Shifting the Paradigm: Alternative Perspectives on Induction 9783110347777, 9783110340273

Citation preview

Shifting the Paradigm

Philosophische Analyse / Philosophical Analysis

Herausgegeben von/Edited by Herbert Hochberg, Rafael Hüntelmann, Christian Kanzian, Richard Schantz, Erwin Tegtmeier

Volume / Band 55

Shifting the Paradigm Alternative Perspectives on Induction

Edited by Paolo C. Biondi and Louis F. Groarke

ISBN 978-3-11-034027-3 e-ISBN 978-3-11-034777-7 ISSN 2198-2066 Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.dnb.de. © 2014 Walter de Gruyter GmbH, Berlin/Boston Printing: CPI buch bücher.de GmbH, Birkach ♾ Printed on acid-free paper Printed in Germany www.degruyter.com

Acknowledgements Any anthology depends on the concerted efforts of a multitude of people. We would like to acknowledge the timely assistance of all the individual contributors, who worked hard to make deadlines, responded patiently to referee reports, and produced a series of refreshingly original and insightful essays on the nature of inductive reasoning. We very much appreciate the assistance of Paul Niesiobedski and Justin Carter, who helped format, proof-read and prepare the final version of the manuscript. We would like to thank Dr. Rafael Huentelmann of Ontos Verlag (De Gruyter) for his enthusiastic support of the project as well as the editorial team at De Gruyter for their guidance throughout the publication process. We wish to thank our colleagues of our respective departments for their support and encouragement. And finally, we would like to thank the publisher for the opportunity of presenting to a wide public a compendium of scholarly essays that provide a much needed corrective to the problematic view of induction generally presupposed by the academic literature. The Editors

Contents Introduction Paolo C. Biondi and Louis F. Groarke

1

Hume’s Disappointingly Accurate Conclusions: General and Specific Peter Loptson

11

Hume and Aristotle on Induction: A Comparative Study Paolo C. Biondi

53

Intelligibility Jude P. Dougherty

123

Induction, Science, and Knowledge James Kelly

135

Induction in the Socratic Tradition John P. McCaskey

161

Socrates and Induction: An Aristotelian Evaluation Joseph A. Novak

193

The Problem of Example Paul Schollmeier

231

The Object of Aristotelian Induction: Formal Cause or Composite Individual? Christopher Byrne

251

From particular to universal: Drawing upon the Intellectual Milieu to Understand Aristotle and Euclid Dwayne Raymond

269

VIII

Not Induction’s Problem: Aquinas on Induction, Simple Apprehension and their Metaphysical Suppositions Matthew Kostelecky

301

Grounding Necessary Truth in the Nature of Things: A Redux Douglas B. Rasmussen

321

Narrative and Direct Experience: A Dialogue on Metaphysical Realism Ernest John McCullough

359

Goethe and Intuitive Induction Jakob Ziguras

385

Lonergan’s Solution to the “Problem of Induction” Hugo Meynell

415

Induction as a Pragmatic Resource Nicholas Rescher

437

Jumping the Gaps: Induction as First Exercise of Intelligence Louis F. Groarke

455

Epilogue Paolo C. Biondi and Louis F. Groarke

515

Contributors’ Biographies

523

Index

527

Introduction 1 Summary Induction, which requires some sort of mental leap from particular instances to a general or universal claim, has remained a puzzling phenomenon for contemporary logicians, epistemologists, and philosophers of science. Yet one cannot account for familiar human experiences of scientific discovery, mental insight, or even artistic inspiration without it. The present volume is intended as a constructive response by a diverse group of experts to the problematic account of induction one encounters almost everywhere in the academic literature. The authors included in this collection criticise the received view and advance alternative answers to key questions about the method and the logical status of induction. They also examine and critically discuss influential historical interpretations of induction. Georg Henrik Von Wright claims that there are really three main problems of induction: (1) the mainly psychological problem of the discovery or origin of inductive inferences in science, (2) the logical problem of analyzing the inferential mechanism of induction, and, (3) the philosophical (or epistemological) problem of the justification of inductive inferences.1 These three problems, he claims, have traditionally been intertwined. But this way of setting out the issues is perhaps misleading. It is not as if we have three separate problems that can be successfully solved in isolation from one another. The authors included in this anthology generally argue that induction is an authentically epistemological (or philosophical) process that has, of course, psychological and logical aspects. They largely resist the suggestion that induction can be construed as either a merely psychological process or narrowly logical process. This book attempts to explain, from a variety of perspectives, why induction can be understood to produce genuinely truthful discourse. In present-day academe, the Humean perspective reigns supreme. According to this way of seeing things, induction is an invalid argument form that generates merely probable conclusions from an incomplete enumeration of instances. Hence the so-called “problem of induction” that has stumped the disciplined minds of so many contemporary philosophers. Briefly stated, the problem is this: I see the sun rise this morning. How can 1

See Georg Henrik Von Wright, A Treatise on Induction and Probability (London: Routledge and Kegan Paul, 1951; rpt. Paterson, NJ: Littlefield, Adams & Co., 1960), 30-31.

2

Introduction

I be assured that it will rise again tomorrow morning? My eyes (i.e., the senses) merely see a bright, golden circle moving across the sky; they do not see (i.e., perceive through the senses) any nature or necessity (either ontological or rational) that will give me a decisive reason to believe it will behave the same way tomorrow. The question arises: What rational inference might I make or what rational justification might I offer to assure myself that what my senses report to me here and now can be relied upon to predict the future behaviour of the sun? None, says Hume. Yet, we (i.e., persons of everyday common sense) make such inferences all the time. But we (i.e., we philosophers) who think rigorously about the foundations of knowledge have no reason to trust these inferences. Hume claims that it is nothing but a mental habit or custom that makes us believe that the future will resemble the past. Reason is unable to arrive at any chain of inference that will prove or establish the point. This is why philosophers since Hume generally view induction as an invalid inference that is logically, epistemologically, and metaphysically inconclusive. Post-Humean accounts of induction reduce it, in many cases, to statistical analysis: the sun rose yesterday; the sun rose the day before yesterday, and the day before that; and before that; but who knows what the morrow will bring, so the best we can say is that the probability is relatively high that it will rise again tomorrow. This is fine as far as it goes, except that probability presupposes a uniformity in the laws of nature that (as mainstream authors insist) can only be discovered through induction. Because probability theory is dependent on induction for its operation, it cannot be used, in any non-circular way, to provide a prior grounding for induction. So this is where we are today. Contemporary philosophers following in Hume’s footsteps have searched diligently, but they have not been able come up with any sort of argument that would secure a rigorous, rational basis for the inductive method. This leaves us in a serious epistemological quandary, for the modern world believes in science, and science is wholly dependent on induction, for its discoveries, for its predictions, and for the universal laws of nature. Without a solid argument for inductive reasoning, the conscientious epistemologist finds it difficult to avoid a slide into a skepticism that would irrevocably undermine pretensions to scientific as well as practical knowledge. Humean worries about induction are not limited to one specialized school or to one narrow group of authors but have been uncritically accepted by the mainstream philosophical community. In addition to the

Introduction

3

specialist’s treatment of induction, one finds that technical literature, critical-thinking textbooks, and pedagogical treatments in formal logic texts trade on the same endlessly reiterated assumptions. Again, one meets with the same approach in epistemology and philosophy of science, and even in more distant discussions that touch on the nature of induction in psychology or philosophy of mind. Perhaps most surprisingly of all, Humean attitudes about inductive reasoning have seeped into critical interpretations and scholarly exegeses of ancient and medieval theories of induction. This results in largely anachronistic readings. Shifting the Paradigm: Alternative Perspectives on Induction challenges the present status quo, providing a constructive response to the usual Humean way of construing induction. The exaggerated attention paid to the so-called problem of induction has unfortunately obscured a more comprehensive and successful way of dealing with the cognitive process we call induction. There is a powerful earlier tradition that we can loosely call the “Aristotelian approach,” which begins with Socrates, is decisively articulated by Aristotle, is revisited by Hellenistic philosophers and enriched by mainstream scholastic treatments until, after being pushed aside by Empiricism, resurfaces in a selective group including philosophers such as Whewell, Veatch, and Lonergan. This book is intended to highlight Aristotelian or Aristotelian-influenced approaches to induction as the main rival to the standard Empiricist-based account. We do not mean to suggest, of course, that individual contributors are in full agreement on every point of contention. For the most part, they attempt to take philosophical explanations and justifications of the inductive process in a more successful direction, in line with overlooked themes found in ancient, medieval and modern thought. Taken together, the essays present a decisive challenge to the majority view. The reflections contained in the volume have interdisciplinary ramifications, for induction is a process that plays an ultimate role in all knowledge formulation. In an age of increasing multi-disciplinary academic research, one could wish for more dialogue among opposing groups and competing specializations within the fields of philosophy and related disciplines. Whereas Aristotelians and Humeans rarely venture out of their own solitudes—discussing pertinent issues among themselves and taking for granted their shared starting points, this anthology is intended to provide an open platform for dialogue and cross-fertilization between specializations and schools of philosophy. The volume raises concerns

4

Introduction

about, and includes important analysis of relevant themes in, science, logic, history of ideas, the philosophy of mind, epistemology, and metaphysics. The essays in this anthology, in the main, seek to rehabilitate induction as a legitimate cognitive process. Many of the authors succeed in dealing with the inductive process in a way that explains its reasonableness and its power. The editors hope that their reflections will nudge academic discussion in a new direction, or at the very least, wake us from our “dogmatic slumbers” by exposing and challenging the often unspoken assumptions on which the prevailing view of induction rests. 2 The Order of Topics Addressed The individual chapters in this book have been arranged according to subject matter. After this short introduction, the book begins with a careful, up-to-date exegesis of Hume’s influential view that induction is ultimately and definitively unreliable. The next chapter provides a scholarly comparison of the Humean and Aristotelian outlook. Having set out those two competing perspectives, we turn our attention to the role of inductive reasoning in science. The three chapters that follow critique the Humean account of science, proposing instead an explanatory realism based on a more confident account of the inductive impetus as well as a concrete investigation of episodes from the history of science. We then move on to an overlapping series of four chapters that analyze, explore and extend the Greek account that begins in Socrates and takes pride of place in Aristotle. The next three chapters consider the medieval account of Thomas Aquinas, Neo-Scholastic approaches to contemporary issues, and, in the only dialogue in the collection, the historical transition that moves from medieval realism to modern skepticism about the reliability of our mental representations of the world. We move on to individually consider alternative modern approaches associated with Goethe, Lonergan, and American Pragmatism. The final paper reviews objections against contemporary accounts and proposes, in an Aristotelian vein, a much wider view of the exercise of the intellection or “intuition” that produces the inductive insight. Finally, a short epilogue suggests further directions for future research. If the reader wishes, the essays could be read in a different sequence. Many essays have more than one feature that could serve as the organizing principle. The reader primarily interested in all things Aristotelian could read together those essays that make his theories a central feature of their analysis. One could instead focus on papers critical of Hume and of the philosophical approaches influenced by him, especially, classical empiri-

Introduction

5

cism, (logical) positivism, and the method of conceptual analysis now prevalent in Analytic philosophy. One could read the essays in chronological order, in according the sequence of historical figures they critically investigate: Socrates, Aristotle, Euclid, Thomas Aquinas, Suarez, Descartes, Hume, Goethe, Veatch, and so on. Someone who is interested in the role of discovery in the sciences could read the contributions that focus on scientific induction in science. And so on. (The brief abstracts that precede each chapter are intended as a guide to the reader. The reader is invited to read these first to get an initial sense of the content of all of the papers.) 3 Chapter Summaries The editors thought it would be remiss if an anthology on induction did not contain at least one sympathetic essay on David Hume. Our first chapter is by Peter Loptson, a well-known Hume scholar. Loptson presents a favorable, though nuanced, view of Hume’s theories. He maintains, to begin with, that nineteenth century critics of Hume’s philosophy who point to alleged flaws in his argument misconstrue Hume’s relentlessly honest pursuit of difficult issues. In pushing the limits of human understanding as far as it can go, Hume does not flinch at skeptical conclusions that are necessitated by an impartial survey of arguments. The second part of Lopston’s essay focuses on Hume’s account of the problem of induction. Loptson shows clearly, through an illuminating and original comparison with Leibniz, why and how Hume comes to his conclusion regarding the a-logical character of induction. Although Leibniz comes close to exposing the problems associated with induction, it is Hume who, through his intellectual courage, exposes them with their full force. The next essay is by one of the editors, Paolo Biondi. It presents an extended, in-depth comparison of Humean and Aristotelian conceptions of induction. The editors believe Aristotle constitutes the main rival to Hume on the topic of induction. Aristotle and Hume may be thought of as the fathers of two opposing and influential traditions in the history of philosophy with respect to how the inductive process is understood. Biondi’s contribution provides the reader with handy summaries of these rival accounts. Biondi argues that Hume restricts induction to sense perception without reason, whereas Aristotle understands it as a cognitive process that features both sense perception and rational insight working together. Induction for Hume is entirely non-rational; for Aristotle, it is eminently rational since the inclusion of reason makes the content of sense perception rational or intellectual. Biondi’s comparison can be seen then as a criticism

6

Introduction

of Humean induction and an argument in favour of Aristotelian induction. He maintains, in the end, that the so-called “problem of induction” can be averted or overcome if induction is rooted in sense perception with reason. The editors have decided to place the three essays dealing with science and scientific practice by Jude Dougherty, James Kelly, and John McCaskey next. Paradoxically perhaps, modern thinkers influenced by Hume, in particular, classical empiricists and (logical) positivists, often take science, especially physics and experimental science, as the paradigm of human knowledge. As these three authors demonstrate, however, classical empiricism and (logical) positivism do not reflect what happens in science. Each one of these papers examines instances of actual scientific practice so as to put on display the problematic nature of the Humean heritage. These papers teach us a valuable lesson. They demonstrate that vigorous scientific knowledge is possible in spite of the skepticism expressed by philosophers who saddle themselves with the task of surmounting Hume’s problem of induction. John McCaskey’s essay moves beyond an examination of scientific practice to consider induction in the Socratic tradition. McCaskey argues that Socrates’ employment of induction to reach universal definitions of moral concepts was a method examined in Aristotle’s Topics. It is a method of induction that differs from the induction of statements described in Aristotle’s Prior Analytics II.23, which presents induction in the form of an argument or deduction. The view that induction provides statements was dominant in the Scholastic period and is dominant today because of Hume; but the Socratic model of induction was dominant at other times and includes Francis Bacon and William Whewell among its leading theoreticians. McCaskey argues for a rehabilitation of the Socratic conception of induction, in part because it is actually employed in the sciences. Joseph Novak’s paper further examines Socratic induction. As Socrates never wrote anything and Aristotle claims that Socrates is to be credited with giving to philosophy the inductive method, Novak uses Aristotle’s views on induction as a lens to turn back the focus on Socrates. Through an extensive survey of relevant passages from the Aristotelian corpus, Novak is able to compose a list of the characteristic features of induction. He then analyzes a representative instance of Socratic induction taken from Plato’s dialogue Hippias Minor to determine which characteristics are found there. This approach, Novak suggests, shows us that Socrates’s method does, in fact, conform to Aristotle’s theoretical description of induction and that we

Introduction

7

can acquire an understanding of Socratic induction through Aristotle’s judicious commentary. Essays that primarily analyze and comment on Aristotle’s views come next. We start with the essays by Paul Schollmeier and Christopher Byrne, both of which consider problems associated with the Aristotelian view of induction. Schollmeier’s essay is representative of a predominant view found among Aristotelian scholars more favourable to the Humean conception of induction. In his chapter, he makes a distinction between, on the one hand, an induction from intelligible species (induction proper) and, on the other, argument from example, which infers generalizations from individual things. In the Aristotle literature, these two kinds of induction are sometimes termed “perfect induction” and “imperfect induction,” respectively. Schollmeier neatly shows how the problems raised by Hume regarding inductive arguments are present in arguments from example because the number of individuals is indefinite (imperfect induction) but not in inductions proper, as these are based on a finite number of species (perfect induction). He concludes then that modern skeptical worries only extend to Aristotle’s treatment of argument from example but not to his treatment of induction proper. This is perhaps why Aristotle considers the former to be a much weaker argument. Byrne examines the nature of the object with which induction is concerned, arguing against a traditional view that we induce only the formal cause of individual substances. Since perceptible individuals are irreducibly composite objects, having a material cause and a formal cause, the induction of their natures must involve an apprehension of both aspects of this composite nature. Part of Byrne’s interpretation of Aristotelian induction also relies upon the contemporary understanding of mathematical induction, which employs a non-enumerative but replicable process in which things to be studied are resolved into their simplest components in a rigorous and logically necessary way. Dwayne Raymond’s essay examines the nature of induction entirely within the context of mathematics through an insightful comparison with Euclid’s geometry. Raymond sheds light on Aristotle’s treatment by situating it within the universe of discourse presupposed by his Ancient Greek intellectual milieu. Inductive generalization is to be understood then along the lines of a Euclidean approach to geometry where universal conclusions are “drawn” from particular geometrical diagrams (and the accompanying text). Apart from illuminating Aristotle’s account of induction, his contribution demonstrates, contra Hume, that we can arrive

8

Introduction

at methods of generalization that do not directly involve an enumeration of different individual instances. The “geometrical approach” presents a serious challenge to Hume’s fork, which radically separates matters of fact (particular diagram) from relations of ideas (text containing universal geometrical proof and conclusion), treating these two types of knowledge as mutually exclusive categories. Although most commentators situate Aquinas firmly within the Aristotelian tradition, Matthew Kostelecky thinks Aquinas’ account differs from Aristotle’s in important respects. Kostelecky presents a concise account of Thomas Aquinas’ views on the cognitive act that enables the human mind to grasp universal knowledge from particular instances, which, for Aquinas, is induction in its broad sense. Kostelecky argues that Aquinas does not have an epistemology in the contemporary sense (that is, one driven by skepticism and seeking a justification of knowledge) because he is not obsessed with defeating skepticism; placing more trust in the cognitive abilities of the human mind, he provides, instead, a metaphysical account of the intellect’s relation to things. Induction in its strict sense is a form of reasoning, and it is understood within Aquinas’ broader theory of cognition, with the fundamental lynchpin being the simple intellectual apprehension of things. Douglas B. Rasmussen’s essay constitutes a detailed criticism of Hume and his philosophical heirs’ account of logical possibility and necessary truth. Relying upon Aristotelian essentialism and distinctions found in Scholastic logic, Rasmussen argues that these philosophers often confuse possibility and necessity as these exist in mere thought and as they exist in reality. Through a nuanced discussion of the nature of abstraction, conception, and logic, Rasmussen is able to argue for the existence of necessity in rerum natura and to show how this necessity grounds fundamental principles of logic. His essay has a two-fold purpose. It undermines Hume’s notion of logical possibility, which contributes to generating the problem of induction, and it lends support to the Aristotelian and Thomistic position on metaphysical necessity, which leads to a metaphysical realism that grounds, in turn, the inductive process. The next chapter is written in the form of a Platonic/Socratic dialogue. Ernie McCullough guides the reader through an imagined conversation that provides a bridge between medieval and modern ways of looking at things. After examining the Greek philosophers Plato and Aristotle, which (McCullough believes) espouse similar doctrines regarding sense perception and intellect and their respective roles in the inductive process,

Introduction

9

he considers how these views are reworked and reshaped by Suarez and Descartes. McCullough’s main message is that induction is a cognitive process that works well within the metaphysical and epistemological context provided in the perennial philosophical tradition rooted in Plato and Aristotle. It only becomes problematic after this context has been radically altered by Suarez and Descartes, who provide a new direction for subsequent philosophical reflections. The narrative form of the dialogue invites the reader to reconsider contemporary forms of philosophical expression, which often emphasize argument, symbolic logic, and scientific method. The chapters that follow these positive accounts of the Aristotelian and Scholastic traditions turn to alternative modern accounts of induction. Although Johann Wolfgang von Goethe is not usually considered a philosopher, Jakob Ziguras perspicuously examines his understanding of science, which involves a conception of ‘intuitive induction’ much like Aristotle's notion of epagǀgƝ. Central to Goethe’s account is the archetypal phenomenon (Urphänomen), which represents an example of a posteriori necessity. The discerning observer moves from a perception of sensible instances to an intuitive grasp of necessary structures discernible within, and explanatory of, the phenomena found in nature. Ziguras believes that Goethe's approach deserves closer attention. It bears a striking resemblance to the Aristotelian model and yet, interestingly, was developed outside the Aristotelian tradition. The last two alternative accounts focus on contemporary philosophers. Hugo Meynell contends that the problems associated with the positivist and classical empiricist views of knowledge can be met by Bernard Lonergan’s renowned account of ‘insight” as a method of knowledge acquisition. Meynell claims that Lonergan’s position provides a robust alternative to the extremes of positivism and radical empiricism. He introduces the reader to Lonergan’s generalized empirical method, which includes attentiveness to experience, fertility in intelligently conceiving hypotheses or possibilities, and reasonable judgement employed in judging whether particular hypotheses are true or not. This three-fold process is equivalent to the practice of rationality. Meynell argues that the real world is nothing other than what is known through Lonergan’s generalized empirical method, a view he calls critical realism. The well-known contemporary philosopher Nicholas Rescher next argues for a pragmatist approach to induction. He maintains that induction is an erotetic procedure, a process for securing answers to questions on the basis of insufficient information. Induction is not really a matter of infer-

10

Introduction

ence but of plausible conjecture and of truth estimation. It involves a search for plausible answers, where plausibility is determined by “cognitive systematicity.” Rescher concludes that a pragmatic approach to induction views inductive reasoning as “inference to the best systematization” rather than as “inference to the best explanation.” In their own ways, the adjacent chapters by Meynell and Rescher acknowledge the lack of certainty and the incompleteness inherent in the acquisition of knowledge. In contrast to the majority of the contributions by Aristotle scholars, which tend to stress the certainty, necessity, and reliability of the inductive process, these contemporary alternatives betray hints of the skeptical influence of Hume. Both authors attempt to sketch out a middle path between Humean skepticism about reason, on the one hand, and Aristotelian confidence in reason, on the other, as the human mind seeks to know the world. Finally, the penultimate contribution by the second editor Louis Groarke aims to accomplish two goals. First, Groarke sets out to demonstrate, point by point, where the Humean account of induction (which he traces all the way back to Hobbes) goes wrong. His criticism of the prevailing view concludes the negative or “destructive” side of the anthology. Groarke lists, second, a number of necessary features he thinks must enter into a more accurate contemporary account of induction, the most important being that induction incorporates a mental leap between incommensurable epistemological categories, notably, between sense cognition and conceptual knowledge. He illustrates his allegedly Aristotelian view by sketching out an analogy between the mental process of induction and a famous experiment by Hertz. In this regard, he continues the positive and constructive side of the anthology. The anthology ends with a short epilogue by both editors, which is intended to indicate future possibilities for research on the topic of induction. Considerations not addressed in Groarke’s paper are explored. After all, if we have succeeded in shifting the current Humean paradigm that constrains our present understanding of induction, this anthology serves merely as a first step in developing a more thorough understanding of the unavoidable first inductive step in our incessant quest for knowledge. Paolo C. Biondi Sudbury, ON, December, 2013 Louis F. Groarke Antigonish, NS, December, 2013

Hume’s Disappointingly Accurate Conclusions: General and Specific Peter Loptson University of Guelph

Abstract: This first chapter, by Peter Loptson, provides an examination of Hume. In the first part of the chapter, Loptson considers nineteenth-century criticisms made against Hume’s philosophy, especially as expressed in the Treatise, in general. Loptson claims that some of these general criticisms have merit, in particular, the inconclusive nature of some of Hume’s reflections; however, Loptson argues the flaws actually demonstrate an intellectually honest pursuit of difficult issues. In the second part, Loptson looks specifically at Hume’s account of the problem of induction. According to Loptson, Hume reaches two conclusions about inductive thinking and its rational justifiability, and conflates them. One is that we humans do not in fact think or reason inductively for rational reasons. The other is that it would not be possible, in principle, for us to think inductively on a rationally justificatory basis. Since Hume does appear at least to gesture toward the distinction drawn here with his seemingly ironic utilization of the Leibnizian model of a pre-established harmony, in the first Enquiry, Loptson compares the two philosophers’ views to show more clearly how Hume is able to come to the conclusion regarding the non-rationality of induction.

Introduction Nicholas Phillipson begins his 1989 study Hume with the opening sentence: “David Hume’s reputation has never been higher.”1 The claim was true then and remained so 22 years later, when he repeats it in the book’s revised second edition, published as David Hume: The Philosopher as Historian (2011).2 Of the major historical philosophers, it would be difficult to be riding higher than David Hume. The year 2011 was the three1

Nicholas Phillipson, Hume (Weidenfeld and Nicolson, 1989), p. 1. Nicholas Phillipson, David Hume: The Philosopher as Historian (Penguin Books, 2011), p. 1. 2

12

Peter Loptson

hundredth anniversary of his birth, so a particularly extensive volume of attention was accorded him during that twelve months’ span and since, most of it highly laudatory. In fact, the general drift of the accounts of Hume’s philosophical ideas has tended over the past few dozen years and more to be extremely positive and typically celebratory. Admirers of the man—widely regarded, as his friend Adam Smith regarded him, as the very model of a philosophical life—and of his philosophical views, are legion. Hume’s works are pored over endlessly, and his interpreters generally vie with one another for the degrees of subtlety and acuity with which they strive to elaborate more perfect interpretations of those seminal texts. Hailed in his time by admirers as ‘le bon David’, the number of those admirers, of the man as well as of the thinker and the ideas that he produced, has become legion in recent time. Hume certainly had a much more negative ‘report card’ at earlier stages, and it remains true that for certain identifiable philosophical constituencies—neo-Aristotelian and (some) Kantian ones, most notably— Hume remains a dark presence, a philosopher who, it is not unreasonable to say, is hated and feared in equal measure—even if held in great respect. But these are, now, at least, minor side notes. In the larger world of philosophy, Hume is just about as big as it gets and as good as it gets. He is taken seriously—very seriously—honoured, and, when dissented from, done so with care, deference, qualification. He is also—just as it happens—viewed as what can only be called a philosophical saint. He is placed in that rare company with Socrates, Spinoza, Mill, and, perhaps, Russell, revered, taken as a model of someone who lived a philosophical life as it ought to be lived. Adam Smith wrote a famous eulogy for his beloved friend, summing up his account of the philosopher’s character and virtues: “Upon the whole, I have always considered him, both in his lifetime and since his death, as approaching as nearly to the idea of a perfectly wise and virtuous man, as perhaps the nature of human frailty will permit.”33 I want to say, indeed, to hasten to say, that I think that Hume’s incredibly high place in current philosophical history is warranted and justified—at least mostly and in general. Hume is a great, in fact a very great philosopher. Hume’s importance can scarcely be overstated. There is a fundamental, coherent naturalist view of the human mind and its operations 3

The passage appears originally in a letter from Smith to William Strahan, dated 9 Nov. 1776—just about two and a half months after Hume’s death. Smith’s letter is regularly published as an appendix or postscript to the several publications in which Hume’s My Own Life appears.

Hume’s Disappointingly Accurate Conclusions

13

in the three spheres of cognition, the emotions, and morality, which is rightly discerned in Hume’s work, together with profoundly important and enduring contributions to the philosophy of science and to the analysis of religion and its bases. In addition, in basic ontology Hume’s work involves and represents movement away from the central prioritizing, or ‘privileging’, of individual objects or substances, the world’s ‘thises’ in Aristotelian vocabulary, which had dominated almost all previous Western philosophy. At the same time, it may be time to review and to some extent to reconsider some parts of the case which was made against Hume’s philosophical work. In his own day, the primary focus of critics was on Hume’s skepticism and irreligion. Several nineteenth-century critics, including Mill, T. H. Green, and L. A. Selby-Bigge, saw a brilliant but massively inconsistent Hume. The present paper reviews some of that nineteenth-century critical case and sees some merit in its account, with Hume emerging nonetheless as a philosophical giant. A thorough sifting of the evidence demonstrates, I will argue, that the most legitimate criticism of Hume’s view, that his skepticism and naturalism are incompatible, is not mistaken or erroneous but an inevitable and accurate reflection of the way things really do appear to an objective, philosophically inquisitive mind. The problem of induction, famously explained by Hume, is an accurate, perhaps unpleasant, comment on the limits of human rationality. In the end, a frank acknowledgment of the non-rationality of induction is what results from a relentlessly honest and objective account of the matter. The disappointing conclusion, that human logic is inconclusive or, more fundamentally, incapable of independent, self-sufficient verification, derives from a correct analysis of this seminal problem. This paper proceeds in two stages. First, I will look at and evaluate Hume’s philosophy from a general, historical perspective. Second, I will consider specifically the origins and the correctness of Hume’s theory of induction. In the first part of the paper, I consider the status of Hume’s present reputation in light of some earlier historical critiques of his Treatise and his general philosophical methodology. In the second part of the paper, I investigate Humean induction with particular reference to Leibniz’s theory of pre-established harmony. I will argue, to conclude, that Hume is, in both cases, fundamentally correct in identifying an irresolvable problem with human rationality. The Humean perspective provides the correct, if disappointing, perspective on human knowledge and the nature of things as they can be known.

14

Peter Loptson

1 Evaluating the General Case against Hume 1.1 Nineteenth-Century Criticism To begin with, I will review some of the charges made by Hume’s nineteenth-century critics; not chiefly for their own sake or to revive contestations in the history of Hume scholarship. Nor will anything like a comprehensive or systematic review of that body of critical literature be undertaken. I will argue that, while the nineteenth-century interpreters exaggerate, and fail to discern the central flowers in Hume’s philosophy, at least some of their concerns are not wholly without merit. Perhaps especially in this period of unqualified, or only modestly qualified, admiring analysis of and judgment upon Hume’s artful brilliance and consistency, there may be value or utility in hearing this more restrained, and sometimes emphatically contrary, note. Hume’s writings returned to scholarly and pedagogical attention after an extended time of neglect, in the 1870s, 1880s, and 1890s. Careful editions were prepared, notably by T. H. Green and T. H. Grose at Oxford in 1874, then by L. A. Selby-Bigge in 1888 and subsequently. It may now seem astonishing to read, or reread, the latter editor’s Introduction to his edition of Hume’s Enquiries. “Hume’s philosophic writings,” Selby-Bigge begins, “are to be read with great caution. His pages, especially those of the Treatise, are so full of matter, he says so many different things in so many different ways and different connexions, and with so much indifference to what he has said before, that it is very hard to say positively that he taught, or did not teach, this or that particular doctrine...”4 More follows in similar vein. Selby-Bigge’s contemporary, T. H. Green, published even more severe strictures on what both interpreters saw as bombast and overenergized effusion, with individual nuggets of brilliance and originality patchworked together into an inconsistent whole. Earlier than either, Mill had called Hume “the prince of dilettanti.”5 Mill was of course a spirited polemicist and controversialist, throughout his career. One basis of his animadversions was what he saw as Hume’s political views. Mill’s critique of Hume expressed in the following passage may be of interest:

4

L. A. Selbey-Bigge, introduction to David Hume, Enquiry concerning Human Understanding [EHU] (L. A. Selby-Bigge, ed.) (Clarendon Press, 1902), p. vii. 5 John Stuart Mill, Essays on Ethics, Religion and Society (Collected Works of John Stuart Mill, Volume X) (University of Toronto Press/Routledge & Kegan Paul, 1969), p. 80.

Hume’s Disappointingly Accurate Conclusions

15

David Hume: a man, the peculiarities of whose mind qualified him to detect failure of proof, and want of logical consistency, at a depth which French skeptics, with their comparatively feeble powers of analysis and abstraction, stopped far short of: Hume, the prince of dilettanti, from whose writings one will hardly learn that there is such a thing as truth, far less that it is attainable; but only that the pro and con of everything may be argued with infinite ingenuity, and furnishes a fine intellectual exercise. This absolute skepticism in speculation very naturally brought him round to Toryism in practice; for if no faith can be had in the operations of human intellect, and one side of every question is about as likely as another to be true, a man will commonly be inclined to prefer that order of things which, being no more wrong than every other, he has hitherto found compatible with his private comforts. Accordingly Hume’s skepticism agreed very well with the comfortable classes, until it began to reach the uncomfortable: when the discovery was made that, although men could be content to be rich without a faith, men would not be content to be poor without it, and religion and morality came into fashion again as the cheap defense of rents and tithes.

This passage appeared originally in Mill’s essay “Bentham”, which had been published in the London and Westminster Review, August 1838. Mill subsequently republished the essay, with modifications, in his Dissertations and Discussions, 1867; among those modifications was a deletion of most of the comments on Hume that had appeared in the earlier published text.6 This nineteenth-century critique is nonetheless all the more significant because it appears well after, and is largely distinct in content from, the opprobrium Hume’s philosophical ideas were accorded by hostile readers in his own time, when chief attention was paid to his religious unorthodoxies and antipathies and his skepticism. In very basic terms, the Humean philosophy belongs in a very large conceptual house, if one may put it that way, that embraces the disparate naturalistic or ‘scientific’ philosophies, from Democritus to Hobbes to Russell, Reichenbach, and Quine; plus the home-based philosophies of skepticism, ancient and modern, and the orientations and projects of the ancient sophists, with their latter-day successors the pragmatists; scientific philosophy, and philosophy of ‘common life’, in Hume’s phrase. The most serious evaluative assessments of Hume’s work will proceed from a stance that at least does not foreclose from the outset on a body of philosophical projects undertaken within the large house metaphorically just identified. 6

The essay, together with Mill’s full Hume comment appearing in an appended endnote, was republished prior to the Collected Works volume, in J. B. Schneewind’s edition John Stuart Mill, Mill’s Essays on Literature and Society (Collier Books, 1965).

16

Peter Loptson

Those assessments will come neither from ‘common sense’ nor from Kantian rationalism. Thomas Reid was the originator of common sense, revived in the twentieth century in the work of G. E. Moore, then later, in the writings of Roderick M. Chisholm.7 This critical perspective basically misses the point of Hume’s skepticism. Another base of oppositional critique of Hume has come, since the 1780s, from the Kantian critical philosophy. Probably the most fundamental difference between them is the ineliminable rationalism of the Kantian perspective. For Kant, the inquiring philosophical mind can think thoughts of possibilities of a world order and of a free rational agency, beyond experience, even if it cannot know the truth in these speculative territories. For Hume, anything along such lines is a very dubious proposition. The negative nineteenth-century critique of Hume is distinct, at least for the most part, from criticisms of Hume’s philosophy made chiefly by some of his eighteenth-century readers from a perspective grounded in philosophical commitments to common sense. Mill is, at least prima facie, a good candidate for providing such critique. Hume’s later nineteenthcentury critics whom we have identified have more broadly Kantian orientations. But they are ‘men of letters’, civilized students of central texts and ideas of their culture, deeply steeped in the literature of Greco-Roman antiquity; all of which also was Hume himself. They are not, to be sure, imbued with the spirit of Democritean, naturalistic, or scientific philosophy—those who were, like Mach, in Germany, warmly embraced Hume— but in other respects they may be said to be writing about and evaluating one of their own. And like Mill, they found much to fault. Hume’s nineteenth-century critics appear to discern, at any rate, to assume, a single Humean philosophy, identifiable in a common body of his philosophical writings, above all the Treatise of Human Nature, as well as the two Enquiries and the Dissertation on the Passions, which are conceived as comprising the reconstructed recasting of the Treatise in reconsidered formulation. That said, their central critical fire usually appears to focus preponderantly or exclusively on the Treatise. The primary criticisms of Hume’s philosophical work which the critics have, and on which my attention here will be focused, are that the philosophy’s frequently very negative argument undermines the possibility of it itself having anything positive to say, that the philosophy is massively 7

See, e.g., G. E. Moore, “Hume’s Philosophy”, The New Quarterly, Nov. 1909, reprinted in G. E. Moore, Philosophical Studies (Routledge and Kegan Paul, 1922); and Roderick M. Chisholm, Person and Object (Open Court, 1976), pp. 37-44.

Hume’s Disappointingly Accurate Conclusions

17

inconsistent, and that it contains as large thematic proper parts elements which appear only superficially to have much connection with each other. These are not for the most part complaints about the detail of analysis and argument which Hume offers, much of which is seen as brilliant and original. There are, however, complaints to the effect that, on a number of important, central philosophical issues, it is difficult or impossible to tell just what Hume’s view is, since he provides textual evidence of holding distinct and incompatible positions. 1.2 Hume’s Treatise: Three Large Shards Hume himself, it is important to say at the outset, was, if only through a kind of back door, in advance of these later critics, at least in part. He himself rejected and repudiated his first published work, the Treatise of Human Nature. Like so many aspects of Hume’s philosophy, this rejection is differently interpreted by Hume’s investigators. For some, it is mostly a merely nominal repudiation, occasioned by what Hume thought were infelicities of style, prompted as much as anything by the wounded vanity of an ambitious author’s not finding his work responded to by its intended audience with the attention, still less the enthusiasm, which he thought its highly original and important content warranted. Many of these interpreters are convinced that Hume intended a second edition of the Treatise that would clarify the (allegedly) minor or merely occasional passages where Hume’s arguments might have been less persuasively formulated or his ideas less sharply advanced; no doubt rendered with extensive revisions of prose style at which the much more polished, and successful, writer of later years had become skilled. Hume may have intended a second edition of the Treatise. In fact, though, the case for this view seems rather dubious. Authorial annotations in a copy of the book and occasional intimations in letters do not make much of a case. Very few authors regard their books as beyond improvement; most would in principle imagine prospects of later editions as welcome ideas. Hume did produce subsequent editions of several volumes of collected essays. He also said that, just possibly, he would go on to a further volume of the History of England, carrying the story up to his own time, at any rate well beyond the Glorious Revolution, where it in fact ends. Hume enjoyed almost a decade of leisurely retirement following his career as a civil servant, first in Paris and later in London. He was in full command of his faculties. He himself said that he was too fat and too rich to

18

Peter Loptson

write much more that was substantive. Yet his editing revisionary work and his vigorous intellectual activity, continued. In any case, Hume did, publicly and formally, repudiate the Treatise. Late in his life, he composed an ‘Advertisement’, which he desired to be inserted in the next and all future editions of the second volume of his ‘philosophical essays’—the volume which contained the two Enquiries, the Dissertation, and the Natural History of Religion. In this piece Hume says: “Most of the principles, and reasonings, contained in this volume, were published in a work in three volumes, called A Treatise of Human Nature: A work which the Author had projected before he left College, and which he wrote and published not long after. But not finding it successful, he was sensible of his error in going to the press too early, and he cast the whole anew in the following pieces, where some negligences in his former reasoning and more in the expression, are, he hopes, corrected...”8 A number of Hume’s letters renounce the Treatise also (some would say still more) emphatically. And Hume had actually published, with the Treatise, an Appendix which claimed to find two fundamental, at any rate, formidable, errors in the work which Hume had been unable to see how to correct. (Needless to say, all of these matters are among the many issues of complexity and varied analysis and interpretation among Hume scholars.) This great, huge work, the Treatise of Human Nature, about which Hume’s own final judgment, and our own, is, summarily, that it is brilliant but flawed, is divided structurally into three ‘Books’, titled, respectively, ‘Of the Understanding’, ‘Of the Passions’, and ‘Of Morals’. There are other significant divisions that may be made of it, but a metaphorical way of dividing the volume would be to say, that it is a union of three large shards, naturalism, skepticism, and his unique account of the moral/social life, which may be thought of as outcomes of projects its author has had. They join only imperfectly, but all matter emphatically, even urgently for Hume. 1.2.1 First and Second Shards: Naturalism versus Skepticism The first shard is composed of a naturalistic attempt at human psychology. Hume aims at a ‘science of man’, as he calls it. The roots of such a project go back in fact to antiquity, but, even though Hume agrees that efforts in the direction of a science of man were initiated in antiquity, he holds that these efforts were wholly vitiated by failures to ground those efforts in a properly empirical methodology. 8

EHU, p. 2.

Hume’s Disappointingly Accurate Conclusions

19

Hume insists that his is an endeavour only inaugurated, indeed, only possible, in the wake of Bacon and Galileo, the respective Britannic and European-continental launchers of modern, that is to say, real and genuine science. There are forerunners within the post-Baconian epoch from whom Hume averts his eyes: most notably, Hobbes. In the deepest and truest sense, A Treatise of Human Nature is Part 1 of Hobbes’s Leviathan, done over, done right, broadly expanded, sharing fully Hobbes’s cold analytical reductionism, but coming (as Hume thinks, not always accurately) to more sophisticated, and, importantly, more social analytical conclusions. The Treatise is also Locke’s Essay Concerning Human Understanding done over and done right. Hume is considerably more explicit about the prefiguring role of Locke. At the same time, Hume means to be—and is—more radical than Locke (it is not clear that he is particularly more radical than Hobbes, though his theories cover what they share far more extensively). Locke is an almost a father-figure, in a Freudian sense, in relation to Hume. Locke is secure, established, famous and influential. One is in his debt, and it is important to show that he is wrong, to whatever extent one can, and one may emerge with views actually much closer to his than one had had in mind that one would. The second shard is skepticism. Hume (like some other philosophers) is riveted, even mesmerized, by the power of radical skepticism, in forms he derives principally from Descartes, Bayle, and Huet, with a substantial additional debt to Berkeley, but which he has also probably to a considerable extent thought through on his own. Hume thinks, or at least affects to think, that his skepticism is closer to his naturalism than it really is. There is an important and intelligible link, but there is also a tension between them that is greater than he is ready to acknowledge. He is in effect addicted to both; his work (for him) must give expression to the cool naturalistic vision of our minds as Democritean constructs out of experience-packages, operating in accordance with regularities as exceptionless as those governing the tides. It also must have cognitive endeavour assailed, blown out of the water, by the impossibility of justifying the existence of anything beyond an immediately occurrent experiencestate. Naturalism presupposes the induction; skepticism, at the very least, doubts its validity. How, then, are we to reconcile the two? How can Hume be equally committed to the inductive method that produces a modern scientific view of man and the world, and to a skepticism which, even in its mitigated varieties, seems to undermine this very aspiration?

20

Peter Loptson

There is no easy, tidy answer to such questions. This conflict or tension in Hume’s oeuvre between naturalism and skepticism only emerges as the dialectic advances. Both the ‘natural’ (and ‘naturalistic’) and the ‘skeptical’ are elastic guides or imperatives, varying in their possible extensions from very small isolable cases to applications they may have which are more or less without limit. Hume doesn’t have the contemporary verb ‘to naturalize’, but he does have the concept, and he means to apply it to all sectors of investigation accessed by his phenomenological methodology. Insofar as naturalizing involves revising everyday or previously-heldtheory concepts, it involves being skeptical about those concepts, and skeptical is precisely what Hume’s inquiries lead him to become. His results include a skepticism about the concept of an atomic or point-like substantial self, and, more globally, about the concept of a substance (in the count-noun sense) as such. He comes to skepticism as well about objective necessity in the mind-independent order, and objective morality; also as to whether human and other animals act (except possibly in some, specialized human cases) in rational or justified-reason-generated ways. On other issues—the case for skepticism as to whether there are hidden powers which objects have, or whether, as Locke held, a ‘double existence’ perceptual theory (inner sensory images corresponding, accurately or otherwise, to objective clusters of sensible qualities—or even, as some insist, to material objects) is true—Hume’s own skepticism is more tentative. There is a reasonable basis for dispute or disagreement as to whether Hume means (at the end of the day, as it were) to be skeptical, or to affirm skeptical results. At any rate, so far, this produces a body of skeptical results that are advocated and defended entirely within a framework of an accepted ‘natural’ causal order, with two subsystems, a mental and a physical one—with Hume viewing their ultimate or underlying mutual relations as unfathomable by us. Still, their distinctness is sufficiently clear that, as Hume tells us, he will confine his investigative theoretical attention almost exclusively to the mental sphere. Hume sees his naturalism and his skepticism as joined from the fact that everything knowable, indeed, thinkable, begins with immediately occurrent experience-states. Two nets are then cast, however: with one of them, the naturalistic net, capturing a syncretistic positive theory that (inductively) assembles an account of the human animal, living successfully, if fundamentally non-rationally (just as do the other animals) within the nomologically closed, profoundly contingent, purposeless causal system of

Hume’s Disappointingly Accurate Conclusions

21

the world; with the other net, the skeptical one, all justificatory enterprise (inductive or otherwise) is sabotaged. One might think of this last skeptical net as launched by a refusal to accept the assumptions underlying naturalizing projects unless they too can be justified in just the sorts of ways that ordinary and previous theory posits had been required to establish their bona fides and been found wanting. In fact, Hume never questions the posits of naturalizing theory; he chooses rather (in Part 4 of Book 1 of the Treatise) to become skeptical about the powers or possibilities of human minds (one of which of course is his own) to reach or grasp or justify those posits. One is faced, however, with an inescapable choice: either one is engaged in a naturalizing enterprise, or one is not. Hume importantly, in Book 1 of the Treatise at least, cannot or, at any rate does not, make up his mind about this. This claim, however, is disputed by some of Hume’s interpreters. The precise role which the skeptical sections of the Treatise are playing in the work is itself variously understood. Some see a straightforward seamless whole—‘no problem’, if we just read Hume with dexterous, gingerly care. Others think that Hume isn’t really talking about radical skepticism—solipsism of the present moment, or a supposed inability to establish anything about anything through reason—at all; that ‘reason’ and others of Hume’s terms are terms of art, which must be understood in the right ways, and when they are it will be seen that Hume actually isn’t even interested in radical skepticism, and has more or less nothing to say about it, other perhaps than to dismiss it as unworthy of serious philosophical attention. Neither of these views seems to be defensible or to survive close scrutiny of what Hume actually says in the Treatise. More promising is the idea that Hume is engaged in something, in the skeptical sections, more complex than at first noticed, viz., that he is not actually laying out his own views or arguments, but speaking ‘in the persona’ of the radical skeptic, as it were, taking on a mantle of ‘hyperbolic’ or exaggerated argumentation, to show what devastating results would ensue if the goal posts—the standards required for justification—were set high enough. The main aim, according to this line of interpretation, is to show utterly convincingly the impotence of human rational endeavour, as a kind of set of case studies contributory to Hume’s anti-reason account of human psychology. That—and the fast and impressive dialectical swordplay the young Hume puts forth (and the depressive reaction in its agent which is either genuinely, or merely rhetorically occasioned by it)— displayed, the main narrative, of the science of man, is resumed.

22

Peter Loptson

Something like this view is encouraged by what Hume (just possibly, it is not him, but another, writing on his behalf but with his endorsement) was to say, a few years later, in the Letter from a Gentleman to his Friend in Edinburgh (1745). This work was written as a response to criticisms of Hume, and the Treatise, held to be sufficient to justify his being rejected for a university chair at Edinburgh. The criticisms include one of radical skepticism. Hume’s response is to say that neither he, nor anyone else, is ever genuinely a skeptic, that some of the most illustrious thinkers (and some of them, like Huet, exemplary Christian clergymen) use skeptical argumentation for exemplary purposes, and that skeptical principles, in all ages, hence also in Hume’s, have figured “as Principles of mere Curiosity, or a Kind of Jeux d’esprit.”9 The claims in the Letter may of course be seen as special pleading in Hume’s circumstances, but, on reflection, this seems unlikely. Hume is studiously, even stubbornly honest, and he usually prefers using correct qualifications when disguising or muting his real views, which he doesn’t do here. The issue is this: is Hume speaking altogether, or, throughout, in his own voice in T 1.4.1, 1.4.2, 1.4.5—and, likely, 1.2.6, which explicitly cites and anticipates the skeptical sections which will come later (and which there may be reason to view as having been written independently of the rest of 1.2, and inserted in its position there)? Or is it, rather, (something like) were I a skeptic, of the most extreme sort, what will be a best case I might forward for my position, including (possibly) some premises I don’t myself actually accept? Here it is… In either case, Hume, in the Treatise, doesn’t explain what he means to be going on with regard to skepticism, the science of man, the rest of the Treatise (Books 2 and 3), and their mutual relations. It certainly may reasonably be doubted whether a consistent, or an interestingly rescuing explanation, could be produced; and the resulting complex, of text, and the challenges to its possible interpretation, are a significant flaw in the work. Not, I will certainly affirm, sufficient to condemn the work, or to dislodge it from the extremely high place at which it justifiably resides. A significant flaw nonetheless, and probably caused by Hume’s inability not to unleash the two passional motivating vectors with which he is animated. By the time of the two Enquiries he is older and wiser. But his youthful indecision is an organic flaw of the work, which Hume, in a famously obscure passage in the Treatise’s Appendix, may 9 David Hume, A Treatise of Human Nature, ed. David Fate Norton and Mary J. Norton (Clarendon Press, 2007), vol. 1, p. 425.

Hume’s Disappointingly Accurate Conclusions

23

perhaps half-recognize. At any rate it is a flaw in the work, which leaves a kind of worrisome imprint on its entirety, a shadow of uncertainty as to just what sort of endeavour this philosopher is engaged in. This ambivalence certainly has been a principal root of the scholarly inquisitions of the Treatise that have occupied philosophical textual investigators for what will soon be 300 years. I have deliberately used the metaphor of three ‘shards’, more conceptually independent of each other than Hume discerns, or than the Treatise displays. Hume’s naturalism cannot be easily connected to Hume’s skepticism. Commentators who favour one or another interpretation almost without exception draw selectively on the text of the work, typically simply ignoring passages that don’t appear to fit or conform to the model or conception of the Treatise as a whole which is favoured; or, at best, they either try to construe problematic passages, usually not very plausibly, so that they will conform, or declare them to be ‘lapses’ or dismissible minor notes, stumbling or incautious departures from main messages. In fact, it is extremely difficult to find a way to make the Treatise’s naturalism, and its skepticism, come into conjunction. The most fundamental tenets of Hume’s metaphysical and epistemological commitments are hard to make out. Consider just one passage that poses a challenge: in the particularly central section entitled “Of skepticism with regard to the senses” (T 1.1.4.2), Hume affirms, as a premise for the argument mounted in the section—as something already proved, earlier, and not seriously open any longer to challenge—the radical idea that we cannot secure or justify a belief in things external to our perceptions. He observes, in passing: “as to the notion of external existence, when taken for something specifically different from our perceptions, we have already shown its absurdity” (T 1.1.4.2.2). Hume then provides a footnote referring the reader back to T 1.1.2.6, where this was allegedly shown. If there is a way to interpret this claim otherwise than with what appears to be its natural meaning, it is not easy to see what it could be. The species of something should be the kind of thing that it is. So, if there were to be something specifically different from a perception, it should be of a species, kind, or type distinct from that of perceptions, whatever that species was. It will be natural, at least, to suppose that the species of a perception will be that of being a mental thing, whatever precisely that might involve or imply. It will also be natural to reflect and suppose that, at least according to common sense—the ideas of ‘the vulgar’—and also according to the views of all but a tiny minority of philosophical and

24

Peter Loptson

scientific theorists, that not everything that exists is mental in character, that is to say, everything is not of the species that perceptions are made of. Indeed, if it will be very widely and very commonly supposed that there are a great many perceptions—that is, a great many things are of the species that perceptions are of—there are also a great many things that are not of that species; in other words, that are specifically different from perceptions. Common sense and most theory will have it that things specifically different from perceptions will typically have an existence which is external to perceptions. Bodies, perhaps especially prototypically, that would have existed whether or not there ever had been perceptions, and which perceptions might be of, would be obvious or natural cases of things that are ordinarily regarded as specifically different from perceptions and at the same time having external existence from those perceptions. Again, if we wanted cases that were arguably more closely parallel in type to but still different from perceptions, we might identify bodily events or purely physical occurrences as playing the indicated role. For Hume, in T 1.1.4, it is a premise, not requiring argument (that argument allegedly having been given earlier), not just that these suppositions of common sense and most theory fall short of being able to be proved, but that they are absurd. Closer investigation reveals that the argument Hume refers his reader to as offered in T 1.1.2.6 is in fact far from successful, or convincing. But, for the present purpose, that isn’t quite the point. The result Hume declares that he reached in the earlier passage is a radical skeptical point, the expression of a radical skeptical position. It will imply—it certainly seems—that it is absurd to suppose that anything exists other than perceptions (or, just possibly, that nothing exists other than some items wholly dependent on or involved in perceptions—sense data, say). But scientists, including scientists of man, don’t—at least, it is far from evident that they would—claim something of this kind as part of their enterprise. Not only is the falsehood of Hume’s claim at least apparently implied by other assumptions they will naturally make (many of which Hume himself also, in other contexts, appears to make), it will also seem irrelevant, in both character and content, to undertaking a scientific project. There is a philosophical position, it is true, which, it may be argued, reconciles the apparent conflicts that we have identified. Present-day philosophical stances are typically, certainly among analytic philosophers, metaphysically realist in character. But this was by no means always the case at earlier stages of analytic philosophy, nor is it universally so among non-analytic philosophers. Widely held positions throughout the nineteenth

Hume’s Disappointingly Accurate Conclusions

25

century and the first half of the twentieth supposed that a postulated real world beyond the horizons of our concepts and our experience was either entirely inscrutable or not a genuinely intelligible posit. These positions have been advocated most notably by Kant and the several varieties of Kantians and neo-Kantians (and Idealists) since his day; by positivists of the original stripe, with either the position articulated by Comte and Mach or that of the 1920s and 1930s in central Europe; and in addition by some neo-pragmatists like Richard Rorty. (The later Wittgenstein can perhaps be placed in this conceptual territory as well). These disparate schools and positions all disparaged and dismissed metaphysical projects aiming to discover the nature of things in themselves, independent of us (and our concepts and ideas), either as literally incoherent or unintelligible or as useless and undoable. Michael Devitt, a robust metaphysical realist who may be taken to be representative of positions extremely widely held by present-day philosophers, identifies two stances which may be assigned to many advocates of the positions referred to. One of these is what Devitt calls Weak, or FigLeaf Realism (and attributed to Kant), viz., “Something objectively exists independently of the mental”—i.e., where the something is wholly unknowable. Another, Devitt names Skeptical Realism: “Tokens of most current common-sense and scientific physical types might objectively exist independently of the mental”—the ‘might’ intended being epistemic.10 None of these later positions and schools, it is important to note, viewed themselves as inherently skeptical in character. Typically, they held, as their surviving advocates continue to hold, that there is a replete and immense fund of knowledge, afforded us in the sciences and in ‘common life’ (to use, in fact, Hume’s phrase), according to canons of justification and evidence, but which simply (if this is simple) does not go beyond the umbra, or perhaps the penumbra, of our concepts and experiences. 10

Michael Devitt, Realism and Truth, second edition (Princeton University Press, 1997), p. 302f. Devitt’s Weak, or Fig-Leaf (or Kantian, or noumenal) Realism, affirms, as Nelson Goodman—who also discusses the position—says, the reality of a world “not worth fighting for” (Nelson Goodman, Ways of Worldmaking (Hackett, 1978), p. 20; cited in Devitt, op. cit., p. 17). One may usefully compare Hume’s remark, in the Enquiry concerning Human Understanding (12.1.17): “Bereave matter of all its intelligible qualities, both primary and secondary, you in a manner annihilate it, and leave only a certain unknown, inexplicable something, as the cause of our perceptions; a notion so imperfect, that no skeptic will think it worth while to contend against it.” (Hume’s italics)

26

Peter Loptson

There is in fact extremely good reason to place Hume within this broad range of anti-metaphysical positions. He says, explicitly, quite a few things richly prefiguring of Kantian, positivist, Idealist, and pragmatist views. There is also some reason—some textual evidence—for hesitating to do so. He at least seems to see the position at which he has arrived by the end of Book 1 of the Treatise as standing at the abyss of radical skepticism. He declares as well that Berkeley’s idealism, which many would also argue belongs in the cluster I have identified, is in fact a skeptical philosophy,11 and he declares further that it would be impossible to be, and that he himself is not, a skeptic. Kant, Comte, Mach, Schlick, Wittgenstein, Carnap, Ayer, and Rorty have no comparable qualms or reservations. And some of Hume’s (at least apparently skeptical, or idealist) claims are stronger than any of those that the named octet would assert; e.g., in one radically skeptical passage, he writes: “’tis impossible our idea of a perception, and that of an object or external existence can ever represent what are specifically different from each other. Whatever difference we may suppose betwixt them, ‘tis still incomprehensible to us; and we are oblig’d either to conceive an external object merely as a relation without a relative, or to make it the very same with a perception or impression.”12

Hume himself appears to see the ‘Pyrrhonian’ or radical skepticism, to which he briefly succumbs in Part 4 of Book 1 of the Treatise, as successfully abandoned by three steps, or reflections, and many of his present-day readers and admirers have wanted to agree with him that it is. First, he notes a psychological fact about ourselves: we simply can’t seriously entertain, and certainly cannot sustain, radical skepticism—we simply cannot help but believe in an ‘external world’ of physical objects and other people. Second, Hume affirms a fallback skepticism, which he calls ‘Academic’ skepticism after the ancient school of that name and otherwise dubs ‘moderate’ or ‘mitigated’ skepticism. This is a position of refraining from dogmatic claims, readiness to revise and reverse positions reached, and similar epistemic virtues. As Hume cleverly notes, this will imply as well being prepared to be skeptical about one’s own skepticism. Third, Hume proposes that cognitive and other inquiries may well have no rational grounding or justification but can be ‘justified’ nonetheless simply as activities which we may choose to engage in because we find them pleas11 12

EHU 12.1.16, n. 1. T 1.4.5.19.

Hume’s Disappointingly Accurate Conclusions

27

ing. That is of course no justification at all, and it is doubtful that anyone devoting themselves to writing books or to a career in cognitive or scientific pursuits could genuinely believe that their projects are on a rational par with, say, preferring strawberry ice cream to chocolate. The latter seems in fact as improbable, psychologically, as the idea that we could sustain radical skepticism. The nature of Hume’s skepticism and its relation to naturalism, at least insofar as this dialectic is played out in Book 1 of the Treatise, remains, it seems, opaque. 1.2.2 The Third Shard: The Moral/Social Life The third shard in this grand ensemble that makes up the Treatise is a construction of a social world: at once the account of our emotions and of moral ideas which, from primitive beginnings in feelings we experience that allow us to place ourselves in the predicaments of others and to compare ourselves across the board with others, effect the assembly of what allows societies and successful political orders to exist and sustain themselves. Norman Kemp Smith, one of the great, important, and original Hume scholars of the first half of the twentieth century, is especially noted as bringing forward the idea of a naturalistic (in contradistinction from a merely skeptical) Hume, one with a positive and systematic philosophy. Kemp Smith didn’t just identify a naturalistic Hume, a would-be Newton of the mind; he also viewed Books 2 and 3 of the Treatise, on the passions and morals, as the more genuine centre of conceptual gravity for Hume than the epistemological investigations of Book 1. Without engaging any of the specifics of Kemp Smith’s views or the case he gives for them, in the present context, it is important to affirm the fact that the account of the affective and normative life which Hume gives is for him an independent locus of his philosophical and—in the Humean sense—scientific attention. Books 2 and 3 are not merely ‘after-thoughts’ or addenda to Hume’s main (cognitive and epistemic) enterprise. They are, as themselves, when set forth and when Hume is working out his ideas within them, ‘the main act’. At any rate, Hume’s naturalism continues and finds new flower in personal, interpersonal, and social life and their investigations. Not so with his skepticism. It is allowed to burn out in the explosive fire of the study of cognition. One could read the whole of Books 2 and 3 without having read Book 1 and never guess that, before the doors to those rooms had opened, a conceptually and theoretically utterly anarchic abyss had been reached. The whole story of the Treatise is, indeed, as some who have studied it characterize it, suffusively informed by the idea of sentiment, feeling actuated by

28

Peter Loptson

principles of imagination. But it is not really a progress of sentiments. A coal-pit was stumbled into, just as Hume’s critic Reid was to say,13 and Hume really just changes the subject and goes on to new themes in which he has (as he did in those that preceded) passionate interest. The ‘shard’ metaphor remains apt, and with it, the intimation of some variety of inconsistency, at least of stress or tension. In the case of the third member of Hume’s triadic ensemble of foci, the stress is as to whether Hume means to, and does, develop a moral theory or rather remains always (some passages suggesting otherwise notwithstanding), in his goals and commitments, (merely) a naturalistic social scientist (as we would now put it) investigating human emotion and the moral sphere of human life. Just as with the naturalism versus skepticism theme, moral realism versus psychology-of-the-normative is played and replayed with dozens of variations of emphasis and detail in the unending secondary literature on Humean philosophy broadly and in the Treatise of Human Nature in particular. There is no question that, if he is a moral realist, Hume is to be placed within the broad camp of anti-rationalist subjectivist and utilitarian positions that begins with Epicurus and was later to number Bentham and Mill (and today includes some like Peter Singer). The still larger anti-rationalist tent includes noncognitivist and error theory positions, as well as the empiricist, subjectivist and naturalist moral stances, and both of those categories have also been argued to be where Hume should be placed. Still, there are at least suggestions in some of the passages in Book 3 of the Treatise (in the Enquiry concerning the Principles of Morals as well, as also in his colleague and friend Adam Smith’s The Theory of Moral Sentiments), that the considered or end-of-the-day stance intended is one that sits on a fence, declining to declare what is on the other side of it (if it is even seen as knowable, or even thinkable, what might be there), and limiting itself to the (allegedly) scientific study of how-we-feel, how-wethink, and how-we-act in these compellingly interesting and important areas of human life. And, it is possible also that, just as it may be that the tension between naturalism and skepticism is not really resolved within the mind of the man himself, so there may be no inner resolution of whether Hume is or isn’t a normativist (even a meta-normativist), and not just a social scientist of the normative. There are also other vectors in the large-plane interpretation of what is going on in the Treatise. Real, significant but, I believe, lesser ones. 13

Thomas Reid, An Inquiry into the Human Mind on the Principles of Common Sense (Pennsylvania State University Press, 2000), p. 23.

Hume’s Disappointingly Accurate Conclusions

29

Among these is Hume’s deep animosity to religion, especially the Christian religion. That animosity seems in fact to grow, just as its tone becomes lighter, in Hume’s post-Treatise writings. There is no question that Hume is often ironical, sometimes indeed quite sportive (even if, often, for him and most of his readers, these are blood sports). At the same time, it is possible, and not rare among his readers, to exaggerate the irony. He is much more frequently to be taken straight and literally than one might think at first. Thus, for example, in the Treatise’s Appendix, Hume provides a theistic footnote, to be inserted, he says, with a preceding paragraph in the main text, right after T 1.3.11, a footnote which many readers find a surprise, or at least puzzling. “The order of the universe proves an omnipotent mind; that is, a mind whose will is constantly attended with the obedience of every creature and being”14 (Hume’s italics). Hume knows well that for orthodox theism, definitely in its Christian versions, the divine will is frequently frustrated by the obduracy of stubborn and perverse humanity. Accordingly, we do well to note Hume’s “that is”. The “omnipotent mind” Hume is affirming here is the natural, deterministic order of the universe, whatever happens instancing — in that sense ‘obeying’ —exceptionless natural laws. Perhaps he does really mean to affirm as well that in some sense or other this order is a realization of mind or thought. At any rate, Hume is here asserting, as we may put it, the existence of Spinoza’s God, probably knowingly. At the time he is writing the Treatise, and, I suggest, for at least many years thereafter, Hume is, in his own view, what may be called a Spinozist deist.15 (So understanding Hume is at any rate one reasonable way to interpret views which Hume assigns, several years later, to Philo, in his 14

David Hume, A Treatise of Human Nature, ed. David Fate Norton and Mary J. Norton (Clarendon Press, 2007), vol. 1, p. 109; the earlier Selby-Bigge-Nidditch edition (Clarendon Press, 1978), prints the Appendix’s directions for insertions of new passages into the text with those passages within the body of the Appendix (as they appeared in the original published edition of the Treatise, in 1740; no subsequent edition was published during Hume’s lifetime). The ‘theistic’ footnote will be found, accordingly, on p. 633 of Selby-Bigge-Nidditch. It seems likely that all of these Appendix ‘passages to be inserted’ are Humean after-thoughts, written after the main body of the Treatise. Though some of them, at least, might conceivably have been written concurrent with or even before the passages to which they were to be added, Hume having had a change of mind as to whether he wanted them published, and at those places, in the work. At any rate, they were published in the work, and are plainly endorsed by its author. 15 An interesting, suggestive exploration of a number of respects in which Spinoza may be viewed as a significant background influence on Hume’s philosophy is Annette C. Baier’s “David Hume, Spinozist”, Hume Studies, 19, no. 2, Nov. 1993, 237-252.

30

Peter Loptson

much-studied ‘reversal’, in Part 12 of the Dialogues concerning Natural Religion—for example, Philo’s claim, there, that the dispute between theism and atheism is merely verbal, both sides, if understood accurately, really just affirming the same thing.16) Hume repudiates both the labels ‘deist’ and ‘Spinozist’, in one setting or other, but that is nonetheless, perhaps, what we may now most usefully call Hume’s position vis à vis matters of God and theology, with the important additional proviso that Hume holds that these are very obscure territories of investigation, the actual truth significantly veiled from us. Nonetheless, Hume does not see himself as an atheist or a (mere) agnostic, and the Appendix footnote can and should be taken as straight, non-ironic, expressing the closest to a literal truth in these quarters that is discernible by us, according to him. Accompanying Hume’s deism, as in most other cases in the early modern period, is a sometimes quite ferocious antipathy to established, public, orthodox, state-enforced (so-called) ‘revealed’ religion—Christianity. As just implied, this is anything but unique among ‘freethinkers’ of the early modern period. They are generally broadly and effusively hostile to Christian orthodoxy, both in its doctrines and in its practices. So it is a clear mistake to think of Hume’s standing out in any distinctive way in this regard (or of him thinking that he did), or of deep or passionate antipathy to Christianity as offering some sort of key, or central nerve, to his philosophical work. Hume thought that his important contributions were staggeringly unique and innovative—and at least to some extent he was right. But, as a Christ-hater, he was one of dozens, perhaps hundreds. Hume does think— and again, he is right—that in the ‘Epicurus’ section (section XI) of the Enquiry concerning Human Understanding, the Natural History of Religion, and (above all) the Dialogues concerning Natural Religion, he comes up with more varied, trenchant, and devastating objections to the rational or argumentative bases people, including philosophers, have thought that they had for religious beliefs, and, he believes, more persuasive—and also trenchant and devastating—analyses of the real psychological grounding of religious conviction, than had ever earlier appeared. Hume was proud of this part of his oeuvre and very keen (concerns expressed by a number of his friends notwithstanding) that it should come to the published light of day. This still will not imply, nor is it the case, that this part of his work, or 16 David Hume, Dialogues concerning Natural Religion (Cambridge University Press (Dorothy Coleman, ed.), 2007), pp. 92-94.

Hume’s Disappointingly Accurate Conclusions

31

anti-theism more broadly, was the only or even among the most important of the arrows in his quiver. 1.3 What to Make of the Nineteenth-century Criticisms Returning to the theme of the central charges made against Hume by his nineteenth-century critics, we note that they include both an attack on his enunciating principles and developing arguments, which (in their skeptical guise at least) seem to imply that there is no possibility of a science of man—the declared aim of the Treatise—or of any other theoretical enterprise; his detractors point out, in other words, that some of the supposed results of the science of man are incompatible with other claims Hume defends and that Hume, more than once, and at critical junctures, essentially abandons his target of investigation (for skeptical motives?) with only the flimsiest, most superficial, or a completely unpersuasive connection leading on to his next target. Furthermore, as we have noted, Hume’s critics think that he will appear to take one basic position in one context, and in another, another, incompatible one. We may give focus to this last complaint by asking some key questions, answers to which are not obvious, that derive from textual passages that appear to imply different conclusions. Is Hume, in strictest terms, a philosophical idealist? Is he, indeed, like Berkeley at least sometimes appears to be, a philosopher for whom no alternative to idealism is even thinkable? Is it rather that Hume’s view is that, although some nonidealist view might be possible—although it is thinkable, or coherent, that there be things that are entirely non-mental—we are completely unable to know whether this may be true? Or, rather, does Hume think that there are physical objects—bodies—the matter not being seriously in any doubt? If there are bodies, do they or do they not have ‘hidden powers’—powers we do not observe, but may infer or may impute to them, which play objective causal roles in what those bodies do? Does Hume, ‘at the end of the day’, believe some sort of ‘double existence’ theory, according to which we, at least normally or frequently, have sensory experiences which are ‘of’ bodies or their sensory qualities, or is any such theory falsehood and illusion? Are experiences (ever) representational at all, such that they correspond (in some degree or other, that degree knowable, or not) to realities external to us, or is this never in fact the case? When someone experiences an impression of blue, for example, is the impression itself blue, or is it not-blue but, rather, of something that is blue? Is Hume an event ontologist? Is he strictly and literally an atheist, or, rather, a kind of

32

Peter Loptson

minimalist deist? When Hume says that there are moral distinctions, does this imply merely that moral ideas and concepts are reasonably clear, and able to be distinguished from each other, or does it imply, rather, that some things are good, bad, right, or wrong? Is Hume a virtue ethicist? Is he a moral realist? (I appreciate that some of my earlier account of Hume’s views will itself imply definite answers to some of these questions. Like other readers of Hume, I certainly find some interpretations more likely right; even if my purpose here is to bring attention to what are frequently severe opacities in Hume’s texts.) Many of these questions may be able to be dodged or subverted with a ‘depends what you mean’ response or with charges of anachronism—‘no one in Hume’s day thought in such terms; at any rate, Hume himself didn’t’. That such responses are inadequate and unconvincing is shown by the fact that Hume’s fellow-Scottish philosopher Thomas Reid, as early as 1764, at least, certainly thought precisely in these terms, in bringing equivalents of these questions to Hume’s texts. And the striking facts are that Hume’s nineteenth-century critics—Green and Grote, at least—also raise these same questions and that present-day Hume scholars and interpreters give, typically, with great confidence and assurance, mutually contradicting answers to each of these same questions. (One of the very striking features of contemporary Hume scholarship is the extent to which its practitioners, including obviously learned, philosophically adroit investigators will write as though passages which problematize, or flatly contradict, their favoured readings, simply don’t exist.) At some point, it seems reasonable to conclude that some matters, and among them some issues that are deep, bearing on the philosophy in its fundamentals, are not sorted out in Hume, or by him. They are certainly inconsistencies. From one point of view they certainly also are flaws. The plea I will make for Hume, with which I will conclude this first section of the paper, is that in at least in one very important sense, these arresting conclusions of honest inquiry into the Humean corpus do not bespeak flaw. They reflect, rather, extraordinary intellectual honesty. Each of Hume’s philosophical missions is, by itself, altogether honourable, serious, important, legitimately motivate-able, and motivated. There is work to be done, and a world to be won, in abandoning old prejudice and presumption by aiming to study the human beast with a minimum of assumptions, through unblinkered eyes, empirically, scientifically. And, independently, there is a cognitive endeavour: aiming to work out what really can be thought, grasped, known, or justified. To determine genuinely

Hume’s Disappointingly Accurate Conclusions

33

what should, surely, be able to be charted from a base in individual subjective experience is a legitimate philosophical venture; if it cannot get very far and ends up in a coal pit or whatever, well, there it is. There will be no use just pretending that we do, somehow, inductively leap beyond that base to outcomes that common life or somebody’s science (making use of the inductive method) says that we do. There are complex, important results to which to aspire as to the character of normative life and thought within the frameworks of human animality, human motivational psychology, and the challenges and imperatives of living together with each other. If Hume’s position is not definitively coherent, it raises the relevant issues. Although some philosophers and scientists have gotten bits of this wide web right, no one has yet grasped the moral, social whole, justified and united in a synoptic explanatory theory and analysis all the competing claims of private self-interest and interactive human gregariousness, or adequately described the intricacies of our psychological makeup which we share with the beasts and the systemic functional rationality which the social system we put together involves and requires. If such inconclusive or disjointed theories unhappily (or happily) coexist in Hume’s oeuvre, that is just the way it is. Hume is not to be dismissed because he, whatever the limitations or imperfections of his work, tells it like it is. Some might say that Hume ought to have written three distinct books. Pity he didn’t have a more judicious, a more taxing editor. Yet, the result would just have been three wildly mutually conflicting books. A better judgment will be found in the concluding words of Spinoza’s Ethics: omnia praeclara tam difficilia quam rara sunt. [“All things excellent are as difficult as they are rare.”] 2 Hume and Induction 2.1 Non-Rational Induction: Describing the Way We Do Behave But let us move on to a more specific investigation of Humean induction. As we shall see, Hume is not alone in his inductive skepticism. There are important philosophical precursors to his views, Leibniz in particular. But, it is important to openly acknowledge, from the start, that Hume reaches two different conclusions about inductive thinking and its rational justifiability and conflates them. One is that observation of human behaviour demonstrates that we humans do not, in point of fact, think or reason inductively on rational grounds or on rationally justificatory bases. The other conclusion is that it is impossible for us to think inductively on a rational basis. These are identifiably different claims. It might be that

34

Peter Loptson

induction is rationally justifiable even if we humans, through habit, laziness, or the priority of feeling in fact come to employ it on purely nonrational bases or because of non-rational grounds. It might even be that we humans—or, possibly, just some clever philosophers among us—could arrive at a rational grounding for our inductive beliefs and practices even though we don’t normally employ those grounds in daily or scientific life. If, however, it is truly impossible to inductively think on a rational basis, such possibilities are inherently contradictory and beyond consideration. Hume’s descriptive case for the first claim, i.e., for the non-rational character of inductive thinking and practice, in human and other animal behaviour, is actually quite a good one, at least in respect of the origins and regularized early-life deployments of such thinking and practice. Even if we eventually achieve a modicum of what we are pleased to call rationality, in both theoretical and practical modes, we, like the other animals, respond to patterns and stimuli in the vicinities in which we find ourselves, essentially from the beginning of life. We have become thoroughly habituated induction practitioners long before maturity, and we do indeed seem irresistibly and automatically to have and apply inductive expectations throughout our experience; above all, in early stages, where significant measures of pleasure and pain are concerned. These formations cannot be evidence-based; they are what we employ to form the ideas that we have of (empirical) evidence. They must, just as Hume claims, have bases in automatically operational features of our minds, whatever the precise mechanisms, in what may be labelled instinct. In this descriptive account of how human beings use induction, Hume is not at all being a ‘skeptic’. This is reasonably good empirical psychology, given even firmer grounding with its coupling with observations stemming from (or at least modest inferences from) animal psychology. When an infant or young child recoils from the reappearance of an observed item that has caused pain on a prior occasion, just as with a young non-human animal, this reaction cannot possibly be a matter of being even a preliminary or earlystage warranted-conclusion-drawing from experience. The fledging creature, human or otherwise, can have had no basis whatever for supposing that previous parallel or similar cases will be in any way relevant to the new case. When the youthful creature proceeds nonetheless as though the alreadyexperienced instance is evidentially relevant to the new instance, this can only be a matter of projection or imposition from something operating more or less automatically and non-rationally in the creature.

Hume’s Disappointingly Accurate Conclusions

35

Not that Hume wishes to withhold at least a version of reason from the other animals—the beasts—any more than from humans. He tells us that “no truth appears to me more evident, than that beasts are endow’d with thought and reason as well as men.” He goes on: We are conscious, that we ourselves, in adapting means to ends, are guided by reason and design, and that ‘tis not ignorantly nor casually we perform those actions, which tend to self-preservation, to the obtaining of pleasure, and avoiding pain. When therefore we see other creatures, in millions of instances, perform like actions and direct them to like ends, all our principles of reason and probability carry us with an invincible force to believe the existence of a like cause... The resemblance betwixt the actions of animals and those of men is so entire in this respect, that the very first action of the first animal we shall please to pitch on, will afford us an incontestable argument for the present doctrine.17

Hume goes on in this section of the Treatise to argue that behaviour, actuated in both beasts and men by interactions with the world that are taken to bear on matters of self-preservation, survival, pleasure and pain, and the like, will have parallel or common causes. Whether found in an animal, a child, an uneducated peasant, or a supposedly rational educated human adult, all behaviour and thought of this kind will be grounded in what Hume (a little misleadingly) calls custom—habit, either originally implanted instinct, or conditioned response from repeated similar experiences. A considerably longer, and in many ways quite a different paper than I offer on the present occasion, would explore more fully the theme of Hume and the beasts. It appears to be an important part of his philosophical project to draw into conjunction and comparison a number of facets of human and animal life. Usually he sees commonalities and similarities. These discussions are presented, typically, in what seems a deliberately provocative way, in opposition to Cartesian and other rationalist philosophies. But this facet of Hume’s enterprise also stands on its own as a significant part of Hume’s naturalism. It is also incomplete. The final sections of Treatise 1.3, 2.1, and 2.2, each take up a topic or theme concerned with animals, their natures, and our similarities or other relations to them. The Parts of Hume’s great work in which these sections appear address themselves to knowledge and probability, pride and humility, and love and hatred. One would have welcomed a still more extensive presence of the beasts in Hume’s account, perhaps especially in his exploration of morality. At any rate, some interpreters have seen degrees of anticipation of 17

T 1.3.16.2.

36

Peter Loptson

Darwinian conceptions in Hume’s discussions of the beasts; though, in fairness, the mere noting of human animality and respects of similarity, including demotions of vaunted human rationality, doesn’t really advance one very far towards the Darwinian synthesis. The controversial— differently interpreted—Part 12 of Hume’s Dialogues concerning Natural Religion, where Hume’s mouthpiece Philo, in ‘Philo’s reversal’, seems to acknowledge greater force to an argument from design than had appeared evident earlier in that work, also speaks against much of a Humean anticipation of genuine natural selection. At any rate, the world, as Hume sees it, is very much a naturalistic world, and we are, for him, not so very impressively different from the other animals. Whether one calls it reason or prefers not to, their behaviour, as well as ours, is fundamentally grounded in instinctual behavioral proclivities and conditioned reflexes. And, that being the case, the idea that our inductive habits and practices and thinking, shared with the beasts, is something that we reason out as we interact with the world that we experience, will be a non-starter. But of course, as we have noted, this won’t all by itself imply that inductive thinking and practice is inevitably or inherently non-rational. Lots of true conclusions are believed on the basis of inadequate arguments or slender or insufficient or wholly non-supportive evidence. It isn’t rare to come to have better reason, or even unqualifiedly good reason, for believing something formerly believed for bad or insufficient reasons. And—a little more exotically—it seems perfectly possible that most or even all humans might, at all stages, believe something that was in fact true with surrounding or supporting confirming evidence that most or all simply invariably miss. Most or all of us might lack necessary capacities to assemble the justifying bases for some result or might have the capacity, but just happen, accidentally and contingently, never to put together relevant clues or evidentiary structures or principles, or their links to the conclusion concerned. The fact that we humans do tend to behave nonrationally does not, in short, preclude the possibility of our behaving rationally. 2.2 Leibniz: Is Rational Induction Impossible? Although Hume does seem to conflate what he thinks is the causal origin of our inductive proclivities in our (and other animals’) inherent habits and ‘instincts’ with the more general or abstract prospects of inductive warrant as such, he does appear nonetheless to gesture toward the distinction drawn here with his superficially ironic utilization of the Leibnizian model of a pre-established harmony, in the first Enquiry.

Hume’s Disappointingly Accurate Conclusions

37

Here, then, is a kind of pre-established harmony between the course of nature and the succession of our ideas; and though the powers and forces, by which the former is governed, be wholly unknown to us; yet our thoughts and conceptions have still, we find, gone on in the same train with the other works of nature. Custom is that principle, by which this correspondence has been effected; so necessary to the subsistence of our species, and the regulation of our conduct, in every circumstance and occurrence of human life. Had not the presence of an object instantly excited the idea of those objects, commonly conjoined with it, all our knowledge must have been limited to the narrow sphere of our memory and senses; and we should never have been able to adjust means to ends, or employ our natural powers, either to the producing of good, or avoiding of evil. Those, who delight in the discovery and contemplation of final causes, have here ample subject to employ their wonder and admiration.18

Though we are proceeding essentially irrationally, Hume says, it is a good thing that we proceed as we do, since our practices correspond to the actual course of nature, ensuring our survival. If nature is in fact sufficiently uniform that human survival depends on supposing that it is and behaving as though it were, there must be some rational basis for supposing that this is so, including for Hume’s supposing that it is, even if Hume himself does not draw this conclusion, or even, perhaps, notice that it is suggested by his claim that human (and other animal) behavioral practice parallels objective patterns of the world. My investigation of Hume and the distinction between how we do behave with respect to drawing conclusions about not-yet-experienced cases and how, at least ideally, it might be possible for us to behave, has followed Hume in citing Leibniz’s pre-established harmony. This view points to a corollary of the primary issue that the present section of this paper is concerned with. Although they appear initially to be profoundly antithetical philosophers, Leibniz and Hume turn out to have many deep commonalities, including a remarkable number in the intersecting clusters that involve human nature, animal behaviour broadly construed, probability, causality, and the uniformity of nature. Still other locations of philosophical convergence may be found to present themselves. Connections between Leibniz and Hume have only occasionally been explored in the secondary literature;19 though one significant 1989 paper 18

EHU 5.2.21. One other paper, in addition to the one to which I will be giving attention, is Vadim Vasilyev, “Hume: Between Leibniz and Kant (The role of pre-established harmony in Hume’s philosophy)”, Hume Studies , 19, no. 1, (1993): 19-30. Carl Schaarschmidt, the nineteenth-century translator of Leibniz’s New Essays into German, adduced similari19

38

Peter Loptson

argues that Leibniz preceded Hume in formulating the problem of induction.20 The case for that view will be explored here, along with other dimensions of Leibniz-Hume mutuality in the general territory of inquiry into induction and its actual and possible rational/normative place in human life and practice. The Hume and Leibniz connection has, as indicated, both historical, or textual, facets, as well as empirical and philosophical ones. The evidence seems persuasive that no philosopher before Hume sees what we think of as the problem of induction in clear, sharp, well-focused terms. Some of Hume’s readers appear to deny that he himself did either, holding either that he is never genuinely skeptical about induction or that he has some other problem in view than the one that posterity generally assigns him. I think that it is difficult to read the relevant sections of both the Treatise of Human Nature and the Enquiry concerning Human Understanding carefully without concluding that posterity has things right in this area. And, while there are partial anticipations of the problem of induction that may be discerned in earlier philosophers, the explicit fully articulated problem, with its special feature of arguing that attempts to justify or rationally ground inductive expectations and inferences seem so regularly to be circular, appears only altogether on the scene with Hume. So at least I will argue. Jonathan Westphal, in his “Leibniz and the Problem of Induction”,21 makes a case for the view that Leibniz essentially formulates the problem before Hume. Leibniz certainly comes very close, very impressively close. Most of the texts Westphal cites will have been unavailable to Hume, so the issue in their regard is whether Leibniz, independently and unknown to Hume, discovered the problem of induction. It is of separate interest whether Leibniz’s reflections and arguments in this area may have some presence in the one Leibniz text that Hume reasonably certainly did read, and then whether Hume may have been at least partly prompted toward his articulation of the problem of induction from that reading.

ties between Leibniz and Hume on a general uniformity of moral conviction implanted in human nature. So Alfred Gideon Langley, who produced the 1896 translation of the New Essays into English, reports. See Gottfried Wilhelm Leibnitz, New Essays concerning Human Understanding, trans. A. G. Langley (La Salle, IL: Open Court, 1949), p. 735. 20 Jonathan Westphal, “Leibniz and the Problem of Induction”, Studia Leibnitiana, 21, no. 2, (1989): 174-187. 21 “Leibniz and the Problem of Induction”, pp. 174-187.

Hume’s Disappointingly Accurate Conclusions

39

We know that Hume read Leibniz. He cites or alludes to him a number of times.22 His library contained the only book of Leibniz’s published in that philosopher’s lifetime, or, indeed, prior to 1765, long after Hume’s two classic works in epistemology and the philosophy of science had been published, namely, the Theodicy of 1710.23 The Theodicy concerns itself with a good deal more than the topic of its title. It provides in fact—in parts and pieces, to be sure—a very extensive exposition of Leibniz’s whole metaphysical system as he saw things by the end of the first decade of the eighteenth century. Interpreters of Leibniz differ considerably about the career-length unity of his system. Some see an essential unity, at one extreme, even from the later 1670s until the end of his life. Others see a very marked periodization. I myself think that a version of the first of these options is the more accurate; in any case, those issues will not enter the discussion here, as I will be reasonably exclusively concerned with the Leibniz of the later part of his career, after 1700, and above all with the Leibniz of the Theodicy—which is very likely the only work of Leibniz’s that Hume will have read. A good number of parallels, similarities, or convergences between Leibniz and Hume may be discerned. It is usual to find anticipations of Hume’s conception of causality, as unmodalized temporally-ordered constant conjunction, in Malebranche. Largely the same idea may be seen as well in Leibniz. Successive monadic states are conceived by Leibniz as 22

In the Abstract to the Treatise of Human Nature Hume cites Leibniz, referring to a passage in the Theodicy (T SBN 646f.). In EHU 5.21 occurs the reference to Leibniz’s ‘pre-established harmony’, as well as to his revived focus on final causes; this passage will receive more extensive consideration below. In EHU 7.29, fn. 17, there is a reference to the vis viva controversy, in which Leibniz was a principal protagonist. In the Dialogues concerning Natural Religion, in Part X, Leibniz is explicitly named, as the first prominent philosopher to affirm that this is the best of all possible worlds, and as having made that thesis “essential to his philosophical system”. Hume, in a footnote, says that William King had promulgated this view earlier, in 1702, as had some others, but “none of so great fame as that German philosopher”. 23 David Fate Norton and Mary J. Norton, The David Hume Library (Edinburgh: Edinburgh Bibliographical Society in association with The National Library of Scotland, 1996), pp. 32, 109. The Hume family library—the library assembled originally by the philosopher and then augmented by his nephew—subsequently included a 1765 volume of Leibniz’s philosophical works (ibid, p. 109). This suggests that Hume continued to interest himself in Leibniz’s philosophy. The early modern thinkers whose philosophical work appears in the library, in editions published prior to 1750, are Bacon, Bayle, Berkeley, Boyle, Butler, Condillac, Saint-Evremond, Galileo, Hartley, Hutcheson, Leibniz, Locke, Mandeville, Montesquieu, Shaftesbury.

40

Peter Loptson

contingently sequential, decreed by God to exist and to occur as they do by virtue of the contribution they make to the best possible world. Leibniz plainly has no place for mere natural necessity. Only strictly contradictory states of affairs would literally be metaphysically or strongly impossible. All else is logically contingent, even if the whole pattern of things is necessitated by divine perfection, which requires that only rational, and morally optimal, paths be taken. This picture is very explicitly and emphatically affirmed in the Theodicy, where Leibniz more than once aligns it with the theological perspective of the advocates of the Augsburg Confession—that is to say, of the Lutheran theological view, the denominational persuasion of his own background and lifelong at least formal commitment. Thus: God can put properties into matter which cause it to operate from a distance. Thus the theologians of the Augsburg Confession claim that God may ordain not only that a body operate immediately on divers bodies remote from one another, but that it even exist in their neighbourhood and be received by them in a way with which distances of place and dimensions of space have nothing to do. Although this effect transcends the forces of Nature, they do not think it possible to show that it surpasses the power of the Author of Nature. For him it is easy to annul the laws that he has given or to dispense with them as seems good to him, in the same way as he was able to make iron float upon water and to stay the operation of fire upon the human body.24

It is to be noted that for Leibniz there are not ever literally miracles; everything the deity does is rule-governed or lawlike. Those requirements have the result that the world is fully deterministic. There are exceptionless regularities, some simpler, some more complex, some instantiated frequently, some only occasionally. All is subject to law and rule and principle—entirely exceptionless. Yet, again, all of these patterns are logically contingent; none if denied implies a contradiction. In principle, any combination of co-instantiated monadic sequential options is possible and is to be found among the infinitely many non-actual possible worlds; it is the constraints dictated by God’s perfection that have limited the world made actual to the one that has in fact obtained, as well as to its having the particular structure of exceptionless laws and their instantiations that it does. Hume, like Leibniz, is a determinist. As with Leibniz, patterns to be found in unthinking nature, or nature apart from such rational consciousness 24

Theodicy 19.

Hume’s Disappointingly Accurate Conclusions

41

and agency as it may contain, are wholly subject to regular law, and so too are the patterns that occur in the thinking or rational parts of the world. Both philosophers are compatibilists. Hume, interestingly, and impressively, makes his case for the problem-free conjunction of exceptionless law governing rational thought and action with similarly exceptionless law governing inanimate nature, not primarily by emphasizing how much rational agents are constrained, but rather by ‘de-fanging’ extra-human nature—by arguing that there is no necessity to be found there, just as there isn’t in rational or animate nature. Everywhere one meets with what is exceptionlessly the case and never with what ‘must’ be the case. Must’s and necessities are to be found only in logic, mathematics, and in projections we observing psychologically-formed minds project—illicitly and unjustifiably—upon the nature we think we are perceiving and about which we reach general conclusions. If Hume, like Leibniz, is, as we have said, a determinist and a compatibilist, both thinkers offer philosophies of the experiencing parts of the world—the minds, including both higher (human) and lower (animal) ones. For both the conception of laws of nature, or laws of the world, is of logically contingent exceptionless patterns. Both also have at least partial (in Hume’s case) accounts of the world apart from the experiencing minds, human and otherwise—philosophies of nature, we may say. And, in both cases, the non-experiencing parts or aspects of the world are subordinate to the experiencing parts or aspects. The subordination is so great that both philosophers have sometimes been interpreted as, strictly speaking, philosophical or metaphysical idealists. This is particularly well-known in the case of Leibniz; one of the primary interpretive positions of his system still in the present day sees it as idealist. Close inspection reveals still more metaphysical remarkable commonalities. At first the contrasts could hardly seem greater. Leibniz is the ultra-metaphysician, the very paradigm case of a rationalist giving his essentially arm chair account of the structure and content that the world must necessarily have. Hume, for his part, explicitly rejects the very possibility or coherence of a metaphysical project at all. It turns out, though, that for Hume there is ‘good’ metaphysics and ‘bad’ metaphysics, and while he wholly repudiates the latter, the former has positive endorsement. (We “must cultivate true metaphysics with some care, in order to destroy the false and adulterate.”25 This theme, and contrast, appears frequently in Hume’s texts.) And, in any case, as his commentators 25

EHU 1.12.

42

Peter Loptson

regularly note, there are ontological—metaphysical—claims and implications of claims met with throughout his work. As for Leibniz, his happy ecumenism is seen on inspection to involve considerable qualification. The several metaphysical systems of the past have much good to be said practically for all of them, but they do need reinterpretation, properly sympathetic adaptations to enable them to fit what we can and should see to be the exigencies of modern advances, the result of the process being that more or less all of them point to Leibniz’s own system. For both Leibniz and Hume, there is a distinction to be drawn between even best-dressed versions of what the theorists think and say, what common sense and common folk—the vulgar—think and say, and the more perspicuous truth that careful theoretical philosophy will express. But the foregoing, it may be said, are generalities, on a somewhat high plane. At a more specific level, Leibniz is a philosopher for whom the concept of substance is central and foundational. His system is a system of individual substances, which are metaphysical atoms, without parts, which endure numerically identical from their apparently miraculous beginnings then forever afterwards. Hume is the philosopher—perhaps the first—who rejects substance; indeed, he argues that we do not have so much as an intelligible idea of what such a thing is or might be (“that unintelligible chimera of a substance,” Hume says 26). As for a self, or mind, its actual reality is to be a ‘bundle of perceptions’. Again, closer views show that things are more complex. Leibniz’s monads are substances, to be sure. But each monad is wholly defined by the complete set—sequence—of states the monad has. No difference is drawn or discernible between some of these states and others of them, whether modally or metaphysically. All are essential to the monad, which is nothing other than the entity constituted by precisely that set of states. Were one of them altered, supplemented, or missing, one would have a numerically different monad. And all of those states are, Leibniz says, perceptions of the monad. The monad is, in short, a bundle of perceptions. There is no individual essence or haecceity that the monad has, which is to be met with throughout its existence or in each of its states. It, the monad, just is that particular bundle of perceptions. And Hume, for his part, is actually happy enough to adopt and make some use of the concept of a substance—so long as that concept is taken only to be the idea of “a collection of simple ideas, that are united by the imagination, and have a particular name assigned them, by which we are 26

T 1.4.3.7.

Hume’s Disappointingly Accurate Conclusions

43

able to recall, either to ourselves or others, that collection.”27 And, as for the conception of a person or self and the bundle theory that Hume advocates for it, Hume notably does not take a path it might have seemed natural for him to take, namely, to assign the unity of the bundles he identifies with the human self to the human or animal bodies that common sense and science say possess those bundles in which they inhere. Obviously, even a brilliant philosopher will not think of every view that a reader or interpreter will see as plausibly or appropriately adopted by the philosopher. But it really does seem hard for naturalist, empiricist philosophy to miss the idea that the identity conditions for perception-bundles should pair them with individual living animals or animal bodies. At any rate, at several junctures of his philosophy Hume resists, or at least fails to opt for, materialist options that might have seemed available to and natural for him, and this is one of them. Humean perception-bundle selves are—it seems—locked within those perceptions. Hume rejects—it seems—double existence indirect perceptual realist views. He also appears to reject philosophical idealism, yet he appears to imply that that is the only view that can make coherent sense of the facts of perception and supposed experiences of and beliefs in an external world of objects. It all looks very Leibnizian, for Leibniz’s monads are of course famously windowless. Also like Leibniz, Hume, somewhat oddly, in fact, never expresses skepticism about the plurality of minds—never raises ‘the problem of other minds’. For all that he is, somewhat notoriously, ‘the great skeptic’ and sometimes explicitly embraces the label of skeptic, his radical skepticism, at least, in so far as it is focused on categories of entity commonly held to be real, is always only about ‘the external world’ of independent objects, and bodies. He does, of course, also raise radical skeptical arguments with regard to conclusions reached by reason. (Hume is also skeptical about substantial selves, substances in general, God, divine providence, objective necessity, an objective morality, induction, etc., but none of these, certainly not in philosophical periods following his own, qualify as particularly radical skepticism.) Hume never seems to conceive as doubtful or problematic that there is a large plurality of distinct experience bundles. In fact, it is Leibniz, not Hume, who explicitly raises the idea that one’s self, some solitary and isolated mind, might be alone in the universe (accompanied, of course, for Leibniz, by God), and says that nothing in that self’s experiences would differ: its content, from beginning to end, would be precisely the same. 27

T 1.1.6.2.

44

Peter Loptson

It is Leibniz also, and only partially and somewhat feebly, Hume, who sees time as a subordinate, reducible feature of the world. For Leibniz’s God, all mental contents exist in an atemporal eternity of co-presence. And, in a sense, the same is true for the created monads as well, since every occurrent monadic state is “pregnant with its future”28—it includes what we will call future-tensed states, hence also, plainly, past-tensed states, that will encompass, from that monad’s “point of view”, of course, not just the whole history of that monad, but the whole history of every other one, hence the whole history of the world. This will clearly point to the idea, at least, of the ultra-radical-skeptical conception of solipsism of the present moment, and it is again in Leibniz, not Hume, that we find this idea implicit. Leibniz gives attention as well, as Hume does, to living beings other than humans in his philosophical investigations. That, of course, rather understates things in Leibniz’s case. His monads comprise a richly diverse hierarchy of animated life forms. Leibniz was hugely interested in and impressed by the developments in microscopy that van Leeuwenhoek, most notably, had achieved. All of nature teemed with life and graded levels of thought or thought-like states. And, although the spirit monads, such as ourselves, comprised a class apart, the ones with consciousness and apperception (as opposed to mere perception), lesser thinkers and life forms have experiential states, very many of them of like kind with those we know. It is common to see Leibniz’s system primarily in a prioristic terms, as the working out of consequences of the postulate of the perfect being, then of the ontological argument that proves that he must exist and the detail of world-creating that must ensue from that. There is, too, a richly empirical content that Leibniz discerns in the world God has made. Leibniz was, of course, a polymath, interested in and creatively contributory to a wide array of research areas, and problems. But it is plain in virtually all expositions of his metaphysical system, including numerous passages in the Theodicy, that he welcomes and draws upon what he takes to be empirical, and latest-science results that he views as illustrating or providing degrees of confirmation of his system. The general character of the comparative picture is that both Leibniz and Hume see humans and other animals as operating largely mechanically and sub-rationally in their experiential interface with the world. Strictly, “the world” is to be understood as “bracketed”, to use the later Husserlian 28

“It is one of the rules of my system of general harmony, that the present is big with the future,” Leibniz says (Theodicy 360; and frequently elsewhere; Leibniz’s emphasis).

Hume’s Disappointingly Accurate Conclusions

45

vocabulary. For Leibniz, and probably also for Hume, nothing is directly or immediately encountered that is other than psychological or intentional ‘content’ that is wholly interior to the experiencer’s ‘mind’. In both cases, there may or may not be exterior realities that ‘correspond’ to that content. In fact, the greater interpretive likelihood—for both thinkers the texts are ambivalent, arguably, flatly inconsistent—is that there are exterior corresponding realities, and if there are, those exterior realities may or may not be themselves ‘non-mental’ in nature. While important for the fuller and more accurate understanding of both thinkers’ philosophies, these are not issues of primary concern in the present context. For our purposes, we can, as both Leibniz and Hume themselves do, proceed in ‘as though’ mode: it is as though human and animal minds encounter and experience an exterior world regularly or very frequently consisting of non-mental objects— ‘bodies’. Even if the full literal rendering, and reckoning, will tell a different tale or interpret—translate—that tale in more esoteric terms, or possibly—in Hume’s case—involve a retreat to agnosticism, proto-Kantian or otherwise, about what is really or literally going on, it will still be meaningful, appropriate, and useful to proceed with a conception of experiencers, human and animal, functioning in causal interface with a world of bodies exterior to them. And, in that picture, for both philosophers, what occurs is largely mechanical, automatic, put in place by ‘nature’, or nature’s master, and non-rational. The chief difference between the two philosophers in this area is that, for Leibniz, there is something additional that some of the experiencers— the rational, conscious, apperceiving ones, notably—have to fall back upon, more precisely, to rise to, while for Hume, evidently, there is not. Reason is real and achievable, according to Leibniz, and is able to ground and justify (at least some) knowledge that goes beyond experience. For Hume, on the other hand, there is no rational or justifying basis to be had. At least in the sphere of interface with and apprehension of anything at all that is beyond the horizons of experience—the horizons “of memory and the senses”, as Hume puts it—all of the experiencers that we know about, among them of course ourselves, are without rational or justifying succour. We can and will continue to proceed instinctually, but this is not to be confused with rational justification. This is, of course, to understand the problem of induction, as well as its imputation to Hume, in classical ways. For many philosophers working on induction in and since the eighteenth century, the issue has been more that, given that inductive inference is rational and justified, in general or in

46

Peter Loptson

principle, what is it that will distinguish the cases where it is warranted and well-grounded from cases where it is not? Some appear to want to assign to Hume himself views or endeavours along these lines. As I have earlier suggested, Hume’s texts don’t imply such interpretive views. I think that Hume is genuinely skeptical about the prospects of human beings being able to achieve a principled ground for their habits and expectations about not-yet-experienced cases. He does, nonetheless, appear to make it clear that he thinks that nature is in fact reliably uniform. His readers are left in the dark as to how Hume himself supposes that he knows this or has even the slightest rational warrant for this view. A reply, on his behalf, that he doesn’t think he knows that nature is uniform, seems harder to sustain with conviction when it is noted that the difficulty will extend to supposing that there is even any relevance that experienced cases will have to not-yetexperienced ones. One of the several interesting features of the Leibniz-Hume-induction cluster is that it develops that, at least on the empirical or experiential side of things, Leibniz is even more skeptical than Hume about induction. Leibniz notes, or affirms, that nature actually isn’t uniform, and will in due course change, hence the human being employing it purely in the animalistic or instinct-guided way really is like Russell’s well-known chicken example—one day the chicken’s expectation that he will be fed by the farmer meets with the grim reality of having his neck wrung. Here is what Leibniz says (in the New Essays Concerning Human Uunderstanding29): That raises another question, namely, whether all truths depend on experience, that is on induction and instances, or if some of them have some other foundation. For if some events can be foreseen before any test has been made of them, it is obvious that we contribute something from our side. Although the senses are necessary for all our actual knowledge, they are not sufficient to provide it all, since they never give us anything but instances, that is particular or singular truths. But however many instances confirm a general truth, they do not suffice to establish its universal necessity; for it does not follow that what has happened will always happen in the same way. For instance, the Greeks and Romans and all the other nations on earth always found that within the passage of twenty-four hours day turns into night and night into day. But they would have been mistaken if they had believed that the same rule holds everywhere, since the contrary was observed during a stay in Novaya Zemlya. And anyone who believed that it is a necessary and eternal truth at least in our latitudes would also be mistaken, since we must recognize that neither the earth nor even the sun exists necessarily, and 29

G. W. Leibniz, New Essays on Human Understanding, ed. Peter Remnant and Jonathan Bennett (Cambridge: Cambridge University Press, 1981), p. 49.

Hume’s Disappointingly Accurate Conclusions

47

that there may come a time when this beautiful star no longer exists, at least in its present form, nor its whole system.

The tone, or note here, is not of course skeptical; except with regard to the epistemic prospects of the senses. Leibniz is confident that secure knowledge of the world is achievable, through reason. But the condition of mere sensory apprehension of the world is lowly indeed, and mechanical. Leibniz goes on, in this same context, to characterize the mental condition of the non-human animals—the beasts—and we see a clear assimilation to, or continuum with, the merely empirical interface with the world as it appears in humans as well. In this light, the following passage is in its own way strikingly proto-Humean. Leibniz writes: ...the senses provide the occasion, and successful experiments also serve to corroborate reason, somewhat as checks in arithmetic help us to avoid errors of calculation in long chains of reasoning. It is in this same respect that men’s knowledge differs from that of beasts: beasts are sheer empirics and are guided entirely by instances. While men are capable of demonstrative knowledge, beasts, so far as one can judge, never manage to form necessary propositions, since the faculty by which they make sequences is something lower than the reason which is to be found in men. The sequences of beasts are just like those of simple empirics who maintain that what has happened once will happen again in a case which is similar in the respects that they are impressed by, although that does not enable them to judge whether the same reasons are at work. That is what makes it so easy for men to ensnare beasts, and so easy for simple empirics to make mistakes.... The sequences of beasts are only a shadow of reasoning, that is, they are nothing but a connection in the imagination—a passage from one image to another; for when a new situation appears similar to its predecessor, it is expected to have the same concomitant features as before, as though things were linked in reality just because their images are linked in the memory...30

Essentially the same views appear also, if more briefly, in the Theodicy, where Hume may have encountered them: The external senses, properly speaking, do not deceive us. It is our inner sense which often makes us go too fast. That occurs also in brute beasts, as when a dog barks at his reflexion in the mirror: for beasts have consecutions of perception which resemble reasoning, and which also occurs in the inner sense of men, when their actions have only empirical quality. But beasts do nothing which compels us to believe that they have what deserves to be properly called a rea30

New Essays on Human Understanding, p. 50f.

48

Peter Loptson

soning sense... Now when the understanding uses and follows the false decision of the inner sense...it is deceived by the judgment it makes upon the effect of appearances, and it infers from them more than they imply. For the appearances of things do not promise us absolutely the truth of things, any more than dreams do. It is we who deceive ourselves by the use we make of them, that is, by our consecutions. Indeed we allow ourselves to be deluded by probable arguments, and we are inclined to think that phenomena such as we have found linked together often are so always... Such an error is pardonable, and sometimes inevitable, when it is necessary to act promptly and choose that which appearances recommend; but when we have the leisure to and the time to collect our thoughts, we are in fault if we take for certain that which is not so. It is therefore true that appearances are often contrary to truth, but our reasoning never is when it proceeds strictly in accordance with the rules of the art of reasoning.31

Some of this—the final sentence in particular—is just rationalist assertion of epistemic superiority over empiricism. But one does well to note, again, Leibniz’s identification of a mode of thinking that he calls consecution, which appears both in humans and the beasts and is a mere semblance of actual reasoning. It proceeds by taking internal images of exterior things for reliable guides to what is there, when in fact so thinking is no more reasonable or rationally better grounded than would be drawing inferences about the world from dreams. I suggest that this does indeed come rather close to an articulation of the problem of induction. Close, even if not quite there. Leibniz fails to bring out the distinctively Humean idea that we do—or many a philosopher would, if challenged—seek to defend inductive thought and practice as justified with the claim that it has proven itself in past instances, failing to see that extrapolating that fact and applying it in yet unobserved cases is presupposing the validity or rational warrant of induction, which was the very thing that was supposed to be backed up or justified. Leibniz, clever as he was, might be regarded as able to come up with this idea had he lingered longer than he did on consecution, probability, and inference-drawing from (mere) sensory experience. But he didn’t linger, and the palm goes accordingly to Hume. They remain though, at least in this territory, very much birds of a feather. Conclusion: The Difference between Hume and Leibniz Let us finish this brief comparison by returning to the problem considered at the outset of the second part of this paper. Descriptively, at least, what we 31

Theodicy 65.

Hume’s Disappointingly Accurate Conclusions

49

call inductive “reasoning” turns out to be, on closer inspection, something more like a non-rational drawing of conclusions based on custom and habit. Given that custom and habit are the modus operandi of normal (or even all) human experience, we are still left with a second question that needs to be resolved. Actual human behaviour aside, is inductive reasoning even theoretically possible? Is a form of reliable, logical inference about future cases or all cases of particular type, in principle, even possible? Here is where Leibniz and Hume, for all their similarities, seem to disagree. Indeed, this could be said to be precisely where the unbridgeable gap between these rationalist and empiricist forerunners lies. Leibniz accepts that we can transcend mere “consecution” and operate on a higher rational plain to arrive at necessary, exceptionless inferences about the world. Induction understood as a form of rational apprehension is, in principle, possible. Hume takes the opposite view, it seems. Hume may often argue as though the world were a certain way, but when it comes to sheer epistemological issues, he refuses to take that second Leibnizian step into rationalism. Wary of self-delusion, of circularity, of obscure metaphysics, of invisible necessities, of substance, of causality, and so on, Hume balks at any final appeal to rationalism, at least when it comes to issues about matters of fact and metaphysical conclusions about the nature of the empirical world. Hume’s parsimonious empiricism, together with his mitigated skepticism, pushes him to a realization Leibniz decisively misses out on. And this is perhaps why Hume correctly identifies a fundamental problem in induction, a problem that Leibniz comes close to identifying until he papers it over — so to speak—with his appeal to rationalism of an epistemologically optimistic sort. As Hume comes to see, we are not so different than beasts after all. We are more intelligent beasts, it is true, but that is all. In Hume’s loosely-organized system, all induction is effectively, to use Leibniz’s terminology, “consecution.” No external or innate source of unempirical reason can shine a light into that darkness and somehow, miraculously, save the day. Without a doubt, Hume’s perspicacious conclusions about the impossibility of rational induction may disappoint the earnestly hopeful human agent, but they have the great epistemological merit of being accurate, and as far as we can rigorously tell, probable or even, as close an approximation to what we can consider to be true.

50

Peter Loptson

Afterword On a more positive note, the possibility that a particular instance of abduction, or inference to the best explanation—which Hume elsewhere (most notably, in his discussion of skepticism about the external world) misses—might afford the best justifying account of inductive inference. This justification would (likely) fall to the standard Humean objection of circularity, but it might plausibly be argued to be a ‘benign’ circularity. The central pattern of this putative justification of induction would be that in undertaking an explanation of past or experienced uniformities, one could consider as significant relevant alternative candidates either (1) that nature has exhibited these uniformities only or merely up to the present, or (2) that nature exhibits at least an approximation of those uniformities at all times and places. The latter (2) could be argued to be the better, because it is a simpler, explanatory alternative. The Humean might argue that this all-ofnature option is held to be simpler only with induction already assumed to be warranted, but to claim—as the opponent of (2) might argue—that a sound explanation of past (successful) patterns can be best or only afforded by reference just to that body of data seems itself arbitrary, ad hoc, and needing justification. The abductive inference, which enlarges the inference to cover the large body of past cases, could, it seems, ground inductive inference broadly and generally.32

32

I would like to thank my colleagues Louis Groarke and Paolo Biondi for their contributions to the final draft of this paper.

Hume and Aristotle on Induction: A Comparative Study Paolo C. Biondi University of Sudbury, Laurentian University

Abstract: According to Hume, induction, considered as the empirical form of reasoning resulting in knowledge of matters of fact, is problematic. Aristotle, on the contrary, thinks that induction can be trusted to provide even the principles of scientific knowledge. This essay argues that the key to explaining the differences between the Humean and Aristotelian accounts of induction lies in their respective attitudes towards human reason: whereas Hume takes an anti-Rationalist (and an anti-rational) approach in his account so that reason is entirely evacuated from the inductive process, Aristotle gives to reason and, in particular, to rational insight (noein or noesis) a significant role in induction. A number of points are compared and contrasted, including the objects of perception, the faculties of the mind involved in induction, and the inductive process. A key to the argument is to note that Hume’s attack on human reason presupposes the Rationalist conception of it, whereas Aristotle’s confidence in reason does not rest on this conception. In fact, Biondi shows how Aristotle’s account of induction is built upon quite different epistemological and metaphysical assumptions than is Hume’s account. Ultimately, an Aristotelian conception of the inductive process offers for us today a viable alternative to the Humean brand.

Introduction Since this anthology presents the Aristotelian tradition as the main rival to the standard Humean account of induction in currency today, it would be beneficial to sketch out a brief comparison and contrast between the views of Hume and those of Aristotle.1 Before presenting their respective accounts of induction, however, we must be aware of two obstacles standing in the way 1

I would like to thank Louis Groarke and Paul NiesiobĊdzki for their helpful comments and suggestions on an earlier draft of this paper.

52

Paolo C. Biondi

of establishing those accounts: the first has to do with problems related to the writings of both philosophers; the second concerns the distinction between the historical Aristotle and the Scholastic portrayal of Aristotle. Regarding Aristotle’s (384-322 B.C.E.) extant corpus, there are several issues. Generally speaking, the treatises are arid and terse. A number of them appear to be lecture notes or summary notes written by Aristotle or, possibly, even by his students or associates. There are various passages which show evidence of having been revised, but it is not easy to determine whether those revisions were made by Aristotle or by others (contemporary students and associates, or later editors). Certain treatises seem quite coherent and complete; others seem to put together disparate writings more or less loosely connected by a common theme. The traditional order of his extant writings follows that established by a later editor, Andronichus of Rhodes, in the first century B.C.E.2 As for Aristotle’s thoughts on the topic of induction, we must consult several works and piece together an account. The most relevant writings in this regard would include the following: Posterior Analytics (Post An) (especially book II, chapter 19), Prior Analytics (Pr An) (especially book II, chapter 23), Topics, Categories, On Interpretation, and On the Soul.3 Short passages from other works could be consulted as offering a brief remark about induction or providing an example of what Aristotle considers to be an induction. To further complicate matters concerning Aristotle, it is important to bear in mind the differences between the historical Aristotle and the Scholastic Aristotle. Aristotle lived and wrote in Ancient Greece in the fourth century B.C.E. His writings were neglected in the West for centuries as the Roman Empire declined and knowledge of Greek withered away. They were gradually reintroduced in Latin translations into a Christianized Europe starting in the 11th-12th centuries, more or less coinciding with the rise of the university and its Scholastic thought and culture. Aristotle’s philosophy, now coloured by Neoplatonic and Christian elements, dominated the medieval universities over the next couple centuries before 2

For an account of Aristotle’s life and writings, see Pierre Pellegrin, “Aristotle” in Greek Thought: A Guide to Classical Knowledge, ed. Jacques Brunschwig and Geoffrey E. R. Lloyd, trans. under the direction of Catherine Porter (Cambridge, MA: The Belknap Press of Harvard University, 2000), 554-75. 3 The English edition of Aristotle followed is The Complete Works of Aristotle: The Revised Oxford Translation, 2 vols. ed. Jonathan Barnes. Bollingen Series 71:2 (Princeton, NJ: Princeton University Press, 1984). Citations may be slightly altered on occasion.

Hume and Aristotle on Induction

53

entering a period of decline, during which time his philosophy and the dialectically rich but empirically poor Scholastic form in which it was often presented were increasingly criticized.4 By Hume’s time, Aristotle was probably still being taught in many universities. Descartes attended La Flèche about a century before Hume did, and “[b]y rule, the Jesuit curriculum [at Descartes’ time] was based on the philosophy of Aristotle, and divided into the then-standard topics of logic, morals, physics, and metaphysics. The Jesuits also included mathematics in the final three years of study. Aristotle’s philosophy was approached through textbooks and commentaries.”5 Hume first attended Edinburgh University where “[h]e read widely in history and literature, as well as ancient and modern philosophy, and also studied some mathematics and contemporary science;” and several years later he attended the Jesuit College of La Flèche where “Hume read French and other continental authors, especially Malebranche, Dubos, and Bayle; he occasionally baited the Jesuits with iconoclastic arguments; and, between 1734 and 1737, he drafted A Treatise of Human Nature.”6 It is not clear to what extent Hume was familiar with the historical Aristotle’s actual writings; his view of the Scholastic Aristotle seemed rather negative, in tune with the general disenchantment prevalent in his time with the Scholastic method, and by association, with Aristotelian philosophy. His critical remarks on the Scholastic notion of three acts of the understanding in Treatise 1, 3, 7 (p. 96, n. 1) and his criticism of “the fictions of the ancient philosophy” concerning substances, substantial forms, accidents, and occult qualities in Treatise 1, 4, 3 offer two examples of Hume’s own criticism of Scholastic philosophy. Hume (1711-1776) first published A Treatise of Human Nature, Being an Attempt to Introduce the Experimental Method of Reasoning into Moral Subjects (Treatise) in 1739 and 1740. It was an explicit attempt at following the scientific and, in particular, Newtonian method in moral philosophy. Unfortunately for Hume, the work “fell dead-born from the 4

For a brief account of the reception of Aristotle’s works into Europe of the Middle Ages, see Paul Vincent Spade, “Medieval Philosophy,” The Stanford Encyclopedia of Philosophy (Spring 2013 ed.), ed. Edward N. Zalta. 5 See § 1.1 of Gary Hatfield, “René Descartes,” The Stanford Encyclopedia of Philosophy (Summer 2011 Ed.), ed. Edward N. Zalta. 6 See § 1 of William Edward Morris, “David Hume”, The Stanford Encyclopedia of Philosophy (Spring 2013 ed.), ed. Edward N. Zalta.

54

Paolo C. Biondi

press.”7 As a result, Hume rewrote the work, publishing in separate volumes revised versions of the three books which made up the original Treatise: Book I was rewritten and published under the title An Enquiry Concerning Human Understanding (Enquiry) in 1748; Book II was truncated and published as an essay titled “Of the Passions” within a volume titled Four Dissertations published in 1757; and Book III was revised and published under the title Enquiry Concerning the Principles of Morals in 1751. Book I of the Treatise and the Enquiry contain the materials which touch upon the topic of induction.8 It is important to note that the Enquiry added chapters on miracles, free will, and the argument from design, which were not included in the Treatise. It omitted, as well, many of Hume’s psychological speculations found in the first work. The consequence of these changes is a debate among Hume scholars over which work to privilege when determining Hume’s position on various matters, including those related to induction. The purpose of noting these obstacles is not so much to meet them as it is merely to alert the reader to the constraints surrounding the elaboration of the following accounts of Hume and Aristotle on the topic of induction. The accounts will be limited to citing or referring to passages found in the relevant writings of both philosophers. There will be little attempt made to defend the selection of one passage over another as representative of either philosopher’s views on a given point. The intent is to give the reader an initial sense of what both Hume and Aristotle could reasonably be held to say about the cognitive process we call induction. There is something philosophically intriguing about comparing Aristotle and Hume on the topic of induction, namely, they share the same empirical origin to acquiring knowledge, and yet, they arrive at very divergent destinations. Both agree that all human knowledge must begin with sense perception: nihil in intellectu nisi prius in sensu. But whereas 7

“My Own Life,” The Philosophical Works of David Hume, 4 vols. ed. T. H. Green and T. H. Grose (London: Longman, Green, 1874-75), 1:2. 8 The editions of the Treatise and the Enquiry followed are those of A Treatise of Human Nature by David Hume, ed. L.A. Selby-Bigge (Oxford: The Clarendon Press, 1888; rpt. 1960); and Enquiries Concerning the Human Understanding and Concerning the Principles of Morals by David Hume, 2nd ed., ed. L.A. Selby-Bigge (Oxford: The Clarendon Press, 1961). Citations may be slightly altered to modernize the English. Footnote entries will generally have the following forms: Treatise book, part, section (page); Enquiry section, part (where applicable), paragraph (page).

Hume and Aristotle on Induction

55

Hume reaches a skeptical conclusion about our abilities to acquire any sort of robust knowledge of such matters as causation and the natures of things, Aristotle confidently asserts we can acquire scientific knowledge of the causes and natures of things. How can we explain such contrary judgments? Evidently, they do not share the same perspective on the cognitive abilities of human beings and the inductive path that must be taken to derive knowledge from sense perception, but why this vast difference in perspective? This essay will argue that the key to explaining the differences between the Humean and Aristotelian accounts of induction lies in their respective attitudes towards human reason: whereas Hume takes an antiRationalist (and an anti-rational) approach in his account so that reason is entirely evacuated from the inductive process, Aristotle gives to reason and, in particular, to rational insight (noein or noesis) a significant role in induction. I will begin with Hume’s account. In order to understand his skeptical attitude towards induction, it is important to understand his attack on human reason as this capacity is conceived in Rationalist terms. As a result, there will be a negative, skeptical account of induction and a positive, naturalist account, which constitutes Hume’s alternative explanation of the inductive process. After presenting Hume’s account, I will add a section to prepare the transition to Aristotle’s account. In this middle section I will briefly examine several secondary topics related to induction and unearth a number of epistemological and metaphysical assumptions undergirding Hume’s construal of induction. I will show how Aristotle’s account is built on quite different assumptions. The reader must adopt these assumptions if they are to understand Aristotle’s account on its own terms. I will then present Aristotle’s account in the third section. In order to understand his confidence in human reason, it is incumbent upon us to see that his conception of reason is not that of the Rationalists. In this manner, an Aristotelian conception of the inductive process will, it is hoped, be seen as offering for us today a viable alternative to the Humean brand. Since the Rationalist conception of human reason will play a fundamental part in my argument, I will briefly describe it at the outset.9 As a label for the philosophies of the early modern philosophers Descartes, Spinoza, and Leibniz, Rationalism signifies “the view that reason, without the aid of sense perception, can give us knowledge of the world.”10 One of 9

The description that follows relies upon summaries of Rationalism found in Garrett Thomson, Bacon to Kant: An Introduction to Modern Philosophy, 3rd ed. (Long Grove, IL: Waveland Press Inc., 2012), pp. 9-10 and 109-12. 10 Thomson, Bacon to Kant, p. 109.

56

Paolo C. Biondi

the characteristics of Rationalism is the employment of strong versions of the Principle of Sufficient Reason, which states that everything must have a rational explanation or, in other words, that there must be a complete explanation of everything that happens. A consequence of this principle is that a priori knowledge of the world is in principle possible. A second characteristic of Rationalism, which follows from the first, is the claim to superiority of reason over sense experience as a source of knowledge. Rationalists consider the ideas of sense perception to be confused and unclear. In comparison with reason, sense perception is generally regarded as an inferior form of reasoning and as incapable of revealing the causal connection between things. With respect to the knowledge of causes, a third characteristic common to the Rationalists is a tendency to assimilate causation to logical demonstration. The result of this assimilation, which again is a consequence of their acceptance of the Principle of Sufficient Reason, is that an effect will be seen to follow its cause(s) with logical necessity, much as the conclusion of a valid argument follows logically from its premises. All truths are thereby seen by Rationalists to be necessary truths. Contingency either does not exist in the world or else, if it does exist, accounting for it becomes problematic. The Rationalist conception of human reason thus presents us with an ideal of knowledge as a deductive system of truths, analogous to a mathematical system: starting with a few self-evident and necessary truths (known intuitively) serving as fundamental principles, the Rationalists share the pretense of deducing a complete and logical explanation of everything (demonstrative knowledge) by means of reason without the aid of sense perception. 1 Hume’s Account of Induction As a scholar of Aristotle and not of Hume, I must acknowledge a certain frustration in trying to compose a coherent account of induction according to Hume. In addition to the debate over which of the two works to privilege, the first book of the Treatise, much more so than the Enquiry, presents a challenge with its apparently meandering passages and seemingly contradictory or conflicting claims. It is not easy, even for Hume scholars, to determine which of the three views present in these writings is to be taken as the dominant theme; that is, Hume scholars are unsure whether, at the end of the day, Hume is a skeptic about the human capacity for knowledge, an empiricist concerned with the origins of knowledge, or a naturalist

Hume and Aristotle on Induction

57

interested in explaining the operations of the human mind and the natural formation of beliefs and knowledge. Without attributing this to Hume as the actual motivation behind his philosophical views, I have found it helpful to construe his dominant motivation as the desire to attack human reason as this was conceived by the Rationalist philosophers. At the end of the day, I believe Hume was an anti-Rationalist/anti-rationalist. From this vantage point, the three dominant strands of his philosophy may be woven into a fairly coherent cloth as follows: the empiricism means that all knowledge must come from sense perception alone, without the aid of reason—a direct denial of the Rationalist position; empiricism thus logically and inevitably leads to skepticism about reason and any Rationalist pretense to knowledge (of the world), simply because there is no reason involved; and finally, without any reason to acquire knowledge, naturalism provides an alternative account in terms of belief formation (not knowledge acquisition) based on the strictly empiricist foundation. This picture seems to me to offer the most coherent and charitable account of Hume on induction.11 1.1 Hume’s Empiricism: The Objects of Perception Let us begin with Hume’s empiricism. What is sense experience for Hume? What are the objects of sense perception? According to Hume, the mind has two kinds of perceptions: impressions and ideas (or thoughts).12 Impressions are the original perceptions the mind experiences, whereas ideas are copies of these impressions. The difference between the two kinds is made with respect to liveliness of perception and intensity of feeling exercised upon the mind. Impressions are strong and lively and are intensely felt by the mind; ideas are feeble and faint and are less intensely felt. Thus, ideas resemble impressions with respect to the perceptual content but differ with respect to the feeling exerted upon the mind when it perceives them. 11

I am indebted to Garret Thomson’s lucid explanation of Hume’s philosophy and of its relation to Rationalism, as found in Thomson, Bacon to Kant. Chapters 19 and 20 as well as remarks made on pp. 248-49, 259, and 276 were of particular assistance in developing my understanding of Hume. Thomson (259) holds that Hume’s philosophy consists of two steps: the first step is from Empiricist principles to skeptical conclusions; the second step is from a rejection of Rationalism to the use of naturalistic explanations. Note that Thomson does not speak of Hume’s having an anti-Rationalist motivation. 12 The account of perception which follows is based upon views found in Treatise 1, 1, 1-3; and Enquiry 2.

58

Paolo C. Biondi

Hume further distinguishes impressions (and consequently the ideas which resemble them) into those derived from outward sentiment and those derived from inward sentiment. In other words, impressions can come to us either through the external senses (impressions of sensation) or through the internal senses, or subjectively experienced passions, feelings, and emotions (impressions of reflection). Thus, we can have perceptions of colours, sounds, textures, and so on, on one hand, and perceptions of pleasure and pain, love and hate, anger, and so on, on the other hand. Furthermore, Hume notes simple ideas can be joined together by the mind to form a complex idea.13 The original/copy relation between impressions and ideas gives an epistemological priority to impressions. Furthermore, Hume takes an atomistic view of impressions; that is, there are fundamental simple impressions which cannot be further divided into other impressions. The result is that any complex idea is to be decomposed into its component simple ideas, each of which must be derived from a simple impression (of sensation or of feeling). Any ideas or any elements of a complex idea which cannot be traced back to simple impressions are to be considered false ideas or figments of the imagination. They are to be banished from philosophical discourse, says Hume.14 This is how Hume understands the derivation of all knowledge from sense experience. He thereby sets relatively strict limits to what can legitimately be thought by the mind. 1.2 Hume’s Empiricism: The Faculties of the Mind At this point, I must confess to some frustration with Hume’s thought. On the one hand, Hume claims, in his famous analogy with the theatre, that the mind is nothing but the perceptions themselves: “The mind is a kind of theatre, where several perceptions successively make their appearance; pass, re-pass, glide away, and mingle in an infinite variety of postures and situations. […] The comparison of the theatre must not mislead us. They are the successive perceptions only that constitute the mind; nor have we the most distant notion of the place, where these scenes are represented, or of the materials, of which it is composed.”15

13

The distinction between simple and complex ideas is found in the Treatise but is not reiterated in the Enquiry. 14 Enquiry 2, 17 (pp. 10-11). 15 Treatise 1, 4, 6 (p. 253).

Hume and Aristotle on Induction

59

Yet, in spite of this clearly stated view of the mind, Hume’s writings contain frequent uses of the word ‘faculty’ and make frequent references to various ‘parts’ of the mind as faculties.16 Such terminology suggests that the mind is indeed something, a place in which perceptions are located, and something that may on occasion actively manipulate those perceptions by means of various cognitive acts. Since this paper will compare Hume to Aristotle, and since in the latter philosopher’s case it can more easily be established that he does conceive of the human mind as something possessing a set of faculties, for the sake of comparison, I will assume Hume’s holding a faculty view of the mind. Thus far, we may say that Hume admits two faculties: (1) the faculty of the outward sentiment or the external senses, which is a capacity to receive and experience sense impressions; and (2) the faculty of the inward sentiment or the internal senses, which is some mental capacity for experiencing pleasures, pains, and other feelings and emotions. Hume’s statement about complex ideas (or impressions) being formed by joining together simple ideas (or impressions) introduces yet another mental capacity, which Hume calls imagination.17 Unlike the first two faculties, which seem to be merely passive channels of perception, imagination seems to be a spontaneous and active ability of the mind. Hume’s statement about ideas being copies of impressions suggests a retentive ability of the mind. This capacity could be delegated to imagination and/or to memory. Let us briefly examine, then, Hume’s thoughts on these two mental abilities. Memory and imagination may initially be understood as mental faculties possessing ideas resembling impressions, thereby retaining copies of impressions. Hume claims “our thought [i.e., our mind] is a faithful mirror, and copies its objects truly,” though the ideas are faint and dull in comparison with the force and liveliness of the original perceptions.18 Hume notes two main differences between imagination and memory.19 The first difference concerns the intensity of the ideas copied: the ideas of memory are stronger and livelier than those of imagination. Memory is said to be a faculty by which the idea copied from the first impression retains a considerable degree of the impression’s initial vivacity, such that it is somewhat intermediate between an impression and an idea in the proper sense. Imagination is said to be a faculty by which the idea 16

See, e.g., Treatise 1, 1, 3 (p. 8); and 1, 1, 4 (p. 10); and Enquiry 2, 13 (p. 19). Treatise 1, 1, 4 (p. 10). 18 Enquiry 2, 11 (p. 18). 19 The two differences are described in Treatise 1, 1, 3. 17

60

Paolo C. Biondi

copied from the first impression entirely loses the initial vivacity. The idea of imagination is thereby described as “a perfect idea.”20 This expression apparently implies that ideas are truly ideas only once the mind is able to perceive them coolly and calmly, so to speak, without being perturbed by the force of feeling which accompanies sensory impressions and, to a lesser degree, memories.21 Imagination, then, designates the mind’s ability to be objective by focusing solely on the perceptual content of perceptions. The second difference between the two mental faculties concerns the order and organization of ideas. Hume remarks that memory tends to preserve the original order in which its objects were presented. Memory lacks any power of variation and is in a manner restrained to the same order and organization found among the original impressions. Moreover, the act of recollection shows that the chief exercise of the memory is not to preserve the simple ideas but to preserve their order and position. The imagination, on the contrary, is not restrained to the same order and organization found among the original impressions. It has the liberty to transpose and change its ideas. In fact, wherever the imagination perceives a difference among ideas, it can easily produce a separation, says Hume.22 Once more complex ideas have been broken down into simpler ideas, or even the simplest ideas, the imagination is then capable of rearranging these elements in new ways. Even though this seems to give to imagination an unlimited ability to the point of imagining things never before perceived, Hume marks out the limits of this liberty.23 On the one hand, “this creative power of the mind amounts to no more than the faculty of compounding, transposing, augmenting, or diminishing the materials afforded us by the senses and experience.”24 In other words, the materials imagination works with must ultimately be derived from at least one of the two channels of perception, the external or internal senses.25 As mentioned already, all complex ideas produced by the 20

Treatise 1, 1, 3 (p. 8). See also the Appendix to the Treatise, pp. 627-28. 22 Treatise 1, 1, 3 (p. 10). 23 See Enquiry 2, 13 (pp. 18-19). Cf. Enquiry 5, 2, 39 (pp. 47-48). 24 See Enquiry 2, 13 (p. 19). 25 As an objection to his view that all ideas of the imagination must ultimately be derived from simple impressions, Hume raises the case of the missing shade of blue (Treatise 1, 1, 1 (pp. 5-6); Enquiry 2, 16 (pp. 20-21)). He thinks a person could use their imagination to fill in the gap, within a continuum of blue shades, of a shade of blue never before seen. Although Hume does not find this objection strong enough to overthrow his position, I would be inclined to wonder what other exceptional cases 21

Hume and Aristotle on Induction

61

imagination must be reducible to, and shown to be derived from, simple impressions of sensation or of reflection; otherwise, the idea will be considered meaningless. With these materials at its disposal, the imagination is free to arrange and compose them in novel ways. On the other hand, the composition of the materials is limited only by “what implies an absolute contradiction;”26 that is, the new organization must respect the principle of non-contradiction. Within these limits, one empirical and one rational, the imagination is otherwise free to order and organize its ideas at will. I find Hume’s views on imagination frustrating. As we will see shortly, Hume relies on imagination instead of on memory in the inductive reasoning process. I find this puzzling since Hume claims memory retains the order among impressions as they are first perceived; thus, the mind is not very free in altering that order. This would seem to give the mind an ability of prediction regarding future events; but Hume does not avail himself of this ability. (We will see in § 3.2 that Aristotle does rely on memory instead of on imagination in his account of the inductive process.) Furthermore, he states, “[t]he memory, senses, and understanding are, therefore, all of them founded on the imagination, or the vivacity of our ideas.”27 This claim seems inconsistent with what Hume says about the ideas of imagination being “perfect” because they lack the intensity that accompanies impressions and memories. But the real source of frustration springs from the fact that Hume’s conception of imagination conceals a significant ambiguity. Hume distinguishes between two meanings of imagination: imagination opposed to memory and imagination opposed to reason.27 When imagination is opposed to memory, it refers to the faculty by which the mind forms fainter ideas; when imagination is opposed to reason, it refers to the same faculty by which the mind forms fainter ideas, but this time excluding demonstrative and probable reasoning processes. The implication of the two meanings is that imagination, when opposed to memory (the first meaning), might implicitly include these two kinds of reasoning, which the second meaning then excludes explicitly. Thus, the two kinds of reasoning mentioned might be considered either acts of the imagination (when it is could be raised. Would not substance, as that which unifies impressions consistently conjoined together, constitute a legitimate exceptional case, too? 26 See Enquiry 2, 13 (p. 18). 27 Treatise 1, 4, 7 (p. 265). 27 This significant clarification is provided in a mere footnote in Treatise 1, 3, 9 (p. 117, n. 1).

62

Paolo C. Biondi

opposed to memory) or acts of reason or the understanding (when these are opposed to imagination). In other words, imagination understood in one sense would actually refer to the mind’s reasoning abilities and include reasoning processes. Given Hume’s empirical criterion about the necessity of all ideas being derived from simple impressions, it is not surprising to find him holding that thinking and reasoning with ideas constitute an act of which the imagination is capable. Hume, perhaps provocatively, claims that the imagination is “the ultimate judge of all systems of philosophy.”28 But attributing the ability to reason to imagination enables him to exclude, or at least to limit the scope of, a separate faculty of reason. In addition, Hume accepts Berkeley’s arguments regarding the inability of the mind to conceive or produce abstract ideas. Abstract or general ideas are merely particular ideas annexed to a general term which gives the particular ideas a more extensive signification and makes them recall other individuals which are similar to them.29 So much for reason’s producing any universal concept or universal proposition. But such a conception of reasoning with ideas is drastically different from that of the Rationalists, for whom reason, not imagination, is the faculty responsible for reasoning processes, which must take place with intellectual or rational concepts and propositions, not with sensory images. (As we will see in § 3.2, Aristotle follows the Rationalists in this regard.) 1.3 Hume’s Skepticism: Hume’s Fork As mentioned in the introduction to Hume, Hume’s empiricism logically and inevitably leads to skepticism about reason and any Rationalist pretense to knowledge (of the world). The road to skepticism has been built so far with his views on what constitutes the objects of perception and with his conception of imagination, which Hume maintains, is capable of either demonstrative or probable reasoning processes. The mention of these two kinds of reasoning brings us to what has become known as Hume’s fork. We will see that it completes the road to skepticism. Hume’s fork refers to the division between the two kinds of “objects of human reason or enquiry” recognized by Hume, namely, relations of ideas and matters of fact and existence.28 Demonstrative reasoning is 28

Treatise 1, 4, 4 (p. 225). Treatise 1, 1, 7 (p. 17). 28 This fundamental distinction is introduced in Enquiry 4, 1, 20-21 (pp. 25-26). It also orients much of Hume’s discussion throughout Treatise 1, 3. 29

Hume and Aristotle on Induction

63

concerned with establishing various logical relations among ideas. (Although our attention is focused on logical relations, it is to be noted that Hume also includes the various branches of mathematics in existence at his time among a priori relations of ideas.) Probable reasoning deals with matters of fact and various ways of relating them together. Though I find Hume is not clear on this point, his conception of what reason is seems to identify it with reasoning, the process of deriving conclusions from premises or evidence.29 It is the mental ability to make inferences. (As will be shown in § 3.2, besides reasoning, Aristotle also adds rational insight and other rational operations as abilities of reason.) It is demonstrative reasoning about the logical relations of ideas that comes closest to the Rationalist conception of reason; however, we have noted how Hume delegates such reasoning abilities to imagination understood as reason rather than to a distinct mental faculty of reason in the Rationalist manner. According to Hume, any reasoning about the relations of ideas involves propositions that are “discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe.” Any demonstrative proposition incorporates “[an] affirmation which is either intuitively or demonstratively certain;” and it implies a contradiction that cannot be distinctly conceived by the mind.30 (The intuitive/demonstrative division is based on the thoroughly Aristotelian distinction between intuition (of terms and immediate propositions) and demonstration (of conclusions). Even though this distinction, which was inherited by the Scholastic tradition, was not rejected by many of the early modern philosophers (unlike other items within the Scholastic tradition), it was retained, yet as it will be shown in the Conclusion below, with a different interpretation.) That is, propositions expressing relations of ideas respect the rational principle of non-contradiction. Such propositions express truths that cannot be denied without thereby generating a falsehood. Any reasoning about matters of fact, on the other hand, depends on sense perception and its impressions. Such probable reasoning involves propositions the contrary of which is still possible because any proposition based on sense experience can never imply a contradiction that can be distinctly conceived by the mind. In other words, the principle of noncontradiction is not applicable in the case of matters of fact. The denial of a statement of fact might also be true. This is significant, for it means sense perception is not rational. It is impossible to violate the principle of non29 30

Thomson, Bacon to Kant, p. 263. Enquiry 4, 1, 20 (p. 25).

64

Paolo C. Biondi

contradiction in probable reasoning about matters of fact. Even though I have observed the sun to rise today and on numerous occasions in the past (every day of my life, in fact), it is still possible for it not to rise tomorrow. Sense perception cannot rule out this possibility, for it neither knows the morrow, nor does it have reason (and its fundamental principle of non-contradiction) to help it avoid this logical (and ontological) possibility. (By ontological possibility, I mean an impression of the world that could be experienced.) Moreover, reasoning about relations of ideas says nothing about the world (i.e., about what exists external to the mind or whatever impressions of reality the mind is actually experiencing through sense perception); it is limited to (the meanings of) the ideas themselves. This implies that demonstrative reasoning is a purely rational kind of thinking: it is an a priori reasoning process of ‘pure reason’ (to anticipate Kant’s terminology). Reasoning about matters of fact and existence, in comparison, does not involve such an a priori reason; it is a posteriori, for such reasoning can only occur either after ideas have been acquired from the impressions of sense perception or with ideas that are associated with actual impressions. Hume claims that these are two mutually exclusive and exhaustive kinds of objects and reasoning processes, hence our understanding them in terms of a fork. The consequences of this fork for Rationalism are dire. In fact, the fork turns out to be “a very important instrument for spearing the heart of Rationalism.”31 By limiting reason in its proper sense to demonstrative reasoning and the manipulation of relations of ideas, Hume has mortally wounded the Rationalist pretense of using reason to acquire knowledge of the world. Such knowledge can only be accessed by means of sense perception. By being concerned only with the logical relations among ideas, and not the ideas themselves, reason’s contact with the world has been severed. He has, in addition, severed the Rationalist tie between logical relations and causal relations. Rational operations employed to establish various logical relations are seen as reflections of the capabilities of reason, not as revealing causal connections between things in the world. The necessary truths discovered by reason are understood to be merely the products of conceptual analysis. The Rationalist conception of demonstration as the manner in which (or the means through which) the causes of things are shown and proven is rejected. (The Rationalist conception, by the way, likely follows the Aristotelian conception of scientific knowledge, as we will see in § 3 below.) 31

Thomson, Bacon to Kant, p. 237.

Hume and Aristotle on Induction

65

With the framework of the fork in place, it is not difficult to see that the Rationalist pretense to rational knowledge of the world in terms of necessary truths and demonstrations of causal relations is no longer tenable. Without the rational principle of non-contradiction governing sense impressions, reasoning about matters of fact and existence can only be probable (as we will soon see). This kind of factual reasoning has traditionally been associated with the inductive process, and Hume claims it is deeply problematic. The issue has become known as the problem of Hume, or the problem of induction.32 But, according to Von Wright, there are really three main problems of induction: 1) the mainly psychological problem of the discovery or origin of inductive inferences in science; 2) the logical problem of analyzing the inferential mechanism of induction; and, 3) the philosophical problem of the justification of inductive inferences. These three problems, he claims, have traditionally been intertwined.33 This is certainly the case with Hume’s presentation. 1.4 Hume’s Skepticism: The Death of Inductive Reasoning This section will focus on the problem of induction, on how Hume reaches skeptical conclusions in his assessment of probable reasoning concerning matters of fact and existence. The next section will present Hume’s own answer to the problem, a positive account of inductive reasoning in naturalist terms. When reading the pertinent passages from Hume’s texts, it is important to keep in mind that Hume’s skeptical conclusions are arrived at, in large part, by showing the limitations of the Rationalist conception of human reason. Hume’s remarks and arguments regarding the inability of reason to know matters of fact presuppose the Rationalist pretense that human reason can provide us with detailed knowledge of everything in the world in terms of necessary truths and causal deductions. With Rationalism as the background, it becomes easier to understand why, for instance, Hume examines how we acquire knowledge of cause and effect, analyses the idea of necessary connection (or power or force), or attempts to show reason’s inability to demonstrate in a priori fashion matters of fact. Rationalist

32

Hume explains the problems associated with probable, or experimental, reasoning mostly in Treatise 1, 3 and Enquiry §§ 4-7. 33 Georg Henrik Von Wright, A Treatise on Induction and Probability (London: Routledge and Kegan Paul, 1951; rpt. Paterson, NJ: Littlefield, Adams & Co., 1960), pp. 30-31.

66

Paolo C. Biondi

reason acts as a foil for Hume’s account of experience and of reasoning about matters of fact and existence. As an Empiricist opposed to Rationalism, Hume considers how we come to know the world by means of the senses. Sense perception, while in activity, provides us with impressions of existing things. When there is no sense perception, we have no impressions and, as a consequence, we cannot be assured of the existence of anything. This view is strikingly stated by Hume with regard to the perception of a self: For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe anything but the perception. When my perceptions are removed for any time, as by sound sleep, so long am I insensible of myself, and may be truly said not to exist.34

Memory can expand the store of impressions by retaining ideas of past impressions. Sense and memory thus constitute the whole of our experience of the world. All the impressions of experience together constitute all the matters of fact there are for consideration. Hume then wonders how human beings can go “beyond the present testimony of our senses, or the records of our memory.”35 Many opinions of the vulgar (i.e., non-philosophers) as well as of some philosophers, in fact, go well beyond the limits of experience and include such beliefs as the persistence of the existence of things even when we no longer perceive them, the existence of substantial subjects which give things their unity, and the existence of natures and powers which account for the way things move and operate. Are we justified in holding such beliefs about the world? Hume thinks that “[a]ll reasonings concerning matter of fact seem to be founded on the relation of Cause and Effect [since it is by] means of that relation alone [that] we can go beyond the evidence of our memory and senses.”36 For example, if we hear voices in the dark, we infer that there are persons speaking nearby because people cause the sound of voices. As a result, we must discover how we come to have knowledge of cause and effect. Hume thinks that knowledge of the causal relation cannot be attained

34

Treatise 1, 4, 6 (p. 252) (italics in original). Enquiry 4, 1, 21 (p. 26). 36 Enquiry 4, 1, 22 (p. 26) (italics in original); Treatise 1, 3, §§ 2 and 6. 35

Hume and Aristotle on Induction

67

by a priori reasoning; instead, it “arises entirely from experience, when we find that any particular objects are constantly conjoined with each other.”37 To understand this claim, let us look at sense perception more closely. Whenever we come across an object for the first time, our senses convey to us sensible qualities, but not the causes which produced them, nor the effects which will arise from them. “[N]ature has kept us at a great distance from all her secrets, and has afforded us only the knowledge of a few superficial qualities of objects; while she conceals from us those powers and principles on which the influence of those objects entirely depends.”38 Without any experience of how these sensible qualities operate, reason would not be able to draw any inferences about matters of fact, such as bread being nourishing for human beings or fire being hot and capable of burning human flesh.39 As a consequence, if we were asked to determine what effect would result from an object presented to our senses for the first time, the mind would have to imagine some event as its effect. This invention of imagination would inevitably be entirely arbitrary.40 Hume takes this scenario as showing that “the effect is totally different from the cause, and consequently can never be discovered in it.”41 For example, observing one billiard ball heading towards a second billiard ball, we could imagine numerous logically possible events unfolding on contact. It is not inconceivable to imagine that the second billiard ball will move to the right, to the left, quickly, slowly, or perhaps, even remain unmoved. Only through experience will the actual particular event become known. According to Hume, if the mind considers only a single instance of the operation of bodies (or the operation of the mind on the body), our external senses (or our internal sense of reflection) could only perceive one event following another. The mind will receive no impression of the force or power by which the cause operates, nor any impression of the (necessary) connection between the cause and its supposed effect.42 To sense perception, “[a]ll events seem entirely loose and separate. […] They seem conjoined, but never connected.”43 Hume thereby concludes that “every 37

Enquiry 4, 1, 23 (p. 27). Enquiry 4, 2, 29 (pp. 32-33). 39 Enquiry 4, 1, 23 (p. 27). 40 Enquiry 4, 1, 25 (p. 29). 41 Enquiry 4, 1, 25 (p. 29). 42 Enquiry 7, 2, 58 (pp. 73-74). 43 Enquiry 7, 2, 58 (p.74) (italics in original). 38

68

Paolo C. Biondi

effect is a distinct event from its cause.”44 Even though Hume says that the statement, ‘Every effect has a cause’, is a logical truth capable of proof, this relation of ideas established by reason does not (necessarily) demonstrate that every event in the world must have a cause (or show what the particular cause of a particular effect is).45 However, Hume does think sense perception can reach some kind of knowledge of causality operating in the world of particular things and events. Such knowledge is obtainable when the mind perceives through its sense impressions that “one particular species of event has always, in all instances, been conjoined with another, […]. We then call the one object, Cause; the other, Effect.”46 Causes and effects can only be discovered through actual experience, by observing on numerous occasions that object A is constantly conjoined with object B. We will continue Hume’s positive account of our knowledge of causality in the next section. For now, we will study Hume’s skeptical conclusions in relation to reasoning about matters of fact. Hume claims that “even after we have experience of the operations of cause and effect, our conclusions from that experience are not founded on reasoning, or any process of the understanding.”47 Hume has the Rationalist view of a priori demonstrative reasoning first and foremost in mind here. It is this kind of reasoning that is not capable of reasoning from experience. However, he also includes probable reasoning based on experience. The inference that the mind makes from its experience may be expressed in the following ways: 1) Based on experience (past and present impressions) these two events have been conjoined. [by the relation of causality] 2) Therefore, all similar events will be conjoined in the future (future impressions). [by 1] Or 1) In all past instances, such sensible qualities have been found to be conjoined with these secret powers. [by the relation of causality]

44

Enquiry 4, 1, 25, (p. 30). Treatise 1, 3, 3 (p. 82). 46 Enquiry 7, 2, 59 (pp. 74-75) (italics in original). 47 Enquiry 4, 2, 28 (p. 32). 45

Hume and Aristotle on Induction

69

2) Therefore, similar sensible qualities will always be conjoined with similar secret powers. [by 1]48 What Hume calls probable reasoning concerning matters of fact takes the form of an inductive inference: based on a sample of a limited number of actual (i.e., actually experienced) cases, the mind reaches a conclusion about all possible cases. There is a generalization; hence, the problem of induction. What is it? First of all, it is the relation of causality that accounts for the conjunction of events (or of sensible qualities and powers) in the premise. This causal relation would also indicate a necessary connection for a Rationalist; but Hume, the Empiricist and skeptic, has rendered the Rationalist view of causality and necessity problematic: if, from the perspective of sense perception, every event is distinct from its cause, then there can be no necessary connection between them. This basic point had already been made when it was stated above (in § 1.3) regarding Hume’s fork that sense perception is not ruled by the principle of non-contradiction. For, if a particular event does not follow from its particular cause with necessity, then it would not be a contradiction to deny the event’s following the cause on any given occasion. Thus, the generalization is merely a probability, and not a certainty. Thus far, my experience shows that object B follows object A; but, who knows what the future will bring. This is one problem with reasoning concerning matters of fact, or “experimental reasoning”: such reasoning can only provide us with probable conclusions that are more or less certain. The higher the frequency with which we observe events A and B being joined together in the past, the greater the probability with which we can foresee that conjunction of events taking place again. In his brief discussions on probability, Hume distinguishes between two kinds of probable arguments: proofs and probabilities. The difference between them is that proofs refer to experiences in which two objects have always been observed to be conjoined and “leave no room for doubt or opposition;” probabilities refer to experiences in which two events are not consistently observed together.49 The variation with which they do occur together affects the probability with which the 48

The two inferences are provided respectively in Enquiry 4, 2, 29 (p. 34) and 4, 2, 32 (p. 37). 49 This distinction is made in Enquiry 6 (p. 56, n. 1) and then again near the beginning of the chapter on miracles in 10, 1, 87 (p. 110). It is also found in Treatise 1, 3, 11 (p. 124).

70

Paolo C. Biondi

mind will infer the future conjunction of the two objects. Thus, proofs offer a higher degree of certainty than probabilities, and probabilities can vary in their degree of certainty. (Hume does remark that sometimes the difference between proofs and probabilities becomes “insensible” so that proofs degenerate into probabilities.50 His skepticism thereby minimizes the distinction and leads him to consider most arguments from experience as probabilities. We will assess this distinction between probabilities and proofs in § 2.4 below.) As noted in numerous contemporary textbooks on critical thinking and logic, another problem is that the inductive inference is invalid from the point of view of a deductive inference. The invalidity of the inductive inference lies in the fact that the mind goes beyond the evidence of experience. From whatever number of past instances the inference is based upon, the mind cannot go beyond its limited experience to state that this will be so in the future, in all cases yet to come about. In short, the mind goes from some cases to all cases, which is an illegitimate rational move. In comparison to demonstrative a priori reasoning, experimental reasoning offers an inferior form of reasoning: it lacks the certainty, the necessity, and the validity of a valid demonstration. It constitutes a humbler type of reasoning in keeping with Hume’s skepticism regarding the pretensions of human reason and understanding. Hume’s skepticism, though, does not stop there. As humble as the conclusions of reasoning about matters of fact may be, Hume wonders whether this inductive inference may still be rationally justified. What is the foundation of conclusions from experience?51 Hume argues for the further insufficiency of human reason by considering three possible routes to justifying the inference from experience: from Rationalism, Hume considers two methods: 1) through reason, we can know that the connection between the two propositions of probable reasoning is intuitive; or 2) through reason again, we can show by demonstrative reasoning that the two propositions are logically connected. Finally, Hume considers the Empiricist method: 3) through the senses, we can seek justification in the evidence of sense experience. Hume rejects the first option.52 First, the two propositions contained in probable reasoning are not the same (in meaning). There is, therefore, an 50

Treatise 1, 3, 12 (p. 131) and 1, 3, 13 (p. 144). This is the final question Hume asks before embarking on a “negative answer” to it. See Enquiry 4, 2, 28 (p. 32). 52 Enquiry 4, 2, 29 (p. 34). 51

Hume and Aristotle on Induction

71

inference from the one to the other. As a result, there is a reasoning process which must go through “a medium.” That is, a middle term or intermediary proposition is required since it is only by means of such a medium that any inference can be drawn. In other words, Hume assumes, as a Rationalist would, that if a link between propositions were intuitive, there would be no inference involved. The connection between them would be immediate, i.e., without a medium. But since probable reasoning incorporates an inference, there cannot be any immediate intuition of propositions. Hume rejects the second option as well.53 In this case, Hume adds a proposition which not only makes the inference evident; it can even make the inference deductively valid: 1) Based on experience (past and present impressions) these two events have been conjoined. [by the relation of causality] 2) The future will be conformable to the past. [by assumption] 3) Therefore, all similar events will be conjoined in the future (future impressions). [by 1–2]54 This additional proposition is an assumption that is, in fact, held by the mind when it infers from experience. If we look carefully at the initial expressions of probable reasoning given above, the mind is actually making the assumption that any future scenario will play out as it has been observed to play out in the past. In other words, the mind is assuming that experience remains constantly the same, or that nature is uniform. Since the mind does presume the principle of the uniformity of nature, this principle is explicitly added as a premise, which then makes the reasoning a valid deduction. However, the justification for reasoning from experience cannot be acquired by means of this demonstrative argument since “it implies no contradiction that the course of nature may change.”55 In other words, Hume doubts that the assumption regarding the uniformity of nature can be rationally justified. From the point of view of sense perception and prior to actual experience, the future is unpredictable. In attempting to foresee the future, imagination’s liberty is not restricted by the principle of noncontradiction, which always binds a priori demonstrative reason. Hume claims that “whatever is intelligible and can be distinctly conceived, implies no contradiction, and can never be proved false by any demonstra53

Enquiry 4, 2, pars. 31-32. Hume asserts the assumption in Enquiry 4, 2, 30 (p. 35) and 32 (pp. 37-38). 55 Enquiry 4, 2, 30 (p. 35). 54

72

Paolo C. Biondi

tive argument or abstract reasoning a priori.”56 Since I can clearly and distinctly conceive, as a future possibility, having the impression of snow that tastes salty, say, or snow that feels hot, reason is incapable of denying this possibility and is not able to determine the truth among the logically (and ontologically) possible thoughts of imagination. Thus, the assumption of the uniformity of nature cannot be defended in a priori fashion. Hume finally rejects the third option as well. In this case, Hume wonders whether we can maintain a valid deduction by justifying the assumption of the uniformity of nature upon the evidence of sense experience itself. However, in this case justification is not possible because the reasoning would end up being circular or end up begging the question.57 For, in making the assumption, we are referring to past experience as support and evidence in favour of it: nature can be assumed to be uniform because experience thus far shows it to be uniform. In addition, the future will inevitably be ‘proven’ to be uniform because it was already assumed so in the assumption. In this manner, attempting to rationally justify experience on the basis of experience itself ties reason up into knots. Therefore, we have no reason to believe that the principle of the uniformity of nature is true or rationally warranted. In this manner, Hume has dealt a serious blow to the Rationalist pretense of a priori knowledge of the world. In the process, he has managed to undermine the rationality of inductive inferences. Though we employ probable reasoning in our everyday lives and find that we cannot do otherwise than accept its inductive conclusions as valid, Hume stresses that philosophers cannot accept this reasoning process because it lacks rational warrant.58 It constitutes a humbler type of reasoning in keeping with Hume’s skepticism towards the pretensions of human reason and understanding. We now turn to Hume’s positive account of probable reasoning about matters of fact and existence. 1.5 Hume’s Naturalism: The Rebirth of Inductive Reasoning With confidence in human reason shaken, Hume proceeds to replace Rationalist justifications with naturalistic explanations in his examination of probable reasoning. We will see that he thereby replaces knowledge claims based on logical connections (necessity) with psychological beliefs based on (non-rational) feelings. 56

Enquiry 4, 2, 30 (p. 35). Enquiry 4, 2, 30 (p.35); and 4, 2, 32 (p. 37). 58 Enquiry 4, 2, 32 (p. 38). 57

Hume and Aristotle on Induction

73

Let us begin once again from an act of sense perception. On the first instance when the mind encounters an object or event, it is incapable of foreseeing what will happen next. But after gaining some experience with the object, the mind may notice the constant conjunction between this object and another; that is, the impressions of the two objects consistently appear together in sensation.59 Hume says that sense perception then becomes capable of reaching some kind of knowledge of causality operating in the world of particular things by perceiving this constant conjunction of events.60 At that point, the relation of causality takes effect and whenever we receive an impression of one object, we tend to imagine the idea of the object that comes after the first because we think the impression of the second is caused by the impression of the first. The repetition of a number of conjoined instances makes the conjunction appear customary. In other words, the imagination develops a habit of connecting the second object with the first whenever the first appears to the senses or memory.61 Upon seeing fire, we imagine the heat and burning sensation it causes. The effect of custom is such that the conjunction perceived in one instance is, after repeated instances, perceived as a connection. The difference between perceiving a conjunction and perceiving a connection is “[n]othing but that now [the person] feels these events to be connected in [their] imagination, and can readily foretell the existence of one from the appearance of the other.”62 We perceive fire and feel it is connected to heat. Hume’s point is simply this: becoming accustomed to certain conjunctions, the mind comes to expect events to follow a certain order. This expectation in the mind is a feeling of determination or inevitability. It is a feeling of necessity. It arises in the mind spontaneously and naturally, without the involvement of reason, merely because the mind is acted upon by the same objects in the same way repeatedly.63 Hume stresses over and again that one instance is not sufficient to ingrain the effect of custom in the imagination; a repetition of a number of similar instances is required.64

59

In Treatise 1, 3, 6 (pp. 86-88), Hume remarks that constant conjunction presupposes contiguity in time or place as well as succession. 60 Enquiry 7, 2, 59 (pp. 74-75), already cited above in § 1.4. 61 Enquiry 5, 1, pars. 35-38. 62 Enquiry 7, 2, 59 (p. 75). 63 This summary of Hume’s point comes from Thomson, Bacon to Kant, 245-46. 64 See, for instance, Enquiry 5, 1, pars. 35 and 36; 5, 2, 38; 7, 2, pars. 59 and 61.

74

Paolo C. Biondi

Only then does the mind acquire the feeling of connection which lies at the heart of this cognitive habit of thinking two objects together.65 Once the mind has become so habituated, the next time it has the perception of an impression through sense or memory, it thinks in terms of the causal relation, which makes it possible for the imagination to infer the object that will follow the impression. The inductive reasoning process explained in naturalist terms may be spelled out as follows: (1) In this new instance, object A has appeared. [by an impression] (2) Experience shows that whenever the first object A (cause) appears, it is followed by the second object B (effect). [by the relation of causality] (3) B will appear (now or very soon). [by 1–2]66 The second object B in the conclusion is an idea of imagination inferred from reasoning about the fact of the impression of object A. The inductive inference involved in this reasoning process is actually nothing other than the effect of custom, the ingrained habit of the mind to go from object A to object B; for, this was how the relation of causality was established in the mind. This explanation of inductive reasoning about matters of fact further explains Hume’s conceptions of necessity and causality. The feeling of inevitability is an impression of reflection. From this impression, the idea of necessity is derived: “This connection, therefore, which we feel in the mind, this customary transition of the imagination from one object to its usual attendant, is the sentiment or impression from which we form the idea of power or necessary connection.”67 As for causality, Hume provides two definitions “from outside” of cause. First, from the experience we have of similar objects always being conjoined with similar objects, cause may be defined as “an object, followed by another, and where all the objects similar to the first are followed by objects similar to the second. Or in other words where, if the first object had not been, the second never had existed.” Secondly, from the experience we have in which the appearance of a cause always conveys the mind, by a customary transition, to the idea of the effect, cause may be

65

Enquiry 7, 2, 61 (p. 78). Enquiry 5, 1, 38 (p. 46). 67 Enquiry 7, 2, 59 (p. 75); Treatise 1, 3, 14 (p. 165). 66

Hume and Aristotle on Induction

75

defined as “an object followed by another and whose appearance always conveys the thought to that other.”68 The first, the objective definition, defines a cause in terms of the constant conjunctions and regularities among the objects or events that can be met in sense experience; the second concentrates on the purely psychological element in the concept of cause, that is, the feeling of expectation engendered in the mind by the constant conjunctions and regularities of sense experience. Neither definition is ‘from inside’, giving us the idea of a necessary connection between events in the Rationalist fashion.69 In this manner, the causal relation, and the inductive inference based on it, is not grounded in reason; it is grounded in the feeling of necessity engendered in the mind through its experience with things. Hume has replaced the logical connections of reason with custom or habit, which has cultivated in the mind a feeling of determination or a sense of inevitability between certain objects. The human mind is habituated to join together certain ideas because they are associated according to the relation of cause and effect, the most important, though not the only, principle of association admitted by Hume.70 The result is a picture of the inductive process from which reason in the Rationalist sense has been entirely evacuated. Induction, which was shown to be problematic for reason, is now an act of probable reasoning performed by the imagination which associates sense (or memory) impressions and ideas of the imagination, the association being rooted in a nonrational feeling of the mind. 1.6 Hume’s Naturalism: Imagination and Belief Before leaving Hume’s account of induction, let us look at how imagination acquires belief. The relevance of this topic to that of induction is 68

The two definitions cited are taken from Enquiry 7, 2, 60 (pp. 76-77). Two definitions of cause, worded differently but essentially identical in meaning to the ones given in the Enquiry, can also be found in Treatise 1, 3, 14 (p. 172). 69 Thomson, Bacon to Kant, pp. 245-46. 70 The importance of knowing the causal relation is stated at Enquiry 7, 2, 60 (p. 76). In the Enquiry (3, 19 (p. 24)), Hume recognizes two other relations, or principles of association, operating in the mind: resemblance and contiguity of time or place. For Hume’s explanation of how these three principles operate, see Enquiry 5, 2, pars. 4144. In the Treatise (1, 3, 1 (p. 69)), he recognizes “seven different kinds of philosophical relation.” Besides the three mentioned so far, he admits these four: identity, proportion in quantity or number, degrees in any quality, and contrariety among the relations of thought.

76

Paolo C. Biondi

twofold: first, it will show how Hume replaces the belief of rational conviction with a sensitive form of belief; and secondly, it will show how imagination’s liberty of thinking is restrained by sense perception. The question we seek to answer is, how can we believe any conclusions of inductive inferences?71 In my presentation of Hume’s position, it has been argued that while he has narrowly confined reason to logical (and mathematical) relations of ideas, Hume has vastly enlarged the scope of imagination. Throughout the presentation, reference has been made to the inapplicability of the principle of non-contradiction in matters of fact and existence; and it has been suggested that when imagination considers matters of fact, it is no longer limited by this rational principle: “whatever is intelligible and may be distinctly conceived” by the imagination is, in this sense, rationally or logically possible, and therefore, ontologically possible (i.e., such an impression of the world could be experienced). Since the act of sense perception is momentary and presents things “entirely loose and separate,” it is always logically possible for imagination to rearrange discrete ideas (impressions) and to conceive a state of affairs that is contrary to the currently perceived matters of fact. It could very well snow in June one day. Fire could one day give me the impression of being cold. A man could never die—which makes me wonder how Hume could have argued against miracles without contradicting himself. There is no logical impossibility because there is no principle of non-contradiction to make the denial of a fact impossible. In short, the rational limit Hume imposed initially on imagination’s liberty in its activity of joining ideas to form new or complex ideas72 seems to have been jettisoned in the course of his analysis of probable reasoning. Imagination becomes limited only by the empirical requirement that its ideas (or their simple elements) be ultimately reducible to (simple) impressions. However, since the imagination has command over all its ideas and is free in how it can arrange them, it is open to generating ideas which, in whole or in part, may not be traced back to simple impressions gained through the external or internal senses; that is, imagination is susceptible to producing fictions or false ideas. Moreover, the mind has a great propensity to spread itself on external objects, by projecting its impressions and ideas 71

In Enquiry 5 Hume presents, in part 1, custom as the nature of the inference involved in probable reasoning, and then, in part 2, the nature of the belief related to this inference; hence, our exploration of belief at this time. 72 This rational limit was noted above in § 1.2.

Hume and Aristotle on Induction

77

onto the external world.73 We are thereby susceptible to mistaking fictions for realities. Imagination is not, therefore, a reliable faculty. In his investigations of human psychology, Hume describes a number of ways in which imagination has a propensity to seek coherence and to complete partial perceptions into a perception of a whole as well as a tendency towards forming unities, such as the opinion of the continued existence of external objects once they are no longer perceived.74 His skepticism with regard to human understanding leads Hume to assert that human imagination is often “seduced” into believing a “false opinion”, an “illusion”, or a “fiction”, that is, to conceive of something non-existent as existent or to conceive of something imperceptible as perceptible. Hume accuses the ancient philosophy of incorporating such “fictions” as substances, substantial forms, accidents, and other similarly “occult qualities.”75 Due to its importance in Aristotle’s account of induction, the example of the idea of substance offers a pertinent case in point. With my imagination, I can make an image of a dog, a collection of simple ideas (a particular size and shape, a furry texture, a shade of brown, this particular smell, a barking sound, and so on) put together into a complex idea (my pet dog, Fido); but the imagination has the tendency to construe such a complex idea as a unity or whole and to give the unity itself a separate idea (designated by the name ‘Fido’): it is the idea of an underlying subject (my dog Fido) in which the simple ideas inhere and by which they obtain their unity. This tendency, Hume suggests, is often a result of language: “The idea of a substance […] is nothing but a collection of simple ideas that are united by the imagination, and have a particular name assigned to them, by which we are able to recall, either to ourselves or to others, that collection.”76 By giving one name to designate the collection as a whole, we might be deceived into thinking the name signifies something else apart from the sensible qualities, that unknown subject in which they inhere and which unifies them. A similar explanation would hold for abstract or general ideas, which are required in Aristotle’s account of induction but which Hume says are not conceivable other than in the way already briefly described (at end of § 1.2 above). We make a mistake if we give a name to the similarity found to 73

Enquiry 7, 2, 60 (p. 77, n. 1). Treatise 1, 4, 2 (pp. 195- 210). 75 Treatise 1, 4, 3. 76 Treatise 1, 1, 6 (p. 16). 74

78

Paolo C. Biondi

be common to many individuals (the animal species dog, and, as Aristotle would say, the substance of my pet dog Fido and of all other particular dogs) and think this name refers to a separate and distinct object which has its own corresponding idea. Given the unreliability of imagination, how, then, can we believe any of the conclusions of inductive inferences? The answer lies in Hume’s explanation of belief, which differentiates it from fiction. According to Hume, belief, or assent, always attends memory and sense perception. Belief is said to be nothing but the vivacity of those perceptions they present. To believe is to feel an immediate impression of the senses or a repetition of that impression in the memory. This alone distinguishes these acts from the act of imagination.77 In other words, belief is the feeling accompanying the act of sense perception. It is sensory stimulation, present or remembered. The significance of this is that the ideas of imagination, which are called perfect because they lack lively feeling (see § 1.2 above), will therefore lack that which will make us believe them. How, then, can we tell the difference between an imaginary fiction and an idea of imagination constituting a belief? Relying upon his empirical criterion, Hume asserts that belief differs from fiction because the former has a sentiment or feeling excited by nature independently of one’s will and which is annexed to the believable idea.78 A fiction lacks this feeling. In Hume’s words: “Belief is nothing but a more vivid, lively, forcible, firm, steady conception of an object than what the imagination alone is ever able to attain”; and “this manner of conception arises from a customary conjunction of the object with something present to the memory or senses.”79 Thus, belief in an idea of the imagination consists in an association between the idea in the imagination and an impression of sense or of memory.80 Or rather, to be more precise, whenever a faint idea of imagination is associated with a strong sense impression or memory, it gains the force or liveliness of that sense impression or memory.81 This borrowed force of feeling makes the idea believable. So the difference between the idea that fire is hot, say, and the idea that fire is cold is explained by the fact that the first idea is or has been experienced, and this experience is accompanied by a strong feeling from the 77

Treatise 1, 3, 5 (p. 86). Enquiry 5, 2, 39 (p. 48). 79 Enquiry 5, 2, 40 (p. 49). See also Treatise 1, 3, 7 (p. 96); and 1, 3, 8 (pp. 102-03). 80 Treatise 1, 3, 6 (pp. 85-86). 81 Treatise 1, 4, 2; and 1, 3, §§ 8 and 10. 78

Hume and Aristotle on Induction

79

sensory stimulation. From the constant but customary conjunction of fire and heat, these two objects eventually acquire a union in the imagination: when the impression of fire becomes present, we immediately form an idea of its usual attendant, heat, because of the feeling of sensory stimulation associated with fire and heat. The feeling makes the idea fire is hot believable. The idea fire is cold remains a figment of the imagination because it does not have the feeling of sensory stimulation associated with it. In this manner, belief is a feeling accompanying sense impressions. The feeling is an impression of reflection, so that both the sense impression and this impression of reflection together give rise to belief. It is important to note, though, the non-cognitive character of this account. Belief is not explained with reference to the similarity in perceptual content between the idea of imagination and the sense impression; it is explained with reference to the feeling of sensory stimulation associated with the sense impression and which will then lead the imagination to believe in the idea that corresponds or is related to the impression. (Oftentimes, it is the impression of a cause, which then leads to the belief in its effect, thus, two objects dissimilar in perceptual content.) Hume’s notion of belief as the feeling of sensory stimulation offers an empirical limit on what imagination can think. Belief offers an empirical criterion guiding what imagination is entitled to think when it considers matters of fact and existence in its probable reasoning. In the terminology of contemporary Analytic philosophy, imagination constitutes the realm of possible worlds; but the actual world is the one measured by the sensory impressions and the feelings accompanying these impressions, past and present. To be of the actual world, imagination must chain itself to sense perception. The relevance of this notion of belief to Hume’s understanding of induction is that belief as a (strong) feeling of sensory stimulation replaces belief as rational conviction. Such a conception limits belief, and any knowledge claims (if any), to sense perception present and past. This circumscribes the potentially wide scope of imagination as well as limiting the scope of conclusions from induction. When all is said and done, Hume’s account of induction is limited to sense perception without the aid of reason. 2 From Hume to Aristotle I find Hume’s entire approach to and conception of induction puzzling and odd. As an Aristotelian, I expect to see something about the formation of

80

Paolo C. Biondi

generalizations. What we find, instead, are discussions about inferences from the past and present to the future, or inferences from the known to the unknown in temporal terms. We find inferences based on sensory images rather than arguments employing propositions and statements. There is an emphasis on causality as the core of these inferences rather than on the similarity of instances, and when Hume does speak about similarity, in terms of the uniformity of nature, it becomes seriously problematic. Given such reactions from an Aristotelian studying Hume, I expect similar reactions from Humeans, and contemporary philosophers influenced by Hume’s account of induction, studying Aristotle. As a result, rather than turning immediately to Aristotle’s account of induction, I think it would be beneficial to prepare the reader first. This preparation will take several steps by briefly examining several secondary topics related to the principal topic of induction. The topics to be considered are the notions of custom, habituation, animals, and experience. The last steps of this transitional section will examine a number of epistemological assumptions that direct the views of the two philosophers on induction. By comparing and contrasting Hume and Aristotle on all these points, I will, it is hoped, be able to accomplish three goals: first, to show several ways in which Aristotle and Hume agree; secondly, to offer several criticisms of Hume’s account from an Aristotelian perspective; and thirdly, to provide the reader with a guide on the adjustments that must be made in order for him/her to receive Aristotle’s account of induction on its own terms. Accomplishing these goals would pave the way towards substantiating my thesis that the major difference between Aristotle and Hume is the former includes reason in the inductive process whereas the latter excludes it. 2.1 Custom As a first step, we will consider the notion of custom, which is the mechanism by which inductive inferences are made, according to Hume’s positive naturalist account. Now custom is a notion mentioned by Aristotle. For the reader who does not have an intimate familiarity with the language of Hume and Aristotle, it would be quite a challenge to know which of the two wrote each of the following statements: 1) “We have already observed that nature has established connections among particular ideas, and that no sooner one idea occurs to our thoughts than it introduces its correlative, and carries our attention towards it, by a gentle and insensible movement.”

Hume and Aristotle on Induction

81

2) “For by the effect of custom the movements tend to succeed one another in a certain order. Accordingly, therefore, when one wishes to recollect, that is what he will do: he will try to obtain a beginning of movement whose sequel shall be the movement which he desires to reawaken.” 3) “Acts of recollection are due to the fact that one movement has by nature another that succeeds it. If this order be necessary, whenever a subject experiences the former of two movements thus connected, it will experience the latter; if, however, the order be not necessary, but customary, only for the most part will the subject experience the latter of the two movements.” 4) “For as one thing follows another by nature, so too that happens by custom; and frequency creates nature. And since in the realm of nature occurrences take place which are even contrary to nature, or fortuitous, the same happens a fortiori in the sphere swayed by custom, since in this sphere nature is not similarly established.” 5) “Here, then, is a kind of pre-established harmony between the course of nature and the succession of our ideas; and though the powers and forces, by which the former is governed, be wholly unknown to us; yet our thoughts and conceptions have still, we find, gone on in the same train with the other work of nature. Custom is that principle, by which this correspondence has been effected [….]”

So, who is the author of each citation?82 Several points could be made. First, we might be surprised to see Aristotle referring to custom given how that notion is readily (and perhaps notoriously) associated with Hume on the topic of induction. Second, we might notice how Aristotle employs the notion of custom in the context of memory and in the act of recollection, unlike Hume, who employs it in the context of imagination engaged in reasoning about matters of fact. Third, we might find it striking to see how both Aristotle and Hume similarly speak of custom and nature, and of some sort of correspondence or parallel between the customary order and the natural order.83 Given this similarity in verbal expression, it becomes even more startling to see how Aristotle 82

If you answered Hume for citations 1) and 5), and Aristotle for citations 2), 3), and 4), you would be correct. The excerpts are taken from 1) Enquiry 5, 2, 41 (p. 50); 2) On Memory 2, 451b28-31; 3) On Memory 2, 451b10-13; 4) On Memory 2, 452a29-b2; and 5) Enquiry 5, 2, 44 (p. 54). 83 One may wonder whether Hume is expressing his own view in passage 5) since the expression “pre-established harmony” comes from the Rationalist philosopher Leibniz and expresses a view that an Empiricist would not seriously take; however, passage 1) seems to be a straightforward remark.

82

Paolo C. Biondi

confidently believes human beings are capable of acquiring scientific knowledge of an objective natural world whereas Hume is skeptical of such an achievement. 2.2 Habituation As a second step, we will consider the notion of habituation, which is inherent in Hume’s understanding of custom. In the case of Hume, we have seen how he understands cognitive habituation to occur. The mind perceives two objects, fire and heat, say, which are repeatedly conjoined. The repetition habituates the mind such that it will eventually be led to connect the two objects whenever it thinks initially about one of them. The mind operates in this way because nature has “implanted in us an instinct, which carries forward the thought in a correspondent course to that which she has established among external objects; though we are ignorant of those powers and forces, on which this regular course and succession of objects totally depends.” This “instinct or mechanical tendency, which may be infallible in its operations” can thus be relied upon.84 Aristotle’s philosophical language shows that he, too, considers the mind as something that requires development through habituation and that this process is something natural. First, he describes sense perception as an “innate discriminative capacity or ability,” that is, as a natural endowment.85 Second, this natural ability can develop into a habit or state of mind, as reflected in the Greek terms dunamis and hexis when applied to sense perception and to other cognitive faculties.86 These two terms designate the two phases of (cognitive) capacity and habituated state (of cognition), respectively. They imply a development of the capacity into the habituated state through the exercise of that capacity. Aristotle employs as well the technical concepts of potentiality and actuality to explain how any capacity of the mind can develop by being exercised on particular objects, with the result being a perfecting of the cognitive capacity and a development of a new kind of cognitive capacity with its own potentiality. That is, the initial innate ability is one kind of potentiality to know, while the developed habit is a second kind of potentiality to know; and once this 84

Enquiry 5, 2, 45 (p. 55). Notice the “harmony” between the natural order and the (customary) order of thought mentioned in the previous section and footnote. 85 Post An II.19, 99b32-35. 86 For uses of these terms with respect to cognitive abilities, see, for instance, Post An II.19, 99b19, 100a10-14, and 100b6; On the Soul II.4, 415a15-22 and III.4-5; and Nicomachean Ethics VI, passim.

Hume and Aristotle on Induction

83

habituated state of cognition has been established in the mind, the mind actually knows in the fullest sense when it is activated from this developed state and exercises its cognition.87 Third, and as we will see below (in § 2.4), Aristotle’s description of experience in terms of many memories of the same thing shows how he, too, acknowledges the need for repetition in cognitive acts in order for experience to grow in the mind of the knower. Fourthly, this development of the mind with respect to cognitive states is either similar to or analogous to the development of moral character, which Aristotle explicitly states is formed by habituation:88 one becomes just by repeatedly doing just acts; similarly or analogously, one learns to perceive a given object by repeatedly perceiving it. All of these points demonstrate that Aristotle is similar to Hume in regarding the mind as requiring some kind of cognitive development, and that habituation is the way in which this development occurs by nature. 2.3 Animals Both philosophers compare human beings to non-human animals. In both the Treatise and the Enquiry, Hume devotes a chapter on “experimental reasoning” in animals titled “Of the Reason of Animals.”89 The title itself reveals how Hume sees non-human animals as being very similar to human animals since he attributes reason, a cognitive faculty traditionally seen as uniquely human, to non-human animals. His conception of reason in the case of non-human animals, however, is not the traditional one, for he defines it as “nothing but a wonderful and unintelligible instinct in our souls, which carries us along a certain train of ideas, and endows them with particular qualities, according to their particular situations and relations.”90 This constitutes a very vague description of reason, indeed; however, experimental reasoning is additionally described as “nothing but a species of instinct or mechanical power that acts in us unknown to ourselves; and in its chief operations, is not directed by any such relations or comparisons of ideas, as are the proper objects of our intellectual faculties.”91 As this citation suggests, the instinct of reason found commonly in both human and non-human animals is different from 87

See On the Soul II.5, 417a10-b26. Nicomachean Ethics II.1, in toto. 89 Treatise 1, 3, 16; Enquiry 9. 90 Treatise 1, 3, 16 (p. 179). 91 Enquiry 9, 85 (p. 108). 88

84

Paolo C. Biondi

reason in that uniquely human sense of thinking in terms of the relations of ideas. Its mode of operation was described above in Hume’s naturalist account of induction, which thus must be seen as a valid account of reasoning from experience for both human and non-human animals. Hume remarks that the uniquely human ability of reasoning in terms of relations of ideas is one that few human beings develop and exercise. Even children are commonly seen as not possessing the uniquely human kind of reason, while the commonly-shared instinct of reasoning is observed in them. As a result, Hume thinks that the instinct of reasoning from experience accounts for the behaviour of self-preservation of the individual and the species observed in all animals. In short, experimental reasoning guides the whole conduct of the lives of both human and non-human animals.92 Though the natural instinct is not exactly identical in both humans and non-humans, it is clear that Hume thinks all animals learn from experience and draw inferences from it in a very similar manner. As for Aristotle, the innate discriminative capacity of sense perception is said to belong to all animals, human beings included.93 In fact, the possession of this capacity is a defining feature of what an animal is.94 Aristotle’s biological treatises are filled with detailed examinations of animal parts and structures, and speculations about their various functions. They provide evidence of someone intimately familiar with a wide variety of animals and an awareness of which sense(s) each species has (or lacks) as well as the discriminative acuity of the senses possessed. Remarks made throughout his writings show the extent to which Aristotle sees human beings as similar to non-human animals.95 In his comparisons between humans and non-human animals, Aristotle, though, tends to mark more sharply than Hume does the differences between human and non-human animals. One in particular is extremely significant and relevant to the matter of the cognitive faculties of the mind, namely, human beings have an intellect, or rational capacity, as part of their mind; all other animals do not. It is with reference to reason that Aristotle defines human beings.96 As the traditional definition puts it, human beings 92

Enquiry 9, pars. 83-84. Post An II.19, 99b32-35. 94 On the Soul II.2, 413b1-4; and III.12, in toto. 95 See, for instance, On the Soul II.2, 413b1-12; II.9, 421a7-25; and III.12-13, in toto. Among the biological treatises, one could consult the History of Animals, the Parts of Animals, and the Generation of Animals for more detailed studies of organs and functions found in human and non-human animals. 96 See Nicomachean Ethics I.7, 1097b21-1098a16; and X.7, 1177b26-1178a8. 93

Hume and Aristotle on Induction

85

are rational animals. (Since this definition is the traditional concept of reason as something uniquely human, Hume’s title Of the Reason of Animals is not only against this long-standing tradition dating back to the Greek philosophers; it is provocatively so.) This ability distinguishes them from all other animals and makes them a different species of animal. Generally speaking, Aristotle would not attribute reason to animals. Hume’s view of reason in terms of the relation or comparison of ideas comes close to this traditional view of reason in its traditional and proper sense, though, as we will see (in § 3.2 below), his impoverished view lacks other rational abilities such as rational insight. Aristotle will stress rational ability whenever he wishes to speak about that which makes human beings unique among animals. Hume, instead, seems to emphasize the close similarity between human and nonhuman animals by attempting to show that both types of animal use empirical reasoning based on habituation and custom. The tone of the Enquiries especially reflects the anti-rational motivation mentioned at the outset of this essay. He seems to manifest a desire to argue that human beings are nothing but animals, perhaps in reaction against the Christian (and Cartesian) view of human nature, which tends to emphasize the rational soul as an immaterial entity unique to human beings. In short, when it comes to discussing reason, there is a noticeable difference in tone or emphasis: Hume seeks to stress similarities between human beings and non-human animals; Aristotle seeks generally to emphasize differences. 2.4 Experience The differences between human beings and non-human animals are also evident in the nature of experience itself. Whereas Hume speaks as if experience and probable reasoning from experience hardly differ at all (except in degree) in the case of both human and non-human animals, Aristotle definitely asserts that “animals other than human beings live by appearances and memories, and have but little of connected experience.”97 Ultimately, experience, too, is a uniquely human kind of knowledge due to the presence of some degree of rationality. Aristotle’s characterization of experience (empeiria) as many memories of the same thing98 is certainly one that could be true of many other animal species besides the human species. As long as an animal possesses a relatively developed faculty of memory, it could likely acquire some level 97 98

Metaphysics I.1, 980b26-27. Post An II.19, 100a4-5.

86

Paolo C. Biondi

of experience through accumulation of memories of the same thing. Up to this point, Aristotle would resemble Hume insofar as both construe experience in terms of sensory images. However, such a characterization is incomplete. Aristotle says experience also requires logos,99 a term that is difficult to translate into English by any one word. In Greek, several fundamental meanings of logos are connected with language (especially the spoken word), with thoughts signified by language, and with reason and reasoning.100 The main point Aristotle wishes to make is that if experience incorporates some degree of logos, it incorporates some degree of rational and/or linguistic ordering and organization of memories. The elements of rationality and language make experience peculiarly human. At this point Aristotle diverges from Hume. Human beings are capable of “connected experience” by organizing memories according to a much wider variety of similarities than non-human animals are. Non-human animals are limited to similarities grounded in the sensible qualities of memories; human beings can select similarities grounded in less sensible qualities and more general or abstract ones. For instance, to say Socrates and Plato and Aristotle are the philosophers that attended the banquet seems to require a perception of qualities that are remotely sensible indeed. Human beings can perceive such a similarity; it is unlikely that dogs, or dolphins, or monkeys can. Hume’s fork and his denial of abstract ideas prevent him from properly acknowledging this human ability. Furthermore, Aristotle gives more credence to the presence of memories in experience than Hume seems to do. Hume, with his “impressions of sense or memory,” seems to make the act of remembering almost identical to actual sense perception simply because both acts are vivid and forceful; but he seems to overlook the fact that a memory contains much more information than a mere past impression of sense. The fact that memories tend to retain not only individual impressions but also a degree of order and organization among them according to the order of their initial appearance to the mind is of immense cognitive value. To describe experience as an accumulation of many similar memories is to recognize that experience already provides a wealth of information 99

Post An II.19, 100a1-2. See H.G. Liddell and R. Scott, A Greek-English Lexicon, Revised and augmented (Oxford: Clarendon Press, 1968), s.v. “logos.” For uses of logos in Aristotle’s writings, see Hermann Bonitz, Index Aristotelicus, 2nd ed. (Graz: Akademische Druck-U. Verlagsanstalt, 1955), s.v. “logos.”

100

Hume and Aristotle on Induction

87

about the organization of things and how they behave generally. Through experience, we can begin to perceive the orderliness, hence the rationality and intelligibility, of external reality (or at least, of the objects the mind thinks about in thinking what is real). If objects repeatedly appear to the mind in a certain order independent of our will, as Hume admits, then why would we not trust what has been presented to our minds in a fairly consistent manner over a significant period of time? Why would we try to imagine what will happen next rather than remember what happened next through past experience? If I was once burned by fire, the next time I see fire, I will not imagine being burned as a possibility having equal chances of occurring as not; I will remember being burned and project that memory as a (highly) probable possibility. We perceive in the light of the past; we do not perceive afresh with each act of sense perception. Hume does not really appreciate the cognitive value of memory’s ability to retain the order of impressions—in fact, to retain an objective order among the appearances of external reality—in his discussion of probable reasoning. For instance, Hume says belief of the existence of any object, when it is not gained by knowledge, is derived entirely from the force and vivacity of the perception; and then he ranks memory first, where this force and vivacity are most conspicuous, and in the next degree comes cause and effect, which is said to be very great, especially when the conjunction is found by experience to be perfectly constant.101 If that is so, then why not rely on memory more than he does? Hume likewise fails to appreciate the significance of resemblance in experience. He correctly points out the necessity for probable reasoning to assume the uniformity of nature or experience: The only reason experience can be applied to a new situation in the present or future is that the present or future case is perceived to be the same as the cases experienced in the past—granted.102 But what exactly does this entail? Does it not make the relation of similarity more fundamental than the relation of causality in probable reasoning? My experience of two objects being conjoined according to, say, the relation of contiguity (in time or place) would make that experience useful the next time I encounter a similar conjunction of objects. The causal relation need not be employed. In other words, without 101

Treatise 1, 3, 13 (p. 153). On numerous occasions in both the Treatise and the Enquiry, Hume notes the role of resemblance in reasoning from experience. He even suggests that resemblance reinforces belief, whereas a lack of resemblance destroys belief; see Treatise 1, 3, 9 (pp. 111-14). 102

88

Paolo C. Biondi

the relation of similarity, past experience would never enter into any probable reasoning about matters of fact; without the causal relation, experience could still be useful. Moreover, this conclusion would make Hume’s claim regarding the relation of causality as the most important principle of association mistaken. In fact, it is even doubtful whether Hume’s empiricism would enable him to claim any sort of perception of causality. The external senses receive impressions of objects. The internal sense, by reflection, perceives their constant conjunction and a feeling of determination or inevitability in thinking the objects together. This seems to be simple correlation or mere association of objects. How does the mind further discern, on Hume’s empiricist principles, the exact nature of that association? I do not think it can without the intervention of reason. Besides, simple correlation and the relation of similarity seem sufficient to explain probable reasoning: objects A and B have been observed to be correlated; here is an object similar to A; therefore, an object similar to B will (soon) appear. No relation of causality is required. As it is often stated in the sciences or in textbooks on critical thinking, correlation does not automatically mean causation. Furthermore, to speak of the uniformity of nature is to introduce the relation of similarity among matters of fact and existence. But Hume maintains that the relation of similarity is a relation of ideas, a comparison of ideas themselves, and it is known intuitively, by an a priori kind of knowledge based on the similar ideas themselves.103 He thereby transgresses the fork he establishes between relations of ideas and matters of fact.104 He does this as well when he says we acquire knowledge of causality by perceiving that “one particular species of event has always, in all instances, been conjoined with another” (already cited above in §1.4). A species is a rational construct, an abstract concept, not a sensible quality; therefore, Hume ought not to speak of “one particular species of event.” What is intriguing about this error is that Hume could be construed as saying (albeit unintentionally) that we intuit similarities among matters of fact, and that probable reasoning would require an intuitive knowledge of similarities. This view would actually be very close to Aristotle’s position, as we will explain (below in § 3.3) about the act of noein (rational insight) and operative in induction. But such an insight must be prepared by prolonged 103

See Treatise 1, 3, 1 (p. 70). To be charitable, this may be a case where a view expressed by Hume in the Treatise was subsequently revised in the Enquiry. 104

Hume and Aristotle on Induction

89

experience, i.e., by first organizing memories of things according to various similarities. Finally, Hume also seems to underestimate the significance of the perception of frequency of instances gained through experience. As already noted (in § 1.4), Hume distinguishes between two kinds of probable arguments from experience: proofs, which are based on the experience of things that happen always and which show no variation in this pattern; and probabilities, which are based on the experience of things that do not always happen in the same way. The latter arguments may be more or less probable depending on the frequency with which we experienced things. The former arguments can provide certainties due to the unvarying regularity of experience. But, there is something odd, if not inconsistent, about Hume’s approach to probabilities. In the context of raising skeptical arguments against probable reasoning about matters of fact and existence, his narrow view of sense perception leads him into thinking things always have an equal chance of happening in a certain way, or not. Whatever we observe, it is always logically possible for facts to be otherwise. Yet, in other contexts, and most notably in the context of arguing against miracles, Hume then acknowledges the two kinds of probable arguments and relies on proofs. But who is to say that what we take currently to be a proof is not really a probability? The toss of a coin has come up heads 100 times in a row. Is that a proof that coins always come up heads? Every human being so far has died. Is that a proof of human mortality? And yet, Hume is surely right in holding that the human mind can, based on experience alone, notice the difference between things occurring always (e.g., humans dying) and things not so occurring (e.g., coins turning up heads). Sense and memory likely cannot go further than notice the fact of regularity. But reason could certainly reflect on it and discern the reason(s) for it, for it is a significant difference about things. Aristotle discerns the significance that could be inferred by reason from such a fundamental difference in frequency of occurrence. He notices that things that happen by nature happen “always or for the most part;” things that happen by chance, instead, happen rarely.105 Thus, frequency of occurrence can be taken as a sign of the presence of an objective nature. He recognizes that such a distinction between always and not always can be helpful in two ways: in perceiving a nature and any essential property belonging to it; and in distinguishing these from accidental properties or 105

For Aristotle’s views on nature and chance, see Physics II.4-9, in toto.

90

Paolo C. Biondi

things happening by chance. Reason can discern and define such natures and essential properties. Hume, because of his fork and his reliance on sense perception alone when dealing with matters of fact, does not take this step. In the context of explaining probable reasoning from experience, Hume is too dismissive of proofs and of the invariable and uniform experience which supports them. And one wonders how he could even maintain the distinction between proofs and probabilities in any case. In closing, if both Aristotle and Hume may be considered empiricists, it is because both philosophers take experience as the source of knowledge; however, their respective understanding of what constitutes experience shows how different that source is. For Hume, experience is completely arational; for Aristotle, it already contains a rudimentary form of rationality. Furthermore, for Hume, experience is the origin and the end of knowledge (more accurately, of belief); for Aristotle, it is the origin but not the end. Reason can continue reflecting on experience to render it even more rational and intelligible, thereby extracting knowledge, and even scientific knowledge, from it. On a final note, several of the criticisms leveled against Hume on the topic of experience could be mitigated if we keep in mind Hume’s aim of showing the limitations of the Rationalist pretension of a priori knowledge of the world through reason without sense perception. We must remain aware of this polemical slant. Hume is right to criticize this pretense. Hume could give more credit to experience and the uniformity of experience if he simply does not accept the Rationalist view, as he actually does for the sake of argument, that everything must be explained. Even Rationalists hold that certain fundamental truths of reason must simply be intuited; they do not explain everything or try to rationally justify everything. As an Empiricist, Hume should take experience as a given or starting point; there is no need to seek to justify it rationally unless he assumes the polemical aim against Rationalism just mentioned. 2.5 Epistemological Assumptions We will end this transitional section by unearthing a number of key epistemological assumptions underlying the views of the two philosophers on induction. By doing so, we will notice that their divergent positions and attitudes are largely the result of their holding contrary assumptions. The reader must adopt Aristotle’s assumptions if he/she wishes to understand Aristotle on his own terms. The assumptions we will consider are the

Hume and Aristotle on Induction

91

following: the perception of external reality; the act of perception and the objects perceived; the status of abstract and universal objects of thought; the relationship between reason and the senses; the existence of an objective natural order; and finally, the attitude each philosopher takes with respect to the human mind. The first assumption to be considered has to do with the perception of external reality, that is, any reality that may be said to exist outside the human mind (and existing independently of its being perceived or known by it). The question is this: can the mind perceive and know external reality or not? The quick answer to the question is that Hume responds in the negative, while Aristotle, in the affirmative. Hume may be said to be an idealist and Aristotle a realist. As we intend it, idealism signifies that Hume thinks the human mind can only perceive things that are found within the mind, namely, its own perceptions, either impressions or ideas. Anything that may exist outside the mind is unknowable to the human mind.106 Realism is intended to signify that Aristotle thinks the human mind can, and does, perceive and know things that exist outside the mind. (Note that this statement is not intended to suggest that, for Aristotle, the mind cannot also know things within it; in a way, it can.) Aristotle would make a distinction between that which the mind perceives and knows, on the one hand, and that through which the mind perceives and knows, on the other.107 Thus, the images and concepts within the mind are not that which the mind perceives and knows; rather, they are the means by which things external to the mind are perceived and known. It is the latter which are perceived and known by the mind. (Whenever the intellect reflects on the image or concept itself, only then does either of these become that which is known. It is in this manner that the mind knows things within itself.) From Aristotle’s perspective, Hume abolishes this distinction. From Hume’s perspective, Aristotle’s acceptance of this distinction expresses 106

According to Thomson (Bacon to Kant, pp. 274-75), the claim that “we can only perceive our own ideas” is one of the “five central pillars of Empiricism.” Moreover, Thomson states that of the three Empiricists, Hume comes closest to recognizing that the claim “apparently implies that we cannot know anything beyond our own ideas.” See, for instance, Treatise 1, 3, 5 (p. 84). 107 In Scholastic terminology, the distinction is that made between quo intelligitur, that by which something is known, and quod intelligitur, that which is known. See R.W. Schmidt, S.J., The Domain of Logic according to Saint Thomas Aquinas (The Hague: Martinus Nijhoff, 1966), p. 116.

92

Paolo C. Biondi

something akin to the vulgar opinion about perception as well as to the incorrect philosophical view about it. Hume criticizes the “unphilosophical” view of the common or vulgar people regarding perception because they take the object itself for the perception, that is, perception and external reality are identified, and it is the latter they say that we perceive. He also criticizes the incorrect philosophical view of his time, which distinguishes the perception from the object and says both exist: the perception exists in and is dependent on the mind, while the object exists outside the mind and is independent of it. Hume thinks this distinction is mistaken, and is to be replaced by the correct philosophical view: the mind perceives its own perceptions only.108 The second assumption is related to the act of perception and the objects perceived in this act. As we will see shortly (in § 3.1 below), Aristotle assumes the act of sense perception is holistic and the things perceived are individual wholes. The three objects of perception do not refer to three separately and independently existing things; they are, rather, three different perceptible aspects of one whole thing. According to Aristotle, individual substances are the things having separate and independent existence; accidents can only inhere in an individual substance.109 This means that the proper perceptible objects (sensible qualities) and the common perceptible objects (quantitative attributes) can only exist in individual things existing substantially; for instance, this dog here and now will be of a certain size and shape and have definite sensible properties. There can be no brown colour floating freely apart from this dog, no canine shape moving about separately from this dog, and no canine nature or substance apart from individual dogs. As we will see (again in § 3.1 below), the act of sense perception, as Aristotle describes it, is simultaneously sensible and intelligible; it requires 108

For his criticisms against both views, see Treatise 1, 4, 2 (pp. 205-06 and 210-17). Note that Aristotle’s position is similar to the common view by maintaining we perceive the external object, and it is similar to the incorrect philosophical view by making some sort of distinction between perception within and object existing outside the mind. 109 There is a debate among Aristotle scholars regarding what Aristotle takes the substance to be: is it the individual composed of a form and matter? Or is it only the form of the individual? Aristotle’s views in the Categories 2 and 5 provide support for the former position, whereas his reflections in the Metaphysics, particularly bks. VIIIX, suggest that form is substance. I opt for the individual as substance view because it can be shown to include the other position since the individual composed of form and matter already includes the form.

Hume and Aristotle on Induction

93

several capacities of perception working together to capture the whole individual. Depending on which faculty of perception is concerned, a different aspect, i.e., object of perception, of the individual whole will be perceived. Each perceptible object could be considered in isolation; but, separateness in thought does not mean separateness in existence. Hume’s language, on the contrary, sometimes suggests that there are such free-floating perceptible objects as if they are individual existing things. For instance, when discussing personal identity, he says, “All these [i.e., our particular perceptions] are different, and distinguishable, and separable from each other, and may be separately considered, and may exist separately, and have no need of anything to support their existence.”110 He conceives of the act and the object of perception in atomistic terms. Each act and object is discrete and completely separable, and apparently separate, from the others. Hume’s guiding principle on the matter is “that whatever objects are different are distinguishable, and that whatever objects are distinguishable are separable by the thought and imagination. […and the inverse is also true, i.e.,] that whatever objects are separable are also distinguishable, and that whatever objects are distinguishable are also different.”111 This epistemological principle signifies that the mind can only know one object in each act of perception. Its acts of thinking and reasoning are a series of discrete objects of thought joined together only according to any one of the principles of association recognized by Hume. In addition, any complex idea, such as that of substance, is merely a collection of discrete simple ideas; whatever unity the complex idea has is merely the result of one of the principles of association operative in the mind. In other words, the collections produced by the mind always appear customary. This view differs from Aristotle’s, according to which individuals can appear to the mind as wholes, in fact, even as natural wholes. The mind does not so much produce as perceive these natural wholes, which present themselves to the mind as such. Another assumption we can examine concerns the status of abstract and universal objects of thought. We have seen that Hume denies that such 110

Treatise 1, 4, 6 (p. 252) (emphasis added). Treatise 1, 1, 7 (p. 18; and reiterated passim). A version of this epistemological principle can be traced at least as far back as Nicholas of Autrecourt in the 14th century C.E. He employed it to serve his skeptical purposes as well. See Richard N. Bosley and Martin M. Tweedale, Basic Issues in Medieval Philosophy, Second edition (Peterborough, ON: Broadview Press, 2006), p. 453. 111

94

Paolo C. Biondi

objects of thought exist in the mind. The Humean brand of empiricism is based upon the epistemological relation between ideas and impressions, namely, all ideas must be copies of impressions and derived from them; otherwise, they are not truly ideas at all. As a consequence, all ideas must necessarily have some sensible element to them, either a sensible quality perceptible to any of the external senses (e.g., brown) or a passion arising from the act of sense perception (e.g., pain), or else an impression of internal reflection (e.g., the inevitability of the constant conjunction of two objects). Any abstract or universal concepts (e.g., philosopher) are impossible because these often lack any sensible element and cannot be derived from any impression. The Aristotelian brand of empiricism is otherwise. We will see (in § 3.1 below) that sense perception is imbued with intellect. Thus, sensory images and the appetites that accompany sense perception do not exhaust all the thoughts available to the mind for thinking. There are also abstract concepts and propositions. Images of imagination or memory are not identical to these rational thoughts. Even though Aristotle maintains that all thinking must be done with images, rational forms of thinking are not reducible to thinking with images alone. Reasoning, understanding, and other such cognitive acts are not identical with imagining or remembering. In other words, Aristotle’s distinction between a sensory image (phantasma or species sensibilis in Scholastic terminology) and an intelligible concept (species intelligibilis in Scholastic terminology) is abolished by Hume, and every thought of the mind is reduced to an idea that must be derived from an impression. Another assumption concerns the relationship between reason or intellect and the senses. Hume’s fork reflects a radical binary division between them. The two faculties operate separately and are concerned with different objects. No cooperation between them is possible. Aristotle, on the contrary, understands them as operating together, at least sometimes. Knowledge gained through the senses can eventually become intellectual or intelligible knowledge, and even scientific knowledge, by means of rational thought processes. From the information gathered through the senses, there can be a progression in knowledge, with knowledge becoming more rational or intelligible or scientific. This is implicitly expressed in Aristotle’s significant distinction between that which is more familiar and knowable to the senses and that which is more familiar and

Hume and Aristotle on Induction

95

knowable by nature and universally.112 We begin with sense knowledge, which is more familiar and potentially intelligible knowledge; it becomes actually intelligible knowledge when reason acts on it, reflecting on it, categorizing it, defining it, and so on. Such co-operation between the senses and intellect was already alluded to in his conception of experience described above (in § 2.4). Yet another assumption has to do with the existence of an objective natural order. It is actually a metaphysical assumption, but it does have epistemological ramifications. As a realist, Aristotle believes that there is a natural order in the way (natural) things exist and that this natural order is (potentially) knowable to the human mind. Thus, the mind, in theory, is able to discover this order and to provide scientific explanations of it. It is able to perceive and know objective natures and causes, and how they normally operate. There are a number of passages which, in their linguistic expression at least, suggest Hume, too, is aware of a natural order of things;113 however, his epistemological assumptions, particularly the idealist assumption and his philosophical skepticism, make such an order imperceptible and unknowable. Thus, the mind is incapable of perceiving and knowing any objective natures of things, or causes, or necessary connections. Any mention of these as ideas is illusory, except when understood in the empiricist way described above (i.e., as an internal impression). A final assumption that may be considered is the attitude each philosopher takes with respect to the human mind. Hume is a skeptic about human understanding. As such, he has a tendency to place limitations on the cognitive abilities of the human mind and to be very careful about making any knowledge claims. He is keenly intent on showing the limits of the knowledge we could acquire from sense perception: “No conclusions can be more agreeable to skepticism than such as make discoveries concerning the weakness and narrow limits of human reason and capacity.”114 Aristotle, on the other hand, places more trust in our cognitive abilities. Unlike Plato, for instance, he does not disparage sense knowledge. Unlike Hume, he does not reject common opinions and consider them antithetical to a philosophical position. Instead, Aristotle thinks both sense 112

See, for instance, Post An I.2, 72a1-5; and Physics I.1, in toto. The Rationalist notion of sense cognition as confused reasoning (the second characteristic noted above in the Introduction) is likely an interpretation of this Aristotelian distinction. 113 Several of these passages were noted above in §§ 2.1 and 2.2. 114 Enquiry 7, 2, 59 (p. 76).

96

Paolo C. Biondi

perception and common opinions provide suitable starting points in the acquisition of scientific knowledge.115 They form a part of the human experience of the world. He accepts this world as familiar to us. He sees that it could offer scientific knowledge if the mind operates carefully and methodically. Starting from such humble cognitive origins, the mind has the potential to arrive at some degree of actual scientific knowledge about many things human beings experience. I would call this attitude realism. Let us now turn to our study of Aristotle’s account of induction. 3 Aristotle’s Account of Induction The previous section prepared the terrain to make it possible for us to understand Aristotle’s account of induction on its own terms. We must put aside Hume’s problematic picture of induction, something that even a number of scholars of Aristotle fail to do. If Hume succeeds in making the reader skeptical of reason, this skepticism must be limited to the Rationalist conception of reason and whatever cognitive capacities this view attributes to reason. Aristotle does not view reason in the Rationalist manner. A major difference with Rationalism lies in his rejection of a priori knowledge of the world. As presented in the previous sections, we have seen several ways in which reason can be said to work with sense cognition, with memories and experience. Reason depends on experience in order to understand the world. At the same time, we must include reason within experience and in the process of induction if we are to explain how scientific knowledge of the world can be acquired from sense perception. This is how Aristotle’s empiricism differs from Hume’s. Post An II.19 constitutes the locus classicus demonstrating Aristotle’s empirical stance. In this famous chapter, he explicitly states that knowledge begins with sense perception, which we saw (in § 2.3) is described as a discriminative capacity shared by all animals including human beings. In Metaphysics I.1, another account of the kinds of knowledge is presented from another perspective. It begins with Aristotle’s well-known assertion about all human beings having the desire to know, and the sign of this desire being the delight we take in our senses because they inform us about the world around us.116

115

This is evidenced by the initial chapters of a number of his treatises. Aristotle usually considers the opinions of his predecessors before expounding his own views. See, e.g., On the Soul I, in toto; and Metaphysics I.3-10. 116 Metaphysics I.1, 980a21-27.

Hume and Aristotle on Induction

97

In Post An II.19, Aristotle confidently asserts that human beings are able to gradually work their way up from sense perception to memory, then to experience.117 We have already seen (in § 2.4) how experience is said to be “many memories of the same thing” and requires an element of logos as well. From experience, human beings can then acquire the principles of science.118 Aristotle calls this cognitive process epagǀgƝ (traditionally translated induction). He equates the process with the mode of operation of sense perception, asserting sense perception instills or implants the universal in the mind “by epagǀgƝ,” i.e., in an inductive manner.119 Once the principles of science have been acquired, they could then be employed to construct scientific knowledge, which Aristotle identifies with the possession of any demonstration of a necessary or essential property inhering in its proper subject.120 The demonstration, which is a deductive inference, constitutes a causal explanation showing the reason why (the cause) the property belongs to the subject (the fact explained).121 (As already mentioned, it is likely that the Rationalist assimilation of causation to logical demonstration, the third characteristic of Rationalism noted above in the Introduction and in § 1.3, took its inspiration from Aristotle’s view of demonstration.) Another significant passage on induction is found in Pr An II.23. In this chapter, Aristotle describes an induction which is really a “deduction which springs out of induction” (ho ex epagǀgƝs sullogismos).122 This induction assists in establishing “primary and immediate propositions” (tƝs 117

Post An II.19, 99b35-100a5. Post An II.19, 100a6-9. Due to a lack of clarity in this passage, there is some diversity of interpretation among Aristotle scholars on the connection between experience and the principles of science. Whereas the Post An passage seems to suggest that experience is somehow identical to the principles of science, Metaphysics I.1 more clearly distinguishes between experience and science, asserting that scientific knowledge is derived from experience (see 981a1-5). 119 Post An II.19, 100b4-5. An increasing number of Aristotle scholars are becoming hesitant about translating epagǀgƝ by ‘induction’ because they are aware that the English term now carries many Humean connotations which do not belong to the cluster of connotations associated with the Greek term. Since one of the aims of this anthology is to provide an Aristotelian account of induction in opposition to the Humean account, we will retain the traditional English translation and leave it to the reader to see how induction is understood from an Aristotelian perspective and how it differs from the Humean conception. 120 Scientific knowledge and demonstration are defined in Post An I.2, 71b9-19. 121 Post An I.2, 71b20-32. 122 Pr An II.23, 68b15. 118

98

Paolo C. Biondi

prǀtƝs kai amesou protaseǀs), which are the sort of proposition scientific demonstrations require as premises.123 The suggestion is that this induction, which incorporates a reasoning process, is also involved in the acquisition of principles of science. We will see (in § 3.3) how both accounts of induction might be understood together. We will also show how Aristotle’s picture contrasts with Hume’s and with contemporary views of induction as invalid deductive forms of argument reaching merely probable conclusions. This section will parallel that on Hume. We will first present the objects of perception recognized by Aristotle. This will be followed by a brief examination of several cognitive faculties of the mind. We will then present Aristotle’s account of the process of induction. 3.1 The Objects of Perception Similarly to Hume, Aristotle analyses perception into objects of perception.124 Taking the external senses as the reference point, he distinguishes between perceptual objects which are perceived per se (kath’ hauta) and those perceived accidentally (kata sumbebƝkos); in other words, he differentiates between those objects which can stimulate any of the external senses and those which cannot. The per se perceptible objects are subdivided into proper (idion) perceptible objects and common (koinon) perceptible objects. The proper are those which can stimulate only one external sense; the common are those which can stimulate at least two external senses and perhaps all of them. For instance, colours can only be perceived by sight, and tactile qualities can only be perceived by touch; but shape, say a square-shaped book cover, could be seen by the eyes looking at the coloured surface of the cover and felt by the hand running along its edges. The proper objects include all sensible qualities (colours, sounds, odours, and so on), while the common objects include quantitative attributes (size, shape, number, unity, motion, and rest).125 As for the third class, the accidentally perceptible object, Aristotle is referring to the substance of an individual sensible thing. By saying substance is accidentally perceptible, Aristotle intends to say that such an 123

Pr An II.23, 68b30-31. Aristotle states that scientific premises must have the characteristics of being primary and immediate in Post An I.2, 71b20-21, 71b25-28, and 72a6-8. 124 The summary that follows is based on On the Soul II.6, in toto. 125 Aristotle lists these six common objects in On the Soul III.1, 425a15-30. Unity is mentioned here but not in the list found in On the Soul II.6, 418a17, which includes the other five objects.

Hume and Aristotle on Induction

99

object is indeed perceptible; however, it is not perceptible to the external senses, hence, the qualification of its being accidental. For instance, by means of the external senses, the human mind is able to perceive per se the proper and common sensible objects of an individual thing (size, colour, shape, texture, and so on); but that individual thing just so happens (this is the meaning of accidental) to be, say, a dog (this is the substance of the individual thing: it is being a dog). Ultimately, it is the intellect (nous) that perceives per se the substance (or nature or essence) of an individual thing.126 Although they are not identical in meaning, for the sake of this essay, substance (ousia), nature (phusis), and essence (to ti esti kata to ti Ɲn einai) can be taken as more or less identical. All three terms refer to the being of an individual thing since its mode of being (ousia) identifies what a thing is (to ti esti). Mode of being is to be understood in a dynamic manner (kata to ti Ɲn einai). That is, contrary to Hume’s definition of substance as an underlying subject, Aristotle’s definition of substance signifies the activity or energy (energeia) displayed by an individual thing (normally, a living whole entity) and which maintains it in existence. This activity is the intellect’s object of perception.127 As Aristotle says, though the act of sense perception is of the individual, say Socrates, the content of perception is of the universal substance, human being.128 In other words, Aristotle acknowledges that the act of sense perception, at least in the case of human beings, is an act in which the external senses and the intellect operate together: Understanding the act of sense perception from the perspective of the external senses, the proper and common sensible objects become perceptible per se; understanding the same act from the perspective of the intellect, however, the intelligible substance, which is accidentally perceptible to the external senses, becomes perceptible per se.129 126

See On the Soul III.6, especially 430b26-30. For a more (biologically) dynamic interpretation of Aristotle’s key philosophical vocabulary, see the English Glossary Aristotle’s On the Soul and On Memory and Recollection, trans. Joe Sachs (Santa Fe, NM: Green Lion Press, 2004), pp. 186203. 128 Post An II.19, 100a16-100b1. 129 This is suggested by Post An II.19 if one interprets the state of nous developed through acts of sense perception as referring to the intellect, the capacity. In On the Soul III.4, 429b10-22, Aristotle says (admittedly not clearly) that two faculties or possibly the same faculty otherwise disposed perceives the essence of perceptible things, and names both the sensitive faculty and nous, which similarly suggests the joint operation of the senses and the intellect. 127

100

Paolo C. Biondi

A major difference between Aristotle and Hume should become evident at this point. Hume does not include perceiving substance among the perceptions of the mind.130 He argues that the idea of substance has no prior impression from which it could be derived. He would say that Aristotle (and any who follow his views on substance) is fooled by a figment of the imagination. We imagine that there is some unifying subject underlying the sensible impressions acquired through the external senses when, in fact, there is none. We are implicitly adding something onto perception without recognizing it, thereby going beyond perception and straying into the metaphysical realm without warrant. In short, substance is a fictional product of the imagination, not an object of perception. What is interesting to note, though, is that Aristotle and Hume are actually closer than they might initially appear. After all, Hume limits perception to the external and internal senses, which capture sensible qualities and feelings. If these are the only channels of perception, then he is correct to conclude that substance is imperceptible to the mind. Aristotle would agree. After all, he does say that substance is not a per se perceptible object of the external senses; it is only accidentally perceptible, which means it is not perceptible at all to the external senses. Although there is no reference made to the internal senses and feelings in Aristotle’s schema outlined above, he does include feelings among the objects of perception in another manner. Similarly to Hume, Aristotle notes that the stimulation of the external senses can be accompanied by feelings of pleasure or pain, which then give rise to other emotions such as desire, aversion, or anger.131 Sense perception, for Aristotle, is generally accompanied by some appetite, which can then be perceived by an internal sense. Therefore, besides their agreement on the external senses as one channel of perception, both philosophers would also admit a second channel, namely that the human mind is capable of perceiving feelings of pleasure, anger, love, and so on; and for both, substance is not perceptible through either of these channels. The only difference between them lies in Aristotle’s accepting, and Hume’s rejecting, the class of perceptible objects called substance (or nature or essence); and the primary reason for this disagreement lies in Aristotle’s acknowledging, and Hume’s not acknowledging, a third channel and capacity of perception in the human mind, namely, the intellect or reason, whose per se perceptible object is the 130 131

Treatise 1, 1, 6. This point was alluded to in § 1.6 above. See On the Soul II.3, 414b1-15; and III.9-11. Cf. Hume, Treatise 1, 1, 2.

Hume and Aristotle on Induction

101

intelligible substance of existing things. Let us now consider briefly the faculties of the mind. 3.2 The Faculties of the Mind In § 1.2, we proposed that both Hume and Aristotle could be said to maintain that the human mind has several cognitive faculties or capacities. If this proposal is somewhat debatable in Hume’s case, Aristotle seems more committed to a faculty view of the mind. It was noted above (in § 2.2) that the language of dunamis (power or capacity or even faculty) and hexis (habit or developed state), when applied to the mind, suggests that there is a mind with various faculties, each of which can be developed through exercising it until it becomes a habitual cognitive state or habitual mental behaviour.132 Since we studied imagination, memory, and reason in our consideration of Hume’s position, we will study these three faculties in our consideration of Aristotle’s. For Aristotle, the initial condition of the mind is analogous to “a writing-table on which as yet nothing actually stands written” or a blank slate: It is nothing before it thinks.133 Through sense perception, it begins to acquire content for thought. The content of sense perception, sense impressions, lasts only as long as the actual act of sensation. Imagination and memory constitute mental faculties that can retain the impressions of sense perception after the act of sensation ceases. Imagination is a movement set up within a percipient as a result of the stimulation of any of the external senses.134 In a manner analogous to Hume’s view that an idea is a copy of an impression, Aristotle maintains that the image of imagination resembles the sense perception and retains it within the percipient subject.135 Once the sensory image is retained in 132

In the key text, Post An II.19, sense perception is said to be a discriminative dunamis which develops into the hexis of nous. See also On the Soul II.4, 415a14-22, which refers to the various cognitive dunameis of the soul; and Nicomachean Ethics VI.3-11, which describes the various intellectual hexeis of the mind. 133 On the Soul III.4, 429b29-430a2; also III.4, 429a18-29. Locke’s description of the initial condition of the mind “to be, as we say, white paper, void of all characters, without any ideas” seems to be a reiteration of Aristotle’s image, except in terms of an updated technology; see John Locke, An Essay Concerning Human Understanding, Book II, ch. 1, § 2. Perhaps today we would speak in terms of a blank computer screen or a blank document file. 134 Most of Aristotle’s views on imagination can be found in On the Soul III.3, especially 428b10-429a9, and in On Memory 1. 135 On the Soul III.3, 428b10-16.

102

Paolo C. Biondi

imagination, it loses any association with the originating impression and the thing that caused the impression. In Aristotle’s terms, imagination considers merely the image in itself.136 This disconnection from the real thing means that the images of imagination may come to mind in ways and times that have no correspondence with how real things were actually perceived (or are currently being perceived). As Aristotle puts it, the images of imagination can be true or false, depending on whether they correspond to things in external reality or not.137 Although this disconnection from reality might seem to lead to a negative consequence—namely, having a false image in mind and being fooled into believing it represents a reality (which Hume notes as well)—it could also have a positive consequence: it makes imagination the suitable faculty for goal-directed action. Such action can take place by bringing to mind an image which could direct animal movement; for example, a hungry animal could imagine its prey, which will help it to find something resembling it as it moves about through its environment searching for something to eat.138 This, according to Aristotle, constitutes the positive function of imagination. In human beings, Aristotle adds another analogous function: imagination is incorporated into thinking since Aristotle claims no thinking can take place without images.139 Even abstract conceptual thinking requires sensory images of some sort. These two functions of goal-directed movement and thinking give to imagination a future orientation by presenting to mind an image of a possible reality (i.e., one that could be perceived in accordance with the image). The future orientation of imagination contrasts with memory’s awareness of the past. Memory works with images retained by imagination but builds upon them. A memory differs from an image of imagination by adding a relation, or an association, to the image. Memory establishes a relation between the image and the original thing of which it is an image, i.e., the thing that caused the sense impression in the first place.140 For instance, the image of 136

On Memory 1, 450b11-451a2. Aristotle describes perceptual error in terms of the three objects of perception at On the Soul III.3, 428b16-30. 138 On the Soul III.3, 428b16-17 and 429a4-8. Note that Aristotle thinks that animal movement, i.e., a goal-directed change of place, also requires desire to work in conjunction with imagination (or thought in the case of some human action). See On the Soul III.9-11 and Movement of Animals 6-10. 139 On the Soul III.7, 431a14-17; and III.8, 432a3-10. 140 On Memory 1, 450a1-451a18. This short treatise contains the bulk of Aristotle’s views on memory. 137

Hume and Aristotle on Induction

103

Socrates in my memory is somehow associated with the real Socrates I saw at the banquet yesterday. Memory is thus said by Aristotle to be “an image related as a likeness to that of which it is an image.”141 A memory is thus a form of internal representation of an experienced reality. He further states that memory is an image that incorporates an awareness of past time.142 In effect, when I remember Socrates, that is, when I call to mind the memory image of Socrates I saw yesterday, what I am aware of is not the image in itself; instead, I am aware of the act of seeing Socrates yesterday, that is, the original act of perception within its spatiotemporal context. The mind is able to perceive this difference in time between the original act of perception and the current act of remembering, and thereby become aware of the perception as having happened in the past. In the act of remembering, the mind is considering the real thing experienced in the past by means of the image related to it through the association effected by memory.143 Aristotle notes, in addition, another significant feature about memory: it retains perceptions in an orderly fashion. Imagination is incapable of this feat. On this point, he and Hume are in agreement; but then he goes further than Hume. Aristotle affirms that memory follows the order of nature, by which he means that the order in which things and events unfold in external reality, in that same order does memory retain the perceptions of things and events.144 Moreover, Aristotle claims that there is also a uniquely human act of remembering: the human mind is capable of what he calls the act of recollection.145 This act is not identical to the act of remembering. The order of things and events perceived and retained in memory makes it possible for the human mind to recollect things and events because recollection involves a rational process of some sort.146 In recollection, the human mind takes any given thing or event that occurred in the past as a starting point and then goes through the succession of events that took place just before or just after that reference point. It differs from the act of remembering by being a more active rather than passive cognitive process (the subject must consciously intend the act of recollection) and by re141

On Memory 1, 451a16. On Memory 1, 449b10-29. 143 On Memory 1, 450b11-451a2. 144 On Memory 2, 451b11-452a4. 145 The second chapter of On Memory covers recollection, while the first is concerned with memory. 146 On Memory 2, 453a5-14. 142

104

Paolo C. Biondi

calling a series of events instead of recalling a single happening, which is the usual focus of the act of remembering. In short, if remembering tends to focus on things, recollection tends to focus on the order among things. Memory and recollection together have the potential to provide the human mind with a broader picture of reality than a single sense impression ever could. In this manner Aristotle goes further than Hume, who limits perception to the perception of impressions and ideas, and limits memory to the feeling of sensation; and he refuses to go beyond the confines of the human mind and into the external world. It can be argued that Aristotle’s realism is rooted in his conception of memory, for what we remember are the real things external to the mind and which caused the memory within the percipient subject. By adding an association with the real thing it represents, memory transforms an image of imagination. As a result, images retained within the percipient subject are transformed from mere fictions to phenomena, from something possibly real to something experienced and actually real. Hume, it was argued (in § 1.6), attempts to separate beliefs from fictions in a non-cognitive manner by associating images of imagination with the stronger feelings accompanying the act of perception of sense or memory. Aristotle’s explanation constitutes a cognitive way of separating fictions from phenomena because the memory image, as a copy of the original thing, itself is an internal representation of (experienced) reality. This cognitive and realist interpretation of memory explains why Aristotle selects memory, and not imagination, as the step that follows upon sense perception in the inductive process. Experience itself is memory, in fact, a solidified memory of reality gained through repetition of similar experiences. As argued in our discussion about experience (in § 2.4), human beings (and all animals) encounter a new situation in the light of the past. Hume is mistaken to think that we will imagine various scenarios upon seeing fire; this is simply not the case. If I was burned by fire, I will remember my past experience with it and respond accordingly. Thus, memory is the crucial retentive capacity in Aristotle’s account of induction; imagination constitutes merely a subordinate step towards the building of memory. Finally, let us consider reason. It was shown (in § 1.2) how Hume’s conception of imagination actually covers a fairly broad range of mental acts. According to one meaning of imagination, this faculty includes certain acts of reasoning, both demonstrative and probable. A consequence of this larger playing field for imagination is a smaller playing field for reason.

Hume and Aristotle on Induction

105

The primary activity of reason is said to consist in reasoning, or drawing inferences. Reason in the proper sense is restricted to reasoning about the logical (and mathematical) relations of ideas, which Hume takes to mean that reason has nothing to say about the world of facts and existence. Reason, apparently, is solely concerned with the meanings of terms and with how various meanings may be logically related to each other and inferred from each other. Such a conception of imagination and reason could certainly explain the primacy and prevalence of imagination in Hume’s cognitive psychology and in his account of induction. Aristotle’s picture of reason differs quite a bit from this one. Even though he maintains that all thinking incorporates images, Aristotle never reduces conceptual thought processes, such as demonstrative reasoning, to thinking about or in terms of images.147 Reason is not identified with imagination; concepts are never identified with sensory images. The object of reason is a universal concept (e.g., dog) or a universal proposition (e.g., Every dog barks); images and memories are not universal but particular (e.g., this dog here named Fido).148 (As a sidenote, Aristotle often contrasts or opposes the universal and the particular as objects of science and of sense perception, respectively.149 However, this opposition (contrary to Hume’s fork) is not mutually exclusive such that the induction of a universal from particular instances becomes impossible; otherwise, Aristotle’s position on the empirical origin of scientific knowledge would not be tenable.) Aristotle does not attribute any form of reasoning to imagination, though he does attribute a form of reasoning to memory in the act of recollection. The act of reasoning, strictly speaking, is the proper act of reason, a mental faculty distinct from imagination and even from memory. Reason could be said to have three basic operations: 1) acquiring concepts, which requires the formation of concepts from images; 2) making judgments, which requires the formation of propositions by joining together two concepts; and 3) reasoning, which requires, at a minimum, joining together two propositions in such a way that a third proposition may be inferred from them. As can be seen, the prior operation is normally required before the following operation can occur: in order to reason, the intellect requires propositions; and these statements must be formed with con-

147

On Memory 1, 450a1-14. Metaphysics I.1, 980b25-981b11. 149 See, for instance, Post An I.2, 71b33-72a5 and I.31, in toto; and On the Soul II.5, 417b16-27. 148

106

Paolo C. Biondi

cepts.150 And concepts are generally not formed in a priori fashion; they are derived from images, which ultimately require sense experience with the world. The objects of reason thus have some connection with the world and can therefore signify and refer to things of the world. As it might be surmised from the brief description of induction given at the beginning of this section (in § 3), the inductive process can be seen to play a part in the first two rational operations. In these operations whereby concepts and propositions are acquired, the third operation of reasoning is not only unimportant; it is not yet possible. What is important is rational insight, or intuition—to use the term employed by Hume and the Rationalists when speaking about reason proper. But whereas these thinkers reserve intuition to a priori reason, Aristotle extends it to include insight into the substance or nature of (images of) particular things. This kind of rational insight is the key missing element in Hume’s account of induction; its presence in Aristotle’s account is crucial and it explains the major difference between the two accounts. Rational insight may initially be described in the following manner. Just as memory considers the same image as the one considered by imagination but in a different way (i.e., it considers the image in relation to the real thing it represents), analogously, reason considers an image or a memory but in a different way, that is, as a universal concept (or perhaps as a universal proposition). Reason (or intellect) conceptualizes the image. It takes an image, which is a potentially intelligible object, and makes it into an actually intelligible object.151 To attempt to describe rational insight or intellectual intuition further would actually take us into Aristotle’s account of induction, so we will stop at this point. There is something paradoxical in this comparison of Hume and Aristotle on reason. Hume does not accept the existence of abstract ideas, which means he does not accept truly rational concepts. There are only particular ideas copied from particular impressions. And yet, reason in its proper sense has no real contact with the content of ideas; somehow, it merely 150

These rational operations are not clearly labelled as such in Aristotle’s writings on logic, though they may be inferred from them. Perhaps Pr An I.1, in toto comes closest to stating explicitly the three operations. Scholastic thinkers more clearly present such a schema; see, e.g., Aquinas, In Aristotelis Libros Peri Hermeneias Expositio (Rome: Marietti Editori Ltd., 1955), Proemium 1-3. Recall Hume’s criticism of this tripartite scheme mentioned in the Introduction. 151 The intellectual capacities responsible for this act are described in On the Soul III.45.

Hume and Aristotle on Induction

107

deals with abstract logical relationships among them, which gives us no knowledge of the world. Aristotle, on the contrary, accepts the existence of abstract and truly rational concepts. There are universal concepts and propositions apart from the particular sensory images of imagination and memory. And yet, reason still maintains contact with the external world since concepts and certain propositions must be acquired from images; and all rational thinking occurs with images. Consequently, reason, in thinking about concepts and propositions derived from images, could provide knowledge of the world. This is especially so when concepts signify the substances or natures of things. Some of the relationships reason establishes among such concepts could reflect relations of essential or necessary properties inhering in substances (i.e., as in primary and immediate propositions) or even causal relations existing between things (i.e., as in demonstrations). In short, Hume is just as Rationalist as the Rationalists in his conception of reason as something capable of knowledge without sense perception. He differs from them by limiting this knowledge to strictly logical relations found in reason itself; he simply denies the Rationalist pretense of a priori knowledge of the empirical world. To know the world, he insists that we require sense perception and experience. Aristotle would concur. But he would then chastise Hume for stopping there, for restricting our knowledge of the world to the senses and memory. Aristotle would take one more step and say that reason can take the material of experience and transform it into rational, intelligible, and even scientific, knowledge. Reason is not completely separated from the world. It has access to it through rational insight or intellectual intuition into the natures of things. We are now ready to consider Aristotle’s account of induction. 3.3 The Process of Induction As already mentioned, Aristotle recognizes several stages or steps in the inductive process: sense perception is said to give rise to memory, and many memories of the same thing result in experience. Then from experience, the human mind is in a position to acquire the principles of science. Science, for Aristotle, refers to having necessary universal knowledge that leads to a demonstration proving the inherence of a property in its appropriate subject.152 The principles of science would therefore include anything that could be used to construct such demonstrations, for example, scientifically adequate universal propositions to serve as premises of the demonstra152

Post An I.2, 71b9-19; I.7, in toto; and I.10, in toto.

108

Paolo C. Biondi

tions.153 A given scientific discipline would contain demonstrations of as many of the necessary or essential properties belonging to the subject as possible. The procedure followed in mathematics, and particularly in geometry, provided Aristotle with an actual example of this model of science as a logically organized body of demonstrative knowledge.154 The key characteristic of scientific knowledge, according to Aristotle, is that it deals with the universal nature of things and demonstrates necessary and essential properties belonging to that nature.155 Establishing appropriate definitions of the subject of a given science and of any of its known properties becomes critical in this quest of scientifically knowing the universal natures of things.156 When a geometer demonstrates that the interior angles of a triangle equal two right angles, this property is true of all individual triangles, including those not yet perceived or even in existence, because each individual triangle satisfies (or will satisfy) the definitions of triangle and of the property of two right angles. If an individual triangle does not satisfy the definition of triangle, then it is not really a triangle at all. Though Hume considers demonstrative knowledge one that is built solely upon relations of ideas and has no need of experience to be known, Aristotle differs from Hume in that he does think it possible to obtain demonstrative knowledge of some things which do require experience to be initially known. That is, Aristotle thinks demonstrations are possible for things Hume would consider matters of fact and, therefore, not objects of demonstration. The realm of natural living things and determining biological species and kinds offers the most obvious case. (Mathematical objects would constitue a separate case. Hume places them under relations of ideas, and as a consequence, they are objects of demonstration; yet, geometrical demonstrations require diagrams, hence sense perception. This ought to make the diagrams matters of fact. Aristotle considers mathematical objects abstractions of the quantitative characteristics found in natural objects (e.g., a square can be abstracted from square-shaped tables). He is aware that geometrical demonstrations require diagrams, hence sense perception, and yet, 153

Post An I.2, 71b20-72b4. For a history of the development of geometry in ancient Greece up to Aristotle’s time, see Sir Thomas Heath, A History of Greek Mathematics, Volume 1: From Thales to Euclid (Oxford: Clarendon Press, 1921; rpt. New York: Dover Publications, Inc., 1981). 155 Post An I.4-6; and II.1-2. 156 The relationship between demonstration and various kinds of definition is examined by Aristotle in Post An II.3-10. 154

Hume and Aristotle on Induction

109

that the demonstration concerns something intelligible and universal (triangle), not the particular sensible diagram (this triangle drawn here).157 Whereas Hume would limit our knowledge of natural things to sensory impressions made by individuals, saying we can have no knowledge of the nature (i.e., the biological species or kind) of that individual, Aristotle would disagree. He would go one step further beyond experiential knowledge of individuals and claim that we can acquire scientific knowledge of natural kinds. Such knowledge would be possible even without experiencing all the individual members of a given species or kind. In other words, though certain sciences, such as the natural sciences, require experience to provide us with initial knowledge of things considered by Hume to be matters of fact, Aristotle thinks science builds upon the foundation of experience and deals with scientific facts which necessarily go beyond experiential knowledge. In short, Aristotle does not accept Hume’s fork: it is possible to have demonstrative reasoning about matters of fact if the reasoning is based on the universal and necessary nature of those facts. (In rejecting Hume’s fork, Aristotle is in agreement with Kant, who attempts to overcome the fork with his notion of the synthetic a priori.) The main reason for this rejection is that Aristotle thinks the human mind is endowed with the ability to perceive and know the natures of individual things; Hume does not. This is the major conclusion to be drawn in our comparison of Hume and Aristotle on induction. We will now begin to see the implications of this conclusion. Aristotle refers to induction as “the path that goes from particulars to the universal,”158 a path that can lead to the acquisition of the principles of science. This path begins with sense perception of individuals, which are normally grouped together in our memory according to relevant or significant similarities. The experience that results from many memories of the same thing is a kind of knowledge that always remains at the level of sensory impressions of particular individuals;159 however, certain significant similarities can be discerned to be a sign of a universal nature common to the particular individuals. The identity of nature supersedes the mere similarities found in the sensory impressions. How do we come to know this common nature?

157

On this last point about Aristotle, see, for instance, On Memory 1, 450a1-14; and Physics II.2, 193b22-194a11. 158 Topics I.12, 105a13. 159 Metaphysics I.1, 980b25-981b9.

110

Paolo C. Biondi

Acquiring universal knowledge of a nature can be accomplished by holding, as Aristotle does, that when we perceive individual things, we perceive not only their sensible qualities and quantitative attributes but also their substance or nature. The reason is that the intellect, which constitutes another channel of perception, works in conjunction with the external senses, imagination, and memory. I have not only individual memories of Socrates, and Plato, and Aristotle whom I met yesterday at the philosopher’s banquet; my intellect is also capable of perceiving something common to the memory images of all these individuals and designate this common similarity by the name ‘philosopher’ or ‘human being’. By means of the intellect, the mind is able to overlook irrelevant differences in sensible qualities presented through the external senses and focus on the underlying similarities of activity. The senses present an image of Socrates the stout and pug-nosed, Plato the broad-shouldered, and Aristotle the slight of build. Despite these very different images of human beings, they may be perceived as being similar because of an identity of activity: they are being human or being philosophical.160 Certain common similarities designate the substance or nature of individuals, and reason is able to form concepts to signify, more or less precisely, this substance. Aristotle thinks the human mind has the ability to classify particular things into categories, or classes, of varying levels of generality. For instance, reason can eventually come to know that ‘All philosophers are human beings’ is a true statement and ‘All human beings are philosophers’ is a false statement; as a consequence, it comes to know that the category of philosophers is narrower and fits within the broader category of human beings. The role of frequency of occurrence of certain features existing in individual things assists in the discernment of reason (as mentioned in § 2.4). Reason compares and contrasts individuals, and distinguishes between essential and accidental features. Gradually, reason discerns and knows which features belong together and which are incompatible. Over time, the intellect’s power of perception becomes habituated into a more refined and more precise perception. In the process, sense perception becomes more rationally informed. Based on such rational insight and discernment, individual things may be defined according to their natures or organized in a variety of ways amenable to scientific knowledge. This is the heart of induction as Aristotle conceives it: by reflecting on our experience of the world, reason elicits universal concepts from 160

This dynamic view of substance as activity of being was already explained in § 3.1.

Hume and Aristotle on Induction

111

similar individual things; and certain concepts enable reason to perceive the natures of those things. The intellect is capable of translating sensible images into intelligible concepts, and translating feelings of necessity binding two objects in the mind into logical relations. This is what it means to conceptualize empirical reality and to render the potentially intelligible into something actually intelligible. This is mostly the work of rational insight and discernment. In this manner, Aristotle’s conception of induction as a path from particulars to universal is not first and foremost a (probable) reasoning process or an inference by causal association or (an invalid) form of argument.161 It is an insightful perception into particular things that leads to an understanding of what they are, i.e., their nature. By observing and experiencing a number of individuals, and by reflecting on the concepts or categories attributable to them, it then becomes possible to understand which concepts are compatible with each other (or not) and what the logical relationships among them are.162 It therefore becomes possible to establish, by means of intellectual perception and rational reflection, a variety of universal concepts and (more or less precise) essential definitions of the natures of things. It also becomes possible to make statements of fact about things and even to establish universal propositions about them when considering their natures. With the introduction of statements and propositions, it now becomes possible to include a kind of reasoning process in the process of induction. It becomes possible to make inferences from one feature or thing to another feature or thing. These inferences depend on the known nature of 161

Groarke astutely notes the significant shift in the conception of induction inaugurated by Hume. Before Hume, the traditional conception followed Aristotle’s definition of induction as the movement from the particular to the general; and induction is opposed to deduction, which is said to move from the general to the particular. Since Hume, induction has instead been defined as an (always) invalid argument; and induction is opposed to deduction, which is a valid argument (when sound). See Louis Groarke, An Aristotelian Account of Induction: Creating Something from Nothing (Montreal & Kingston: McGill-Queen’s University Press, 2009), pp. 31-40, 95-155. 162 This sentence contains the seed of my puzzlement with Hume’s a priori relations of ideas and certain practices of philosophical analysis or conceptual analysis found within Analytic philosophy. It seems to me that the role of concepts and their meanings must somehow be related to the individual things (in external reality) and their various features which the concepts are intended to signify and to refer to. At least certain concepts and their ‘logical’ relations can only be known through the experience and understanding of individuals, not through any a priori analysis of (ontologically empty) ideas or concepts or meanings.

112

Paolo C. Biondi

the thing, not merely on our experience of it. Let us now look at the induction said to produce propositions. Aristotle speaks of a “syllogism coming from induction,” by which we can deduce “immediate and primary propositions,” that is, propositions having the requisite features of a scientific premise for demonstrations.163 As explained by Aristotle, the deduction from induction accomplishes this feat by attributing one property, A, to all instances of a group of individuals perceived to have that property, and then by enumeration of those same individuals, a second property, B, is observed to belong to all of them as well.164 Consequently, it, too, may be attributed to them all. As long as certain conditions are met,165 then one can legitimately infer by reasoning from this induction that ‘Every B is A’, a universal conclusion uniting the two properties (designated by universal concepts). Aristotle’s stipulation of certain conditions regarding the convertibility of terms explains the conversion of (2) the minor premise in the sample syllogism that follows. The conversion is required to make the deduction valid and have it conclude universally. Here is a sample deduction from induction: (1) Socrates, Plato, Aristotle, each (C) is a rational animal (A). [by induction] (2) Socrates, Plato, Aristotle, each (C) is a human being (B). [by induction] (3) Every human being (B) is Socrates, Plato, and Aristotle (C. [conversion of (2)] 163

Pr An II.23, in toto. This important text is a source of much dispute among Aristotle scholars. One source of disagreement is whether the induction presented here is supposed to start from individuals or from species. I claim the former since the induction from species necessarily presupposes a prior induction from individuals to species, thus making it impossible not to have recourse to individuals. In Post An I.18, in toto, Aristotle states that demonstration depends on universals, but universals require induction, induction requires perception, and perception is of particulars. 164 In the previous section (§ 3.2), it was stated that reasoning is not possible without first having acquired propositions and concepts. This claim must be restricted to reasoning in the strict sense, which requires universal propositions, which in turn, contain universal concepts. The kind of reasoning tied to induction is not so in the strict sense because each of the propositions contains one universal concept and one term that is not a universal concept, but rather, a (set of) particular sensible thing(s); hence, no inconsistency in claims. 165 The pertinent conditions are stated at Pr An II.23, 68b24-27. Aristotle studies the conditions of the convertibility of terms in Pr An II.22, in toto.

Hume and Aristotle on Induction

113

(4) Every human being (B) is a rational animal (A). [by (1) and (3)]166 Aristotle maintains, then, that it is possible for the human mind to go from an experiential knowledge of a limited number of individuals and mere statements of fact about them (premises 1 and 2) to a scientific knowledge of their natures and universal statements about the nature of those individuals (conclusion 4). For the process of reasoning from induction to reach a universal proposition, it is necessary that the mind perceive with understanding (noein) that both properties belong to each and every instance of the individuals enumerated (conversion of premise 2 to 3). In other words, in order for the convertibility of the minor premise to be effected, Aristotle claims it is necessary that “we grasp (noein) all the particular instances of C; for induction proceeds through an enumeration of all the cases.”167 This means the intellect understands that the two concepts are logically compatible because all the individuals enumerated are observed to possess the same nature and therefore both properties designated by both concepts. The intellect further understands that things cannot be otherwise. The expression “cannot be otherwise” conveys the notion of the necessity of the connection between the two properties. It is not sufficient to perceive that A and B are both connected because both properties are observed to belong to the same individual (as in Hume’s notion of constant conjunctions); it must be perceived and understood that they are necessarily so connected. This necessity is what is perceived in the act of noein, which is a perception that incorporates an understanding that what each of the two properties is, somehow includes the other in its being (i.e., in its ‘what it is to be’ or nature, say, a rational animal). It expresses a form of rational 166

Contemporary readers, accustomed to philosophical discussions about zombies, computer minds, brains in vats, and other such things, may find this example anodyne or a trite tautology. However, the fact that this paper must argue for an Aristotelian conception of human reason that differs from the Rationalist and Humean conceptions shows, I believe, that the nature of human reason is not so obvious a priori. The example obviously carries the Aristotelian meaning of human rationality, which was contrasted with Hume’s conception above in the sections on animals (§ 2.3) and experience (§ 2.4) especially. Besides, I have already expressed my doubts about a priori conceptual analysis in n. 162 above. 167 Pr An II.23, 68b27-29. Both the nature of the act of noein and the demand that enumeration must be of all the cases pose numerous problems for many Aristotle scholars.

114

Paolo C. Biondi

conviction (i.e., that of the immediate and primary proposition). (The other form of rational conviction is the necessity of an inference and comes with the possession of any valid deduction.) Unlike Hume, Aristotle is not skeptical about the mind’s abilities to accomplish this rational insight into necessity. He does not think it problematic that the induction has not gone through every single human being that was, is, and will be—an impossible task and unnecessary if one correctly perceives and understands the nature of the individuals and the universal nature’s necessary and essential properties. It is worth reiterating that, for Aristotle, human perception is not restricted to the external senses (and the internal senses). Sense perception (aisthesis) is said to be a capacity (dunamis) that, through being exercised, develops into a habit or state (hexis) of mind. This state of mind is said to possess the principles of science. Aristotle uses the term nous, a term cognate with noein, to designate this cognitive state of mind. He even says it grasps truth without reasoning (i.e., the third rational operation of reasoning with universal propositions), which is an intellectual quality.168 Let us be very clear about this: Aristotle maintains that sense perception, a capacity or disposition human beings share with every other nonhuman animal, can eventually become a cognitive state of mind unique to human beings. This cognitive development occurs through an inductive process that begins with sensory impressions and images, but ends with the acquisition of universal concepts and even universal propositions. In the process, empirical reality becomes conceptualized and sensory images are rendered intelligible because human perception can now perceive individuals through concepts (e.g., human being; rational animal). Perception incorporates understanding. A kind of reasoning plays a part in this inductive process, at least in the acquisition of scientific propositions; but, it is not the heart of induction. The whole process revolves around first gaining a rational insight into the universal nature of individuals aided by the intellect’s ability to conceptualize the sensible. Aristotle shows none of the skepticism displayed by Hume. Hume admits neither such an intellectual perception nor the mind’s ability to produce abstract or general concepts (categories) which make the perception called rational insight possible. In fact, Hume’s naturalist account of induction merely reaches the level of beliefs grounded in the certainty of sense perception. Knowledge, in the sense of rational or scientific knowledge, is not obtainable through induction as Hume construes it. 168

Post An II.19, 100b5-8; and see also Nicomachean Ethics VI.6, in toto.

Hume and Aristotle on Induction

115

Aristotle’s account, instead, opens the door to rational conviction and scientific knowledge. Induction and inductive reasoning are not a problem for him. Hume is somewhat right to think that something is ‘added’ to sensory images when the mind considers the substance of things. But it is not a figment of the imagination; it is concepts formed by reason. But such rational concepts are not really additions so much as the means by which the mind is able to see into what those images are. If we do not do this, then we will never get beyond the images and associations of Humean experience. On a final note, I would like to suggest that Aristotle’s account of induction as explained above actually constitutes an answer to Hume’s skeptical attacks on induction. In the course of raising skeptical doubts concerning the inference made from experience in probable reasoning about matters of fact in Enquiry 4, Hume makes the following demand: “But if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connection between these propositions is not intuitive. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact. […] You say that the one proposition is an inference from the other. But you must confess that the inference is not intuitive; neither is it demonstrative : Of what nature is it, then?”169

The answer to this demand, I contend, lies in the deduction coming from induction. The medium of this inference are the individuals, the matters of fact. However, these individuals must be perceived as instances of a universal concept: they instantiate the property or nature designated by the concept. This requires rational insight or intuition, which then anchors the inference or deduction. The reasoning is not a demonstration in the proper sense, for each of the premises does not join together two universal concepts; they join together a universal concept with a sample of individuals perceived to possess that concept. At a certain point in the induction, the concepts which are initially perceived to belong to the individuals are finally perceived to belong to each other. This is how the inference from statements about singular instances to a universal proposition occurs. Rational understanding occurs when the two concepts are seen to be compatible (or incompatible, if two concepts necessarily exclude each 169

Enquiry 4, 2, 29 (p. 34); and 4, 2, 32 (p. 37).

116

Paolo C. Biondi

other). Experience has now become knowledge. And the inference is justifiable with reference to the natures and definitions of the two concepts involved. Ultimately, the course of nature refers to the natures of the individuals concerned, and the uniformity of nature is grounded in those natures. Conclusion This paper argued that the main difference between Hume and Aristotle on induction is that the former does not, whereas the latter does, incorporate reason, and particularly rational insight into the natures of things, in the inductive process. The reason for this difference may be found in Hume’s polemical stance against the Rationalists, in particular, their pretense to know the world through reason without the assistance of sense perception. Hume’s skeptical attacks against the abilities of human reason and understanding to accomplish such knowledge of the world must be restricted to the Rationalist conception of reason, which is not identical to Aristotle’s conception of reason. Aristotle’s reason, unlike the Rationalist reason, relies on sense perception to assist it in coming to know the world and the natures of things in it. By acknowledging that reason has the ability to perceive and know the natures of things in the world, Aristotle bridges the divide between matters of fact and relations of ideas generated by Hume’s fork. In other words, Aristotle rejects Hume’s fork, which was the principal tool employed by Hume to slay the Rationalist pretense that reason, without the assistance of sense perception, can acquire knowledge of the causal and necessary relations of things in the world. Regarding induction, Hume’s portrayal of it has a negative and a positive account. The negative account refers to the skeptical attack on the Rationalist pretense of acquiring a priori knowledge of the world. The inference involved in inductive reasoning is shown to be problematic (for the Rationalist especially) in several respects. The positive account refers to the naturalist account of inductive reasoning. This account presents induction in terms of ideas and a reasoning process whose core is a mental habit of associating ideas together (by means of the relation of causality), a habit acquired after repeated instances of perceiving that such ideas are constantly conjoined. The naturalist account of induction relies on sense perception (or memory) and imagination, and it results in beliefs about what ideas are joined together in the mind.

Hume and Aristotle on Induction

117

Aristotle’s portrayal of induction begins with sense perception and moves through to experience, which is described in terms of memories of the same thing and incorporates an initial element of rationality in the way experience is organized. Memory and rational insight into the natures of things known through experience are crucial in Aristotle’s account. Reason or intellect is able to perceive the intelligible natures of things first known through experience. This ability of reason translates the potentially intelligible experience of things into rational knowledge of things. Rational insight, an intellectual perception incorporating concepts, constitutes the distinguishing feature present in Aristotle’s account of induction and absent in Hume’s. To conclude this comparison and contrast between Hume and Aristotle on induction, we may make the following related remarks. Hume is right about sense perception insofar as he claims it cannot provide any knowledge of the natures of things and almost no knowledge of their causes. On this point, he actually confirms the Rationalist view that the senses cannot provide any clear and distinct knowledge of the natures and causes of things (see the second characteristic of Rationalism in the Introduction). However, Hume is wrong to think that we cannot have any knowledge of nature and that our knowledge of causality is merely from the “outside” of things due to its being limited to an awareness of a subjective feeling of the mind. Knowledge of nature and of causality is possible, but it requires reason. The Rationalists are right on this point, but they went too far in their estimation of the powers of reason. Hume is right to be skeptical of the Rationalist pretense to know the world through reason without the aid of sense perception. But he is mistaken in thinking that our access to the world is restricted to the senses without the input of reason. When it comes to acquiring knowledge of the world, the opposed philosophical camps of Empiricism and Rationalism emphasize one source of knowledge to the (almost) complete exclusion of the other: either sense perception or reason (and not both). Aristotle, instead, accepts both sources of knowledge and relates them in a hierarchical manner. Where these philosophical camps see mutual exclusion regarding the two sources of knowledge, Aristotle sees co-operation and complementarity. Aristotle combines the best of both Empiricism and Rationalism, and shows how the senses and reason can and must work together to obtain rational and scientific knowledge. This opposition regarding the source of knowledge is the main reason for the inappropriateness of labeling Aristotle in either Empiricist or

118

Paolo C. Biondi

Rationalist terms. He is really neither since he does not oppose sense and reason. With this warning in mind, though, Aristotle may be said to be similar to Hume in holding that knowledge of the world begins with sense perception; Aristotle differs from him by incorporating reason in sense perception and in the process of induction. Aristotle may also be said to be similar to the Rationalists (rather, they are similar to him if we wish to avoid any anachronism) because he thinks that knowledge of the causes and the natures of things is gained through reason and demonstration; he differs from them because he insists reason cannot accomplish this without relying on the material furnished through sense perception and experience of the world. In addition, Aristotle limits rational knowledge of the world to the natures of things. He recognizes that the sensible individuality of things escapes the necessity of nature and reason. As a result, he admits some contingency in the world of individual things. It is not possible for human beings to have rational or scientific knowledge of everything, that is, to hold a strong version of the Principle of Sufficient Reason. On a few occasions, brief references were made to Kant’s philosophy. Aristotle is similar to Kant, who is also noted for combining elements of Empiricism and Rationalism in his philosophy. Both accept that human beings have acquired knowledge and that science does exist. It is a fact. Just as Kant then seeks to discover the conditions of its possibility through his critical philosophy, Aristotle similarly provides an explanation of what constitutes science and how it might be acquired. The things said about rational insight in Aristotle’s account of induction make this ability analogous to Kant’s categories of the understanding. These constitute two ways of making sense experience intelligible and orderly. They offer two ways of accounting for scientific knowledge of necessary and causal relations. Hume’s skepticism about the feeble powers of the human mind seems unreasonable at times, especially given the history of science since his time. Human beings have amassed an enormous amount of information and scientific knowledge about the natural world and its workings. Compared to Hume’s, Aristotle’s position is closer to the scientific method, which has both empirical and rational components: observation requiring sense perception and explanation requiring reason (hypotheses and theories). Of course, the level of observation and the kind of rational explanation are very different between Aristotle’s model of science and contemporary scientific methods. Water may have been defined by Aristotle as a natural body moving in a linear motion towards the center of the

Hume and Aristotle on Induction

119

universe with a natural resting place on earth (i.e., it is lighter than earth). This is quite different from our contemporary scientific definition of water as H2O, a definition in terms of chemical elements and their combination determined by valence. But in both cases the nature of water has been defined and other properties of water are shown to be logically connected to it in accordance with the respective models of explanation. Similar remarks may be made about Aristotle’s biological classification, which did not have the luxury of genetics as we do today in the biological sciences where classification can be done according to the DNA of living things. And we cannot overlook another major difference between Aristotle’s method and most contemporary scientific methods, namely, the contemporary reliance on experiment and the controlled arrangement of variables within an empirical situation. This is almost entirely absent in Aristotle, who at most resorted to the dissection of plants and animals to assist in the natural observation of internal organs and anatomical structures. Nevertheless, Aristotle’s model parallels the method of contemporary science in its broader outlines, which combine sense perception and reason. Throughout this paper several brief comments of a historical nature were made. To follow these conjectures would have been beyond the scope of this paper; nevertheless, it would be interesting to undertake a history of ideas of certain key notions. Such a study could better demonstrate the differences between Aristotle’s philosophical views as they may be gleaned from his own works and the Scholastic portrayal of Aristotle, which is what the early modern philosophers knew of him and which is what a number of contemporary philosophers influenced by the early moderns know of him still today. For instance, it was noted (in §§ 1.3 and 3) that the third characteristic of Rationalism, namely, the identity of causal necessity with logical necessity in demonstration, has likely an Aristotelian inspiration since for Aristotle, the demonstration reveals the cause of a fact. Another point that would merit historical study concerns the intuition/ demonstration distinction. Given the increasing doubts, shown by contemporary Aristotle scholars influenced by Hume’s empiricism, regarding interpreting the state of nous in Post An II.19 as an intuitive ability of the mind, it is somewhat amusing to see Hume retain the Scholastic distinction between intuitive and demonstrative knowledge within his relations of ideas. This distinction (noted in § 1.3) is likely rooted in Aristotle’s views found in Post An II.19, as understood in the Scholastic tradition, and in Post An I.3 (72b19-25), where Aristotle maintains the indemonstrable

120

Paolo C. Biondi

(hence intuitive) character of the knowledge of the principles of demonstration. Though early modern philosophers found much to object to in Scholastic Aristotelian philosophy, it seems the thoroughly Aristotelian distinction between intuition (of terms and immediate propositions) and demonstration (of conclusions) was not rejected by many of them.170 However, a significant shift in understanding the nature of intuition seems to have taken place. As we argued, intuition, or rational insight, is, for Aristotle, related to induction from sense perception. With the Rationalists, intuition refers to an a priori rational ability. Without this reliance on sense perception, intuition no longer has any connection with the world. How and when did such a change come about? Could it be that at some point, reason became skeptical of the senses? Then, along came Hume, who, it seems, paid back that skepticism in kind: the senses became skeptical of reason. Somehow, reason and the senses became opposed to each other instead of remaining complementary partners in the enterprise of knowledge acquisition. Another historical point of interest concerns the claim that Hume is an idealist. Such a claim likely seems outrageous in the eyes of Analytic philosophers especially. The Analytic approach in philosophy arose, in large part, in opposition to idealism, particularly the British idealism influenced by the German tradition (Hegel). Hume is often revered by Analytic philosophers for his hard-nosed, anti-metaphysical empiricism. Yet, idealism, defined as the view that we know our ideas or perceptions within our minds, and not necessarily the external world, would make of Hume an idealist. He is stuck in his own mind and its perceptions, just as much as Descartes, the father of Rationalism and even of idealism, is. Hume and Descartes are equally skeptical about the external world, in large part, because of this shared idealist position. How is it that these points seem to have been obscured over time? It seems we sometimes forget that the labels Empiricism and Rationalism were given to the early modern philosophers after the fact. Certain philosophers placed in one camp are actually very similar to certain philosophers placed in the other camp when particular points of their respective philosophies are compared.171 Idealism is shared by most Rationalists and Empiricists. In fact, it could reasonably be claimed that the 170

See, for instance, rule 3 in Ch. 1 of René Descartes, Rules for the Direction of the Mind; and John Locke, An Essay Concerning Human Understanding, Book IV, ch. 2, §§ 1-7. 171 This point is very clearly made in Thomson, Bacon to Kant, pp. 5-7 and passim.

Hume and Aristotle on Induction

121

labels Rationalism and Empiricism reflect a subdivision within idealism and merely refer to the different views regarding the origin of the ideas. Regardless of the origin, most early modern philosophers falling within either division may be considered idealists because they maintain that the mind knows its ideas only. It could even be argued that the characteristic feature of modern philosophy lies in this idealism. This feature of knowing ideas within the mind distinguishes the modern tradition from the tradition of philosophy that preceded Descartes, which, generally speaking, accepted realism, defined as the use of ideas as a means to knowing the world itself, the things in the external world. The shifts in our understanding of idealism, realism, empiricism, and rationalism would all be an interesting matter for historians of philosophy to trace out. Our paper began with the claim that both Aristotle and Hume are empiricists in the sense that both think knowledge begins in sense perception. However, it was also stated that they arrive at opposite conclusions about the process of induction that originates in sense perception, and consequently, they differ drastically about the results of this cognitive process. This difference between them revolves around the intellect as a channel of perception because Aristotle admits such a source, while Hume does not. It is the presence of intellect and reason that makes Aristotle’s conception of experience different from Hume’s and enables him to claim scientific knowledge can be derived from experience. The epistemological assumptions presented above (in § 2.5) help to shed some light on why Aristotle and Hume reach such divergent positions. With respect to several of the assumptions, it can be seen that distinctions accepted by Aristotle are not accepted by Hume. An Aristotelian would likely see Hume’s position on some of these matters as an oversimplification and impoverishment of human thought. A Humean would see Aristotle’s position as containing metaphysical illusions and Hume’s skeptical empiricism as an antidote to these illusions, a healthy skeptical purging of the mind. There are likely other points of comparison that could have been made in the course of this study; however, this relatively brief essay is intended as merely an introductory study of Aristotle and Hume on induction. An interesting question we could ask ourselves is this: was the attitude taken by each philosopher regarding the cognitive abilities of the human mind the source or the consequence of their respective positions taken with respect to the epistemological assumptions we examined (in § 2.5)?

122

Paolo C. Biondi

Whichever answer one gives to the question, the least that can be said is that Aristotle and his tradition offer another way of dealing with Hume’s empiricism and its consequent rational skepticism regarding the inductive process. This comparison and contrast, at the very least, assisted in unearthing certain assumptions underlying Hume’s philosophy and offers another set of assumptions about the human mind, how it operates, and its relation to the (external) world it perceives

Intelligibility Jude P. Dougherty The Catholic University of America

Abstract: In an essay published in 2004, the French sociologist, Pierre Bourdieu, raised a concern about the possibility for a historical activity such as scientific activity to produce trans-historical truths independent of history, detached from all bonds with place and time, and which are therefore eternally and universally valid. In this chapter, Jude P. Dougherty shows how, from an empiricist or positivist perspective, Bourdieu’s concern is challenging to say the least. The empiricist, by limiting human knowledge to sense experience, in effect, reduces science to description and prediction. Dougherty shows how removed from actual practice in the natural sciences is the positivist account of scientific enquiry, by focusing primarily on the limitations of the empiricism of David Hume and the positivism of the Vienna Circle. Science seeks to provide explanations of phenomena, which answers to the human aim of intelligibility. Dougherty demonstrates his point with examples from the work of Newton, Curie, Fermi, and several other scientists.

Introduction In an essay published in 2004, the French sociologist, Pierre Bourdieu rhetorically put the question: “How is it possible for historical activity such as scientific activity to produce trans-historical truth independent of history, detached from all bonds with place and time and therefore eternally and universally valid?”1 The answer is readily found in Aristotle’s Posterior Analytics and in St. Thomas’s appropriation of Aristotle’s doctrine of the agent intellect and its power of abstraction. Presupposed, of course, is a conception of nature and of human nature, of the immaterial character of the human intellect and the intelligibility of nature itself.

1

For a discussion of Bourdieu’s fundamentally Aristotelian approach and from whom this remark is taken, see Loic Wacquant, “Bourdieu” in Key Contemporary Thinkers, ed. Rob Stones (New York: Macmillan, 2006).

124

Jude P. Dougherty

For those working within a modern empiricist or positivist perspective, finding an adequate answer to Bourdieu’s question is challenging to say the least. As David Hume explains it, the empiricist limits knowledge to sense experience, in effect, reducing science to description and prediction. This is in line with a familiar model of scientific investigation that has scientists doing two things: producing descriptions, framed mathematically, so as to accurately grasp the matter under consideration; and testing the predictions that follow from their hypothesis. Scientific success, on this account, is limited to accurate prediction that correctly describes what happens. The intent of this essay is to show how removed from actual practice this positivist account of scientific inquiry is. What we are pursuing in science is not bare description, nor even mere prediction. What we are looking for, ultimately, is an explanation. Mere experience of things joined in space and time (in the Humean sense) is not enough to satisfy the inquiring mind. The question of why we experience things conjoined surely begs to be answered. Two events conjoined sequentially or by proximity may be causally related or perhaps not. To call something the cause of something else is to attempt to explain it by means of this prior event. We want to uncover a mechanism, a cause and effect process of some determinate sort that can elucidate as well as predict the precise nature of the object of under study. Only through a reasoning process does the intellect grasp the mechanism responsible for the causal bond if such is the case. This pursuit of scientific explanation turns out to be impossible from the modern empiricist or positivist viewpoint. I will focus here primarily on the profoundly influential empiricism of David Hume, which naturally developed, over time, into the radical positivism of the Twentieth Century Vienna Circle. I will not discuss at any length sense perception and abstraction as developed in the more successful “empiricist” accounts of Aristotle and Aquinas, which seem to be well covered by other contributions to this volume. In answering Bourdieu’s question, examples of actual practice will be drawn from the work of practicing scientists such as Isaac Newton, Marie Curie, and Enrico Fermi. We will also consider disagreements in scientific practice between Ludwig Boltzmann and Ernst Mach as well as between Max Planck and Arnold Sommerfeld. We will end by briefly considering Paul Churchland’s attempts to provide a science of human beings.

Intelligibility

125

1 Newton Some date the beginning of modern science to Isaac Newton because of the role that mathematics plays in his natural philosophy; yet it must be acknowledged that ever since Pythagoras, Western science has tended to view nature in mathematical terms. A century before Newton, Galileo looked upon mathematics as the instrument by which man is called to understand the script God employed in creating the universe. Kepler shared this view when he wrote, “Just as the eye was made to see colors, the ear to hear sounds, the human mind was made to understand quantity.”2 In fact, much of the activity we associate with the natural sciences is an attempt at description, framed mathematically, rather than explanation. Yet the natural sciences also consist in more than an account of quantitative relations and variations, more than an attempt to grasp accurately the matter under consideration. The mind is not easily content with mere description. It seeks to know the intrinsic nature of things, why things are and behave as they do. Much of that knowledge is attained by inference. The knowledge we have of the submicroscopic is by inference, the mental mechanism by which we hold that knowledge entails the creation of models, of plausible mechanisms responsible for the phenomena observed. Those models may be either sententional (equations, for example) or iconic (a mental picture or a diagram). Thus, for example, in the history of theoretical physics we find successively sophisticated schema for depicting the atom as our knowledge has increased; and we are led to recognize that our knowledge of nature is open-ended, the focus of an intellectual quest that is never fully satisfied. A classic example illustrative of the nature of scientific method is found in Isaac Newton’s Mathematical Principles of Natural Philosophy (1687), called one of the most important single works in the history of modern science. We speak of modern physics up to the coming of quantum mechanics as Newtonian physics. With Newton we enter the age of Galileo, Kepler, Boyle, Halley, Descartes, Gassendi and Leibniz, intellectual giants all. Throughout the seventeenth century physics had begun to replace qualitative analysis with quantitative precision. Newton himself wrestled with the problem of how to relate the common new algebraic analyses of modern approaches with the venerated methods of the ancients. For him, large questions loomed: When is a geometrical construct exact? What guarantees the applicability of geometry to mechanics? 2 Johannes Kepler, Opera I, 31, as quoted by Christopher Dawson in Progress and Reality, (Garden City, N.Y.: Doubleday, 1980).

126

Jude P. Dougherty

A clear account of Newton’s method is described by William L. Harper.3 Harper traces the steps by which Newton argued from the phenomena of orbital motion to centripetal forces and then to universal gravity. This in turn enabled him to calculate the masses of the sun and planets from orbits about them, and, further, led to his decisive resolution of the problem of deciding between geocentric and heliocentric world systems. Newton concluded that neither is completely accurate because both the sun and the earth are moving relative to the center of the solar system. The sun, he finds, never recedes very far from the center of this mass, thus making it possible to achieve approximate calculations of the complex motion of the planets by successively more accurate models. If, as the positivist model of scientific investigation would have it, hypotheses are verified by conclusions to be drawn from them, or, put another way, empirical success is determined by and limited to accurate prediction, Newton begs to differ. He believes that successful scientific theory must be an attempt to explain phenomena. A true explanation turns theoretical questions into ones which can be empirically answered by measurement of relevant parameters; but more than that, the theoretical propositions inferred from phenomena, when successful, may provisionally serve as guides to further research. Newton’s argument for universal gravity and its application to the solar system, Harper points out, bore fruit in Kepler’s use of physical causes to overcome the empirical equivalence between heliocentric and geocentric world systems. Newton employed the notion of gravity as a physical cause to explain planetary motion, even though he was unable to find the initial cause of orbital motion itself. He further generalized his theory of gravitation to all celestial bodies. All are kept in their orbits by the centripetal forces of gravity, and Newton calculated those forces to be the inverse of the square of the distance from their centers. In this manner, in collaboration with Kepler’s later work, the theory of gravitation served to explain more phenomena. The theory explained sense observation and then went beyond it to account for more than the original phenomenon under observation. 2 Curie Philosophers who grapple with the problem of universals and the abstractive power of the human intellect and who work as strict empiricists or 3 See William L. Harper, Isaac Newton’s Scientific Method: Turning Data into Evidence about Gravity and Cosmology (Oxford: Oxford University Press, 2011).

Intelligibility

127

materialists often go to absurd lengths to avoid reference to the nonmaterial character of human knowledge. Causal mechanisms are often inferred and are rarely visually encountered, but they are important nonobservables posited in physical theory that work to facilitate understanding. A good example is found in the work of Marie Curie. When Madam Curie first began her study of minerals, her attention was drawn to the mineral pitchblende, uraninite. She reasoned that its emission of rays could only be explained by the presence in the ore of an unknown substance or substances. Joined by her husband, Pierre, she undertook to resolve the question. Using sophisticated measuring techniques, by measuring the action of the rays given off on magnetic fields, the Curies proved the existence of varying amounts of three types of particles—electrically positive, negative, and neutral ones, particles that Sir Ernest Rutherford later called alpha, beta, and gamma rays, respectively. The varying amounts of the particles, it was eventually determined, were caused by the radioactivity of radium and thorium. The term “radioactive” was first introduced by Marie in 1898. The investigative techniques of the Curies, in the same year, led them to deduce the existence of two previously unknown elements, later called polonium (in honor of Marie’s home country) and radium. Clearly their discoveries were not the product of an observed sequence. Rather, what we find in their work is a reasoned explanation of something otherwise unintelligible. The explanatory principle involved in the Curie example is the principle of efficient causality. Expressed in its simplest form, the principle states: Things or events, which do not fully explain themselves with respect to their origins or properties, must be explained in terms of something other than themselves. Mere experience of things joined in space and time does not suffice. The scientist needs to answer the question, “Why do we experience things conjoined?” The fact that two things are always conjoined sequentially or by proximity may be due to the fact that they are causally related or perhaps not. Only through a reasoning process does the intellect grasp the mechanism responsible for the causal bond if such is the case; and to call something the cause of the other is an attempt to explain the other. 3 Fermi In l933 the state of particle physics was such that it seemed necessary to postulate the existence of a particle as yet undetected. The Italian physicist, Enrico Fermi, assuming its existence, built his theory of beta decay upon it and gave the undetected particle the name, “neutrino,” Italian for little one.

128

Jude P. Dougherty

Even with the support from Niels Bøhr, he was subject to remarks about his “poltergeist” since no one had empirically shown it to exist in spite of its theoretical necessity. It remained a hypothetical entity until Clyde Cowan (a colleague when I joined the faculty at The Catholic University of America), with access to a particle accelerator at Hanford, Washington, performed an experiment that confirmed the neutrino’s existence. He duplicated the experiment in l956 at the Savannah River Laboratory in Georgia. And, as is said, the rest is history. This example illustrates clearly the principle of sufficient reason, sometimes called the principle of efficient causality, wherein an explanation is sought for something otherwise unintelligible. The neutrino episode illustrates what often happens in scientific practice: one arrives at a concept that is needed for explanation, which only later comes to be useable as a means for making the kind of narrow predictions that are needed for testing hypotheses. One can think of other examples of “invisible beings” that principally serve an explanatory function in science. Think to Louis Pasteur’s discovery of germs too small to see or Michael Faraday’s demonstration of invisible lines of force emanating from a magnet (revealed by metal filings). Germs and force fields do not merely provide for some sort of empirical predictability; they supply a mechanism that explains what is going on. Once we know about such things, we have a cause for disease and a cause for the way a particle bends beside a magnet. This captures the difference between scientific realism and positivism. Science is not just about predicting things; it is about capturing and communicating the relations of causality (that go beyond correlation) that structure and regulate the world. 4 Planck and Sommerfeld Historians of science remind us that there is no obvious point at which Newtonian physics replaced Aristotle’s natural philosophy or for that matter when the old order of physics associated with Newton gave way to the new order of quantum physics. Sheilla Jones in The Quantum Ten, has written a fascinating account of one of the most exciting periods in the history of modern physics.4 Max Planck is credited with introducing the word “quanta” into the lexicon of physics in 1900, and he was to play a significant role in the “quantum revolution” of the mid-1920s. In classical physics, it was assumed that energy flows in a continuum; but in quantum 4 Sheilla Jones, The Quantum Ten: A Story of Passion, Tragedy, Ambition, and Science (Oxford: Oxford University Press, 2008).

Intelligibility

129

physics, energy is thought to come in chunks or quanta which can only be described mathematically. For most physicists it is not necessary to visualize the quantum world so long as their calculations match their experimental results. It does not matter that the symbols and mathematics they use might or ought to have any link with the physical world. Jones quotes Murray Gell-Mann as saying: “We all know how to use it and apply it to problems; and so we have learned to live with the fact that nobody can understand it.”5 After more than 90 years, physicists are still having trouble reconciling the classical and quantum worlds. (A distinction has to be made, of course, between quantum theory and quantum mechanics, although we speak of the package as quantum physics.) This difference between physics understood as calculation and physics understood as a matter of explanation can be illustrated by the difference between the work of Max Planck and that of Arnold Sommerfeld, a difference that Seth Suman calls the difference between the “physics of principles” and the “physics of problems.”6 Suman characterizes the work of Planck, as well as that of Einstein, as subsuming all physical phenomena under a few general axioms, principles transcending particular data; hence, the physics of principles. For Planck the place of experiment within theoretical practice was limited to testing conclusions. Sommerfeld, on the other hand, started with experimental data. His interest was in real-world engineering problems; hence, the physics of problems. Theoretical physics as practiced by Sommerfeld was an interdisciplinary creation drawing upon mathematics and technical mechanics as well as physics. His was a search for specific solutions to specific problems, a search for a mechanism or a process rather than a general postulate. Unlike Planck and Einstein, he did not want to get into abstract theory and waste time disputing with philosophers. The two styles of pursuing physics proved to be mutually illuminating. Sommerfeld’s investigation of atomic spectra led him to suggest that elliptical orbits replace circular orbits of the Bøhr atom. From this idea, he postulated the azimuthal quantum number and later introduced the magnetic quantum number as well. So his interest in real-world engineering paid off in a remarkable way. Seth Suman relates that of the ten doctoral dissertations supervised or co-supervised by Sommerfeld in Munich between 1908 and 1931, eight discussed some aspect of electromagnetism. 5

Jones, The Quantum Ten, p. 15. Seth Suman, Crafting the Quantum: Arnold Sommerfeld and the Practice of Theory, 1890 - 1926 (Cambridge, MA.: The MIT Press, 2010).

6

130

Jude P. Dougherty

Sommerfeld’s students, because of their training in hydrodynamics and electromagnetism, and because their work on gyroscopes had military implications, became known during World War I as “ the Kaiser’s physicists,” given their contribution to the German war effort. So even in the very abstract, mysterious domains of quantum physics, the building of explanatory physical models that point to something more than predicted quantities was fruitful scientifically. 5 Boltzmann and Mach It was the failure of Newtonian physics in the nineteenth century to construct a mechanical or atomic model of matter and aether, one that would explain thermal and magnetic properties, which led Ludwig Boltzmann (1844-1906) to develop his probabilistic physics. In a seminal article in 1887, a little more than a decade after Planck had introduced the notion “quantum,” Boltzmann in his statistical mechanics not only assumed the existence of invisible molecules but in his work relied on mathematical probabilities instead of experimental measurements. For that he earned the scorn of Ernst Mach and the positivists of the Vienna Circle. Mach’s positivism, following the lead of the French philosopher Auguste Comte, denied the power of the intellect to reason from the seen to the unseen and led Mach to oppose the use of atoms and probabilities in scientific explanation. The only meaningful statements a scientist can make, Mach held, are about what can be measured, counted, tested, or which otherwise rest on the experience of the senses. Mach refused to accept the existence of atoms even when presented with experimental evidence. Sheilla Jones, from whom this account is taken, was led to remark: “‘Positivism’, perhaps more accurately called ‘negativism’, had all but killed theoretical physics in France.”7 The dramatic shift from Newtonian physics to the puzzling world of quantum physics gave rise to many a philosophical treatise. Aware of the philosophical landscape at the time, Jones, in a humorous passage, offered her assessment: “Positivism has no God and no external world; logical positivism has no God and no external world but it does have mathematical logic; Kantianism has no external world, but it does have God; and realism allows for both God and the external world.”8 German mathematicians and physicists, while not philosophically illiterate, did not demonstrate philosophical leanings, at least on the job, and for the most part did not try to 7 8

Jones, The Quantum Ten, p. 124. Jones, The Quantum Ten, p. 126.

Intelligibility

131

bring their scientific activity into logical connection with their philosophy. By 1930 most physicists simply abandoned the need for a philosophical theory of quantum physics. Mach’s positivism was behind his rejection of the atom. In his case, positivism was combined with a radical phenomenalism (what we see is real) whereas other, more recent positivists, given the highly abstract nature of quantum physics, take refuge in mathematics, substituting unexplainable formulae or algorithms for any description of causal mechanism. Given the central role of probability in quantum physics—the Heisenberg uncertainty principle, for example—causal mechanisms are, to some extent, out of reach; so the tendency is to focus on accurate prediction without trying to lay bare physical causes, which remain somewhat unintelligible. Still, the basic models underlying phenomena such as electromagnetic radiation, constructive and destructive interference, the wave-particle duality, quantum entanglement, and quantum tunneling from nothing are more than attempts at prediction. However difficult it may be to fully fathom, these theoretical constructs exemplify a search for causal mechanisms, in addition to a search for predictability. 6 Churchland No matter how useful mathematical techniques may be in the study of nature, subject matter yet determines method. The way we ordinarily talk about mind and human nature, for example, does not fit well with our understanding of the world derived from theoretical or mathematical physics. The realm of reason, the realm of judgment, of belief, and of desire is independent of physical or biological facts about human agency. We may be every bit a part of nature as are the elements that surround us, but there are important facts about what we do and what we think that have no counterparts when the subject is human nature. To explain human behavior in the language of physics or chemistry, or by causal accounts that cast human beings as a collection of physical particles, is to miss that which is distinctive about human beings. Philosophers who grapple with the problem of universals and the abstractive power of the human intellect and who work as strict empiricists or materialists often go to absurd lengths to avoid reference to the nonmaterial character of human knowledge. A frequent mistake in this area of research is to confuse mind with brain activity, to assume that the nervous system and the brain are the cause of what goes on in consciousness. From

132

Jude P. Dougherty

an Aristotelian point of view, mind is clearly bodily and cannot be discussed apart from brain activity. Discussions of intellect are something else. While intellection cannot take place apart from sensation, the two are not the same. How one discusses the relationship depends first on a clear distinction between sensation and intellection. Sense knowledge obviously provides the material for the intellectual formation of concepts, universals that transcend sensory experience. Recognition of the transcendent or nonmaterial aspects of human knowing entails a modeling of human nature that finds its prototype in Aristotle, in contrast to materialistic or reductionist accounts that ignore or falsify data in the interest of simplicity. A valuable study of the Posterior Analytics, wherein Aristotle sets forth his conception of abstraction, is found in Louis Groarke’s An Aristotelian Account of Induction.9 Paul Churchland, in developing his philosophy of science, does not deny that abstraction takes place or that we hold most of our knowledge in terms that employ universals; however, his materialism forces him to deny not only the immaterial character of the human intellect but even the notion of intellect itself. It is the brain, not the self, nor the I, which constructs and holds our knowledge of the external world. In a work entitled Plato’s Camera, Churchland compares the human brain to a camera.10 “The eye,” he writes, “constructs a representation or ‘takes a picture’ of the landscape or configuration of the objective spatiotemporal particulars currently displayed in the lens. This picture-taking process is completed in milliseconds; the eye does it time and again and again, because its targeted landscape is typically in constant flux. The learning brain, by contrast, very slowly constructs a representation, or ‘takes a picture’ of the landscape or configuration of the abstract universals, the temporal invariants and the enduring symmetries that structure the objective universe of its experience. This process takes months, years, decades, and more because these background features take time to reveal themselves in full.”11 Churchland’s novel account of abstraction eludes proof and is at best a metaphor of what takes place in the everyday knowing process from a materialist perspective. Churchland posits a correlation between brain maps and observation/experience. He denies any invisible, immaterial dimension 9

Louis Groarke, An Aristotelian Account of Induction: Creating Something from Nothing (Montreal: McGill-Queens University Press, 2009). 10 Paul M. Churchland, Plato’s Camera: How the Physical Brain Captures a Landscape of Abstract Universals (Cambridge, MA.: MIT Press, 2012). 11 Churchland, Plato’s Camera, p. vii.

Intelligibility

133

or aspect of the intellect as the ultimate cause or explanation of consciousness. But turning the mind into a mere physical mirror of some sort, even built up over a long period of time (if that is possible), seems too meager an account to suffice as a full-fledged explanation of human nature. Even if we could correlate thoughts and brain states, even if we could predict the former from the latter, our linking of this with that makes for a very thin model of science. The immaterial property of consciousness, however precisely described or construed, provides a fuller explanation, but that is because it invokes a different power, principle, or level as causal origin. Conclusion We began with Bourdieu’s question: “How is it possible for historical activity such as scientific activity to produce trans-historical truth independent of history, detached from all bonds with place and time and therefore eternally and universally valid?” From an Aristotelian perspective, there is more in the sense reports that make up individual experience than the senses themselves are able to appreciate. Reason can uncover the veiled agency in things. Positivism and radical empiricism inadvertently restrict science to a study of correlation. Their narrow restriction of knowledge to the data of sense perception leads them to overlook the causal nexus on which trans-historical truths depend. Aristotelian realism views scientific practice as a search into causes. This traditional perspective rests, however, on the prior establishment of the immaterial character of abstract knowledge and, of course, the immaterial character of the human intellect itself, a perspective that has prevailed across the ages from Plato and Aristotle to the present. It is a perspective shared by Newton, Kepler, and Galileo. Galileo, it should be noted, was as much a scholastic as was Newton and Descartes. Aristotle’s physics was found wanting and was superseded but not his theory of knowledge which remains perennially viable.

Induction, Science, and Knowledge James Kelly Stanford University

Abstract: In order to understand the role of induction in knowledgeformation, it is important to take into account not only its role as a form of reasoning, but also its place in concept formation and in judgment. Science is inductive, not only because it includes induction within its method of reasoning, but also because it begins from and ends with sense experience. Classical empiricists and positivists sometimes presume that natural science, particularly physics, is the model form of human knowledge. Thus, inductive reasoning in science is often presumed to set the standard for all learning through experience. This essay counters these presuppositions, arguing it would be mistaken to treat scientific knowledge as fundamental or to judge other forms of reasoning by their conformity to the scientific method. Kelly defends the claim that scientific induction would not be possible unless there were both pre-scientific knowledge and philosophy. Although pre-scientific knowing is less perfect than science, nonetheless it has some priority, both because it comes first and because science would be impossible without it. Moreover, science is built up on certain presuppositions, for instance, that the world is intelligible or that it is valid to employ the mathematical method. But science cannot itself defend such premises; this task belongs to philosophy. A related conclusion Kelly makes is that the term ‘induction’ is used analogously, as there can be pre-scientific, scientific, and philosophical forms of induction.

Introduction In order to understand the place of induction in the sciences, it is helpful to include within this term not only reasoning that takes the mind from the individual to the universal, but more generally the interaction between the senses and the intellect in the process of knowing. Understanding ‘induction’ solely as the argument that all things of a particular type share a particular characteristic could lead someone to neglect other examples of sense experience playing a role in science and even in all human knowledge. Scientific knowledge is inductive not only because it some-

136

James Kelly

times involves that inductive form of reasoning, but also because it begins and ends in sensation. The effort of the natural sciences that rely on experimental method (here I am thinking especially of physics, chemistry, and biology) is to account for or explain the phenomena, and a scientific theory is tested by its agreement with observation. The aim of this essay is to argue, within the limited scope of the concept of induction, that these experimental sciences are truly objective, in the sense that they obtain consensus and can be confirmed through repeatable experimental results. On the other hand, they are not self-sufficient. If there were no prescientific knowledge, science would not be achieved. Pre-scientific knowledge also depends on sense experience. And science is limited in scope. It is a free human activity, and natural science, especially physics, is not directly derived from any other form of knowledge. But physics cannot explain or justify itself. When science reaches its limits, one must turn to philosophy to answer the remaining puzzles and questions. Although philosophy deals with abstract concepts (e.g., necessity and possibility), it too must seek support from the evidence of the senses. And so I will argue that we should recognize different related forms of induction: first, prescientific induction, which should be understood to include concept formation; second, induction as used in experimental science, which will henceforth be called “scientific induction”; and philosophical induction, which incorporates and complements in various ways the other two forms. Further, these forms of induction have important aspects in common. One of these features is that judgments are inductive because they involve testing against sense experience. Before going further, we could examine briefly an important and influential alternative view on experimental science and its relation to philosophy. Positivism argues that mankind is now in a third historical period; in ancient times there was a religious period, followed by a metaphysical period, and now we are in the positive period. This could be regarded as a kind of myth, not surprising given the outlook of Auguste Comte, the founder of positivism. I would argue that this myth continued to have a hold on the thought of J.S. Mill and of the logical positivists, even though they put aside the religious aspects of Comte’s thought. Until the present time, it is often presumed by some that if human beings know anything at all, what they know is physics. If this view is correct, the primary understanding of induction and its best examples are found in experimental science. Whatever inductive reasoning apparently found outside the bounds of such science would need to be justified in terms of

Induction, Science, and Knowledge

137

induction in physics, or it would not be objective or reliable and should not be trusted. In this essay, I offer some reflections that cast doubt on this particular view and, implicitly, on the positivist mythology. The proposition that knowledge, and in particular induction, is best explained in experimental science leads to important difficulties. The argument of the paper follows the following line. First, both the physical theory of Isaac Newton and that of Albert Einstein rely on inductive reasoning. But that inductive reasoning is of a special kind, involving idealization, simplification, and mathematical abstraction. This leads to the suggestion that natural science is objective, but that its relation to physical reality is mediated. Second, it seems implausible to argue that Newton and Einstein (and everyone else in the world) had no knowledge of the physical order (again, as a consequence of inductive reasoning) prior to developing their theories. Put in another way, natural science must build on some forms of pre-existing knowledge. For Galileo, for example, that preexisting knowledge includes elementary truths about physical objects (such as a tower, or a ball, or a pendulum, or a planet). Third, there was philosophical knowledge prior to the development of modern natural science, but it needs to be modified in some ways, taking into account what physics and other sciences have shown about the world and about knowledge. This philosophical knowledge is also derived from experience, and it should now deal with the relation between scientific models and theories, on one hand, and the natural order, on the other. The development of science makes manifest aspects of the human capacity for knowledge which were not as clearly understood before. In this discussion of induction, a good point of reference could be John Vickers’ long entry in the Stanford Encyclopedia of Philosophy entitled “The Problem of Induction.”1 He notes that the definition of ‘induction’ given in the Oxford English Dictionary is limited to the transition from single instances to a general law. This definition corresponds to the idea which was the object of David Hume’s critique of knowledge of the principle of causation, and implicitly of induction, though he himself does not use the word ‘induction’. This definition seems outdated, the author notes. During the twentieth century, the concept of induction has been greatly amplified, so that some eminent philosophers have referred to all reasoning about contingent matters as inductive. Probability theory has offered another perspective on inductive reasoning. 1

John Vickers, “The Problem of Induction,” Stanford Encyclopedia of Philosophy (Fall 2010 ed.), ed. Edward N. Zalta.

138

James Kelly

Also, studies in the nineteenth and twentieth centuries have examined closely the relation between logic and mathematics. These factors have broadened the understanding of induction and have often made the traditional “problem of induction” seem less crucial. While grateful for the clarifications of Vickers, it seems necessary to go further. Hume’s argument represented part of his effort to do for the understanding of the human mind what Newton had done for natural philosophy. Implicit in this manner of reasoning is that Newton’s method can be used in every type of human knowledge, and that those who have studied any discipline without being familiar with that method have not accomplished anything worthwhile. Much of the discussion of the “problem of induction” presupposes that natural science is the paradigmatic form of human knowledge, and that scientific reasoning is likewise the model for all inductive reasoning. These presuppositions are not contradictory, but they do not give a good account of human reasoning. Although Newton’s method set a pattern, science has evolved and diversified, and likewise inductive reasoning is more varied. Chemistry and biology, while they still borrow from physics, have achieved a certain autonomy, and they have the advantage of being closer to sense experience. Further, scientific argument should not be treated as independent and self-sufficient. Philosophy has as part of its purpose to express clearly and to defend the first principles of the various sciences. This should not be understood in the positivist fashion, as if it were merely a question of correct logical form and consistency. Philosophy examines dialectically the presuppositions of the sciences and shows what they imply about the structure of the world. All of this reflects that ‘induction’ must be an analogous concept: there are common features of prescientific, scientific, and philosophical analyses of nature, but they are not the same.2 Scientific induction develops especially from late medieval philosophy, which introduced both a recursive model for inductive reasoning and an application of mathematics in reasoning in the natural sciences. Experimental method transformed this manner of reasoning, but a crucial element is the return to the information accessible to the senses.

2

Others might want to express this relation in terms of “family resemblances” instead; but I would argue that testing against sense experience is a common feature of the various forms of induction, and that this justifies the use of ‘analogy.’

Induction, Science, and Knowledge

139

1 Induction in Science Galileo and Newton, the great founders and developers of modern physics, begin from the inductive methods of their predecessors, and they highlight their reliance on mathematical formulations. The work of these natural philosophers has been taken by many as an ideal pattern of inductive reasoning and argumentation. In this essay, I defend the objectivity of the scientific arguments of Newton and Einstein, and thus of many other arguments of a similar kind. On the other hand, this scientific form of induction is insufficient to provide a full understanding of human knowledge. Isaac Newton’s Principia Mathematica (1687) has been repeatedly and carefully examined, because it has been seen for hundreds of years as a model of scientific reasoning. Here we will just highlight a few features, relying on some recent studies. It is widely accepted that Newton formulated his laws of motion in the Principia Mathematica in such a way that he could test and revise them against experience. We can characterize this approach as both inductive and mathematical. As I. Bernard Cohen noted in commenting on his translation of the great Newtonian work, “An important feature of Newton’s mature science is the union of mathematical analysis and the data of experience as manifested in experiment and critical observation.”3 Newton avoided the lengthy reflections of Descartes, who took a more a priori approach to the study of nature. Nonetheless, he did offer his thoughts on the place of mathematics in physics, as in the following passage:4 Mathematics requires an investigation of those quantities of forces and their proportions that follow from any conditions that may be supposed. Then, coming down to physics, these proportions must be compared with the phenomena, so that it may be found out which conditions of forces apply to each kind of attracting bodies. And then, finally, it will be possible to argue more securely concerning the physical species, physical causes, and physical proportions of these forces. Let us see, therefore, what the forces are by which spherical bodies consisting of particles that attract in the way already set forth, must act upon one another, and what sorts of motions result from such forces.

3

I. Bernard Cohen and George Smith, The Cambridge Companion to Newton (Cambridge: Cambridge University Press, 2002), in the Introduction, p. 8. The Principia, Mathematical Principles of Natural Philosophy, trans. I. Bernard Cohen and Anne Whitman (Berkeley: University of California Press, 1999), pp. 588-9.

140

James Kelly

In order to formulate laws based on the movement of heavenly bodies, Newton develops an ideal system built up from points of mass acting under forces consequent upon that mass. Of course, there are no mass points without extension given in nature; the idea of a point may express the operation of the imagination on what is perceived. This ideal system formed the basis for Newtonian mechanics. His definitions and arguments refer directly to the mass points and only indirectly to the Earth, the Sun, and other heavenly bodies, such as the other planets. This idealization and simplification could remind us of Galileo, who set aside the effect of friction in his table-top experiments. This partially fictitious basis for natural philosophy5 could be referred to as “forming the scientific object.”6 Scientific laws deal with schematized and idealized objects, which can be understood through mathematical laws. Newton formulated abstract concepts of space and time which better allow for measurement and for articulation of such laws. He also developed particular definitions of such terms as force and acceleration; he differed from Galileo and Huygens by making ‘force’ a theoretical quantity. All this brings out clearly that the object of the sciences is not simply given, but must be shaped in accord with the goal of the research. It is a familiar reflection that modern science focuses on ideal models, partial aspects, and immediate causes. The nature of this formation varies according to the science and its methods. Especially for physics, the definition of terms is related to the instruments of measurement and mathematical methods available. What is given in ordinary experience is not yet a scientific object. Early natural philosophers, especially Galileo and Newton, devised a method for understanding nature. When Galileo studied the behavior of pendulums or of falling bodies, he sought to devise an experiment that would yield numerical results and could be formulated as a law in simple notation. We considered earlier Newton’s idealization of the solar system. This is what is meant by the formation of the scientific object. Newton secured the agreement of others for his definition of terms and his measurements. People might generally agree about the meaning of ‘pendulum in motion’ or ‘falling body,’ but the scientific object is much more closely specified and seeks to eliminate ambiguity. Forming this object prepares the way for an experiment which could be repeated by anyone. 5

‘Natural philosophy’ would be the term used by Galileo or Newton, and their contemporaries for the work they were doing. 6 Cf. Mariano Artigas, Knowing Things for Sure (Lanham, MD: University Press of America, 2006), pp. 62ff.

Induction, Science, and Knowledge

141

Using the basic theoretical terms, Newton formulates some propositions permitting theory-mediated measurement of parameters; measurement is crucial to this type of argument. Success in measurement and increasing precision both formed part of the evidence in support of the theory. As George Smith noted, “Newton is using mathematical theory to turn otherwise recalcitrant questions into empirically tractable questions.”7 The terms allow for the use of mathematics, and Newton skillfully applies his mathematical tools to the measurements of the movements of the planets, treated as points. In contrast to the view of Newton held by some writers, he does not subscribe to the idea that the mathematical conception of the world precisely matches real events, as is reflected in the following affirmations: By reason of the deviation of the Sun from the center of gravity, the centripetal force does not always tend to that immobile center, and hence the planets neither move exactly in ellipses nor resolve twice in the same orbit. There are as many orbits of a planet as it has revolutions, as in the motion of the Moon... But to consider simultaneously all these causes of motion and to define these motions by exact laws admitting of easy calculation exceeds, if I am not mistaken, the force of any human mind.8

Newton thus did not believe in an exact correspondence between his description and physical reality. Still, he explores the discrepancies as a way of improving the theory. For example, he focuses on deviations from Kepler’s rules. Cohen and Smith comment on this in the following passage: First, in every case in which he deduces some feature of celestial gravitational forces, he has taken the trouble in Book I to prove that the consequent of the ‘ifthen’ proposition licensing the deduction still holds quam proxime [that is, approximately] as long as the antecedent holds quam proxime ...Second, in every case in which Newton deduces some feature of celestial gravitational forces, mathematical results obtained in Book I allow him to identify specific

7

George Smith, “Turning Data into Evidence,” a series of three lectures given at Stanford University in the spring of 2007. The manuscript is available at the web-site of Stanford University, under the heading of the Patrick Suppes Center for the Interdisciplinary Study of Science and Technology. 8 Newton, “De motu corporum in gyrum” in D.T. Whiteside, ed., The Mathematical Papers of Isaac Newton, vol. 6 (Cambridge: Cambridge University Press, 1974); English translation in A. Rupert Hall and Marie Boas Hall, Unpublished Scientific Papers of Isaac Newton (Cambridge: Cambridge University Press, 1962), pp. 239-292.

142

James Kelly

conditions under which the phenomenon from which the deduction is made would hold not merely quam proxime, but exactly.9

Working in this way, Newton imposed order on the irregular patterns he mentions in the earlier quotation. His manner of argument, built from ‘ifthen’ propositions and the quam proxime counterparts, is rigorously deduced from the laws of motion. The main risk for this type of reasoning, in Cohen’s view, is a discovery that would call into question the evidential reasoning that led to the formulation of a law. This risk comes from the huge inductive leap that is part of Newton’s manner of reasoning. He begins from ordinary sense-perception, then uses theoretical terms, sometimes understood in a new way. He chooses to understand the planets and their motion in an idealized way, seeking to formulate laws which will account for observed behavior. The idealization is then shown to conform, even if not perfectly, to what can be perceived through the senses. In Book 3 of Principia, Newton seeks to apply the gravitational law to unresolved problems somewhat remote from the phenomena on which it was based: first, the non-spherical shape of the earth and the variation of surface gravity with latitude; second, the area-rule violation in the orbit of the Moon, the motion of its nodes, and its fluctuating inclinations; third, the tides; fourth, the precession of the equinoxes, and fifth, the trajectory of the comets. It could be said that he pushes the theory for all it is worth; that is, that he tries to draw out many and varied consequences, to see whether experimental results will be in agreement. Again, Newton tries to show discrepancies between theory and observation that would tell the researcher more about the world.10 From this summary treatment of Newton’s method, it could be noted that he relies heavily on an accumulation of data, which is gathered in view of his mathematical formulation of the theory. In addition to the abstraction involved in using a mathematical method, he deliberately idealizes and simplifies. Newton labored to build a stock of basic terms, isolating features which could be measured and compared to one another. He outlined his methods of measurement and observation, and in general his fellow natural philosophers agreed with him. The consequence of all this was one of mankind’s great achievements. Of course, it can be objected that he looks on his work as definitive and does not anticipate the 9

Cohen and Smith, The Cambridge Companion to Newton (Cambridge: Cambridge University Press, 2002), p. 156. 10 Cohen and Smith, eds. The Cambridge Companion to Newton, p. 159.

Induction, Science, and Knowledge

143

possibility of a different understanding, as would be expressed in relativity theory. He lacked historical perspective, not realizing that his theory could one day be replaced; but few people realized this until the nineteenth century, when other developments called into question previously unquestioned presuppositions. We will consider next Einstein’s manner of reasoning. Does the Newtonian method, or something like it, remain that of physics, in Einstein’s proposal of a new theory? Authors disagree about what is central in the great physicist’s method. Popular representations have sometimes contrasted Einstein’s work with that of Newton, because Sir Isaac was a great experimentalist, while the re-founder of physics relied principally on the results of others’ experiments. But some recent critical studies of Einstein’s work argue that he also relied on inductive reasoning. John Norton affirms that Einstein discovered the general theory of relativity through “eliminative induction.”11 He describes this in the following way: a researcher might begin by defining a universe of theories or hypotheses that may serve to explain some phenomena, then marshal evidence and arguments at hand in such a way as to eliminate members of this universe either by deductive or inductive inference.12 This eliminative induction can be derived from Mill’s canons. In some sense, this seems an accurate description of what happened, because Einstein dealt with alternative explanations of phenomena (especially phenomena that were anomalous for the Newtonian theory). He thought something was awry with the classical account, and we will see a bit later that this inner conviction arises in part from unfeasible but possible and imaginable physical experiences; in some way, this is inductive. Jon Dorling describes Einstein’s way of proceeding as deductive, though he focuses on similarities between the methods of Einstein and Newton.13 He introduces his argument with an expression that resembles those of Cohen and Smith concerning Newton.

11 “Eliminative Induction as a Method of Discovery: How Einstein Discovered General Relativity,” in The Creation of New Ideas in Physics, ed. Jarrett Leplin (Dordrecht, Boston, London: Kluwer Academic Press, 1995). 12 Cf. “Eliminative Induction,” p. 29. 13 “Einstein’s Methodology of Discovery was Newtonian Deduction from the Phenomena,” The Creation of New Ideas in Physics, ed. Jarrett Leplin (Dordrecht, Boston, London: Kluwer Academic Press, 1995).

144

James Kelly

Newton taught us how to deduce a theory from the phenomena, an explanans from one or more of its own explananda, by adding suitable higher level constraints, such as his own laws of motion. 14

Dorling argues that Einstein followed a similar strategy, supporting his argument first with reference to his own work on photons in 1905. The central argument from Einstein’s 1905 paper on special relativity can be seen as a Newtonian deduction from the phenomena. There the constancy of the velocity of light, including frame-of-reference independence, is taken as given. Experimental confirmation for the existence of ether had failed, in the Michelson-Morley experiment, and the initially surprising result was that the speed of light remained always the same, regardless of the point of reference. The Lorentz transformation equations, which serve to explain this fact, are deduced from the phenomena through higher-level theoretical constraints, such as the principle of special relativity, which affirms the physical equivalence of all inertial systems. Some other more innocuous theoretical constraints, such as the linearity of the appropriate coordinate transformations, must also be accepted.15 A discussion of induction in Einstein should include some reference to his use of thought experiments. On one occasion he remarked the following: Then there occurred to me the happiest thought of my life, in the following form. The gravitational field has only a relative existence, in a way similar to the electric field generated by electromagnetic induction. Because for an observer falling freely from the roof of a house there exists—at least in his immediate surroundings—no gravitational field. Indeed, if the observer drops some bodies, then these remain relative to him in a state of rest or uniform motion, independent of their particular chemical or physical nature (in this consideration the air resistance is, of course, ignored). The observer therefore has the right to interpret his state as ‘at rest.’16

Einstein here appeals to possible experience, to an experiment that could be carried out; even though it is taken for granted that the results will be as he

14

“Einstein’s Methodology,” p. 97. Cf. “Einstein’s Methodology,” p. 98. 16 “Einstein’s Luckiest Thought,” trans. A. Pais from the manuscript in the Pierport Morgan Library; Pais, ‘Subtle is the Lord…’ The Science and the Life of Albert Einstein (Oxford: Clarendon Press, 1982), p. 178. 15

Induction, Science, and Knowledge

145

suggests.17 Perhaps such a ‘happy thought’ can also be integrated into the idea of forming a scientific object, in the sense that it involves idealization and simplification. Einstein’s idealization is analogous to that of Newton. In trying to understand his method, it is important to take into consideration some deep theoretical concerns which he spoke about: It seems to me that a physical theory can only be satisfactory if its structures are put together from elementary foundations. The theory of relativity is just as little satisfying as, for example, was classical thermodynamics before Boltzmann had interpreted entropy as probability. If the Michelson-Morley experiment had not brought us into the greatest perplexity, no one would have accepted the theory of relativity as a (partial) salvation.18

Einstein’s words reflect the close interplay between theoretical considerations and experimental method. The results of the MichelsonMorley experiment contributed to a crisis, but as yet no fully satisfactory theory had been reached. John Stachel questions the possibility of identifying clearly a method Einstein deliberately followed.19 His progress towards various breakthroughs seems a consequence of apparently providential circumstances, fortuitous rather than part of a research strategy. His own research concerns, and even some errors, led him along a path that proved to be fruitful. These several points suggest an unplanned development of Einstein’s theory. Still, it is not easy to define ‘method,’ and the great physicist’s writings indicate that he acted deliberately and not randomly. These are only two examples of scientific reasoning, but both are significant, and they share some common features. First, for both Newton and Einstein, experimental results were crucial. Newton reflected for years and accumulated data in order to ensure that he would be prepared to defend his theory. Einstein and others waited eagerly for the results of 1919 measurements of the distortion of paths of light taken during a solar eclipse. This is the more directly inductive component. Second, mathematics takes 17

Cf. “Einstein’s Luckiest Thought,” Roberto Torretti, in The Creation of New Ideas in Physics, ed. Jarrett Leplin (Dordrecht, Boston, London: Kluwer Academic Press, 1995). 18 In “The Manifold of Possibilities,” Stachel translates from Michael Eckert and Willibald Pricha, “Die erstenBriefe Albert Einstein’s an Arnold Sommerfeld,” Physikalische Blätter, vol. 49 (1984), pp. 29-34. 19 John Stachel, “The Manifold of Possibilities,” in The Creation of New Ideas in Physics, ed. Jarrett Leplin (Dordrecht, Boston, London: Kluwer Academic Press, 1995).

146

James Kelly

on great importance in scientific reasoning, most especially in physics. One theory replaced the other, but both were tested against observation. As was noted, science deliberately forms its object (that is, it identifies qualities of physical reality that can be measured and compared), and preliminary to this is a long process of defining terms, developing standards and instruments of measurement as well as conventions about measurement and experimentation. It can be argued that such scientific argumentation achieves objectivity, both because consensus is reached among those who know about a particular field (in this case, physics), and because there are external measures and references (the experimental results) accessible to everyone. Induction plays a part in this scientific method, but it is in fact difficult to separate that one strand and to study it in isolation. Scientific method combines induction and deduction, often in very rapid succession. But induction relates to sensation, and this is critical; the results that different parties consider must be accessible to the senses. It is in this sense that induction is crucial for science and its method. 2 Pre-scientific Induction Neither the physical theory of Newton nor that of Einstein should be taken as a paradigm of human knowledge. Both reflect the incredible power of a method for studying observable and measurable phenomena. It could be added that they fulfilled the hopes of Francis Bacon for practical knowledge that would yield control and domination of nature. Methodical induction yields very fruitful results. But the results of scientific induction have a genuine but mediated relation with physical reality. Sense experience lies at the basis of natural science. The Newtonian terms (e.g., force) do not correspond to some quality that can be directly perceived, but to a feature that can be measured, and thus can be accessible to all observers who agree on some definitions and standards of measurement. Likewise, the experimental results are accessible to all. One theory prevailed, and then the other, because of ongoing experimental confirmations of each respective theory. Something similar could be said of the success of practical applications of the theoretical findings. On the other hand, the idealization, simplification, and mathematization mean that neither theory closely corresponds to physical reality. This does not take anything away from the achievement nor from its power; it is simply the character of experimental science as it has developed. This view of the matter helps resolve the problem of one theory replacing another. From this perspective, there would be no reason to think that Newtonian

Induction, Science, and Knowledge

147

theory could be definitive; nor that Einsteinian will be. Puzzling features of the theory become less problematic when a perfect fit is not anticipated. This position can be maintained while conceding that mathematics has served the development of science with astounding power. From the point of view of induction, it could simply be said that mathematical formulations help the researcher to focus on measurable features, and this facilitates the articulation of a scientific argument. We could ask where mathematics comes from and whether it is somehow derived from nature by induction. This is not the focus of this paper, but it could be said that induction plays a role in a person forming the idea of bodies, planes, triangles, and numbers; but that it involves concepts which can be understood apart from the material order and are not tested against that order. On the other hand, there is a sometimes amazing correspondence between aspects of mathematics and real features of the world, as the Greeks discovered with regard to music and as Eugene Wigner mentions in his striking article.20 Also noting the difficulties introduced by mathematical abstraction, Bas van Fraassen has argued against scientific realism. In a recent work, discussing various understandings of representation, he wrote, “Since the scientific description of the world is couched throughout in mathematical language, we can put it this way: the scientific image itself harbors vagueness and ambiguity, at each historical moment of its development— but this only comes to light in retrospect.”21 He takes examples of representation in art and points out how images are always produced with a view to some purpose, and so the relation between a picture or a model and what it represents will only be clear in view of the context and the aim of the depiction. Nancy Cartwright wrote in a similar vein of the difficulties caused by abstraction: “I have repeatedly said that I do not believe in theoretical laws.”22 This could be related to the earlier quotation from Newton, concerning the disparity between theoretical laws and physical processes. That is, the human mind can represent physical reality through a theoretical law, and the law may be instrumental for some exercise of 20 Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Physical Sciences”, in Symmetries and Reflections (Bloomington, IN: Indiana University Press, 1967). 21 Bas C. van Fraassen, Scientific Representation: Paradoxes of Perspective (Oxford: Clarendon Press, 2008), pp. 39ff. 22 Nancy Cartwright, How the Laws of Physics Lie (New York: Oxford University Press, 1983), p. 8.

148

James Kelly

dominion over nature, but the abstraction involved in forming the scientific object leaves behind some features of the reality understood. Cartwright argues that phenomenal explanations and causal accounts remain closer to what they account for, while theoretical laws are excessively abstract. Both Cartwright and van Fraassen argue in different ways that a person representing the natural order would be misled were she to aspire to a perfect correspondence, because mathematical abstraction leaves behind significant dimensions of what is represented. And they would refer to such a misconception as realism, or more precisely scientific realism. The limitations of scientific knowledge do not in themselves manifest the need for some more fundamental cognition, but all of the previous argument suggests such a possibility. If Galileo, Newton, and Einstein had no knowledge prior to their experimental reasoning, it would have been impossible for them to begin. Galileo came to understand, partly through the use of a telescope, that the moon has a rough surface; this type of knowledge preceded his application of mathematical reasoning to the motions of the heavenly bodies. He understood something concerning the height of towers and the time needed for an object to fall from the top of the tower. He had watched rolling objects descend along slopes. Scientific method clarified and perfected this initial knowledge, but it could not do without it. The story of an apple falling on Newton’s head is apocryphal, but it does reflect that it occurred to Newton to see a connection between ordinary objects falling and the behavior of the heavenly bodies. Newton explored many phenomena deliberately and methodically, but he could not have begun from nothing. Einstein’s appeal to a body falling freely through space also indicates a connection between theory and a pre-scientific awareness about falling bodies and space. It could be said that the thought of a freely falling body only acquired importance because it occurred to Einstein, but nonetheless his reasoning suggests a relation between science and ordinary knowledge. Science perfects and even corrects aspects of people’s everyday convictions. At one time, it seemed in accord with common sense that heavy and light objects of similar shape and size would fall with different velocities, but measurement showed otherwise. Most forms of human enterprise involve inductive reasoning. Sherlock Holmes often speaks of deduction, but in fact he reasons inductively. Gregor Mendel crossbred plants, observed and recorded the results, and eventually hypothesized an explanation. Historians have pointed out the resourcefulness of certain medieval monks, who observed the gradual depletion of the soil and learned the benefit of rotating their

Induction, Science, and Knowledge

149

crops, thus increasing productivity. This does not in itself depend on awareness that chemicals found in the soil can be used up and that changing what is planted in a particular field could allow them to be replenished, but it does express reflection about what has been observed. This was a type of activity that would eventually be raised to the level of a science. The impulse towards science is already seen in the project of applying thought and experience to improving agricultural methods. Many arts involve some knowledge of technique and materials, without being strictly scientific. Here I will not give attention to the distinction between pure and applied science, which is important and interesting. My focus is more on the foundation of experimental science, which could be either pure or applied. Some of the truths known pre-scientifically are capable of more rigorous justification, as are some scientific truths. This role could be attributed to philosophy. Galileo and Newton both thought of themselves as natural philosophers, and several generations of twentieth century physicists were themselves quite philosophical concerning relativity and quantum mechanics. The natural philosophers, especially Galileo, continued to rely on a logic developed by the Aristotelians who preceded them, such as Iacopo Zabarella.23 Zabarella developed a form of inductive reasoning which he referred to as regressus, and which suggests Galileo’s method. In that period, there was discussion of demonstrations in mixed sciences, of which the mechanics of Galileo and Newton could be considered an example: demonstrations involving both physical and mathematical components. Such demonstrations were distinguished because logicians accepted a difference between physical and mathematical objects, and consequently arguments. Intrinsic to the argument of this paper is that this is a valid distinction and that it serves to explain some of the puzzles and problems of contemporary physics. An area of natural reasoning which has both a pre-scientific and a philosophical aspect might be termed ‘concept formation.’ Learning a language means gradually entering into a way of thinking. G.E.M. Anscombe suggested this in her discussion of David Hume’s treatment of causality, a point certainly relevant to the consideration of induction. She says the following about learning the causal concept:

23

Cf. William Wallace, The Modeling of Nature (Washington, D.C.: Catholic University of America Press, 1996), pp. 240ff. On this topic, Zabarella (1533-1589) wrote De regressu. He commented on the works of Aristotle and was influential during the Renaissance.

150

James Kelly

The truthful—though unhelpful—answer to the question: ‘How did we come by our primary knowledge of causality?’ is that in learning to speak we learned the linguistic representation and application of a host of causal concepts. Very many of them were represented by transitive and other verbs of action used in reporting what is observed. Others—a good example is ‘infect’—form, not observation statements, but rather expressions of causal hypotheses. The word ‘cause’ itself is highly general. How does someone show that he has the concept cause? We may wish to say: only by having such a word in his vocabulary.24

This reflection, applied here to the concept of cause, is relevant to our discussion of induction. Anscombe’s use of the word ‘infect’ could be taken as an example: a person learns about infection, and this is inductive reasoning. Nancy Cartwright points to the case of someone realizing that spraying swamps will serve to impede the spread of malaria, whereas burning the blankets of victims will have less effect.25 Anscombe is trying, I think, to disarm Hume’s argument, and she does so by pointing out that the source of the concept of cause is not private (repeated experience of an individual), but linguistic and hence public and common to many. Learning a new word is not truly induction, but learning language is related to inductive reasoning. In this sense, Galileo could not have first used inductive reasoning in developing his theory. Rather, he had been accustomed to correctly applying causal concepts in his learning to speak and write in Italian and in Latin. Also implicit in Anscombe’s argument is the following reflection: a person who tries to call into question the reality of causal relations can slip into contradiction.26 It is difficult for Hume himself to avoid this. Even if he offers psychological reflections about the source of concepts, he is arguing that certain experiences cause in us the formulation of particular concepts. He could be taken to argue that psychology trumps philosophy, but I do not think he succeeds.27 Hume attributes the causal principle to imagination, 24

Causality and Determination: An Inaugural Lecture (New York: Cambridge University Press, 1971), p. 9. 25 Nancy Cartwright, How the Laws of Physics Lie, p. 10. 26 This has some similarity to Aristotle’s argument concerning the principle of contradiction (Metaphysics IV, 4, 1008b). 27 D. Hume, Treatise on Human Nature 7, 1, 1, 6. He thinks that his explanation is psychological, but this does not seem to matter with respect to reliance on causality. He affirms at the very beginning of the book that he seeks a scientific treatment of these matters, the application of Newtonian method. R. Harré and E.H. Madden in their Causal Powers (Totawa, NJ: Rowman and Littlefield, 1975) show interesting parallels between Hume’s approach to causality and other historical examples of skepticism.

Induction, Science, and Knowledge

151

and this in some way explains his view that there is no reason to expect one result more than any other in the succession of events in the natural order. A critic of my view might respond that all philosophers have suggested reform in the use of particular terms, beginning with Socrates’ examination of the meaning of ‘justice’ or ‘piety.’ These are moral terms, but that was the field where Socrates appealed to induction. Aristotle gave technical meanings to ordinary terms. Both these points can be granted. But what Anscombe notes is that a philosophical account that seems to lack awareness of the ordinary understanding of basic terms is at a grave disadvantage. Anscombe’s argument does not reach the level of proof, because the words we use (‘infect’, or ‘cause’) could be considered ambiguous or misleading. But the argument does cast doubt on an entire line of reasoning. Hume denied that there are examples of causal relations given in sense experience, and Anscombe points out that ordinary language is full of such examples. If so, [that is, if understanding ‘cause’ is having the word as part of one’s vocabulary] then the manifest possession of the concept presupposes the mastery of much else in language. I mean: the word ‘cause’ can be added to a language in which are already represented many causal concepts. A small selection: scrape, push, wet, carry, eat, burn, knock over, keep off, squash, make (e.g., noises, paper boats). But if we care to imagine languages in which no special causal concepts are represented, then no description of the use of a word in such languages will be able to present it as meaning cause. Nor will it even contain words for natural kinds of stuff, nor yet words equivalent to ‘body,’ ‘wind,’ or ‘fire.’ For learning to use special causal verbs is part and parcel of learning to apply concepts answering to these and many other substantives. As surely as we learned to call people by name or to report from seeing it that the cat was on the table, we also learned to report from having observed it that someone drank up the milk or that the dog made a funny noise or that things were cut or broken by whatever we saw cut or break them.28

Again, this argument approaches the matter at the level of a pre-scientific understanding. Anscombe calls into question the reasonableness of suggesting a problem in deriving the concept of causality from experience. Speaking English involves using general concepts related to experience. The person who tries to do without such concepts could say that they are not sufficiently clear or well-defined, but the burden of proof should fall on

28

Causality and Determination, pp. 9-10.

152

James Kelly

that person. Neither Hume’s argument nor the positivist myth offer convincing evidence that the idea of causality is inconsistent.29 Earlier in the same essay, Anscombe discusses more generally the meaning of causality, and how it should not be confused with determination, in the sense of one thing following of necessity from another, as Hume suggests. …[C]ausality consists in the derivativeness of an effect from its causes… For example, everyone will grant that physical parenthood is a causal relation. Here the derivation is material, by fission. Now analysis in terms of necessity or universality does not tell us of this derivedness of the effect; rather it forgets about that. For the necessity will be that of laws of nature; through it we shall be able to derive knowledge of the effect from knowledge of the cause, or vice versa, but that does not show us the cause as source of the effect. Causation, then, is not to be identified with necessitation. 30

Here she is not speaking merely of features of language, but of characteristics of the natural order. To focus on derivativeness does direct attention to one aspect of the ordinary use of the term, but at the same time it expresses a philosophical position. She broadens the examples of causal relations to forestall the possibility of reducing causality to pushing or pulling, that is, simply mechanical relations. In view of our earlier discussion, Anscombe’s affirmations could be taken to imply that a description that omitted this derivativeness in some correlation might be outlining some aspect of determination, rather than being concerned, strictly speaking, with causality, which requires this element. I do not follow Anscombe this far; rather, it seems to me that ‘cause’ simply applies differently to the two cases. (I would call this analogous use.) The motion of one billiard ball can produce motion in another, or two parents can produce a child, and ‘cause’ refers to a feature of both relations. When Crick, Watson, et al, built models of the DNA strands, they were seeking a causal explanation for observed behavior. Motion could be attributed to gravitation, understood as an intrinsic property of all matter (by Newton) or as part of the structure of space (by Einstein). Some philosophers have extended the analogy to a first cause or ultimate cause, an original cause of the being and order of things. This means affirming that there is something in common between producing change in a thing and producing the thing 29

A developed discussion of this question can be found in R. Harré and E.H. Madden, Causal Powers (Totowa, NJ: Rowman and Littlefield, 1975). 30 Causality and Determination, pp. 7-8.

Induction, Science, and Knowledge

153

itself. ‘Cause’ used in these very different situations is clearly not univocal, but according to this view not simply equivocal. To summarize this section of the argument, all human beings use causal reasoning in their ordinary discourse. Part of learning a language is to learn what ‘cause’ means, and to learn a host of other words referring to causal relations. Although everyone has a sense of what ‘cause’ means, this is ordinarily a confused and uncritical understanding. Nonetheless, if we examine the concept closely, we realize that essential to causality is the dependence of one entity on another, as in the case of generation, or of one aspect of experience on another, as in the case of gravity and motion. Taken together, these affirmations imply that there is pre-scientific induction which is essential in order for there to be experimental science, and that there is a more reflective philosophical induction, which is necessary if there is to be an articulate science, capable of defending its results and methods. In learning language, the child learns to use concepts and to understand their relations, and this will also involve sense experience. Philosophical induction implies recognition of objections and difficulties (such as those of Hume and others) and an ability to respond to them. 3 Philosophical Induction This presentation can lead us from the consideration of pre-scientific to philosophical induction. Anscombe’s argument generally concerns the learning of a language. When she focuses her attention on the word ‘cause,’ she stresses the philosophical aspect of this matter. Our contention is that, apart from learning the use of words, the person is recognizing concepts. Anscombe mentions both verbs with some causal implication, such as ‘scrape’, ‘push’, ‘wet’, etc., and a few nouns, such as ‘body’, ‘wind’, and ‘fire.’ Both the concept ‘cause’ (which is implicit in the various verbs), and those of more concrete agents (such as wind, body, and fire) correspond to types of things given in sense experience. These concepts have a foundation in experience, even though the terms used vary from language to language. Although it might be concluded that such terms are less useful for the study of nature than are ‘mass’, ‘velocity,’ and ‘impetus,’ in part because of being less susceptible to measurement and therefore not easily expressed mathematically, they express in some way the intelligibility of nature, a necessary presupposition for science.

154

James Kelly

Some philosophers of science have treated the learning of language as an example of inference to the best explanation, also called abduction.31 Noam Chomsky pointed out that people acquire the capacity to judge whether a sentence they have never heard before is acceptable or not in their language, even though they have heard only a limited set of statements, and much of what they have heard is incorrect (either incomplete or ungrammatical). This led the linguist to revive the conception of a universal grammar, something based on human brain capacity and anatomy. For Peter Lipton, this account is an example of inference to the best explanation: the person is reaching a principle, even though that principle is underdetermined by the evidence. Abduction is a form of induction, and so Lipton would make Anscombe’s argument experience-based. But although the grammar of a particular language is a kind of theory, there are significant differences between scientific theories and grammars. A scientific theory could be replaced by a newer theory, as Newton’s theory of gravity was replaced by Einstein’s, even though Newton’s theory still serves for most ordinary purposes. The overturning of a grammar would seem to be the dying out of a language, so that there are no longer speakers, or even students, of that language. In addition, that the various conceptions of causality and of “powerful particulars”32 belong to a language does not establish that they are useful for the understanding of natural science. Anscombe’s argument does cast serious doubt on Hume’s account, because he argued there are no examples of perception of causality; it is true that causality is not an object directly perceived. But Anscombe replied that we use causal concepts daily, they are related to simple ordinary experiences, and we would find it very difficult to communicate without them. We could readily agree with Hume that the senses do not perceive causality, but this affirmation is more strongly supported by observed collisions than by generation, where the observed stages will manifest a relation. Still, a further step would be beneficial, in order to show that the concept of a causal relation is coherent and with foundation in experience.

31

Peter Lipton, Inference to the Best Explanation (London and New York: Routledge, 1991), pp. 15ff. 32 Rom Harré and E.H. Madden, Causal Powers (Totowa, NJ: Rowman and Littlefield, 1975).

Induction, Science, and Knowledge

155

John Searle discusses the question of experience of causation.33 He begins from the frequently argued point that human beings can directly experience their own causal agency, mentioning how the patients of Dr. Penfield distinguished between what they did and what he caused their bodies to do, by stimulating the appropriate neurons with micro-electrodes. He quotes from Elizabeth Anscombe, who mentioned in lectures the case of a person who is sitting at a desk and jumps when a car backfires outside. This fits well with her argument mentioned above, that what is essential to causality is “derivativeness,” as is well illustrated by physical generation. In Searle’s view, these examples can easily be extended to other experiences, because we recognize causality when we see another person, or some other object, pushing a car; we relate these perceptions to our own experience of pushing the car. When discussing this problem, Rom Harré and E.H. Madden tried to follow a different path. They argue that the concept of ‘power’ is needed for an understanding of change. The human mind recognizes individual things in terms of what types of things they are and what they can do. If we were to identify a metal by its appearance, but it turned out that its melting point was not what had been anticipated, we would be inclined to think that our initial identification was incorrect. Acceptance of induction is related to this conviction about the suitability of the human mind to understand the natural order. Seen from a certain perspective, i.e., that of the usefulness of perception and understanding for survival, it would be possible to attribute this conformity to the process of evolution. Such an explanation is not without its difficulties, as can be seen in accounts of art or altruism or theoretical mathematics; these realities are not of clear use for survival and therefore remain unexplained. Aristotle recognized a biological aspect of knowing, but he viewed nature as acting as if for a purpose. The lower faculties, more clearly advantageous for survival, provide a foundation making knowledge possible. 4 The Connections among Pre-science, Science, and Philosophy All human knowledge seeks patterns, and this holds true for natural science, for pre-scientific knowledge, and for philosophy. Pre-scientific recognition of patterns comes first, and this could develop into science, adopting the method of Newton or one analogous to it. Aristotle argues that 33 John Searle, Mind (New York and Oxford: Oxford University Press, 2004), pp. 142ff.

156

James Kelly

we can reach some understanding of change through what precedes and what follows the change. Change, the individuals in potency, and later the individuals in act (that is, having reached their final state or goal) are accessible to the senses. Sense perception, in this view, is the starting point and foundation for all human knowledge. Aristotle attributes the discovery of induction to Socrates34, and he uses the term to refer to this aspect of the development of knowledge. This view of change in terms of potency and act seems derived principally from living things (e.g., acorns and oak trees, the embryo and the fully developed animal). Still, it can be applied analogously to inanimate realities. Copper has the capacity to conduct electricity, for example; this would qualify as a potency, which would be in act when the current is actually flowing through it. When studying the structure of a particular atom, only certain orbits are possible. Some atoms can be split, and doing so will yield great quantities of energy. Even these sub-atomic changes can be understood within the framework of potency and act. Anscombe’s analysis links causality to the recognition of tendencies or inclinations, potencies or powers, in particular entities. Ordinary conversation offers representations of what exists in the world (e.g., ‘the cat drank the milk’). Natural science offers a different form of representation, often expressed mathematically. Using the same example, science could study the digestion of the cat. Philosophy could attribute a qualitative change, what Aristotle would call accidental change, (that is, features of the cat change, but it remains the same substance) to the cat and a substantial one to the milk (when digested, it is no longer the same substance). The cat instinctively recognizes milk as something that contributes to its well-being. The digestive system of the cat has the capacity to break the milk down and to use the chemicals to rebuild or heal the cat. Ordinarily, the various representations will not conflict with one another, and they serve different purposes. Every scientific theory depends both on judgments that precede the theory (e.g., it seems that balls of different weight undergo the same acceleration when dropped from a tower), and on some presuppositions (e.g., Newton’s rules for reasoning, which include the principle of induction). Often, people take scientific induction as the pattern for all inductive reasoning, in large measure because of its apparent success. As is stressed in Vickers’ article, there are a number of ways in which science employs induction. Even Karl Popper, who accepted Hume’s critique of induction, offered as a discerning mark of scientific discourse that it could be tested 34

Metaphysics XIII.4.1078b 22-33.

Induction, Science, and Knowledge

157

against experience, and that means using inductive evidence.35 Since scientific discourse depends on pre-scientific judgments and on philosophical judgments which science itself cannot justify, the success of scientific induction also lends credibility to these judgments which are not in themselves scientific. This capacity is exercised spontaneously in prescientific knowing. In different ways, natural science and philosophy impose method and discipline on the work of reason. Pre-scientific reason recognizes changes in qualities (such as growth or movement) and substantial changes (such as death), and also basic kinds (such as oak trees or giraffes). Philosophy should take into account both the pre-scientific and the scientific patterns. The pre-scientific are closer to direct experience, and so they provide a check on both scientific and philosophical ideas. On the other hand, both science and philosophy can serve to correct uncritical judgments based on first impressions. Newton and Einstein shared basic perceptions and conceptions of falling bodies, but they offered very different theoretical accounts to explain what can be perceived. This essay has not addressed the puzzles concerning causality posed by certain aspects of quantum mechanics. One expression of contemporary physics is quantum theory, and it has puzzling features, such as waveparticle duality, the Heisenberg Uncertainty Principle, the use of imaginary numbers, not being able to localize the trajectory a photon follows to reach the screen, and so on. The so-called EPR (Einstein-Podolsky-Rosen) paradox34 has been central in twentieth-century debates about this field of study. It concerns two detectors, with parallel polarization filters. Each detects the photons passing half the time, in random order. The traditional causal model would have two options: either the photons are preprogrammed or the detection events influenced one another. But John Bell showed in 1964 that the pre-programming hypothesis conflicts with the quantum mechanics predictions for a variety of orientations of the filters. The second idea (mutual influence of the detection events) would conflict with the theory of relativity, which indicates a finite maximum velocity for physical interactions at a distance. Anscombe might argue that the paradox supports her contention that causality and determination are distinct concepts. From her perspective, there would be no inconvenience in not being able to identify a relation between the photons. In fact, she seemed to think that some physical 35

Popper regards the possibility of empirical testing as characteristic of science. It is not clear what he would think of multi-dimensional universes, with no possibility of sense experience of them.

158

James Kelly

indeterminacy of this kind is needed in order to argue for free will. I would prefer a different approach. What was said earlier about mathematical abstraction could be taken as a partial explanation for puzzles and paradoxes in quantum mechanics, or in relativity theory. Because the theories are so heavily dependent on mathematics, there may be features which, in order to be represented in mathematical terms, are affected by the separation from what is given to the senses. This account does not directly resolve the paradox, and it calls for further explanation of how to give an account of it. It does seem, though, that physics is the science that relies most on mathematical theory, and it suffers from such puzzles more than other sciences (e.g., biology). We might contrast Watson and Crick’s construction of possible models for DNA and choosing the one that best accounted for the data (this seems relatively close to the senses), and discussions in physics about whether the Higgs boson has been identified (this seems more theoretically mediated). The paradoxes do not count tellingly against what has been proposed in this paper: that induction in natural science yields objective results, both achieving consensus and confirmation through results accessible to the senses. On the other hand, it would be mistaken to think of physics (or experimental science) as paradigmatic for all human knowledge. In fact, it could not arise without previous knowledge, and it could not explain or justify itself without philosophy. Both pre-scientific knowledge and philosophy rely on induction, and induction provides different ways of measuring theory with reference to sense experience. Crucial to this view is the proposition that there can be common understanding of terms such as ‘induction’ and ‘knowledge’, even when no single definition covers all uses of the terms. The word ‘analogy’ has often been used to characterize such terms. It may be of interest to consider what should be taken as the central example for induction. Anscombe proposed her example (physical generation) as evident, and this seems accurate. To recognize it as an instance of causality could remain at the level of the pre-scientific, because causality plays an important role in ordinary human dealings, such as trials, and any determination of responsibility. For many of the classical writers, induction in philosophy involves finding patterns. Plato spoke of patterns or models somehow found outside of nature, while his student Aristotle insisted that the understandable structure (what might today be called information) is distinguishable from the thing itself, but does not exist apart from the individual entity whose structure it is. In scientific induction, something comparable is achieved. In the case of biology, the discovered

Induction, Science, and Knowledge

159

structure may in fact be visible or tangible. In the case of physics, it seems that the understandable structure has an aspect of artifice, related in some way to the various types of abstraction involved in such reasoning. But the physicist also finds ways to test his theory inductively, and so his reasoning can be compared to simpler more spontaneous types of thought, more directly derived from experience. This essay has only touched briefly on the relation between induction and mathematics, a point which divided Plato and his great student. On the one hand, for Aristotle induction would be the source of mathematics, while for Plato mathematics helps us to discover what is unchanging in the order of nature. On the other hand, Aristotle expressed concern that physics not become overly mathematical, lest it lose its close relation with real physical processes. His concern was pushed aside by many others, going back even to Roger Bacon. But the development of twentieth-century physics suggests that, while mathematics lends great power to physical theory, it may also contribute to the paradoxes of quantum physics. And the reliance on mathematics can lead to developments, as in string theory, which are accepted without possible empirical confirmation. This may contribute to the argument that the mathematically based induction of experimental science cannot be ultimate, but must draw on other forms of knowledge, both pre-scientific and philosophical.

Induction in the Socratic Tradition John P. McCaskey Stanford University

Abstract: Aristotle said that induction (epagǀgƝ) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Induction in the Scholastic and the (so-called) Humean tradition has presumed that Aristotle meant going from particular statements to universal statements. But the alternate view, namely that Aristotle meant going from particular things to universal ideas, prevailed all through antiquity and then again from the time of Francis Bacon until the mid-nineteenth century. Recent scholarship is so steeped in the first-mentioned tradition that we have virtually forgotten the other. In this essay McCaskey seeks to recover that alternate tradition, a tradition whose leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. The examination is both historical and philosophical. The first part of the essay fills out the history. The latter part examines the most mature of the philosophies in the Socratic tradition, specifically Bacon’s and Whewell’s. After tracing out this tradition, McCaskey shows how this alternate view of induction is indeed employed in science, as exemplified by several instances taken from actual scientific practice. In this manner, McCaskey proposes to us that the Humean problem of induction is merely an artifact of a bad conception of induction and that a return to the Socratic conception might be warranted.

Introduction Aristotle said that induction (epagǀgƝ) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Did Aristotle mean particular things and universal ideas, or did he mean particular and universal statements? Induction in the Scholastic and the (so-called) Humean tradition has presumed the second. Recent scholarship is so steeped in this tradition that we have virtually forgotten the other. But the alternate view prevailed until late antiquity and then again from the time of Francis Bacon until the mid-nineteenth century. This essay seeks to recover that alternate tradition, a tradition whose

162

John P. McCaskey

leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. 1 There have been times when philosophers were stressfully aware of the ambiguity. In 1439, Lorenzo Valla said that Socrates and Cicero had the correct view and Boethius was evil for promoting the other: Boethius was like a thief who steals a horse and tries to hide the crime by cutting and dyeing the horse’s hair.2 Rudolph Agricola (d. 1485) agreed that induction was the Socratic practice.3 In a book of 1542, Agostino Nifo, in commentary on Aristotle’s Topics 1.12, said there were now several open questions about what induction is.4 In 1551, in the first edition of the first logic textbook published in English, Thomas Wilson took the Scholastic view, that induction was propositional inference made good by conversion to a syllogism. But in the second edition, “newly corrected,” published only one year later, Wilson added a new section on the other kind of induction, “called … Socrates[’] induction.”5 The debate waned after Bacon and his followers adopted the Socratic understanding, but it returned in the nineteenth century. The revisionist logician Richard Whately found it necessary to add to the fourth, 1831, edition of his Elements of Logic an acknowledgement that he was using the term “induction” in the Scholastic sense not in the “original and strict sense.”6 The whole Mill-Whewell debate over induction was essentially a disagreement over which of the two meanings was correct. In an 1874 textbook, Mill’s follower Alexander Bain warned his students against the Baconian or Socratic usage. “By Induction, we arrive at Propositions, … [It is not Induction] where what we arrive at is a Notion or Definition.”7 Bain’s students heeded his injunction—and most of 1

For comments on drafts of this paper, I thank Daniel Schwartz, Greg Salmieri, and Travis Norsen. None of them agrees with everything I say here. 2 Lorenzo Valla, Repastinatio dialectice et philosophie, ed. Gianni Zippel (Padua: Antenore, 1982), pp. 345–52. 3 Rudolph Agricola, De Inventione Dialectica, 2.18, p. 265. 4 Agostino Nifo, Aristotelis Stagiritae Topicorum (Venice: Girolamo Scotto, 1557), f. 18r–v, first published 1542. 5 Thomas Wilson, The rule of reason, conteinyng the arte of logique, set forth in Englishe (London: Richard Grafton, 1551), ff. 64v–68r; (London: Richard Grafton, 1552), f. 66r, f. 32v in subsequent editions. 6 Richard Whately, Elements of Logic, 4th ed., bk. 4, ch. 1, sect. 1, n. 2. In later editions, this note was moved into the body of the text. 7 Alexander Bain, “Meaning and Scope of Induction,” Logic, bk. 3, ch. 1, sect. 1, p. 1. Italics in original. “Notion” was Bacon’s technical term for a concept, the cognitive content corresponding to a word.

Induction in the Socratic Tradition

163

us have done the same. We take Aristotle to have meant that induction is a proceeding from particular statements to a universal statement—that is, a kind of propositional inference—not fundamentally a proceeding from observation of particular things or groups of things to an abstract concept. But this is not what Aristotle meant.8 He uses the term epagǀgƝ frequently enough, but always without preface or preparation. He always assumes his student knows what he means. And what his student would have known by the term was that distinctive practice by which Socrates pursued the identifying characteristics that justify grouping things together as a class. When Aristotle said, “Two things may be fairly ascribed to Socrates—inductive reasoning and universal definition,”9 Aristotle was not listing two unrelated inventions. He was describing two aspects of one project, what Valla, Agricola, and Wilson knew as “Socratic induction.” Unfortunately the word epagǀgƝ (Cicero translated it as inductio) is not used in the Socratic dialogues, and so we are left to infer exactly which part of Socrates’ practice Aristotle would have considered induction. I have argued elsewhere for the part that I presume here,10 but the focus in this paper is philosophical, not historical. My goal is to sketch out what I believe is a promising approach to induction, and I will label the proposal as being for induction in the “Socratic tradition.” But whether Aristotle, Cicero, Valla, Agricola, Wilson, Bacon, and I are right to give the historical Socrates credit will not be central to the presentation here. Moreover, not everyone working in this tradition agrees with all the others or with me. I will gather what I think are the most promising parts and say of their authors what we say of the generous colleagues from whom we learn: None has seen the final product, and none should be held responsible for its errors.11

8

I have argued this in detail in “Freeing Aristotelian EpagǀgƝ from Prior Analytics II 23,” Apeiron: A Journal for Ancient Philosophy and Science 40, no. 4 (December, 2007): 345–74. 9 Metaphysics, M4 1078b24–29. Ross’s translation, slightly modified. Cf. a similar passage in Nicomachean Ethics, bk. 6, ch. 3; 1139b26–33. 10 “Freeing Aristotelian EpagǀgƝ.” 11 For an entry to the sparse literature on Socratic induction, see Mark L. McPherran, “Socratic EpagǀgƝ and Socratic Induction,” Journal of the History of Philosophy 45.3 (2007): 347–64 and Hugh H. Benson, “Socratic Method,” Cambridge Companion to Socrates (Cambridge: Cambridge University Press, 2010). Other scholars have not espied in Socratic epagǀgƝ exactly what I have, but I think some have been hampered by looking for what those in the twentieth and early twenty-first centuries would call induction, not what Socrates’ successors would have called epagǀgƝ.

164

John P. McCaskey

1 Socrates Less contested than the nature and role of induction in Socrates is the importance there of the search for answers to the question, “What is it?” or, as we often say in this regard, “What is F-ness?” In the Republic, “What is justice?” In the Laches, “What is courage?” In the Meno, “What is Virtue?” Elsewhere, “What is beauty?” “What is it to be skilled?” “What is a good ruler?” “What is piety?” Consider this last, from the Euthyphro.12 Socrates asks: What is piety? Euthyphro replies that it is prosecuting a wrongdoer, even if the wrongdoer is one’s own father. Socrates does not dispute that this is an instance of piety but asks for something else: “I did not bid you tell me one or two of the many pious actions but that form (eidos) itself that makes all pious actions pious.”13 Euthyphro appreciates the difference and proposes that piety is doing what pleases the gods. Socrates likes this proposal, but it is ambiguous: Which gods? After further discussion, they agree that what is pious is what pleases all the gods. Euthyphro and Socrates have reached some sort of definition. What pleases all the gods is pious, and whatever is pious pleases all the gods. The two sets are coextensive. Socrates, however, is not satisfied. He does not just want a definition that marks out the boundaries of the concept. He wants rather to identify “that form (eidos) itself that makes all pious actions pious.” Which fact, he wants to know, causes the other? Euthyphro is at first confused, and Socrates explains. Euthyphro then appreciates the difference but realizes he is not sure which causes which. Socrates notes then, that even though what is loved by all gods may be pious and what is pious may be loved by all gods, “the god-loved is not the same as the pious.”14 Socrates suggests they start over. And where he starts is important: Piety, he proposes, is a kind of justice. All that is pious is of necessity (anagkaion) just, but not all that is just is pious. Socrates is proposing a genus. Euthyphro embraces the proposal, and Socrates calls for a differentia. “See what comes next: if the pious is a part of the just, we must it seems, find out what part of the just it is.”15 Euthyphro proposes that piety is justice in service to the gods. The other part of justice is in service to men. The conversation now turns to understanding what would make

12

Euthyphro, 5c–6e. Euthyphro, 6d, emphasis mine. 14 Euthyphro, 10d. 15 Euthyphro, 12d. 13

Induction in the Socratic Tradition

165

something of service to the gods. The question comes round very close to the original one. Euthyphro tires of the investigation and begs his leave. Socrates has pursued not just a definition of piety, not, that is, just a delineation that identifies what is or is not pious. He demands to know what makes a pious thing pious. What is the form? What is the cause? What predicate fills the blank, “It is piety because it ____”? To answer this, Socrates proposes to survey some instances, accepting that they are indeed instances, and to repeatedly compare and contrast instances of the one sort with instances of other sorts. He decides that the best approach is to first identify a genus and then use more compare-and-contrast to find the distinguishing differentia. Knowledge of such a form would be remarkably powerful. When, in Hippias Major, Socrates seeks the form of fineness (beauty, kalon), he says he wants to know “what when added to anything—whether to a stone or a plank or a man or a god or any action or any lesson—anything gets to be fine.”16 Note that it is not necessarily knowledge of a Platonic Form that Socrates seeks. As Aristotle reports, just after saying Socrates was concerned with inductive reasoning and universal definitions, “Socrates did not make the universals or the definitions exist apart; his successors, however, gave them separate existence, and this was the kind of thing they called Ideas.”17 The metaphysical status of a form is separate from its identification. 2 Francis Bacon From Aristotle’s time until late antiquity, inductio and epagǀgƝ were as closely associated with Socrates as induction nowadays is with David Hume. After the mid-seventeenth century, that association shifted to Francis Bacon. Bacon came to induction late. Though reared and trained for a lawyerly and courtly life, he always had an interest in natural philosophy and experimental science. Worldly explorations and the new sixteenth-century industries interested him as a boy.18 In 1592, when he turned thirty-one, he expressed a wish that he could purge systematic knowledge of its errors by his own “industrious observations, grounded conclusions, and profitable

16

Hippias Major, 292d, emphasis in Woodruff’s translation. Metaphysics, bk. M, ch. 4; 1078b30–32. Translation by McPherran, after Barnes. 18 Benjamin Farrington, Francis Bacon: Philosopher of Industrial Science (New York: Collier Books, 1961), ch. 2. 17

166

John P. McCaskey

inventions and discoveries.”19 Later that decade, he would enjoy retreats outside London to an estate at Twickenham Park, where he could perform experiments.20 Bacon’s scientific discoveries did not in the end amount to much, but—to take just a few examples—his study of specific gravity was the result of commendably careful experimentation,21 his theory of the tides earned Galileo’s consideration,22 and Robert Boyle modeled his early experimentation on Bacon’s posthumously published natural history, Sylva Sylvarum.23 By around 1603, when Bacon was in his early forties, he had become engaged with a theoretical problem arising in the practice of natural philosophy:24 How does one effect a property in materials that have never had that property? How does one attempt something never before done and know what will happen? The problem, Bacon decided, had two dimensions, what he called certainty and liberty. The first, Bacon thought, was easy enough if one ignored the second. It takes no great genius or much method to know that the next dollop of butter thrown on a hot skillet will melt.25 We can continue doing what we have always done, and we know what will happen. But what of lard? What about cheese? Wax? Clay? What about a new artificial material, envisioned but not yet produced? As we exercise our liberty, as we try things increasingly dissimilar, we lose our certainty— at least without a proper method. Bacon wanted a method that would allow liberty without sacrificing certainty. 19

Letter to William Cecil, 1st Baron Burghley, The Works of Francis Bacon, ed., James Spedding, Robert Leslie Ellis, and Douglas Denon Heath (London: Longmans & Co., 1857), (hereafter “Spedding”), v. 8, p. 109. 20 Lisa Jardine and Alan Stewart, Hostage to Fortune: The Troubled Life of Francis Bacon (New York: Hill and Wang, 1998), p. 138. 21 Historia densi et rari, Spedding, v. 2, pp. 242–305; History of Dense and Rare, Spedding, v. 5, pp. 339–400. 22 Letter to Bacon from Tobie Matthew, Spedding, v. 14 pp. 36–7; Jardine and Stewart, Hostage to Fortune, pp. 306–7; and Paolo Rossi, Aspetti della rivoluzione scientifica (Naples: Morano, 1971), pp. 163–9. 23 “I must inform you that many of the Particulars which we are now considering, were in my first Designe collected in order to a Continuation of the Lord Verulam’s Sylva Sylvarum, or Natural History. And that my intended Centuries might resemble his, to which they were to be annexed.” Robert Boyle, “A Proemial Essay,” Certain physiological essays, (London: 1661), p. 14. 24 Valerius Terminus, ch. 11; Spedding, v. 3, pp. 235–41. 25 My example, not Bacon’s. His involved reproducing the color white in any material, including liquids.

Induction in the Socratic Tradition

167

To solve his problem Bacon turned to three concepts he found in Aristotle—kata pantos, katholou proton, and formal cause.26 A property that is true kata pantos is true for all members of a class. But a property that is true katholou proton, is true of all and only all members of a class. Thus a proposition predicating a katholou proton property is convertible; that is, subject and predicate can be swapped. All triangles have angles that sum to 180°, and any plane polygon whose angles sum to 180° is a triangle. This suggests a rule: If you want a polygon whose angles sum to 180°, make a triangle. But even if the properties are katholou proton, a rule like that may not be useful. Even if you have found several properties that counterpredicate, you need to know which is “more original.”27 It is not enough to know that properties “cluster and concur,”28 it is important to identify which is the cause. But which cause? Bacon dismissed the final cause as inapplicable in cases outside of human actions. And he thought knowing just the material and efficient causes can provide certainty but not liberty. Such knowledge would help only to “achieve new discoveries in material which is fairly similar.”29 What is needed, Bacon says, is to identify what is “formative,”30 what is the “form or formal cause,”31 what the “received philosophies” call the “true difference.”32 To find this Form (the term is often capitalized in Novum Organum), this formal cause, Bacon proposes that the researcher first gather instances, and counter-instances against which they can be compared. Such comparisons are used to identify a genus. Further comparisons, especially those guided by some helpful rules, will identify the differentia and consequently the formal cause, the Form, that which makes something the kind of thing it is. When, as an example, Bacon investigates the Form of heat, he concludes 26

Valerius Terminus, ch. 11; Spedding, v. 3, pp. 236, “This notion Aristotle had in light, though not in use”; Advancement of Learning, bk. 1, sect. 17, para. 12; De Augmentis Scientiarum, bk. 6, ch. 2. In Latin, the first two went by the names de omni and universaliter, respectively, but Bacon preferred either the Greek, as in his published works, or the Ramist forms “rule of truth” and “rule of prudence,” as in Valerius Terminus. 27 Valerius Terminus, ch. 11; Spedding, v. 3, p. 240. 28 Valerius Terminus, ch. 11; Spedding, v. 3, p. 240. 29 Novum Organum, bk. 2, aph. 3, Silverthorne’s translation. 30 Valerius Terminus, ch. 11; Spedding, v. 3, p. 241 31 Valerius Terminus, ch. 11; Spedding, v. 3, p. 239. Cf. Novum Organum, bk. 2, aph. 2. 32 Valerius Terminus, ch. 11; Spedding, v. 3, p. 239. Cf. Novum Organum, bk. 2, aph. 1.

168

John P. McCaskey

that heat is a kind of motion, “an expansive motion which is checked and restrained and acting through particles, expanding in all directions, [etc.]” Armed with this knowledge, he boldly claims, If in any body you can arouse a motion … [of this certain kind], you will certainly generate heat. It is irrelevant whether the body is elementary (so-called) or imbued with heavenly substances; whether luminous or opaque; whether rare or dense; whether spatially expanded or contained within the bounds of its first size; whether tending toward dissolution or in a steady state; whether animal, vegetable or mineral, or water, oil or air, or any other substance whatsoever.33 It is not that there will be this motion and the motion will then make some heat. It is that the motion is heat. If you arouse this motion, you will generate heat—because that is what heat is. This is a part of what Bacon means when he says that knowledge is power. Knowledge of formal cause provides both certainty and liberty. (Notice as well that the final cause in this case ends up being also a material cause and an effective cause, but it is qua formal cause that these provide certainty and liberty. Thus, one way to characterize Bacon’s contribution to science is that he changed formal cause from being a substance to formal cause being reducible to one or more of efficient, material, or final cause.34) Bacon’s conclusion is inescapable. If, in fact, that is what heat is, then if you effect that motion, you effect heat. If Socrates could find the form—the formal cause—of fineness (kalon), then wherever the cause was found, there would be fineness, whether in a stone or a plank or a man or a god or any action or any lesson—in anything. The conclusion becomes true by the very definition of the term, by the very essential nature of the concept (of the notio in Bacon’s language). Bacon, however, did not say his conclusion was true “by definition.” Somewhere between writing his first notes in or around 1603 and others in 1607 and 1608, Bacon came to say his conclusion was trustworthy because 33

Novum Organum, bk. 2, aph. 21. Italics in Bacon’s original. The proposal here should go a long way toward reconciling what many commentators have thought to be tensions or inconsistencies in Bacon’s thought. I suggest that the tensions are really false dichotomies, artifacts created by scholars trying to put Bacon into their own this-or-that buckets rather than understand him as participating in a Renaissance conversation already underway about the nature of causes, induction, and productive powers. For a spirited cataloging of such artifactual problems, see “Francis Bacon and the Progress of Knowledge,” Journal of the History of Ideas, 53, no. 3 (1992), by Brian Vickers, who is himself not immune to the siren of artifactual dichotomizing.

34

Induction in the Socratic Tradition

169

it was reached by “a true induction:” Bacon does not make the connection between his method and the term “induction” in Valerius Terminus, written in or around 1603. The Advancement of Learning of 1605 only hints in the direction. The association appears in the manuscript Partis Instaurationis Secundae Delineatio et Argumentum of 1607 and is strong in Cogitata et Visa de Interpretatione Naturae, also of 1607. I speculate that he picked up the term from interactions with William Harvey, who learned a similar method at the medical school of Padua, a method Harvey called regula Socratis, “the rule of Socrates.” But whether from Harvey, Wilson, another humanist,35 or even Aristotle,36 Bacon came to the view that his universal claim was true by induction, and by that he meant a compare-and-contrast method that results in identifying the true cause, the essential nature, the Form of something. The identification does result in a definition, but a certain kind of definition, a causal, essential one, not just a nominal one. Bacon was tracing the same steps Socrates had, and it was surely these to which he referred when he said, “[The correct procedure] has not yet been done, nor even certainly tried except only by Plato, who certainly makes use of this form of induction to some extent in settling on definitions and ideas.”37 3 William Whewell The last major induction theorist to work in the Socratic tradition was William Whewell. (I will here skip over but will return later to John F. W. Herschel. I will also skip Thomas Reid.) As with others in the tradition, for Whewell induction is a process of classifying and defining. He presumes, that is, that induction is a progression from particular things or groups of things to universal concepts, and only derivatively a progression from particular statements to universal statements. To understand his theory of induction, we must understand the basic outline and terminology of his overall theory of conceptual knowledge. Whewell claims that his whole philosophy rests on recognition of the difference between thoughts and things. Our Thoughts are something which belongs to ourselves; something which takes place within us; they are what we think; they are actions of our minds. Things, on the contrary, are 35

William Temple, England’s leading Ramist, is another candidate. Bacon knew his Aristotle more than he is given credit for. In about a page of introductory remarks to the Novum Organum (in the Distributio Operis), Bacon uses or cites technical terms or issues in recent Aristotelian scholarship forty-one times. 37 Novum Organum, bk. 1, aph. 105, Silverthorne’s translation. 36

170

John P. McCaskey

something different from ourselves and independent of us; something which is without us; they are; we see them, touch them, and thus know that they exist; but we do not make them by seeing or touching them, as we make our Thoughts by thinking them; we are passive, and Things act upon our organs of perception.38 These “organs of perception,” however, do not themselves provide us with perceptions, merely with sensations. Sensations are given a perceptual form, automatically, by means of a few fundamental ideas, such as space and likeness, with the result that we perceive objects: “Perception is Sensation, along with such Ideas as make Sensation into an apprehension of Things or Objects.”39 From this apprehension of objects, knowledge is built up hierarchically, using conceptions. We gather knowledge from the external world, when we are able to apply, to the facts which we observe, some ideal conception, which gives unity and connexion to multiplied and separate perceptions… Our conceptions, thus verified by facts, may themselves be united and connected by a new bond of the same nature; and… man may thus have to pursue his way from truth to truth through a long progression of discoveries, each resting on the preceding, and rising above it. Each of these steps, in succession, is recorded, fixed, and made available, by some peculiar form of words; and such words, thus rendered precise in their meaning, and appropriated to the service of science, we may call Technical Terms.40 Thus, conceptions bind facts together, and words (or technical terms) fix those conceptions and make then usable. Finally, to round out Whewell’s terminology of items in the cognitive hierarchy: A second conception, broader than another, is called an idea. The difference between conception and idea (when Whewell makes one), is hierarchically contextual, like that between species and genus. What is an idea at one level can be a conception at another. An idea, such as space or causality, broader than all or nearly all other conceptions is one of the above-mentioned fundamental ideas. 38

Philosophy of the Inductive Sciences, 2nd ed. (London: John Parker, 1847), bk. 1, ch. 2, sect. 1, “Thoughts and Things”; v.1, p. 17. Whewell’s emphases. 39 Philosophy, 2nd ed., bk. 1, ch. 2, sect. 10, “The Fundamental Antithesis inseparable”; v. 1, p. 43. Cf. bk. 8, ch. 1, art. 2, “Unity of the Individual”; v. 1, pp. 467–8. Whewell’s capitalization in text and title. 40 Philosophy, 2nd ed., bk. 1, ch. 3, art. 1; v.1, p. 51. The first two emphases are mine, the latter Whewell’s. The spelling is Whewell’s.

Induction in the Socratic Tradition

171

The way in which perceptions, things, facts, conceptions, terms, ideas, and fundamental ideas are structured into a body of scientific knowledge involves two complementary processes, the explication of conceptions and the colligation of facts. Like analysis and synthesis, or differentiation and integration, explication and colligation are not necessarily sequential, either temporally or logically. They are simply two complementary, primary processes involved in scientific knowledge. To explicate a conception is to clarify it by identifying what it contains, by “unfolding” it, as Whewell often says.41 This may include, to begin, surveying and examining examples. When Whewell explicates the conception symmetry,42 he lists as examples the right and left sides of animals and the three faces at the summit of some crystals. He also identifies several kinds of symmetry: simple, triangular, tetragonal, pentagonal, and oblong. To explicate is also to identify implications. One implication of symmetry is that symmetrical members are affected in like ways by like circumstances. An implication of the conception of the earth as a globe43 is that the earth casts a circular shadow, as during a lunar eclipse. Another task of explication is to determine in what way a conception is an instance or modification of a more general idea. The result of all these considerations may be a definition. “The Definition gives the last stamp of distinctness to the Conception; and enables us to express, in a compact and lucid form, the … propositions into which the … Conception enters.”44 Note that the definition is the final, not the initial, step. “The Conception must be formed before it can be defined.”45 In fact, “though Definition may be subservient to a right explication of our conceptions, it is not essential to that process.”46 The essential part of explication is the identification of the constituent facts included in the conception.

41

Philosophy, 2nd ed., bk. 11, ch. 1–2, sect. 1; vol. 2, pp. 3–11. Philosophy, 2nd ed., bk. 7, ch. 1, art. 1, “Explication of the Idea of Symmetry”; v. 1, p. 439. 43 Philosophy, 2nd ed., bk. 11, ch. 6, art. 11; v. 2, p. 84. Cf. also the fold-out “Inductive Table of Astronomy.” 44 Of Induction, with Especial reference to Mr J. Stuart Mill’s System of Logic (London: 1849), reprinted in Butts, Theory of Scientific Method, ed. Robert E. Butts (Hackett, 1989) as “Mr. Mill’s Logic,” §35, p. 284. See also Philosophy, 2nd ed., bk 11, ch. 2, sect. 2, “Use of Definitions”; v. 2, pp. 11–16. 45 Mr. Mill’s Logic, Butts, p. 284. Whewell’s emphasis. 46 Philosophy, 2nd ed., bk. 11, ch. 2, art. 9; v. 2, pp.13–14. Whewell’s emphasis. Fundamental Ideas cannot be defined. They are simply acknowledged in “self-evident 42

172

John P. McCaskey

Colligation is the complementary process of “binding”47 facts together. Whewell stresses that it is not just that “we find something in which the facts resemble each other.”48 A conception is not merely a binding of multiple instances of a common attribute. It is rather a cognitive binding of the facts themselves—not just the common attributes, not just the definition, but indeed all the attributes and even propositions associated therewith. The conception of universal gravitation, for example, includes the fact of heliocentric motion, includes the fact of the precession of the equinoxes, includes the conception of terrestrial weight, and so on.49 This is why Whewell says explication is an unfolding. It is an exposing of what has already been bound together in the colligation. The process of colligation is a normative process. It can be done properly or improperly, and Whewell calls the proper method induction. “Induction is a term applied to describe the process of a true Colligation of Facts by means of an exact and appropriate Conception.”50 The first step in an induction—in a successful colligation, a successful binding—is selection of the broader (possibly fundamental) idea that contains the facts under investigation. Before an induction of planetary observations can proceed, for example, it must be decided whether these observations are instances of physical motion or are instances of supernatural whim. Thus, an induction presupposes that all the observations are instances of one already known universal. An induction is not the creation of a new generalization per se. It is the narrowing of an already existing generalization. Every conception is, for Whewell, a modification of an existing (possibly axiomatic) idea. Ultimately, all conceptions are modifications of space, the inescapable, fundamental idea presupposed in the very act by which we perceive objects. Once the facts and the broader-level idea have been identified, the first step of colligation is complete. The second step is the construction of the conception. This involves a creative act that Whewell calls invention. He observes that such invention is often performed by means of hypotheses—“by calling up before our minds truths,” that Whewell calls “Axioms.” Philosophy, 2nd ed., bk. 11, ch. 2, sect. 3, “Use of Axioms”; v. 2, p. 16–23. Also bk. 1, ch. 2, sect. 3; v. 1, p. 21. 47 Philosophy, 2nd ed., bk. 11, ch. 1, 2:5. Also bk. 11, ch. 4, art. 1; v. 2, p.36. Also bk. 11, ch. 4, art. 11; v. 2, p. 45. 48 Mr. Mill’s Logic, Butts, p. 284. Whewell’s emphasis. 49 Philosophy, 2nd ed., bk. 11, ch. 6, art. 1; v. 2, p. 75. Whewell himself uses such italics when making this point. 50 Philosophy, 2nd ed., “Aphorisms Concerning Science,” aph. 13; v. 2, p. 468; Whewell’s emphases.

Induction in the Socratic Tradition

173

several suppositions, and selecting that one which most agrees with what we know of the observed facts.”51 How does the discoverer select from among the invented hypotheses? Before Whewell answers this, he stresses that a colligation, the formation of a conception, can still be meritorious and useful even if erroneous. The task of the colligation is to bind the facts together so that they can be cognitively manipulated as a unit. He offers the example of fuga vacui, nature’s abhorrence of a vacuum. Water rising in pumps, the operation of a bellows, an infant’s sucking action, respiration in animals, and many other facts were usefully bound together by this conception, even though aspects of the conception were later found erroneous. With this preliminary made and stressed, Whewell proceeds to offer criteria for the testing of hypotheses. His tests for hypotheses include the following. First, an induction must be consistent with the facts. This consistency must be overwhelming, but not necessarily absolute. Whewell cites the orbit of Uranus. “If we find that Uranus … deviates from Kepler’s and Newton’s laws, we do not infer that these laws must be false; we say that there must be some disturbing cause.”52 As mentioned above, a valid hypothesis must also be a modified instance of a broader idea. A valid hypothesis must also be consistent with whatever facts follow deductively from it.53 Whewell furthermore claims that “our hypotheses ought to foretel phenomena which have not yet been observed; at least all phenomena of the same kind as those which the hypothesis was invented to explain.”54 For example, “the Epicyclical Theory of the heavens was confirmed by its predicting truly eclipses of the sun and moon, configurations of the planets, and other celestial phenomena.”55 But Whewell then, famously, goes further: The evidence in favour of our induction is of a much higher and more forcible character when it enables us to explain and determine cases of a kind different from those which were contemplated in the formation of our hypothesis. The instances in which this has occurred, indeed, impress us with a conviction that the truth of our hypothesis is certain. No accident 51

Philosophy, 2nd ed., bk. 11, ch. 5, art. 6; v. 2, p. 54. Criticism of Aristotle’s Account of Induction (Cambridge: 1850), reprinted in Butts, pp. 315–6. John H. W. Herschel made the same point in A Preliminary Discourse on the Study of Natural Philosophy (London: 1830), p. 165. 53 Philosophy, 2nd ed., bk. 11, ch. 6, art. 18; v. 2, p. 93. 54 Philosophy, 2nd ed., bk. 11, ch. 5, art. 10; v. 2, pp. 62–3. Whewell’s emphasis and spelling. 55 Philosophy, 2nd ed., bk. 11, ch. 5, art. 10; v. 2, p. 63. Whewell’s emphasis. 52

174

John P. McCaskey

could give rise to such an extraordinary coincidence.56 Whewell gives a special name to this kind of evidence. He calls it “Consilience of Inductions.” He gives as an example the fact that Newton’s inverse-square law of universal gravitation, developed to explain orbits, turned out to explain something seemingly unrelated, the precession of the equinoxes.57 Whewell believes consilience to be one of the most powerful confirmations that a hypothesis can have. He says consilience has never supported a hypothesis later found to be false.58 Consilience gives rise to Whewell’s final criteria, simplicity. One hypothesis that encompasses multiple, seemingly unrelated, phenomena is simpler and better than multiple independent hypotheses. All these criteria—agreement with facts, prediction, consilience, simplicity—are not arbitrarily chosen. They are direct results of Whewell’s theory that an induction is the successful construction of a conception. A conception, by the nature of its universality must include all facts of the class, not just those already observed; therefore a valid induction must be able to make predictions about the unobserved. Because a conception includes all attributes of a fact, including its relations, the conception must be consistent with deduced implications. The discovery of a consilience demonstrates that facts earlier included in two or more conceptions are in fact instances of a single conception, strengthening and broadening the conception and increasing simplicity and the unity that is the goal of the binding. Since an induction is a successful construction of a conception, Whewell’s criteria for a valid induction follow from the nature of a conception. Whewell frequently says that every valid induction is accompanied by a new properly formed conception. The “Inductive Step” is “the Invention of the Conception.”59 “In every inference by Induction, there is some Conception superinduced upon the Facts.”60 This conception includes the facts, but it is not merely the facts. Something is added, a bond that holds the facts together.61 The group of facts is then “seen in a new light”62 56

Philosophy, 2nd ed., bk. 11, ch. 5, art. 11; v. 2, p. 65. Whewell’s emphasis. Philosophy, 2nd ed., bk. 11, ch. 5, art. 11; v. 2, p. 66. 58 Philosophy, 2nd ed., bk. 11, ch. 5, art. 11; v. 2, p. 67; Mr. Mill’s Logic, Butts, p. 295. 59 Philosophy, 2nd ed., bk. 11, ch. 6, art. 17; v. 2, p. 91. 60 Philosophy, 2nd ed., bk. 11, ch. 5, art. 11; v. 2, p. 65. First emphasis mine, second Whewell’s. 61 Philosophy, 2nd ed., bk. 11, ch. 6, art. 3; v. 2, p. 77. 62 Philosophy, 2nd ed., bk. 11, ch. 6, art. 12; v. 2, p. 85. Whewell’s emphasis. 57

Induction in the Socratic Tradition

175

and takes on “a new shape.”63 The penultimate step (a definition may be the ultimate) is creation or new application of a word, phrase,64 or technical term. Whewell offered ninety pages65 on how such terms have been and should be formed. He himself coined several (including scientist, physicist, anode, cathode, and ion). It is by the creation of such conceptions— completed by creation or application of a word or phrase—that inductions, for Whewell, are performed. 4 Whewell, Bacon, Socrates Note some similarities and differences between Whewell’s system and those of Bacon and Socrates. The latter two took for granted that we already have a concept, that we can identify its instances, and that we can readily get a description (or overlapping descriptions) that provisionally function as a definition. Then, in order to remove ambiguity, add precision to our knowledge, and raise it to the level of scientific understanding—to the level of Aristotelian epistƝmƝ—we use induction to identify the essence, the formal cause, of what we are studying. Once we have identified that essence, we can legitimately make some unqualified universal statements. Whewell, on the other hand, drew attention to the fact that, in much scientific inquiry, the researcher in fact does not begin with a ready-formed concept. The forming of the concept (or “conception”) itself can, he claims, be a crucial part of scientific discovery. For example, Newton’s integration of facts about falling apples, revolving moons, planetary orbits, tides, comets, and so on did not merely result in better definitions of old concepts such as gravitas but, more importantly, in the formation of the new concept mass. Newton had at hand some facts, but the facts were not cognitively held as a single unit. They were expressed in statements, paragraphs, lists, tables, even whole chapters and books. Newton’s inductive breakthrough, Whewell says, was to integrate (“colligate”) a variety of facts into a single cognitive unit, assign to it a term (“technical term”), and then, as the final step, identify its definition. Bacon stresses the importance of forming one’s concepts from the ground-up, rising slowly. Whewell, on the other hand, thinks all concepts are formed by filling in a conceptual hierarchy that has individual perceptible three-dimensional things at the bottom and axiomatically known 63

Philosophy, 2nd ed., bk. 11, ch. 6, art. 3; v. 2, p. 77. Mr. Mill’s Logic, Butts, p. 271. 65 Philosophy, 2nd ed., “Aphorisms concerning the Language of Science”; v. 2, pp. 479–569. 64

176

John P. McCaskey

concepts at the top. All definitions are then, for him, formed of genus and differentia, even if the genus is something as broad as “thing.” We often speak this way: “What is that?” “Oh, it’s something [genus] that … [differentia].” For Whewell, more so than for Socrates and Bacon, the boundaries of concepts could be refined as a science matures. Socrates assumed (or played along as if to assume) that the men who were supposed courageous really were. Bacon assumed that, in seeking the definition of heat, we already knew what to include as instances and what to include as counterinstances. But Bacon included spicy food as an instance. We would not. He did not indicate how exactly, if at all, his theory could accommodate dropping spicy food from the class.66 Whewell, on the other hand, thought it not only untroubling but positively necessary and useful that, in the process of induction, we clarify and sometimes even move the boundaries of our classifications. All inductions, for Whewell, end with forming—or reforming—a concept. Appropriately, then, he does not automatically abandon a concept when a counter-instance, or class of counter-instances, is discovered. Against the twentieth-century model, for Whewell, at least in some stages of a science’s maturation, a counter-instance does not necessarily invalidate an inductive conclusion. He thought fuga vacui was a valuable concept on the road to our understanding of gases.67 A large difference between Socrates and (especially) Bacon is that Socrates gave no guidelines on how one should proceed in an inductive search for an essence. He merely frustrated his interlocutors until they walked off. Bacon provided explicit rules. But to appreciate the purpose of those rules and the context in which Bacon developed them, we must go back again to ancient Greece. 5 Handbooks on Induction In ways obscure to us now, the back-and-forth, give-and-take that we see exemplified in Socratic dialogues evolved in Athens into a pedagogic, dialectical sport, something like our high-school debate competitions. Aristotle’s early work, the Topics, is a handbook for those engaged in such competitions. The handbook is a catalog of maneuvers and the associated 66

Daniel Schwartz claimed to me, and I think rightly, that Novum Organum bk. 1, aph. 118 and bk. 2, aph. 25 indicate Bacon does believe his theory accommodates such changes. 67 For John Herschel’s insistence that one should not commit to classification boundaries too soon, see Preliminary Discourse, p. 138.

Induction in the Socratic Tradition

177

principles that make those maneuvers effective. Each maneuver-andprinciple pair came to be called a topos, later, in Latin, a locus, literally a place. The reason for the name, too, is obscure, but because the term “topic” took on such specialized meaning, the etymology matters little. (I envision something as mundane as a teacher laying out on the ground potshards with notes, each in its place, its own topos, as we would place notecards on a table, and instructing a student to retrieve a particular notesshard based on the competitive situation he confronted.) Nowadays, the topics are often introduced by saying they are a kind of “informal logic” and noting that the strategies can be persuasive but often do not adhere to standards of formal logic. This is misleading if it suggests that topics-logic is sloppy logic, a kind of arguing that is not fully valid and is useful only for swaying the gullible. Aristotle did not see it this way. Much is made of Aristotle saying that, in dialectical reasoning, a premise need not be true. It can merely be what is widely believed. But normally, Aristotle’s point is not that one should persuade the gullible by reasoning from premises they foolishly hold. His point is usually that a debate regularly begins with some opinion held by a majority or by those considered wise68 and then proceeds to test whether that opinion leads to any contradiction. He says, without suggesting his view is unconventional, that the technique he presents in his handbook are equally applicable to conversations, to one’s own mental training, and to philosophical science. The techniques allow one to discern “truth and falsehood on every point.”69 At times, Aristotle’s Topics seems like a repetitive grab-bag. At the highest-level, however, the organization is simple, plain, and profound. When one is faced with assessing the truth of any proposition, the nature of the predication is the primary issue. Aristotle identifies four types of predication: the predicate is an accident, a genus, an idion (later, proprium in Latin; distinguishing property), or a definition. In Aristotle’s treatise, all of its eight books except the first and last, are organized around this fundamental division. Books 2 and 3 treat accidents, book 4 treats genus, and so on. Nothing is more fundamental to Aristotelian reasoning— whether in gymnastic debate, in one’s own thinking, or in science—than identifying this aspect of a statement’s predicate. For example, the very first topos is to check whether an opponent has predicated as an accident something whose relation is not in fact accidental.70 68

Topics, bk. 1 ch. 1; 100b23. Topics, 101a26–7, a37. 70 Topics, bk. 2, ch. 2; 109a34. 69

178

John P. McCaskey

In the statement, “The sky is blue,” the nature of the predication is unstated. It must be supplied either by the context or by qualifiers. And the scope varies whether one says, “The sky is blue today,” “The sky is naturally blue,” “The sky is always blue,” or “The sky is blue, roses are red, bananas are yellow.” Like any cognitive content, predication is contextual. So, to evaluate Euthyphro’s claim that it is pious to prosecute wrongdoing, even if done by one’s own father, one must identify the nature of the predication. By considering the context, Socrates can see that Euthyphro has not actually proposed a definition of piety but has instead given an example. The predication—using the framework Aristotle describes in the Topics book 2—was that of a particular accident not of a universal accident, let alone that of a universal genus, idion (pl. idia), or definition. But Socrates wants a different sort of predication. Euthyphro proposes, “Piety is what pleases the gods.” This has the potential to be predication of an idion, a characteristic distinctive to piety and only to piety, and Socrates begins subjecting it to some tests, tests like those that Aristotle codifies in the Topics book 5. Unfortunately for Euthyphro, the proposal fails the tests, because the predicate cannot be made unambiguous in the ways necessary. Socrates proposes that he and Euthyphro start over; he proposes they start with predication of a genus. Aristotle might later say to his students: Socrates and Euthyphro jumped too quickly from book 2 to book 5, too quickly from accidental predication to distinguishing predication; they should have first identified the genus. Socrates proposes that all acts of piety are just, that piety is a kind of justice. Euthyphro readily accedes and the interlocutors are ready to proceed to definitional predication—book 6 of the Topics—when Euthyphro decides he is no longer having fun and begs his leave. I have argued elsewhere71 that, for Aristotle, epagǀgƝ is a compareand-contrast method used to identify idia, the distinguishing characteristics that counter-predicate with their subjects. Maybe that is too narrow and the term covered the quest for universal accidents as well, or maybe my proposal is too broad and Aristotle (or at least others in antiquity) would have the method cover only the identification of defining characteristics. The evidence is too slight to be completely sure. But whatever the scope, epagǀgƝ in antiquity was a logic of classification, a process of compareand-contrast used to form, refine, and define one’s concepts, especially predicate concepts. Because it was so, it was the foundational method by which valid general and universal statements could be made. In the ancient 71

“Freeing Aristotelian EpagǀgƝ.”

Induction in the Socratic Tradition

179

world, Aristotle’s Prior Analytics was a handbook for deductive logic, and the Topics a handbook for classificatory, or inductive, logic. Interest in this latter sort of logic waned after the Alexandrian Neoplatonists recast induction as a kind of propositional inference like but inferior to deduction and whose definitive treatment was supposedly Prior Analytics B 23. But later, especially after the 1540s, interest in induction and the Topics—and the Posterior Analytics, where the logic of definitions is central—increased. It was in this period that Nifo said there were now important questions about what induction is. In the next generation, Wilson documented the two kinds of induction. And in the next generation, William Harvey, studying under the new humanist Aristotelians in Padua, learned his compare-andcontrast method for identifying essences, the method he called the rule of Socrates. Aristotle’s Topics and Posterior Analytics were thus the main treatises on inductive logic until 1620, when Harvey’s older contemporary Francis Bacon published his Novum Organum. Book 2 of that work replaced Topics book 5 as the most complete set of rules for identifying distinguishing characteristics and, as Bacon saw it, for going even further and identifying a Form, a formal cause, an essence, a definition. As with so many momentous books, it is remarkable how large are the parts of Novum Organum seldom read anymore. We frequently enough reprint and re-read the sections in book 1 about the idols, but those sections merely fleshed out a known problem in Renaissance philosophy of mind.72 Bacon’s real innovation was to show how a valid solution to that problem would also allow man to make universal statements of practical use in (what we would call) science, technology, and engineering. That solution comes in the much longer book 2. Book 2 begins with the claim that the goal of productive human activity is, primarily, to generate freely and with certainty some nature (natura) in a given body that does not have—and may never have had— that nature. The nature might be heat, transparency, strength in glass, a particular color. Bacon concurs with the common judgment of natural philosophers that effecting a given nature requires a knowledge of causes. But, he says, the usefulness of knowing merely efficient and material causes limits one’s power to materials that are similar. And final causes are irrelevant in physical sciences. The key is to find the formal cause, or 72

Concepts (notiones, conceptus) were conceived to be mental images or representations (imagines, species). An idol was a faulty representation, a “vain phantasm,” a false image, a notion hastily made or ill-defined.

180

John P. McCaskey

“Form, or true difference, or causative nature or the source of its comingto-be.”73 Sadly, he says, others regard the search for formal causes as useless, and man’s progress is thus limited. Bacon puts his call in italics: “find another nature that is convertible with a given nature, and yet is a limitation of a better-known nature, as of a true genus.”74 This is done by a “true and proper induction.”75 In a work 313 pages long, Bacon’s example of finding the nature of heat takes fifty-four pages. He has shown how comparing and contrasting can identify a genus and then identify the distinguishing differentiae. And as mentioned earlier, he then lays claim to a universal and indisputable statement: Whenever motion of the sort he describes is effected, heat is produced, because heat is that motion. But his example has been illustrative only. He finally gets to his specific guidelines for a true and proper induction. He provides 139 pages—over forty percent of the whole work— describing twenty-seven kinds of instances (more with all his subcategories) whose comparisons are particularly useful in performing such an induction: solitary instances, instances that have nothing in common with other particulars except for the one nature under investigation; parallel instances, such as feet in animals and fins in fish; instances of divergence, in which two properties usually found jointly, such as heat and light, appear by themselves; crucial instances, which can indicate which of two theories is correct; instances of dominance, of which there are nineteen kinds and which are motions that can be precisely measured. Unfortunately, the handbook is incomplete. Bacon says that he has yet to add sections explaining aids to induction, how to refine an induction,76 how to adapt induction to concrete subjects, and more. Yet what was completed was already unwieldy. In the early nineteenth century, one of Bacon’s vigorous advocates, John Herschel, in his Preliminary Discourse on the Study of Natural Philosophy, gently mocked those who committed themselves too zealously to categorizing instances into Bacon’s twentyseven.77 Herschel reordered and simplified Bacon’s list and placed that list in a broader framework of inductive experimentation. 73

Book 2, aph. 1. “autem naturae Formam, sive differentiam veram, sive naturam naturantem, sive fontem emanationis.” “These are the words we have that come closest to describing the thing”; “ista enim vocabula habemus, quae ad indicationem rei proxime accedunt.” 74 Novum Organum, bk. 2, aph. 4. 75 Novum Organum, bk. 2, aph. 10. 76 See note 66 above. 77 Preliminary Discourse, pp. 183–4.

Induction in the Socratic Tradition

181

For Herschel, induction has three steps. The first78 is the observation of facts and collection of instances. And Herschel offered specific criteria, such as variety and reproducibility, for judging the value of facts. The facts need to be recorded, reviewed, and reduced to measurements, and imprecision in measurements has to be accounted for. Classification is the second step.79 Names must be assigned, but initial classifications can and often should be tentative. The classifications will get finalized in the third step, the induction proper. The first stage80 of that last step is identification of proximate causes and inductions of the lower levels. Here, Herschel expands Bacon’s three tables a little but then reduces Bacon’s twenty-seven types of prerogative instances to ten rules, such as to reject candidates that are not present, not rule out a cause just because its mechanism is not discernible, consider contrary facts, and isolate one factor and test with an experiment. The second stage of the third step is to extend the inductions to higher levels. Here the source material is not experiments and other direct sensory experience, but the results of the lower-level inductions. Herschel explains how to address problems distinct to these higher-level inductions. Among other things, he cautions against wanton hypothesizing. The frontispiece to Herschel’s book included a portrait of Bacon, but Herschel did not just repeat Bacon’s guidelines. He regularized them, made them more mathematical, and in general updated them. He had, after all, the benefit of looking back on two centuries of inductive science. Though the procedure Herschel recommended was different than those recommended by Bacon or Aristotle, induction was for him as it was for them: the “juxta-position and comparison of ascertained classes, and marking their agreement and disagreement,” so as to obtain a “just and accurate classification of particular facts, or individual objects, under general well considered heads,” and continuing to do so with ever higher levels of generality until “at length, by considering the process, we arrive at axioms of the highest degree of generality of which science is capable.”81 These classifications make possible scientific laws when they are based on verae causae, causes that truly make something the kind of thing it is.

78

Preliminary Discourse, ch. 4. Preliminary Discourse, ch. 5. 80 Preliminary Discourse, ch. 6. 81 Preliminary Discourse, p. 102. Herschel’s hyphenation. 79

182

John P. McCaskey

The treatise on induction by Herschel’s good friend William Whewell82 was the most theoretical in the Socratic line of induction, less of a step-by-step cookbook than Herschel’s. Whewell’s criteria for good inductions, such as consilience and factual agreement, are more grounded in a theory that relates the formation of concepts to the establishment of universal predication. The man after Herschel most famous for developing concrete guidelines for induction was not Whewell, but John Stuart Mill. Mill reduced inductive criteria to just four “methods of experimental inquiry,” but he completely swapped out the theoretical foundations being developed by Herschel and Whewell, turned induction—as the medieval Scholastics had done—from a logic of classification back into a (usually defective) logic of propositional inference, and concluded that “anything like a scientific use of the method of experiments, in these complicated cases [he was discussing medicine but went on to list many others], is out of the question.”83 The better scientists of the future would, Mill was sure, be using deduction, not induction. For a while, at least, those scientists stayed with what was working. In fact, the zenith of science in the Baconian framework was the period from Herschel in the early nineteenth century until, let us say, John Maynard Keynes in the early twentieth. Though Keynes is now better known for his work in economics in the 1930s, his 1921 A Theory of Probability made a major contribution to the turn away from the Baconian conception of induction. In the book, Keynes noted that even though people do not associate David Hume with induction, they should.84 6 Examples of Socratic Induction in Science Whewell called his three-volume history a history of the inductive sciences; similarly with his three volumes on philosophy. But in all these volumes he found no need to discuss Hume, the uniformity principle, probability, Bayes, or white swans. These were just not part of his conception of induction or his intended readers’. One major difference between their conception and ours is that nowadays induction is taken, by its very essence, to be a kind of uncertain inference, yet Baconians thought it was 82

On their relationship see Laura J. Snyder, The Philosophical Breakfast Club (New York: Crown, 2011). 83 John Stuart Mill, System of Logic, Ratiocinative and Inductive (1843), bk. 3, ch. 10, sect. 8. 84 John Maynard Keynes, A Treatise on Probability (London: Macmillan and Co, 1921), p. 272.

Induction in the Socratic Tradition

183

induction that provided scientific certainty. Baconians were always a little cautious about the syllogism, since it seemed to be about words and not things. (Note that while Mill was debating induction with Whewell, parallel conversations were underway elsewhere about whether the syllogism was a valid form of inference at all. See, for example, discussions about quantification of the predicate. Also, any inability to prove a uniformity principle was, at first, considered as much a threat to syllogistic inference as to induction.) Let me briefly review how, in four cases considered in the nineteenth century to be hallmarks of inductive science, induction produced unqualified certainty.85 For his textbook example of inductive science in action, Herschel chose William Charles Wells’ investigation into the nature of dew, an investigation widely admired.86 Wells began by limiting his subject to what is “properly … called dew.”87 Herschel describes that as “the spontaneous appearance of moisture on substances exposed in the open air when no rain or visible wet is falling.”88 Wells had a nominal definition, sought the cause of his subject (the “real cause” or “vera causa,” Hershel or Whewell would say), and could—once that cause was found—replace his nominal definition with a causal or essential one. Using a wide range of experiments, involving many temperatures, weather conditions, seasons, times of day, locations, and materials, and by recognizing that the cause is a specific instance of known general laws of heat, Wells was able to identify dew as a condensation of water vapor that occurs when the dewed surface is cooled by radiation faster than warmed by conduction. This explains dew’s complex dependency on thermal conductivity, cloud cover, wind speed, and other factors. The boundaries drawn by the new causal definition allow more universal and certain claims than were possible with the earlier, nominal definition. It could now be said, for example, that dew cannot form on certain materials. If water was found there, it could not be what was now classed as dew. Sure enough, later in the nineteenth century, some botanists studied drops of water found on plants in the morning, superficially similar to dew. By the earlier classification, they were dew. But these drops, it was 85 For more on three of these four, see John P. McCaskey, “When Induction Was About Concepts,” Concepts, Induction, and the Growth of Scientific Knowledge, Richard Burian and Allan Gotthelf, editors (forthcoming). 86 Preface to William Charles Wells, An Essay on Dew and Several Appearances Connected with It, edited, with annotations by L. P. Casella (London: 1866) 87 Wells, Dew, pt. 1, sect. 1. 88 Herschel, Preliminary Discourse, sect. 163. Herschel’s emphasis.

184

John P. McCaskey

discovered, had a different cause, the forcing of liquid out through pores. Botanists chose to call these drops not dew, but guttation. Based on similarity of symptoms, certain ailments were, as early as Celsus (c. 25 BC–50 AD), identified as cholera. But into modern times, little was understood of the disease. General statements could be made about it, but few universal, unqualified, exceptionless ones could be. By the midnineteenth century, physicians were grouping cases of cholera into categories. The so-called Indian type of cholera was particularly severe, frequently fatal, and often epidemic. By the 1870s, it was thought to be caused by a “specific organic poison.”89 In 1884, the German Robert Koch claimed to have identified the poison: a particular bacillus shaped like a comma. But the truth of his theory depended on what one meant by “cholera.” Koch himself very soon began distinguishing “real (wirklich, echt)” cholera from other diseases classified as cholera. By the early 1890s, reference works were adopting Koch’s distinction and by 1910, the presence of Koch’s comma bacillus, Spirillum cholerae asiasticae, was the defining characteristic of cholera. A nominal definition that allowed many general but few universal statements was replaced by a causal, essential (Aristotelian), formal (Baconian) definition. It became possible to say with complete certainty, without reservation or qualification, that if a person is kept away from Spirillum cholerae asiasticae the person positively will not, cannot contract cholera. He may get a bellyache, he may vomit, he may have diarrhea, he may spread his illness to others, and he may die of it, but if what he had was not caused by Spirillum cholerae asiasticae, then he did not have cholera. A host of universal, exceptionless, scientific statements about cholera could now be made. Historians of electrical science say that Ohm’s law, the law that resistance is the ratio of voltage to current, was discovered by Georg Ohm in the 1820s. But that can be misleading, for the three constituent concepts did not yet exist. At the time, one could report how many pairs of copper and zinc plates were in a Voltaic pile, how large each plate was, the dimensions of a wire joining the metals, and how far a nearby compass needle deflected. But the distinctions between electromotive force, voltage, potential, current, power, charge, charge density, and so on were still being worked out. Some conceptions proved inconsistent; some were too poorly defined to be useful. It took a couple decades for the concepts of voltage and current to reach some maturity. Only as they did could Ohm’s theory about 89

John M. Woodworth, The Cholera Epidemic of 1873 in the United States (Washington: Government Printing Office, 1875), p. 8.

Induction in the Socratic Tradition

185

the relationship between compass deflection, wire length, and dimensions of a battery take the form it did. In 1834, Michael Faraday called Ohm’s proposal a beautiful theory but still called it just a theory. In 1843, Charles Wheatstone wrote, “It will soon be perceived how the clear ideas of electromotive forces and resistances, substituted for the vague notions of intensity and quantity which have been so long prevalent, enable us to give satisfactory explanations of the most important phenomena, the laws of which have hitherto been involved in obscurity and doubt.”90 By 1850, Ohm’s theory was being called a scientific law. In 1873, James Clerk Maxwell summarized the history like this: “Here a new term is introduced, the Resistance of a conductor, which is defined to be the ratio of the electromotive force to the strength of the current.”91 Ohm’s Law was now true by definition, resistance defined to be the ratio of voltage to current. Can one simply define scientific laws into existence? Maxwell continues: “The introduction of this term would have been of no scientific value unless Ohm had shewn, as he did experimentally, that it corresponds to a real physical quantity.”92 Ohm’s Law was not established by an application of hypothetico-deductive experimentation. Rather, classifications were worked out, a conceptual framework was constructed, and essential definitions were formulated. To know whether the universal statement applies, we do not now say, “The resistance of this device obeys Ohm’s Law; the resistance of that one does; so too does this other—does the resistance of all devices obey Ohm’s Law?” Rather, we ask, “Is this device a resistor?” If what we are measuring does not obey Ohm’s Law, then what we are measuring is not resistance. What was shown to be true by induction is what was shown to be true by definition. Tides were long identified as the flux and reflux of the seas, and mariners had many general things to say about them. But their cause was, until Isaac Newton, unclear. And after Newton, it was another two centuries before mathematics and mathematical science had advanced enough to make practical use of Newton’s discovery. These advances made possible highly valuable predictions of the rise and fall of the seas. The predictions, however, were not always highly accurate. For another problem presented 90

Charles Wheatstone, “The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit,” Philosophical Transactions of the Royal Society of London 133 (1843), p. 304. 91 James Clerk Maxwell, Treatise on Electricity and Magnetism (Oxford: Clarendon Press, 1873), p. 296, my emphasis. 92 Maxwell, Treatise, p. 296. Maxwell’s spelling.

186

John P. McCaskey

itself. Newton accounted for the celestial factors, but many non-celestial factors can causes bodies of water to rise and fall regularly. There are daily temperature variations, barometric cycles, seasonal rain patterns, seiches, and even man-made causes such as ships’ passages or industrial releases of water. On August 25, 1882, Lord Kelvin, who had by this time done much to promote the mathematical analysis of tides, began an evening lecture by saying, “The subject on which I have to speak this evening is the tides, and at the outset I feel in a curiously difficult position. If I were asked to tell what I mean by the Tides I should feel it exceedingly difficult to answer the question. The tides have something to do with motion of the sea. Rise and fall of the sea is sometimes called a tide; but ...” 93 He proceeded to cite many problems with this definition—with what we may call a nominal definition. Kelvin was here reflecting on the development of tidal science in the two hundred years since Newton proposed what causes the sea to rise and fall and Newton’s successors worked out the physics, mathematics, and data-gathering techniques to make it possible to predict such risings and fallings. And Kelvin had to acknowledge that all that science left him unable to tell the sea-captain for sure where the water level will be at a certain time, because all that tidal science has left temperature variations, barometric cycles, and the coming and going of ships out of the equations. Kelvin returned to his theme, “What are the Tides?” and answered, “I will make a short cut, and assuming the cause without proving it, define the thing by the cause. I shall therefore define tides thus: Tides are motions of water on the earth, due to the attractions of the sun and of the moon.”94 Centuries of inductive research into what causes tides and Kelvin announces the result: A tide is, by definition, caused by attractions of the sun and of the moon. The sea may flux; the sea may reflux; but if some particular fluxing and refluxing has some other cause, it is by definition not a tide. Statements about tides need no longer be just generalizations. They could be unqualified, certain, universal. For they could be deduced from the very definition of a tide.

93

Lord Kelvin (William Thomson), “The Tides: Evening Lecture to the British Association at the Southampton Meeting, Friday, August 25, 1882,” Harvard Classics 30 (Collier and Son, 1910), pp. 287–314. 94 Ibid. My emphases.

Induction in the Socratic Tradition

187

7 Certainty and the Maturity of Concepts95 It is by concepts that we organize our thinking. There is only so much we can do with poorly formed ones, as Socrates’ interlocutors learned. Bacon was explicit: “The syllogism consists of propositions, propositions of words; and words are the tokens of notions. Therefore if the notions [notiones, concepts] themselves—this is the foundation—are confused and rashly abstracted from things, there is nothing firm to what is built above.”96 Concepts are also personal. They are cognitive products of individual minds. There are no concepts outside of minds, and no concept of yours is numerically identical to any concept of mine. There may be similarities, but yours is yours and mine is mine, Ohm’s was his and Maxwell’s his. Concepts are mental integrations of things we observe but their referents are more than the individuals we observed in forming the concept. Concepts, that is, are ampliative. When I say or think, “house,” I am referring to all individual things sufficiently similar and yet sufficiently different from other things—and to all such things past, present, and future, actual and imagined. But concepts are not the referents or the open-ended sets. They are the cognitive processes and the results of those processes. They are mental integrations. As such, they change over time. As an infant, I had a certain concept of soap. Over time, my concept changed. The mental integrations grew wider, deeper, and stronger. I made connections I had not made earlier. I more sharply distinguished boundaries of inclusion. Little by little, I even altered those boundaries. I could have kept the old boundaries, but I got on better in life by doing otherwise. Whether your 95

The reflections in this section have been heavily influenced by my understanding of Ayn Rand’s theory of concepts. See Ayn Rand, Introduction to Objectivist Epistemology, expanded second edition, ed. H. Binswanger and L. Peikoff (New York: Meridian, 1990), first edition (1979). Although I believe my understanding is consistent with Rand’s published work, some scholars more studied in her theories, including some who spoke with Rand about these topics, believe my understanding is flawed. For valuable treatments, see Concepts and Their Role in Knowledge: Reflections on Objectivist Epistemology, ed. Allan Gotthelf and James Lennox (Pittsburgh: University of Pittsburgh Press, 2012). For a theory of induction based on Rand’s theory of concepts that does not rely on a distinction between general and universal statements, as my reflections here do, see David Harriman, The Logical Leap: Induction in Physics (NAL, 2010), especially ch. 1. 96 Novum Organum, bk. 1 aph. 14, my translation. See comparable statements in Advancement of Learning, bk. 2, ch. 13, par. 4; Instauratio Magna, “Plan of the Work”; and De Augmentis Scientiarum, bk. 5, ch. 2, Spedding v. 1, p. 621. For a seventeenth-century translation and comment, see John Webster, Academiarum examen (London: 1654), ch. 4, par. 3, p. 34.

188

John P. McCaskey

concept of soap includes precisely the same integrations, differentiations, classificatory boundaries, clarity, or distinctness as mine, I do not know. If my getting on in life requires that yours and mine are similar and I suspect they are not, I will suggest we each write down our definitions (or consult a third party’s) so that our concepts have at least the same referents. If it serves me better, I might go on modifying mine without concerning myself much with that of anyone else. Koch did that with his concept of cholera. When my concept was immature, there were things I could say about soap that were generally true, but not universally so. The more my concept advanced, the more general could be my statements. Truly exceptionless, unqualified, universal statements required mature concepts not only of my subject, soap, but of predicate concepts as well, of clean, wash, soft, hard, solid, liquid, dissolve, salt, fat, dye, and so on, and so also of my concepts of predication itself. I had to mature to the point where I could distinguish the difference between Aristotle’s accident, genus, idion, and essence. I needed to learn advanced concepts such as every, all, must, and always. To say things that are universally true about soap, my knowledge needed to advance to where I knew something about what makes soap, soap, and to understand differences in kinds of predication. The more I knew of the essential nature, the formal cause, of soap, the larger could be the scope of my generalizations. Now that I have scientific knowledge of soap, now that I have Aristotelian epistƝmƝ, I can make unqualified, exceptionless, universal statements about soap. My concept of soap is now so mature that I can make statements about soap that could be denied only on pain of contradicting my mature definition of soap. I have come to this maturity through many compare-and-contrast operations, ones I have done myself and ones I have heard from reliable informants. There are now unqualified statements I can make that are true by induction and true by definition. (I mean to leave open the possibility of similarly certain and universal statements based on idia that are not definitional.) On similar grounds, I can now make not only general statements, but universal statements, about bachelors, triangles, and prime numbers. When Koch began his work, a physician in Missouri had a concept for the disease he called cholera. So too did a doctor in London. The concepts were similar but not numerically identical. In fact, the mental integrations were substantially different. Both physicians classed as cholera ailments involving nausea, vomiting, and diarrhea. But the London physician had formed strong mental connections to water wells, contagion, and ships from India, that is, to what he had thought were causally related. The

Induction in the Socratic Tradition

189

Missouri doctor, on the other hand, would immediately consider season and what the patient had eaten. Robert Koch would immediately consider bacteria. By the time Koch discovered the comma bacillus, he had used the most rigorous standards of classificatory logic—the most rigorous standards of induction, standards that could be traced back through Whewell, Herschel, Bacon, Aristotle’s Topics, and Socrates’ haranguing—to conclude that for the physician to do his job well, he should have a concept for the intestinal disease caused by that bacteria. So many cases that the London physician knew as cholera were in fact caused by this bacteria, and so many of the symptoms, treatments, and courses were exactly as the Londoner knew them, that Koch was recommending that physicians not say, “But I have cases of cholera not caused by your comma bacillus, so your theory must be wrong,” but to say, “If I just make some small changes to the boundaries of my classification, I can retain and use almost everything I know about cholera and begin making universal and not merely general statements about cholera. And I could become a better doctor.” For the physician in Missouri, many more mental connections needed to be severed and many more new ones formed. But he too found the effort worthwhile. He—or at least his successors—reclassified cases, began making certain claims about how to prevent cholera, and cured more patients. Notice Maxwell’s statement above about Ohm’s Law. Maxwell said “so many conductors have been tested that our assurance of the truth of Ohm’s Law is now very high.” This sounds to us like a claim that a sufficiently large number of experiments have been conducted and enough confirming instances have been found to warrant a high probability that some hypothesized relationship is true. But that is not the situation Maxwell describes in the sentences immediately preceding. He said that enough experiments had been conducted to suggest the value of forming a concept for a property “defined to be the ratio of the electromotive force to the strength of the current.” He continued, “The introduction of this term would have been of no scientific value unless Ohm had shewn, as he did experimentally, that it corresponds to a real physical quantity” (my emphasis now added). When Maxwell then wraps up by saying, “so many conductors have been tested that our assurance of the truth of Ohm’s Law is now very high,” he does not mean that a sufficient number of experiments have provided a sufficiently high correlation. He means many conductors have

190

John P. McCaskey

been found that fit the definition and much good will come to the engineers who class these conductors as resistors. On the first day of a course I teach on the history of scientific method, students read Robert Hooke’s publication of what is now known as Hooke’s Law: force exerted by a spring is proportional to the compression or extension of the spring. Students see that Hooke tested his theory on a remarkable range of materials, forces, and displacements, and students consider whether Hooke had conducted enough experiments, whether he could be certain, whether maybe the next spring might not obey the law. The philosophy students bring up swans and Bayes and Hume and uncertainty and try to outdo each other in their inductive skepticism. Eventually a physics student who had been puzzled and quiet and increasingly uncomfortable joins the discussion: “If it doesn’t follow Hooke’s Law, it’s not a spring. Following Hooke’s Law is what makes a spring a spring.” A semester of philosophers and scientists trying to understand each other has begun, as has a long discussion about what Socrates’ search for the definition of piety has to do with experimentation, scientific knowledge, induction, and certainty. 8 Two Conceptions of Induction There are two conceptions of induction. By the first, which prevailed in antiquity and in the period from Bacon to Whewell, induction is a logic of classification. As such it is a logic by which we abstract and form our concepts. The second prevailed from late antiquity until the Renaissance and then again starting in the late nineteenth century. It holds that induction is a logic of propositional inference. By it we derive universal statements from particular statements. This second takes the work of the first for granted. It assumes we already have concepts of swans and water and soap and asks whether some universal statement about them can be legitimately inferred from particular statements about them. But there is simply no way to know whether all swans are white, all cardinals red, and all zebras striped without standards for classifying things as swan, cardinal, or zebra. The first conception of induction holds that propositions are only as good as the concepts on which they are based. Crude and immature concepts may enable statements that are generally true, but few that are universally so. Propositions are only as good as their constituent concepts, but they can be fully as good as their constituent concepts. By the Scholastic and modern conception of induction, constituent concepts are taken for granted. But by the Socratic conception, concept-formation is a normative process.

Induction in the Socratic Tradition

191

It can be done poorly and it can be done well. If done well, universal propositions become extensions—explications, let us say—of what is contained in the concepts. Yes, evacuation of Spirillum cholerae asiasticae will always cure cholera. Yes, you can say that this is “just” true by the very definition of cholera and of Spirillum cholerae asiasticae. But those definitions were not chosen on whim. They were selected by human discretion for the objective benefits the classification bestowed on the classifiers. The classifications were not arbitrary. Sufficiently good concepts can ground unqualified universal statements, but such concepts do not emerge ex nihilo. Scientists, nay all human beings, pull their cognitive selves up by their bootstraps. A simple concept of soap enables rough generalizations about cleaning, itself a crude concept at first. New observations about soap and about cleaning and about how other materials interact enable refinements to the mental integrations that are the concepts of soap and of cleaning. The process is iterative, or better, spiral. Eventually, a thinker sufficiently concerned with soap will so refine his conception that he can make many exceptionless universal statements about soap that he could never have made using his earlier concept. Concepts of increasing and better delimited scope enable propositions of greater generality and more universality—more freedom and more certainty, Bacon would say. This makes sense—predicate concepts are, after all, concepts themselves. And predication is a kind of classification. Both conceptions of induction hold that one can justifiably infer universal statements from particular statements, but the Socratic conception grounds these universal statements in universal concepts. It holds that in human cognition, ampliation takes place—fundamentally and primarily—at the conceptual not the propositional level. Induction in the Socratic tradition is not exclusively, but is fundamentally and primarily, a logic of classification. It holds that if, and only if, one gets the concepts right can one make unqualified universal statements. The tradition, when it was still active, sought the criteria by which such mature concepts could be formed, their maturity marked, and universal statements therefrom derived. The tradition deserves a revival.

Socrates and Induction: An Aristotelian Evaluation Joseph A. Novak University of Waterloo

Abstract: The employment of induction by Socrates is broadly accepted, on the basis of Aristotle’s authority, to be one of his fundamental contributions to philosophy. In this essay Novak attempts to clarify the nature of Socratic epagǀgƝ by studying what manner of induction Aristotle was attributing to Socrates. As a first step, Aristotle’s description of induction is achieved through a schematic representation of its logical form as well as through an examination of numerous passages in his writings containing the word epagǀgƝ and several of its related or cognate terms. From this description, Novak extrapolates the major characteristics in Aristotle’s conception of induction. As a second step, a concrete example of Socratic induction, taken from Plato’s dialogue Hippias Minor, is then presented and analysed in terms of Aristotle’s major characteristics. Novak demonstrates that this case of Socratic induction illustrates a number of these characteristics. He claims that an elucidation of the various applications of epagǀgƝ by Aristotle allows one to evaluate more precisely his claim that one of the major contributions of Socrates to philosophizing was the use of epaktoi logoi. Likewise, an examination of passages in Plato which display Socrates’ using such types of reasoning renders concrete the Aristotelian claim. The essay concludes by raising a few questions concerning epistemological issues involved in the process of epagǀgƝ.

įȪȠ ȖȐȡ ਥıIJȚȞ ਚ IJȚȢ ਗȞ ਕʌȠįȠȓȘ ȈȦțȡȐIJİȚ įȚțĮȓȦȢ, IJȠȪȢ IJ’ ਥʌĮțIJȚțȠઃȢ ȜȩȖȠȣȢ țĮ੿ IJઁ ੒ȡȓȗİıșĮȚ țĮșȩȜȠȣ. There are two things which one might rightly ascribe to Socrates, inductive accounts and defining the universal. (Metaphysics 1078b27-29)

194

Joseph A. Novak

ਲ ȝ੻Ȟ Ƞ੣Ȟ ਥʌĮȖȦȖ੽ ੒ʌȠ૙ȠȞ IJȓ ਥıIJȚ, įોȜȠȞ. It is obvious what sort of thing induction is. (Topics 157a7-8) Introduction Socrates is recognized as the representative figure of philosophy in the West and as the most influential force in philosophical movements since Antiquity. Diverse ancient schools of philosophy comprised of Platonists, Stoics, Skeptics see him as their source of inspiration; key modern thinkers, even such antithetical ones as Nietzsche and Kierkegaard, consider him a foundational marker for rational thinking. Nonetheless, very little is known about the historical Socrates. One twentieth century scholar noted that practically nothing about him is certain; another cited the monumental work of K. Joel who said that the famous Socratic dictum, ‘I know only that I know nothing’ could be applied most appropriately to the problem of the historical Socrates itself.1 Socrates himself is not said to have written any autobiography nor published any treatise or even handbook containing his philosophical beliefs.2 The seeming ignorance of Socrates’ philosophical contributions seems counterbalanced by the presentation of his ideas by the four main authorities who have influenced the ideas later thinkers have had about Socrates, namely, Aristophanes, Xenophon, Plato, and Aristotle. It is the last of these thinkers who has presented us with some very brief claims about the contributions of Socrates to Western philosophy. As quoted above, Aristotle writes that both induction and general definition are things that can be attributed to Socrates. Aristotle’s accuracy as a historian of thought has been questioned. His survey of the development of Pre-Socratic philosophers has appeared to some as too self-serving as an evolutionary pre-staging of his fourfold distinction of causes.3 Moreover, Socrates’ death 1

O. Gigon in his Sokrates: Sein Bild in Dichtung und Geschichte (Bern: A. Francke, 1947) writes, “Of practically every assertion about Socrates the opposite can also be asserted with good reasons,” p. 12 (trans. mine). A. H. Chroust in his work Socrates: Man and Myth (London: Routledge and Kegan Paul, 1957) writes, “barring a few and very meager data, there exist no reliable reports on Socrates,” p. xiii. 2 In Plato’s Phaedo (60d-61b), he is said to be putting verses together in response to a divine urging, but even these are of a poetic sort and contain as their subject the fables of Aesop. 3 H. Cherniss, Aristotle’s Criticism of Presocratic Philosophy (New York: Octagon Books, 1971), p. xii: “Aristotle’s belief that all previous theories were stammering

Socrates and Induction

195

in 399 B.C. occurs well before Aristotle’s birth (384 B.C.) and more than thirty years before his admission to the Academy of Plato, who did have personal knowledge of Socrates (367 B.C.). Given that Plato himself is seen as placing his own doctrines, e.g., the theory of transcendent Forms, into the mouth of Socrates, any second-hand knowledge Aristotle had of Socrates might with good reason seem tainted.4 All this notwithstanding, Aristotle’s willingness to distinguish Plato and Socrates with regard to this matter of Forms provides sufficient reason to consider his report as carrying some validity. Without necessarily endorsing the skepticism tending to see the reports of all ancient writers about Socrates as a literary artifact (‘Dichtung’ is the term of Gigon), perhaps it would be safest for an investigator simply to assume the Aristotelian report as accurate and then examine what the philosophical details of the claim might be. First, then, a closer look at the words of Aristotle himself seem warranted: “for two things may be fairly ascribed to Socrates—inductive arguments and universal definition, both of which are concerned with the starting-point of science):—but Socrates did not make the universals or the definitions exist apart.”5

Just a little earlier (b17-19) in the text Aristotle had noted that Socrates was engaged in a definition process and seeking the universal: “But Socrates was occupying himself with the excellences of character, and in connection with them became the first to raise the problem of universal definition.”6

Just a little later than this passage, at b23-27, one reads:

attempts to express his own aids him in interpreting those theories out of all resemblance to their original form.” 4 A. E. Taylor has been one to claim that the Platonic portrayal of Socrates is indeed accurate; see his Varia Socratica: First Series (Oxford: Parker, 1911), p. xi. 5 įȪȠ ȖȐȡ ਥıIJȚȞ ਚ IJȚȢ ਗȞ ਕʌȠįȠȓȘ ȈȦțȡȐIJİȚ įȚțĮȓȦȢ, IJȠȪȢ IJ’ ਥʌĮțIJȚțȠઃȢ ȜȩȖȠȣȢ țĮ੿ IJઁ ੒ȡȓȗİıșĮȚ țĮșȩȜȠȣā IJĮ૨IJĮ ȖȐȡ ਥıIJȚȞ ਙȝijȦ ʌİȡ੿ ਕȡȤ੽Ȟ ਥʌȚıIJȒȝȘȢ)ā – ਕȜȜ’ ੒ ȝ੻Ȟ ȈȦțȡȐIJȘȢ IJ੹ țĮșȩȜȠȣ Ƞ੝ ȤȦȡȚıIJ੹ ਥʌȠȓİȚ Ƞ੝į੻ IJȠઃȢ ੒ȡȚıȝȠȪȢā (Metaphysics 1078b2731). The following abbreviations will be used in references after the first citation of a title from the Aristotelian corpus: Metaphysics (Metaph); Topics (Top); Prior Analytics (Pr An); Posterior Analytics (Post An); Sophistical Refutations (Soph Ref); Rhetoric (Rhet); Eudemian Ethics (EE). 6 ȈȦțȡȐIJȠȣȢ į੻ ʌİȡ੿ IJ੹Ȣ ਱șȚț੹Ȣ ਕȡİIJ੹Ȣ ʌȡĮȖȝĮIJİȣȠȝȑȞȠȣ țĮ੿ ʌİȡ੿ IJȠȪIJȦȞ ੒ȡȓȗİıșĮȚ țĮșȩȜȠȣ ȗȘIJȠ૨ȞIJȠȢ ʌȡȫIJȠȣ

196

Joseph A. Novak

“but it was natural that Socrates should be seeking the essence, for he was seeking to syllogize, and ‘what a thing is’ is the starting-point of syllogisms; for there was as yet none of the dialectical power which enables people even without knowledge of the essence to speculate about contraries and inquire whether the same science deals with contraries.”7

With regard to this last passage, one should note the role of “syllogizing” and finding the principles of syllogism. It seems important then, in an attempt to understand what these epaktikoi logoi (epagogic reasonings) in which Socrates is engaged are, to understand what the role of reasoning is for Socrates. Of course, one does not want to go too far afield, but it seems that the “inductive” side of Socratic reasoning cannot be understood—at least as it is being viewed by the Aristotelian account—without some context of reasoning (syllogizing) in general for Socrates. The first task will be to examine what meaning can be deduced from the passages here and what manner of induction Aristotle was attributing to Socrates. This will be attempted in Parts One and Two. The second task appears more daunting, namely, to proffer some instances indicative of the Socratic technique. This will be attempted in Part Three. These would presumably exemplify what Aristotle meant by his designating at least part of the Socratic activity as induction. Given the paucity of reports in Aristotle about Socrates as well as the lack of particular instances of Socratic reasoning in the corpus of the Stagirite, evidence brought forward in the analysis of induction will default to the Platonic text. 1 Aristotle’s Description of Induction If Aristotle is attributing the method of epagǀgƝ to Socrates—although the very use of this term is not applied by Aristotle to Socrates himself at 1078b28 or elsewhere in the Aristotelian corpus—it is important to note that the meaning of this phrase epaktikoi logoi is not disparate from the notion behind the term epagǀgƝ which occurs not thrice but multiple times throughout the corpus. For instance, Aristotle does join the epaktikous logous with the definition of universals by their common (ampho) role in the grounding of science (peri archen epistemes).8 He also notes in the Topics the role played by the consideration of like things in epagogic reasonings (ਥʌĮțIJȚțȠઃȢ ȜȩȖȠȣȢ), hypothetical reasonings (ʌȡઁȢ IJȠઃȢ ਥȟ 7

ਥțİ૙ȞȠȢ į’ İ੝ȜȩȖȦȢ ਥȗȒIJİȚ IJઁ IJȓ ਥıIJȚȞā ıȣȜȜȠȖȓȗİıșĮȚ Ȗ੹ȡ ਥȗȒIJİȚ, ਕȡȤ੽ į੻ IJ૵Ȟ ıȣȜȜȠȖȚıȝ૵Ȟ IJઁ IJȓ ਥıIJȚȞā įȚĮȜİțIJȚț੽ Ȗ੹ȡ ੁıȤઃȢ Ƞ੡ʌȦ IJȩIJ’ ਷Ȟ ੮ıIJİ įȪȞĮıșĮȚ țĮ੿ ȤȦȡ੿Ȣ IJȠ૨ IJȓ ਥıIJȚ IJਕȞĮȞIJȓĮ ਥʌȚıțȠʌİ૙Ȟ, țĮ੿ IJ૵Ȟ ਥȞĮȞIJȓȦȞ İੁ ਲ Į੝IJ੽ ਥʌȚıIJȒȝȘā 8 Metaph 1078b.

Socrates and Induction

197

ਫ਼ʌȠșȑıİȦȢ ıȣȜȜȠȖȚıȝȠઃȢ) and in the production of definitions (IJ૵Ȟ ੒ȡȚıȝ૵Ȟ).9 He then goes on to say that, in the case of the epaktikoi logoi, we arrive at the universal (epagein to katholou) by an epagǀgƝ on particulars: “because we maintain that it is by induction of particulars on the basis of similarities that we infer the universal. For it is not easy to employ inference if we do not know the points of similarity.”10

A consideration of many of these passages should reveal what Aristotle himself thinks that epagǀgƝ is and thereby, indirectly, one can get a better sense of what Socrates’ method is. Aristotle himself provides a very clear statement of what epagǀgƝ is, and it is easily schematically presented in contrast to two other modes of reasoning in his system. Late in the second book of the Prior Analytics, c. 23, we seem confronted with what appears to be a classic precise description of induction: Now induction, or rather the syllogism which springs out of induction, consists in establishing syllogistically a relation between one extreme and the middle by means of the other extreme, e.g. if B is the middle term between A and C, it consists in proving through C that A belongs to B. For this is the manner in which we make inductions. For example let A stand for long-lived, B for bileless, and C for the particular long-lived animals, e.g. man, horse, mule. A then belongs to the whole of C: for whatever is bileless is long-lived. But B also (‘not possessing bile’) belongs to all C. If then C is convertible with B, and the middle term is not wider in extension, it is necessary that A should belong to B. For it has already been proved that if two things belong to the same thing, and the extreme is convertible with one of them, then the other predicate will belong to the predicate that is converted. But we must apprehend C as made up of all the particulars. For induction proceeds through an enumeration of all the cases.11 9

Top 108b7-9. ʌȡઁȢ ȝ੻Ȟ Ƞ੣Ȟ IJȠઃȢ ਥʌĮțIJȚțȠઃȢ ȜȩȖȠȣȢ, įȚȩIJȚ IJૌ țĮș’ ਪțĮıIJĮ ਥʌ੿ IJ૵Ȟ ੒ȝȠȓȦȞ ਥʌĮȖȦȖૌ IJઁ țĮșȩȜȠȣ ਕȟȚȠ૨ȝİȞ ਥʌȐȖİȚȞā Ƞ੝ Ȗ੹ȡ ૧઻įȚȩȞ ਥıIJȚȞ ਥʌȐȖİȚȞ ȝ੽ İੁįȩIJĮȢ IJ੹ ੖ȝȠȚĮ (Top b10-13). The translation is that of E. S. Forster, Loeb ed., Cambridge: Harvard University Press, 1966. The elements just mentioned in the passages referred to are also characteristics found in Socratic dialectic as will be noted below. 11 The Greek reads: ਫʌĮȖȦȖ੽ ȝ੻Ȟ Ƞ੣Ȟ ਥıIJȚ țĮ੿ ੒ ਥȟ ਥʌĮȖȦȖોȢ ıȣȜȜȠȖȚıȝઁȢ IJઁ įȚ੹ IJȠ૨ ਦIJȑȡȠȣ șȐIJİȡȠȞ ਙțȡȠȞ IJ૶ ȝȑı૳ ıȣȜȜȠȖȓıĮıșĮȚ, ȠੈȠȞ İੁ IJ૵Ȟ ǹ ī ȝȑıȠȞ IJઁ Ǻ, įȚ੹ IJȠ૨ ī įİ૙ȟĮȚ IJઁ ǹ IJ૶ Ǻ ਫ਼ʌȐȡȤȠȞā Ƞ੢IJȦ Ȗ੹ȡ ʌȠȚȠȪȝİșĮ IJ੹Ȣ ਥʌĮȖȦȖȐȢ. ȠੈȠȞ ਩ıIJȦ IJઁ ǹ ȝĮțȡȩȕȚȠȞ, IJઁ į’ ਥij’ મ Ǻ IJઁ ȤȠȜ੽Ȟ ȝ੽ ਩ȤȠȞ, ਥij’ મ į੻ ī IJઁ țĮș’ ਪțĮıIJȠȞ ȝĮțȡȩȕȚȠȞ, ȠੈȠȞ ਙȞșȡȦʌȠȢ țĮ੿ ੆ʌʌȠȢ țĮ੿ ਲȝȓȠȞȠȢ. IJ૶ į੽ ī ੖Ȝ૳ ਫ਼ʌȐȡȤİȚ IJઁ ǹ (ʌ઼Ȟ Ȗ੹ȡ IJઁ ī 10

198

Joseph A. Novak

Aristotle’s standard assignment of variables would enable one to set up the syllogism as follows. Where ‘B’ stands for “bileless”, ‘A’ stands for ‘longlived’ and ‘C’ for particular long-lived animals, such as ‘man’, ‘horse’, ‘mule’ we arrive at the following syllogism: B–A C–B C – A ,i.e., All things that are bileless are long-lived Men, horses, and mules are bileless Men, horses, and mules are long-lived. Of course this appears to be a demonstrative syllogism, a deduction rather than an induction.12 However, it is the convertibility of C and B that gives us our induction for it allows us to establish the connection in the major premise B – A, yielding the representation which follows below. Aristotle notes at the end of this description that there is an “enumeration of all the cases” that is at work. ȝĮțȡȩȕȚȠȞ)ā ਕȜȜ੹ țĮ੿ IJઁ Ǻ, IJઁ ȝ੽ ਩ȤİȚȞ ȤȠȜȒȞ,ʌĮȞIJ੿ ਫ਼ʌȐȡȤİȚ IJ૶ ī. İੁ Ƞ੣Ȟ ਕȞIJȚıIJȡȑijİȚ IJઁ ī IJ૶ Ǻ țĮ੿ ȝ੽ ਫ਼ʌİȡIJİȓȞİȚ IJઁ ȝȑıȠȞ, ਕȞȐȖțȘ IJઁ ǹ IJ૶ Ǻ ਫ਼ʌȐȡȤİȚȞ. įȑįİȚțIJĮȚ Ȗ੹ȡ ʌȡȩIJİȡȠȞ ੖IJȚ ਗȞ įȪȠ ਙIJIJĮ IJ૶ Į੝IJ૶ ਫ਼ʌȐȡȤૉ țĮ੿ ʌȡઁȢ șȐIJİȡȠȞ Į੝IJ૵Ȟ ਕȞIJȚıIJȡȑijૉ IJઁ ਙțȡȠȞ, ੖IJȚ IJ૶ ਕȞIJȚıIJȡȑijȠȞIJȚ țĮ੿ șȐIJİȡȠȞ ਫ਼ʌȐȡȟİȚ IJ૵Ȟ țĮIJȘȖȠȡȠȣȝȑȞȦȞ. įİ૙ į੻ ȞȠİ૙Ȟ IJઁ ī IJઁ ਥȟ ਖʌȐȞIJȦȞ IJ૵Ȟ țĮș’ ਪțĮıIJȠȞ ıȣȖțİȓȝİȞȠȞā ਲ Ȗ੹ȡ ਥʌĮȖȦȖ੽ įȚ੹ ʌȐȞIJȦȞ (68b1529). The above is the translation of A.J. Jenkinson in the Ross edition, Oxford University Press, 1928, vol. 1. H. Tredennick in the Loeb (Cambridge: Harvard University Press, 1967) reads: “Induction, or inductive reasoning, consists….” whereas in the revised Oxford edition by J. Barnes, The Complete Works of Aristotle (Princeton: Princeton University Press, 1984), vol. 1 one reads: “Now induction, or rather the deduction which springs out of induction, consists in deducing a relation between one extreme and the middle by means of the other extreme….” Pacius (Aristotelis Peripateticorum Principis Organum, Frankfurt, 1597, 2nd ed.; rpt. Hildesheim: Georg Olms, 1967) reads, “Est igitur inductio, et syllogismus ex inductione, cum….” The use of the term ‘deduction’ is consistent with its translation for syllogismos throughout the Barnes translation. Robin Smith in his Aristotle: Prior Analytics (Indianapolis: Hackett Publishing Company, 1989) also uses ‘deduction’ to translate syllogismos. Tredennick wants to drop the phrase equivalent in his translation to “for whatever is bileless is long-lived.” The phrase is bracketed but retained in the Barnes version. 12 Here, of course, the term deduction is being used in the sense present in the classic bifurcation Aristotle made between induction and deduction earlier in the Pr An 42a3-4 and later at 68b13-14, 68b35-37, 71a5-6, 71a9-11, 81a39-41, and elsewhere.

Socrates and Induction

199

Aristotle seems to maintain that there is a strong contrast between deduction and induction. The classic bifurcation between these two is clear from many passages in Aristotle, such as Prior Analytics 42a3-4 and later at 68b13-14, 68b35-37, 71a5-6, 71a9-11, 81a39-41, and elsewhere. A useful diagram for portraying the differences is one that can be found in C. S. Peirce, who contrasts what he takes to be three fundamentally different types of reasoning in Aristotle and which he also considers basic to human inferential activity. He sets up the contrast under the larger division of inference into deductive and synthetic and then subdivides the later into induction and hypothesis.13 He casts them as following: Deduction (apodeixis - ਕʌંįİȚȟȚȢ)14 Rule—All beans from this bag are white. Case—These beans are from this bag. ? Result—These beans are white. Induction (epagǀgƝ - ਥʌĮȖȦȖ੾) Case—These beans are from this bag. Result—These beans are white. ? Rule—All beans from this bag are white. Hypothesis/Abduction (apagoge - ਕʌĮȖȦȖ੾) Rule—All beans from this bag are white. Result—These beans are white. ? Case—These beans are from this bag. 13

Collected Papers of Charles Sanders Peirce, Elements of Logic, vol 2 (Cambridge: Belknap Press of Harvard University Press, 1965), p. 375, para. 2.624: Inference Deductive or Analytic

14

Synthetic Induction

Hypothesis

Aristotle does put many constraints on what is a demonstration in a strict sense; he would not consider this example to be of that sort.

200

Joseph A. Novak

While leaving out of consideration the last schema, that of hypothesis, consider the contrast between the first two.15 The first clearly is an analytic deduction of the conclusion from the two given premises, while the second derives the rule or generalization on the basis of the two premises. Clearly Peirce seems to be saying much the same that Aristotle is saying. The general statement (“rule”) is established by means of the premises among whose terms is the link (“middle”) for the inference to succeed. In comparing Aristotle’s understanding of induction to even a very basic textbook contemporary approach, one finds Aristotle’s last qualification in the quotation above to make a remarkable difference. In a contemporary “syllogistic” presentation of induction, the conclusion appears to be a “leap” from a limited number of cases to a generalization, or it appears to be a leap from a number of given cases to yet another case that is said to fall under the same predicate. In other words, portrayed schematically, we have either: Schema I:

Schema II:

X1 is P X2 is P X3 is P Xn is P All x’s are P

X1 is P X2 is P X3 is P Xn is P Xn+1 is P

To put it briefly, the problem for contemporary philosophers is that from a limited number of cases one concludes to a generalization that is effectively a universal or one concludes to the affirmation of a property to another particular instance. Both of these moves seem questionable to philosophers moving within the gambit of a highly empirical approach to science. The induction advanced by Aristotle above would seem to take on the form: Men, horses, and mules (C) are long-lived (A) Men, horses, and mules (C) are bileless (B) All things that are bileless (B) are long-lived (A)

15

The last schema is presumably based on Pr An II, c. 25, but as R. Smith points out there are many textual problems with this chapter.

Socrates and Induction

201

As this syllogism stands, it would be invalid by Aristotle’s own syllogistic rules since it is a third figure AAA.16 However, if the condition is granted that B and C are convertible and co-extensive, one arrives at an acceptable inference. This schema became the point of departure in the discussion of the representation of Aristotle’s theory; it can be found in von Fritz and Schmidt as well as in some older logic texts.17 Although this structural representation might give some insight into the form of a syllogistic induction, especially as it stands in contrast to a deduction, one must not think that all that Aristotle means to express by it is contained therein.18 Actually, Aristotle does go beyond this in other passages relating to epagǀgƝ. Aristotle will reiterate that the induction does seem to rest on showing that all the individuals are exhaustively considered whereas, if one wants to speak of the reference to a single case, one is dealing with a paradeigma (example) which stands in contrast to an epagǀgƝ.19 However, he also seems to draw comparisons between logical and rhetorical reasoning, aligning paradeigmata (examples) with epagogai and enthymemes with syllogisms (Post An 71a9-11). Induction does have the quality of being more accessible than a deduction—it is more knowable to us whereas a syllogism is more knowable in itself (72b28-30). He does seem to make epagǀgƝ transcend a single instance when he remarks, in connection with his famous illustration of the contrast between two types of demonstration—the demonstrations of the fact that (੖IJȚ - hoti/quia) and the reasoned fact (į઀ȠIJȚ - dioti/propter quid)—that the general statement “what does not twinkle is near” is gotten by epagǀgƝ or by perception. Presumably here the epagǀgƝ would encompass more than a single individual (something had by perception); it would seem to be more than an induction of a new single instance as is had in the case of enumerative generalization (78a33-37). It is, however, the case that induction is “from the particulars,” whereas 16

See the treatment in the Prior Analytics, but from the perspective of traditional logic the scholastic rule of distribution would be violated. 17 Werner Schmidt, Theorie der Induktion: Die Prinzipielle Bedeutung der EpagǀgƝ bei Aristoteles (München: Wilhelm Fink Verlag, 1974); Kurt von Fritz, Die ‫݋‬ʌĮȖȦȖ‫ ޤ‬bei Aristoteles (München: Verlag der Bayerischen Akademie der Wissenschaften, 1964). In von Fritz the syllogistic representation can be found on p. 15. 18 See Schmidt, p. 81. 19 Pr An 69a16-18. The enumerative type of induction, where the conclusion is to a new singular instance of a type rather than to a generalization, resembles the nature of an example.

202

Joseph A. Novak

demonstration is from the universals.20 Aristotle thereupon notes that there is a certain dependence operative in scientific activity, for it is impossible to behold the universals except through induction and impossible to get an induction (empachthenai) without sense perception which reaches the particulars.21 So, there seems to be the following relation of epistemic dependency among these elements: the universal Æ induction Æ sense perception Æ particulars. Of course, for Aristotle, it is not the case that we would be said to know (ਥʌ઀ıIJĮıșĮȚ - epistasthai), in a strict sense, everything down to the particulars; these last are gotten by a sensing. Aristotle’s language reflects this by speaking of these as falling under our awareness (ȖȞȦȡ઀ȗİȚȞ - gnǀrizein). 2 Varieties and Complexities of Induction This fairly standard talk about the nature of induction might incline one to think that Aristotle is only speaking about the origin of the knowledge of the essence of indivisible natures, simples grasped by the intellect such as the essence of a triangle or even an animal. However, an examination of multiple passages in Aristotle should make it clear that the terminus of the process of induction is not simple the grasp of a simple essence whose multiple instances have provided an experiential base for its cognitive apprehension in a simple intuition. It does seem that the famous chapter Post An II, 19, with its mention of the individual man Callias as opposed to the universal man and the genus animal may well be an important factor in focusing the discussion of induction on the formulation and/or grasp of an individual essence. Consider, however, the variety of ways in which induction seems to occur in Aristotle. First of all, it becomes clear that Aristotle is also willing to talk about truths or propositions that are arrived at in this way. For instance, in the De Caelo he writes, “Again, a place in which a thing rests or to which it moves unnaturally, must be the natural place for some other body, as induction shows” (276a12-15). What precisely this induction is, Aristotle does not say. (Aquinas does, however, fill in the induction. In his commentary on the passage, he writes: “And this becomes believable on the basis of induction: for earth is moved upward against its nature, however, fire according to its nature; and conversely fire is moved downward against its 20

Post An 81a40-b1: ਩ıIJȚ į’ ਲ ȝ੻Ȟ ਕʌȩįİȚȟȚȢ ਥț IJ૵Ȟ țĮșȩȜȠȣ, ਲ į’ ਥʌĮȖȦȖ੽ ਥț IJ૵Ȟ țĮIJ੹ ȝȑȡȠȢ. 21 Post An 81b5-6: ਥʌĮȤșોȞĮȚ į੻ ȝ੽ ਩ȤȠȞIJĮȢ Į੅ıșȘıȚȞ ਕįȪȞĮIJȠȞ.

Socrates and Induction

203

nature but earth according to its nature.”22) However, it is clear that what is being established here is the proposition that “a place in which a thing rests….” This becomes a premise ultimately for a proof that (i.e., conclusion) the body of the universe is not infinite. So, the induction not only yields universal natures, it also gives truths (i.e., universal propositions) about these natures. Here Aristotle is formulating statements (theorems?) about a body’s natural movements. Nonetheless, Aristotle is also able to use induction to cover the relationships of basic concepts. In the case of concepts, he uses induction to show their oppositional relations. This use need not be seen as a case of legitimizing general statements, nor arriving at a definition expressing the essence of a thing, nor even grasping a nature in its simplicity, but rather indicating a relational property possessed by a concept. It could be claimed that the opposition between concepts is expressed in a proposition and that each of the instances cited can also be framed propositionally. The example that Aristotle employs at Categories 13b36-14a6 is that of the opposition of evil to good. The passage deserves being cited in full: “That the contrary of a good is an evil is shown (įોȜȠȞ) by induction: the contrary of health is disease, of courage, cowardice, and so on. But the contrary of an evil is sometimes a good, sometimes an evil. For defect, which is an evil, has excess for its contrary, this also being an evil, and the mean which is a good, is equally the contrary of the one and of the other. It is only in a few cases, however, that we see instances of this: in most, the contrary of an evil is a good.”

Two important features of Aristotelian induction become clear here. First, as already noted, the cases here seem to be simple concepts that are instanced. This is not to say that the analysis is being shifted to a purely linguistic or conceptual level, i.e., that the term ‘good’ is opposed to the term ‘evil’ or even that we are not dealing with a good thing or a bad thing, but only that we are not necessarily dealing with propositional formulations about the more complex nature of the movements of the elements as noted above. Secondly, it becomes clear that only a very limited number of cases are used in the supportive induction: health is opposed to disease (evil)— instance1, courage is opposed to cowardice (evil)—instance2. Despite this limited number, Aristotle seems to think that the truth has been made obvious (įોȜȠȞ). However, with regard to the converse, the same claim of 22

Aquinas, De Caelo et Mundo, Bk I, c. vii: “Et hoc credibile fit ex inductione: nam terra movetur sursum praeter naturam, ignis vero secundum naturam; et e converso ignis deorsum praeter naturam, terra vero secundum naturam.” (Leonine, vol. 3, p. 61).

204

Joseph A. Novak

opposition cannot be made, for only sometimes is it the case that the contrary of an evil is a good. To establish this Aristotle does not cite any particular instances but only the more general truth that a defect is opposed both to the excess and to the mean. This presumably is a reason offered in support of the claim; it is not an induction. It should be clear that Aristotle does view induction as furnishing the ground for knowledge by providing instances or enumerating them in view of some general claim. The attempt to ground knowledge claims in terms of elements that are more basic and known in some way prior to the knowledge claim itself is fundamental throughout his writing. At Metaphysics 992b30-33, he seems to utilize the basic bifurcation between demonstration and induction to make the point that all learning presupposes things already in some way known. Thus, a demonstration presupposes something already known to effect the proof, e.g., definitions (which are among the principles of demonstration) must have terms that are already known, and similarly inductions rest on the instances that are known: “Yet all learning is by means of premises which are (either all or some of them) known before, whether the learning be by demonstration or by definitions; for the elements of the definition must be known before and be familiar; and learning by induction proceeds similarly.”23 Definitions are presumably broken down into terms (their elements) while inductions must presumably rest on knowledge of particulars or particular instances. If there are inductions that succeed, presumably on the supposition that they include all instances, are there inductions that fail? In other words, can there be false inductions?24 One would think so a priori. Perhaps one might argue that such would not be inductions at all, just as Aristotle suggests that geometrical proofs that fail are not really bad proofs, they are not geometrical proofs at all.25 At Metaphysics 1025a10, he speaks of a “false result of an induction” (Ross translation). The particular example he chooses to show this is taken from a Platonic Dialogue, the Hippias Major. This dialogue will be of special focus below so only brief mention will be made here. How does the induction fail so as to produce a false result? The

23

Metaph 992b30-33. The bifurcation between demonstration and induction seems to be indicated by the use of ੒ȝȠ઀ȦȢ į੻ țĮ੿ ਲ įȚ ਥʌĮȖȦȖોȢ. Rather than a simple “and”/ țĮ੿, the lengthier conjunction seems to imply some deeper contrast. 24 Alexander Aphrodisias uses the expression “through a false induction” (įȚ’ ਥʌĮȖȦȖોȢ ȥİȣįȠ૨Ȣ). Aristotle himself simply says IJȠ૨IJȠ į੻ ȥİ૨įȠȢ ȜĮȝȕȐȞİȚ įȚ੹ IJોȢ ਥʌĮȖȦȖોȢ. 25 Post An 77b16-33.

Socrates and Induction

205

false result seems to be “he who is willingly bad is better.”26 Ross in his commentary takes this as the result of the induction; this is also true of J. Tricot’s reading.27 However, it seems to be established on the basis of a single instance, namely, that of a man willingly limping as (physically) better than one who is unwillingly limping, namely, one who is by nature lame. It seems that one might fault the induction because it is only based on a single instance. However, it appears more likely to be the case from the accompanying remarks of Aristotle that the failure is due to this particular instance offering inadequate support, since the limping is not a genuine instance but only a mimic of a limping. Alexander seems to add “and upon other such pretensions,”28 thereby understanding other such like premises in addition. Aristotle also seems to indicate that an epagǀgƝ can show something not to be the case. In other words, the epagǀgƝ need not arrive at something positive, it can conclude to something negative. At the beginning of his analysis of the rankings of the sciences in Metaphysics Bk VI, Aristotle, alluding to medicine and explicitly mentioning mathematics, notes that all the sciences investigate causes and principles, with various degrees of exactitude, and that each is occupied with a single subject or genus but none of them purport to demonstrate essence (1025b5-10). He then mentions that “from such an induction as this” (ਥț IJોȢ IJȠȚĮȪIJȘȢ ਥʌĮȖȦȖોȢ) it is clear that there is no demonstration of essence (b15). In other words, from a review of the common absence of demonstration of essence in these various sciences, one can claim that such a demonstration does not exist. This becomes an issue Aristotle will discuss at length in his Posterior Analytics, but here he seems to think that the overview and comparison of the disciplines will reveal this to be the case. In a parallel passage at 1064a, using almost the same language, Aristotle draws the same conclusion, but he does so by citing as instances that the definitions are gotten by perception and by hypothesis in sciences that are productive or practical. Here it seems that the positive provisioning of essential knowledge in each of the sciences by

26

IJઁȞ ਦțȩȞIJĮ ijĮ૨ȜȠȞ ȕİȜIJȓȦ (1025a9). Aristotle’s Metaphysics, vol. 1 (Oxford: Clarendon Press, 1924), p. 348; “on y donne la préférence à celui qui est méchant volontairement. Mais cette dernière assertion repose sur une fausse induction,” La Métaphysique, vol. 1 (Paris: J. Vrin, 1970), p. 331. 28 ਥʌ੿ IJ૵Ȟ ਙȜȜȦȞ IJ૵Ȟ IJȠȚȠȪIJȦȞ ʌȡȠıʌȠȚȒıİȦȞ (In Metaph, 437.10). 27

206

Joseph A. Novak

perception and hypothesis allows one to conclude, by epagǀgƝ, that there is no demonstration of essence.29 Aristotle further seems to indicate that epagǀgƝ is not only linked to indivisible essences, or even to statements of the definitions of things, but it can contribute to the understanding of a concept by being employed over a number of analogies which elucidate the meaning being sought. Thus he focuses on the key concepts of potentiality and actuality, which can be grasped by an overview of the relation of the following items: construction to the constructible, waking to sleeping, seeing to functional eyes, what is shaped from matter to the matter, and what is wrought to the unwrought.30 This conceptual relation becomes obvious by an epagǀgƝ on particulars (ਥʌ੿ IJ૵Ȟ țĮș’ ਪțĮıIJĮ IJૌ ਥʌĮȖȦȖૌ). He then goes on to add that in such analogies some things stand as movement to potency or as substance to some matter. As he notes, “take an overview of the analogous.”31 What Aristotle seems to being describing by this series of analogies is the otherwise undefinable concepts of actuality and potentiality. An important question that arises here is whether the epagǀgƝ is prior to the formulation of a hypothesis endorsed by someone, or whether the epagǀgƝ simply provides the authentication of the hypothesis after it is proposed. In dealing with relationships again, Aristotle enunciates at 1054b31-32 the conjunctive proposition that, “contraries are different and contrariety is a kind of difference.”32 The multiplicity of instances alluded to seems to show that Aristotle is beginning with a hypothesis that is in need of being established and the induction is a way of doing this: “That we are right in this supposition is shown by induction.”33 He goes on to 29

The parallel between the two conclusions is striking: Metaph 1025b14-16: įȚȩʌİȡ ijĮȞİȡઁȞ ੖IJȚ Ƞ੝ț ਩ıIJȚȞ ਕʌȩįİȚȟȚȢ Ƞ੝ıȓĮȢ Ƞ੝į੻ IJȠ૨ IJȓ ਥıIJȚȞ ਥț IJોȢ IJȠȚĮȪIJȘȢ ਥʌĮȖȦȖોȢ, ਕȜȜȐ IJȚȢ ਙȜȜȠȢ IJȡȩʌȠȢ IJોȢ įȘȜȫıİȦȢ and Metaph 1064a8-10: įȚઁ țĮ੿ įોȜȠȞ ਥț IJોȢ IJȠȚĮȪIJȘȢ ਥʌĮȖȦȖોȢ ੖IJȚ IJોȢ Ƞ੝ıȓĮȢ țĮ੿ IJȠ૨ IJȓ ਥıIJȚȞ Ƞ੝ț ਩ıIJȚȞ ਕʌȩįİȚȟȚȢ. It should be noted that Ross notes some problems with the presentation by Aristotle, especially regarding the passage at 1025. See ibid., vol. 1, p. 352. 30 Metaph. 1048a35-b4. 31 țĮ੿ Ƞ੝ įİ૙ ʌĮȞIJઁȢ ੖ȡȠȞ ȗȘIJİ૙Ȟ ਕȜȜ੹ țĮ੿ IJઁ ਕȞ੺ȜȠȖȠȞ ıȣȞȠȡ઼Ȟ. 32 IJ੹ į’ ਥȞĮȞIJȓĮ įȚȐijȠȡĮ, țĮ੿ ਲ ਥȞĮȞIJȓȦıȚȢ įȚĮijȠȡȐ IJȚȢ. 33 ੖IJȚ į੻ țĮȜ૵Ȣ IJȠ૨IJȠ ਫ਼ʌȠIJȚșȑȝİșĮ, įોȜȠȞ ਥț IJોȢ ਥʌĮȖȦȖોȢ (1054b32-33). The sense of hypothesis or supposition that Aristotle has in mind is developed at greater length in the Posterior Analytics. Although the term does occur even in Plato’s earlier dialogues, the so-called Socratic ones and although, as will be noted below, terms related to the verb hypotithemi are put in the mouth of Socrates, generally the term applied to his method is the elenchus. Please see below about the movement in Plato from elenchus to hypothesis to the later method of “Collection and Division.”

Socrates and Induction

207

propose that “contrariety is the greatest difference” and also that “the extremes from which changes proceed are contraries,” noting that both of these are known by induction.34 In the case of the first proposition he provides really no enumeration but rather offers philosophical reasons in support. In the case of the second proposition he does raise cases of the equal-unequal, like-unlike, virtue-vice. Of course one might forgive Aristotle for not actually providing the induction in the text; often in the Prior Analytics he might speak of something being provable by echthesis without actually providing the terms of such a proof.35 However, in what follows shortly thereafter at 1058a9 in arguing that difference in genus is a contrariety, and that this is clear from induction he seems to provide no enumeration. Ross himself notes here “nor does what follow bear any resemblance to an ਥʌĮȖȦȖ੾.”36 Nonetheless, at 1067b12-14, Aristotle articulates a proposition whose warrant (pistis) comes from epagǀgƝ: “Change which is not accidental is found not in all things, but between contraries, and their intermediaries, and between contradictories. We may convince ourselves of this by induction.”37 Here he does provide an analysis of cases in support but the induction is not done on individuals but on types, types that are products of philosophical theorizing. In the Meteorologica 378b14, by contrast, in claiming that the hot and cold are active while the dry and moist are passive, he seems to be alluding to concrete cases and notes that this can be shown by induction (ਥț IJોȢ ਥʌĮȖȦȖોȢ), adding in the next line that this is clear “in all cases (ਥȞ ʌ઼ıȚȞ).” When he speaks this way he seems to encompass first the active in different types of activity of the first two causes (heat and cold) of the elements as well as the passive in the different things upon which they are active (moist and dry)—various determinations are seen as present in isolation and in conjunction. The number of cases here seems extensive, but Aristotle does not enumerate them in detail; here the epagǀgƝ is presumably left to the reader. Aristotle adds that this can also be seen as a result of their logoi.38 Here he seems to mean that, as it is the nature of the hot or cold to pull things together (presumably the melting of separate bits of 34

At 1055a4-5: ਩ıIJȚ IJȚȢ țĮ੿ ȝİȖȓıIJȘ įȚĮijȠȡȐ, țĮ੿ IJĮȪIJȘȞ ȜȑȖȦ ਥȞĮȞIJȓȦıȚȞ. ੖IJȚ į’ ਲ ȝİȖȓıIJȘ ਥıIJ੿ įȚĮijȠȡȐ, įોȜȠȞ ਥț IJોȢ ਥʌĮȖȦȖોȢ.; at 1055b16-17: ਥȟ ੰȞ Ȗ੹ȡ Įੂ ȝİIJĮȕȠȜĮ੿ ਥıȤȐIJȦȞ, ਥȞĮȞIJȓĮ IJĮ૨IJĮ. ijĮȞİȡઁȞ į੻ țĮ੿ įȚ੹ IJોȢ ਥʌĮȖȦȖોȢ. 35 See Pr An 28b14. 36 Ibid., vol. 2, p. 301 (on passage). 37 ਲ į੻ ȝ੽ țĮIJ੹ ıȣȝȕİȕȘțઁȢ ȝİIJĮȕȠȜ੽ Ƞ੝ț ਥȞ ਚʌĮıȚȞ ਫ਼ʌȐȡȤİȚ ਕȜȜ’ ਥȞ IJȠ૙Ȣ ਥȞĮȞIJȓȠȚȢ țĮ੿ ȝİIJĮȟઃ țĮ੿ ਥȞ ਕȞIJȚijȐıİȚā IJȠȪIJȠȣ į੻ ʌȓıIJȚȢ ਥț IJોȢ ਥʌĮȖȦȖોȢ. 38 At 378b20-1: ਩IJȚ į’ ਥț IJ૵Ȟ ȜȩȖȦȞ įોȜȠȞ, ȠੈȢ ੒ȡȚȗȩȝİșĮ IJ੹Ȣ ijȪıİȚȢ Į੝IJ૵Ȟā

208

Joseph A. Novak

snow or that of metal into a liquid or the freezing of flowing water into a solid is a combining and combining is active), so these causes are active. Thus, an analysis of the processes and the concepts involved shows the nature of the causes of the elements. This contrast of epagǀgƝ to an approach kata ton logon also arises elsewhere, namely, in the De partibus animalium, where the subject under consideration is the composition of animals. The principle which he is there trying to defend is that “the order of development and the order of substance are always the inverse of each other.”39 This can be done by induction (ਥț IJોȢ ਥʌĮȖȦȖોȢ) and by reasoning (țĮIJ੹ IJઁȞ ȜȩȖȠȞ). Using the former Aristotle cites the case of bricks and stones which exist for the sake of the house; using the latter Aristotle cites the analysis of the generative process, while nonetheless attaching examples to illustrate it, man generating man, plant generating plant. Of course this does raise the persistent question: “how great is the number of instances to effect a good induction?” At Physics 185a12-14, Aristotle puts forward the hypothesis (ਲȝ૙Ȟ į’ ਫ਼ʌȠțİȓıșȦ) that all or some natural things are in motion. This hypothesis is supported by induction. Given that the hypothesis is disjunctive, one need not do an analysis on all natural things. Still, the question remains concerning the number of instances that would be sufficient to warrant the claim that some natural things are in motion—perhaps one would be sufficient. Thus there would be an interconnection between the number of instances looked at and the scope of the type of hypothesis being proposed. However, Aristotle is not quite clear how the consideration of the instances is achieved. At Physics 224b 28-30, he writes, “change which is not accidental on the other hand is not to be found in everything, but only in contraries, in things intermediate between contraries, and in contradictories, as may be shown by induction.”40 His following remarks gives no citation of instances, although he does provide examples (ȠੇȠȞ) of intermediates as the central note (in the case of sound) and of grey (in the case of color). Ross’ remark on this passage is rather puzzling since it implies that the induction is done by a 39

At 646a25-27: ਫʌİ੿ į’ ਥȞĮȞIJȓȦȢ ਥʌ੿ IJોȢ ȖİȞȑıİȦȢ ਩ȤİȚ țĮ੿ IJોȢ Ƞ੝ıȓĮȢā IJ੹ Ȗ੹ȡ ੢ıIJİȡĮ IJૌ ȖİȞȑıİȚ ʌȡȩIJİȡĮ IJ੽Ȟ ijȪıȚȞ ਥıIJȓ, țĮ੿ ʌȡ૵IJȠȞ IJઁ IJૌ ȖİȞȑıİȚ IJİȜİȣIJĮ૙ȠȞ. Admittedly, the ‘always’ of the Ross/Barnes translation is not explicitly in the Greek but the formulation shows it accurately captures the idea. Despite this addition, their translation is more succinct than that of A.L. Peck in the Loeb (Cambridge: Harvard University Press, 1968), vol. 12, p. 109: “Now the order of things in the process of formation is the reverse of their real and essential order.” 40 ਲ į੻ ȝ੽ țĮIJ੹ ıȣȝȕİȕȘțઁȢ Ƞ੝ț ਥȞ ਚʌĮıȚȞ, ਕȜȜ’ ਥȞ IJȠ૙Ȣ ਥȞĮȞIJȓȠȚȢ țĮ੿ IJȠ૙Ȣ ȝİIJĮȟઃ țĮ੿ ਥȞ ਕȞIJȚijȐıİȚā IJȠȪIJȠȣ į੻ ʌȓıIJȚȢ ਥț IJોȢ ਥʌĮȖȦȖોȢ.

Socrates and Induction

209

review of the per se change cases, in effect, a review of the complement of the accidental change. To cite Ross: “Aristotle means that if you reviewed all the cases of per se change you could think of, you would satisfy yourself of the truth of what he said.”41 Presumably “all the cases” would be types of cases, but even then the connection of this review as an induction in support of the claim about accidental change remains obscure. Yet at 229a30-b10, when dealing with the claim that “contrary motions are motions respectively from a contrary to the opposite contrary and from the latter to the former,” Aristotle notes that one can say, on the basis of epagǀgƝ (ਥț IJોȢ ਥʌĮȖȦȖોȢ) what kind of things these contraries are, and he provides instances: getting sick as opposed to getting well, learning as opposed to being misled, moving back as opposed to moving forward, moving right as opposed to moving left, and moving up as opposed to moving down. Here we find quite a concrete listing, but it is unclear whether this is a listing of cases taken exemplifying the claim or of instances providing the basis for the generalization. On the other hand, at Physics 244b2-3 the claim “nor again is there anything intermediate between that which undergoes and that which causes alteration” is said to be made obvious by induction (ਥȟ ਥʌĮȖȦȖોȢ), and this rests on what happens in all cases (ਥȞ ਚʌĮıȚ).42 Here Aristotle does provide a number of cases dealing with qualities, and since he deals with animate and inanimate cases and furnishes cases from many (albeit not all) of the senses, it would seem the universalization might be grounded in fact.43 In the last book of the Physics, Aristotle maintains that one who espouses a theory should not merely assert it, but explain its cause—he should not make any mere assumption or lay down any unreasoned axiom but should employ either inductive or demon41

Ross, Aristotle’s Physics (Oxford: Clarendon Press, 1936), p. 616 (on passage). Two earlier lines are needed to make the text comprehensible: ijĮȞİȡઁȞ ੖IJȚ IJȠ૨ țĮIJ੹ IJȩʌȠȞ țȚȞȠȣȝȑȞȠȣ țĮ੿ țȚȞȠ૨ȞIJȠȢ Ƞ੝įȑȞ ਥıIJȚ ȝİIJĮȟȪ. 244b.2: ਕȜȜ੹ ȝ੽Ȟ Ƞ੝į੻ IJȠ૨ ਕȜȜȠȚȠȣȝȑȞȠȣ țĮ੿ IJȠ૨ ਕȜȜȠȚȠ૨ȞIJȠȢ. IJȠ૨IJȠ į੻ įોȜȠȞ ਥȟ ਥʌĮȖȦȖોȢā 43 Actually, Aquinas does list in detail all the senses and their relevance and then concludes to the generalization. However, his interpretation poses two problems: first, his text seems to be following the textus alter (an alternate text); second, he places this reasoning under a proof through argument rather than through induction, “hoc probat primum per inductionem … probat idem per rationem.” In Physicam VII, lect. iv (Naples: D’Auria, 1953), par. 1827-29. The value and nature of the textus alter is discussed at length by W.D. Ross in his Physics (Oxford: Clarendon Press, 1936), pp. 11-19. That two different texts existed even in antiquity was already noted by the commentator Simplicius. Aquinas’ detailed list rests on the enumeration given in the textus alter. 42

210

Joseph A. Novak

strative reasoning.44 The bifurcation of reasoning into these two grand types is here again clear. If one looks at what are probably the works that would likely be reflective on the nature of epagǀgƝ, the Topics and the Rhetoric seem to stand out. What is operative at Topics 103b2-19 is the bifurcation of proving into doing so either by epagǀgƝ or by syllogismos, i.e., by induction or deduction. The concrete proposition raised here is whether the four (five) predicables, i.e., genus (difference), species, property, and accident adequately account for the types of things to which and from which arguments proceed.45 He thinks that this can be established first by induction (įȚ੹ IJોȢ ਥʌĮȖȦȖોȢ)—one looks around at presumably all cases of arguments to see whether the predicables’ division covers all instances, stating that one looks at each of the premises or problems.46 This demand really seems quite stringent since there are a potentially infinite number of propositions. Moreover, this infinite number will mean that the epagǀgƝ could never be finished. The deductive argument for the same proposition proceeds in a much more abstract and finite manner.47 Still, after distinguishing the two types of logoi, epagǀgƝ and syllogismos, at 105a10-12,48 Aristotle does provide a succinct definition for the former method: epagǀgƝ is the method from the particulars to the universal.49 He provides some examples of this by listing two types of individuals, the pilot and the charioteer, noting that if these are skilled in their profession, then they are the best. From this one is entitled to conclude that generally (੖ȜȦȢ) the one who is skilled in anything is the best. This is practically a snapshot section of a Socratic dialogue, not only in terms of the limited number of instances 44

Physics 252a 23-26: ਕȜȜ੹ țĮ੿ IJȠ૨IJȠ įİ૙ IJઁȞ ȜȑȖȠȞIJĮ ȝ੽ ijȐȞĮȚ ȝȩȞȠȞ, ਕȜȜ੹ țĮ੿ IJ੽Ȟ ĮੁIJȓĮȞ Į੝IJȠ૨ ȜȑȖİȚȞ, țĮ੿ ȝ੽ IJȓșİıșĮȚ ȝȘį੻Ȟ ȝȘį’ ਕȟȚȠ૨Ȟ ਕȟȓȦȝ’ ਙȜȠȖȠȞ, ਕȜȜ’ ਲ਼ ਥʌĮȖȦȖ੽Ȟ ਲ਼ ਕʌȩįİȚȟȚȞ ijȑȡİȚȞā 45 Topics 103b2-3: ੖IJȚ į’ ਥț IJ૵Ȟ ʌȡȩIJİȡȠȞ İੁȡȘȝȑȞȦȞ Ƞੂ ȜȩȖȠȚ țĮ੿ įȚ੹ IJȠȪIJȦȞ țĮ੿ ʌȡઁȢ IJĮ૨IJĮ. Pacius distinguishes the use of the prepositions here with the first two applying to propositions and the last, to problems. 46 Topics 103b4-5: IJȚȢ ਥʌȚıțȠʌȠȓȘ ਦțȐıIJȘȞ IJ૵Ȟ ʌȡȠIJȐıİȦȞ țĮ੿ IJ૵Ȟ ʌȡȠȕȜȘȝȐIJȦȞ. Pacius translates this as “singulas propositiones et problemata.” In his comments on the passage, Robin Smith explains: “the examination of individual problems and premises to see that each one always falls under the fourfold division,” in Aristotle’s Topics: Books I and VIII (Oxford: Clarendon Press, 1997), p. 72. Italics in the text above are mine. 47 Smith provides a very good diagram to represent this argument; see ibid., p. 72. 48 Ȥȡ੽ įȚİȜȑıșĮȚ ʌȩıĮ IJ૵Ȟ ȜȩȖȦȞ İ੅įȘ IJ૵Ȟ įȚĮȜİțIJȚț૵Ȟ. ਩ıIJȚ į੻ IJઁ ȝ੻Ȟ ਥʌĮȖȦȖȒ, IJઁ į੻ ıȣȜȜȠȖȚıȝȩȢ. 49 At 105a13-14: ਥʌĮȖȦȖ੽ į੻ ਲ ਕʌઁ IJ૵Ȟ țĮș’ ਪțĮıIJĮ ਥʌ੿ IJઁ țĮșȩȜȠȣ ਩ijȠįȠȢ.

Socrates and Induction

211

enumerated but also in terms of the concept of skill which so often finds its way into the Socratic dialectic. The advantage of epagǀgƝ, he adds, is its four features of being more convincing, clearer, more knowable perceptually, and more accessible to a greater number of people than is the syllogism.50 He seems to note that epagǀgƝ functions to help understand the nature of a thing even when there is not a definition of it; a considering of particulars that are similar seems to allow one to get a grasp of a concept.51 (Although it does seem that one is forced to be content with a kind of “family resemblance” of the cases rather than a covering concept that clearly demarcates a class.) Of course this likeness or similarity is recognized by Aristotle to be important in induction as well as the other procedures in the reasoning process:52 “it is useful for inductive arguments, because it is by means of an induction of particulars in cases that are alike that we claim to induce the universal.”53 This passage is of especial interest, first of all, since it pulls together three expressions, epaktikous logous, epagǀgƝ, and epagein, effectively showing their equivalence, and secondly, it shows that by epagǀgƝ upon similar particulars one induces a universal. This is precisely the approach that is so stereotypical of the activity of Socrates in the early Platonic dialogues. Inductive reasoning can be applied as well in the case of the implications involved in basic logic relations, including those of immediate inference. Aristotle discusses this starting at Topics 113b15, where he shows how the oppositions of contradictories, contraries, privation/possession, and relations can be grasped by induction (ȜĮȝȕȐȞİȚȞ į’ ਥȟ ਥʌĮȖȦȖોȢ). The exact import of the word lambanein here is unclear.54 It is not obvious whether it means that one formulates these general principles of opposition by looking at a number of cases drawn from experience such as those Aristotle suggests, e.g., of man, animal, not-man, not-animal, pleasant, not-pleasant, etc. or if these particular cases simply illustrate the general principle oppositions. His 50

Topics 105a16-18. Topics 105b25-27. 52 The other items here, Aristotle says, are hypothetical deductions (IJȠઃȢ ਥȟ ਫ਼ʌȠșȑıİȦȢ ıȣȜȜȠȖȚıȝȠȪȢ) and furnishing definitions (IJ੽Ȟ IJ૵Ȟ ੒ȡȚıȝ૵Ȟ ਕʌȩįȠıȚȞ). 53 Topics 108b9-11: ʌȡઁȢ ȝ੻Ȟ Ƞ੣Ȟ IJȠઃȢ ਥʌĮțIJȚțȠઃȢ ȜȩȖȠȣȢ, įȚȩIJȚ IJૌ țĮș’ ਪțĮıIJĮ ਥʌ੿ IJ૵Ȟ ੒ȝȠȓȦȞ ਥʌĮȖȦȖૌ IJઁ țĮșȩȜȠȣ ਕȟȚȠ૨ȝİȞ ਥʌȐȖİȚȞ. R. Smith translates the explanatory clause: “ because it is by means of bringing in particular about similar cases that we claim a right to bring in the universal ,” op. cit., p. 19. 54 Pacius translates this as “accipere.” The same Greek terminology occurs also at 113b29, 115a5-6, 122a19. 51

212

Joseph A. Novak

use of the phrase “look to see whether”55 inclines toward the first option, that one investigates the oppositions on the basis of experience. Moreover, at 114b37 Aristotle speaks of “the commonplaces of more and less” (IJȩʌȠȚ IJȠ૨ ȝ઼ȜȜȠȞ țĮ੿ ਸIJIJȠȞ) and, in speaking of the first of four of these, i.e., “see whether a greater degree of the predicate follows a greater degree of the subject”, he notes that it is to be “taken by induction,” so that a rule or commonplace is to be established, seemingly, by evidence from experience.56 At Topics 122a17-19, Aristotle moves on to speak of predication “in what it is”, i.e., in the order of essence. The principle Aristotle has at work is this: when one genus is predicated in the category of essence, all the rest, if predicated at all, will be predicated in the category of essence. He states that this should be secured by induction. Presumably Aristotle means that if there were a series of subordinated genera, beginning with P1, and moving upwards with ever-broadening genera, P2, P3, P4, P5, and so forth, all the superordinate genera will be predicated essentially. The securing of this truth by induction (įȚ’ ਥʌĮȖȦȖોȢ) could mean checking vertically as far up (or down) as one might wish or using as many different species as one might wish, horizontally, which in itself would mean checking again, vertically, the new lines of superordinate genera that are introduced. Aristotle does not specify here how many instances either vertically or horizontally that one should examine. Aristotle’s frequent use, explicit or implicit, throughout this chapter of the Topics of the verb ıțȠʌİ૙Ȟ carries the flavor of consulting particular instances to verify the principle but also showing how it is illustrated in the concrete. This same duality of verification and illustration also seems to be present at Topics 123b1ff., where even the additional aspect of examination seems to be present. The principle in question is: “If there is a contrary to a species it should be found in the same genus if there is no contrary to the genus; if there is a contrary to the genus, see whether the contrary of the species exists in the contrary genus.”57 Aristotle notes that both of these 55

At 113b27: ਫʌ੿ į੻ IJ૵Ȟ ਥȞĮȞIJȓȦȞ ıțȠʌİ૙Ȟ İੁ. The same terminology occurs at 113b29, 115a5-6, and 122a19. 56 Pacius translates the phrase at 115a5-6 (IJȠ૨IJȠ į’ ਥʌĮȖȦȖૌ ȜȘʌIJȑȠȞ) as “hoc autem inductione sumendum est” using “sumere” instead of his earlier “accipere.” Both terms seem to incline toward experience as the base of the rule or topos rather than merely exemplifying it. In a note on this passage Pacius adds, “Hoc axioma de eo quod est magis vel minus, confirmandum est inductione.” The use of confirmandum seems to imply again that experience is somehow warranting the topos itself. 57 Or as Aristotle writes: ıțȠʌİ૙Ȟ İੁ IJઁ ਥȞĮȞIJȓȠȞ ਥȞ IJ૶ ਥȞĮȞIJȓ૳ā (123b5). This rule might at first seem puzzling if one considers Aristotle’s remark in the Categories that

Socrates and Induction

213

conditionals need to be made “obvious through induction.”58 It seems as though Aristotle is here supposing that the principle is true but that it is being used as a rule to determine what is true of a particular case rather than simply using the case as an instance exemplifying a rule or as a particular for deriving the rule. There follow other rules in this section and Aristotle’s explicit or implicit use of the verb ıțȠʌİ૙Ȟ seems to imply that induction is to be used throughout. That induction is linked to the universal seems reinforced at Topics 155b21-22, where Aristotle indicates that the role of certain premises is to establish a universal (presumably by induction), i.e., premises that serve “inductively to secure the universal premise being granted.”59 One should note here that epagǀgƝ is involved with premises (ʌȡȠIJȐıİȚȢ) so that the universal does not seem to be an item grasped in a simple intuition as an indivisible, as an essence apprehended by induction on particulars. More specifically, at Topics 155b34-156a1, Aristotle recommends a strategy for argumentation whereby a necessary premise is secured by induction or deduction. The establishment of the truth of a premise such as “knowledge of contraries is one” can be effected either by deducing it from a premise such as “knowledge of opposites is one” or by induction on particular cases.60 Aristotle provides no examples here, although the items in question do seem to be propositions, if one can trust the immediate contextual reference. However, this much is clear, that the inductive method is less clear (ਕįȘȜȩIJİȡȩȞ) for obtaining the result, i.e., in making obvious what is the general proposition being sought.61 Yet, in making a contrast between

substance has no contrary as he applies this to many other things, citing quantity as an example. Pacius, however, does provide a good illustration of the passage by noting species in the category of quality, for science and ignorance are contraries as are virtue and vice, yet virtue is not a species of science nor vice of ignorance (although surely Socrates would disagree on this). Pacius also refers to the principles under investigation as rules (regulae). 58 ijĮȞİȡઁȞ į੻ IJȠȪIJȦȞ ਪțĮıIJȠȞ įȚ੹ IJોȢ ਥʌĮȖȦȖોȢ. 59 Barnes’ translation. Smith’s translation which has these premises, “for the sake of induction and giving the universal” (p. 20), although quite literal, is somewhat puzzling unless “and” is taken epexegetically. One suspects that what Aristotle means is that induction is used to get the universal. Pacius’ translation hints at this: “vel enim sumuntur inductionis causa ut detur quod est universale” i.e., those are assumed for the sake of an induction that there be given something that is universal. 60 At 155b34-35: įȚ’ ਥʌĮȖȦȖોȢ ȜȘʌIJȑȠȞ ʌȡȠIJİȓȞȠȞIJĮ ਥʌ੿ IJ૵Ȟ țĮIJ੹ ȝȑȡȠȢ ਥȞĮȞIJȓȦȞ. 61 Pacius translates the Greek term as “obscurius.”

214

Joseph A. Novak

induction and a method of likeness,62 Aristotle does point out that the particulars are the base upon which the universal is grasped.63 Further, Aristotle distinguishes the collective activity of induction in contradistinction to the distinguishing activity of division (įȚĮ઀ȡİıȚȢ/diairesis)—a contrast that is foundational to Plato’s later method of Collection and Division which Socrates’ character formulates in the Phaedrus and which is utilized in the later dialogues, although the beginnings of these two correlative dialectical activities can be detected in the properly Socratic dialogues as well.64 In all this Aristotle does note the popular appeal of the inductive style of argumentation: “deduction should be employed in reasoning against the dialecticians rather than against the crowd; induction, on the other hand, is most useful against the crowd.”65 It is no wonder, then, that Socrates would employ this method so often in his dialogues. Aristotle’s remark might even be generated by the actual success in this regard of the historical Socrates. Moreover, even if the procedure did not focus on a nameable universal, there would still be something to which the cases adduced were directed.66 Another area of philosophical debate against which background Socrates is generally seen as active is that of rhetorical argumentation. While Socrates’ opponents are portrayed as sophistical rhetoricians and Socrates himself is seen, by contrast, as employing against them a dialectic (elenchic) technique, there can be little doubt both types of debaters are in some sense rhetores (rhetoricians/debaters). Hence in addition to the Topics, Aristotle’s Rhetoric can provide useful insight into the method used 62

At 156b10: įȚ੹ IJોȢ ੒ȝȠȚȩIJȘIJȠȢ. The example provided here is: “as knowledge and ignorance of contraries are the same, so too perception of the contraries is the same.” 63 At 156b15: ਕʌઁ IJ૵Ȟ țĮș’ ਪțĮıIJĮ IJઁ țĮșȩȜȠȣ ȜĮȝȕȐȞİIJĮȚ; Pacius: “ex singularibus sumitur universale.” 64 An example Aristotle gives of diairesis is at 157a10-11: “the distinction of the sciences into speculative, practical, and productive.” Although this particular tripartite division is very familiar from Aristotle’s analysis of episteme, this contrast of induction and distinction (division) has resonances of Plato’s method of Collection and Division. One can detect a faint similarity of the particular threefold distinction to the three groups of people Socrates examines in his response to the oracle of Delphi and noted in the Apology: the poets, politicians, and engineers. 65 The ‘crowd’ is translating, of course, the many (Ƞੂ ʌȠȜȜȠ઀). 66 In some cases it is possible for the one engaged in induction to ask the question in its universal form (਩ıIJȚ į੻ ਥʌ’ ਥȞȓȦȞ ȝ੻Ȟ ਥʌȐȖȠȞIJĮ įȣȞĮIJઁȞ ਥȡȦIJોıĮȚ IJઁ țĮșȩȜȠȣ), in others, not (157a21-22).

Socrates and Induction

215

by Socrates, surely more so than an attempt to understand his method by consulting the Posterior Analytics where the emphasis falls on the deductive side of reasoning and the apodictic syllogistic approach. In comparing rhetorical forms of reasoning to those in dialectic,67 Aristotle, at Rhetoric 1356a35-1356b11, juxtaposes the dialectical epagǀgƝ (induction) and syllogismos (deduction) to the rhetorical paradeigma (example) and enthymema (rhetorical syllogism): “just as in dialectic there is induction on the one hand and syllogism or apparent syllogism on the other, so it is in rhetoric. The example (ʌĮȡȐįİȚȖȝĮ) is an induction (ਥʌĮȖȦȖȒ), the enthymeme (ਥȞșȪȝȘȝĮ) is a syllogism (ıȣȜȜȠȖȚıȝȩȢ), and the apparent enthymeme is an apparent syllogism. I call the enthymeme a rhetorical syllogism, and the example a rhetorical induction.68

Noting that the comparison had already been made in the Topics, Bk I, c. 12, Aristotle elaborates by saying that in induction dialectic works on the many and similar cases just as in example rhetoric does upon the same.69 Induction, as is the case with the example and the rhetorical syllogism, must deal with what is contingent and capable of being otherwise for the most part (ʌİȡȓ IJİ IJ૵Ȟ ਥȞįİȤȠȝȑȞȦȞ ੪Ȣ IJ੹ ʌȠȜȜ੹ ਩ȤİȚȞ ਙȜȜȦȢ—1357a1415). In comparing the example to the induction, Aristotle indicates that the example does not carry the relation of whole to part, part to whole, or whole to whole, but rather of part to part (1357b27-29). The part-to-whole relationship would seem to cover that of the multiple individuals to the

67

It is clear that Aristotle here is considering dialectic to cover the “scientific” understanding of logic. Through much of his corpus Aristotle indicates that there is a strong contrast between dialectical arguments, which are often propaedeutic or preliminary to serious proof, and definitive arguments. 68 At 1356b1 (the last sentence): țĮȜ૵ į’ ਥȞșȪȝȘȝĮ ȝ੻Ȟ ૧ȘIJȠȡȚțઁȞ ıȣȜȜȠȖȚıȝȩȞ, ʌĮȡȐįİȚȖȝĮ į੻ ਥʌĮȖȦȖ੽Ȟ ૧ȘIJȠȡȚțȒȞ. The translation is by W. Rhys Roberts in the Oxford translation. A. F. Didot translates paradeigma as exemplum: Voco autem enthymema quidem, oratorium syllogismum; exemplum vero, inductionem oratoriam, Aristotelis Opera Omnia (Paris, 1848), Vol. 1, p. 314. 69 At 1356b14-15: IJઁ ȝ੻Ȟ ਥʌ੿ ʌȠȜȜ૵Ȟ țĮ੿ ੒ȝȠȓȦȞ įİȓțȞȣıșĮȚ can become either an epagǀgƝ or a example but, if a conclusion is drawn as true universally or for the most part (ਲ਼ țĮșȩȜȠȣ ਲ਼ ੪Ȣ ਥʌ੿ IJઁ ʌȠȜઃ - vel in universum, vel plerumque) from certain principles (IJȚȞ૵Ȟ ੕ȞIJȦȞ ਪIJİȡȩȞ IJȚ įȚ੹ IJĮ૨IJĮ ıȣȝȕĮȓȞİȚȞ - quibusdam positis, aliud quid ex his evenit praeter haec, as Didot translates), one is then confronted with a syllogism in dialectic or an enthymeme in rhetoric.

216

Joseph A. Novak

universal whole, precisely what seems to be occurring in an epagǀgƝ that Aristotle notes at 1393a26, as “the foundation of reasoning.”70 Yet, the way in which an example is used is very close to the way an induction may unfold.71 In order to support by example the statement, “we must prepare for war against the king of Persia and not let him subdue Egypt,” a speaker can use many complex and isolated instances that may even be tied to the past (ʌȡ੺ȖȝĮIJĮ ʌȡȠȖİȖİȞȘȝȑȞĮ) rather than simple and present (or timeless) generic instances. Two examples are brought up of conquering kings, Darius and Xerxes, who both conquered Egypt before each crossed the sea to reach Greece.72 The speaker would conclude, “if [therefore] the present king seizes Egypt, he also will cross [the sea], and therefore we must not let him.” Since the conclusion is simply to a particular, it would not as such be an induction. It would, moreover, differ even from the format of an enumerative induction since other factors in each of the antecedent cases would likely cause this last to bear less of the lawlike similarity to them. Aristotle had included this use of past facts as one member of a division whose other member is subdivided into illustrative parallels (ʌĮȡĮȕȠȜ੾/Į઀) and tales (ȜȩȖȠȚ) as in the case of Aesop).73 With respect to the first he speaks of its use by Socrates, “the Socratic parallel” (ʌĮȡĮȕȠȜ੽ IJ੹ ȈȦțȡĮIJȚțȐ). Due to its relevance to the topic of this paper, it is worth quoting at length: “The illustrative parallel is the sort of argument Socrates used: e.g. ‘Public officials ought not to be selected by lot. That is like using the lot to select athletes, instead of choosing those who are fit for the contest; or using the lot to select a steersman from among a ship’s crew, as if we ought to take the man on whom the lot falls, and not the man who knows most about it.’”74 70

What the Barnes’ translation yields for ਲ į’ ਥʌĮȖȦȖ੽ ਕȡȤȒ (1393a28). Rhet 1393a32-b4. 72 J. E. Sandys, The Rhetoric of Aristotle (Cambridge: Cambridge University Press, 1877), vol. 2, p. 197 has a note regarding the historical accuracy of these examples. 73 At 1393a28, he distinguishes the two species (İ੅įȘ) of examples, the first dealing with past factual items, the second dealing with items of fancy. These two species had fallen under the first member of the set of two genera (įȪȠ IJ૶ ȖȑȞİȚ), example and enthymeme. 74 Barnes’ translation. Note however, that the neuter plural seems to make reference to a number of references in Socrates or writings attributed to Socrates. Aristotle also refers to the Socratic words (ȜȩȖȠȚ) in the Poetics 1447b12 and Rhetoric 1417a21, and even to Socratic dialogues (IJ૵Ȟ ȈȦțȡĮIJȚț૵Ȟ įȚĮȜંȖȦȞ) in one of the Fragments (Ross, Fr. 3). 71

Socrates and Induction

217

Had this reasoning gone on to generate a conclusion such as: “It is always the wise man who should be chosen to direct a given task that requires a skill” one would have an induction at work. Since, however, it is directed to a single case of public officials which is the focus of these parallel support examples, one is presumably not dealing with such a generalization.75 The relative distinction of example and an inductive instance is something that Aristotle explicitly addresses at 1394a9-16. Aristotle states that if in a given situation one has not an enthymeme, one should use examples; if one has an enthymeme, one should use examples only after the argument is given— the argument itself will carry most of the probative force and the example is only supplementary (ਥʌȚȜȩȖ૳). If one were to use several examples in advance (ʌȡȠIJȚșȑȝİȞĮ) of the proof, the argument itself would “seem like an induction (਩ȠȚțİȞ ਥʌĮȖȦȖૌ).”76 This passage lends support to the construal that induction is not the application of a given rule to an instance but the justification and/or establishment of a rule through multiple instances.77 At Rhetoric 1398a33ff., Aristotle provides probably more illustrations how inductions utilize instances to formulate a general rules than elsewhere in his work. There are three principles he is trying to establish, the first dealing with the reliability or accuracy of maternal love, the second addressing the role of trust in the face of past misdeeds, and the third concerning the respect due to wise men. In support of the first he offers three instances involving three sets of characters in three different cities.78 In the case of the second principle he invokes two different types of 75

The resemblance to, yet difference from, the argumentation in the Apology about the poets, engineers, and statements is striking. This, of course, becomes the basis of the craft analogy that exerts such a powerful influence throughout the Platonic dialogues and of the doctrine that virtue is knowledge. See Sandys, ibid., pp. 197-199. 76 Rhet 1394a11-12. 77 One finds a good indication of this at Soph Ref 174a30-37: “Also when, in dealing with particulars (ਥʌ੿ IJ૵Ȟ ȝİȡ૵Ȟ), a man grants the individual case (IJઁ țĮș’ ਪțĮıIJȠȞ), when the induction (ਥʌȐȖȠȞIJĮ) is done you should often not put the universal (IJઁ țĮșȩȜȠȣ) as a question, but take it for granted and use it: for sometimes people themselves suppose that they have granted it, and also appear to the audience to have done so, for they remember the induction (IJોȢ ਥʌĮȖȦȖોȢ) and assume that the questions could not have been put for nothing.” Of interest here in the background is the issue whether the audience might be asking for more instances to validate the universal, a query that can be avoided if the arguer does not proceed to explicitly draw the induction, i.e. induce the universal. 78 For this and the following details Sandys provides considerable historical analysis, ibid., pp. 259-263.

218

Joseph A. Novak

instances of human skilled behavior, noting that it should apply in similar cases.79 In the case of the final principle he offers five sets each comprised of different countries, agents, and recipients of respect. Although there might be variety in the sampling, the question again arises concerning the sufficient adequacy of the base support.80 Aristotle does speak of enthymemes that are based upon inductions from one or more similar cases (IJ੹ į੻ įȚ’ ਥʌĮȖȦȖોȢ ਥț IJȠ૨ ੒ȝȠȓȠȣ, ਲ਼ ਦȞઁȢ ਲ਼ ʌȜİȚȩȞȦȞ), and these enthymemes would also become, once the universal is arrived at, the means for arriving at particulars.81 Notice the one very different use of epagǀgƝ which occurs in De Spiritu 482b14-16 in connection with the three motions connected to breathing: respiration, pulsation, and the third “which introduces and assimilates the nutriment (ਲ IJ੽Ȟ IJȡȠij੽Ȟ ਥʌȐȖȠȣıĮ țĮ੿ țĮIJİȡȖĮȗȠȝȑȞȘ). Later at 483a9, there is talk of this third as “the reception of food” (IJોȢ ਥʌĮȖȦȖોȢ). Although this is clearly a case of homonymy, there is a certain ‘in(tro)duction’ of the food into the system, a certain ‘leading up to’ that is involved. It must be noted, however, that this work is considered spurious.82 One would expect that Aristotle’s use of epagǀgƝ would also occur in his ethical writings and that, just as Socrates’ enterprise was to a large extent motivated by ethical concerns, more light should be thrown on the method itself by looking at its usage in these works. Aristotle uses epagǀgƝ to establish a basic truth articulated at the beginning of Book II of the Eudemian Ethics. He makes two assumptions (ਫ਼ʌȠțİȓıșȦ), one of which is that “excellence is the best disposition or state or faculty of each class of things that have some use or work. This is clear from induction (ਥț IJોȢ ਥʌĮȖȦȖોȢ), for we posit this in all cases (ਥʌ੿ ʌȐȞIJȦȞ Ȗ੹ȡ Ƞ੢IJȦ IJȓșİȝİȞ): for instance…” (1218b37-19a2). He then goes on to cite a number of instances, i.e., a garment, a vessel, a house, and a soul, that will presumably enable the final conclusion. Less clear is the induction he speaks of at Eudemian Ethics 1220a26-29, where the principle being addressed is that “every disposition is both produced and destroyed by the same things applied in a certain manner, for example health by food and 79

More precisely he writes (1398b9), “if this is true of everything else alike (Ƞ੝țȠ૨Ȟ İੁ ੒ȝȠȓȦȢ ਥij’ ਖʌȐȞIJȦȞ)”. 80 Sandys remarks about this section, “The rudimentary kind of induction, of which alone Rhetoric admits; two or three similar cases being adduced to prove a general rule, from which the inference is drawn as to the present case,” ibid., p. 259. 81 İੇIJĮ ıȣȜȜȠȖȓıȘIJĮȚ IJ੹ țĮIJ੹ ȝȑȡȠȢ—1402b16-18. 82 See Die Philosophie der Antike, Band 3: Ältere Akademie—Aristoteles—Peripatos, ed. by H. Flashar (Basel/Stuttgart: Schwabe, 1983), p. 289.

Socrates and Induction

219

exercises and climate; these points are clear from induction (ਥț IJોȢ ਥʌĮȖȦȖોȢ).” Aristotle himself provides no further cases, although V. Décarie points to a passage in the Historia Animalium which is helpful.83 Quite detailed, on the other hand, is the passage at Eudemian Ethics 1220b27-1221a15, where Aristotle is arguing for the principle: “In all cases the mean in relation to us is the best.” In its support he adopts two approaches, through induction and reason (įȚ੹ IJોȢ ਥʌĮȖȦȖોȢ țĮ੿ IJȠ૨ ȜȩȖȠȣ), arguing first by reason that the extremes are mutually destructive, and then by induction which seemingly is shown by example (ʌĮȡ੺įİȚȖȝĮ) and a detailed outline (ਫ਼ʌȠȖȡĮijોȢ). There follows the long list of virtues and vices, fourteen in number, which seem to act as an inductive base in support of the thesis. Further at EE 1248b19-20, he presents a principle: “those ends are noble which, existing for their own sakes, are praised.”84 He uses induction (įȚ੹ IJોȢ ਥʌĮȖȦȖોȢ) to show not only the positive cases in support such as justice and temperance that are praised but also the negative cases in support such as health and vigor which are not praised. Induction is applied beyond the particular propositions noted above to more general principles. In Nicomachean Ethics 1098b3-4, he writes, “Now of first principles (IJ૵Ȟ ਕȡȤ૵Ȟ) we see some by induction (ਥʌĮȖȦȖૌ), some by perception, some by a certain habituation, and others too in other ways.” But what would be an example of a first principle had by induction? H. Apostle thinks that these would be general principles of a science. 85 Presumably one would after a (random?) number of observations be said to have successfully completed an induction; these observations would no doubt be had by means of perception. This is entirely in consonance with what Aristotle says later at 1139b26- 31, where he notes that induction is the beginning point (ਕȡȤ੾) even for the universal (IJȠ૨ țĮșȩȜȠȣ). Since the universals are the basis of the syllogism (IJȠ૨ țĮșȩȜȠȣ), if one wishes to avoid an endless regress of establishing them in turn by other syllogisms, epagǀgƝ must be invoked. What allows the induction (ਲ ਥʌĮȖȦȖȒ) to be the beginning point for the universal is, as ‘Aristotle’ says in the Magna Moralia at 1182b18, that it 83

Aristote: Ethique à Eudème (Paris: J. Vrin, 1978), p. 87, ft. 46. The passage begins at 601a35 and focuses on the effects of weather on various animals. Aristotle cites various types of birds and fish responding to specific weather conditions. 84 IJȠȪIJȦȞ į੻ țĮȜȐ, ੖ıĮ įȚ’Įਫ਼IJ੹ ੕ȞIJĮ ʌȐȞIJĮ ਥʌĮȚȞİIJ੹ ਥıIJȓȞ. 85 In commenting on this passage he writes, “like the principle that bodies of specific gravity greater than that of water sink in water,” Aristotle’s Nicomachean Ethics (Grinnell, IA: The Peripatetic Press, 1984), p. 216. Of course, this very principle is not so articulated by Aristotle.

220

Joseph A. Novak

shares with the definition (੒ ੒ȡȚıȝઁȢ) in the focus on something common (IJઁ țȠȚȞȩȞ).86 The connection of these three concepts will also be something important for Socrates in his quest in the early Platonic dialogues via the elenchic method which searches to formulate definitions on the basis of an induction on similar cases, cases which have something in common. He later (1182b32), in commenting on the limitations of political science, offers an induction: “But neither has it to speak of the common element as arrived at by induction (țĮIJ੹ IJ੽Ȟ ਥʌĮȖȦȖ੽Ȟ țȠȚȞȠ૨.). Why so? Because when we wish to show some particular good, we either show by defining that the same description applies to the good and to the thing which we wish to show to be good, or else have recourse to induction (IJૌ ਥʌĮȖȦȖૌ); for instance, when we wish to show a that magnanimity is a good, we say that justice is a good and courage is a good, and so of the virtues generally, and that magnanimity is a virtue, so that magnanimity also is a good. Neither then will statecraft have to speak of the common good arrived at by induction of the common (țĮIJ੹ IJ੽Ȟ ਥʌĮȖȦȖ੽Ȟ țȠȚȞȠ૨), because the same impossible consequences will ensue in this case as in that of the common good conformable to the definition.”87

There is an intriguing mixture here using an inductive listing but also a syllogistic deduction at the end. Nonetheless, the mention of the different virtues by names gives the rudimentary epagǀgƝ for Aristotle’s conclusion. After this examination of a rather large and diverse set of excerpts from Aristotle’s corpus and before casting an eye upon Socrates’ use of induction, it is necessary to review the major characteristics in Aristotle’s conception of induction that seem to emerge from these passages. This will be a useful summary of the interesting aspects of induction present in Aristotle’s own theorizing and will also facilitate a better understanding of what he means in attributing the use of induction to Socrates. First of all, induction seems to have an assignable syllogistic format; it stands in contrast to deduction/demonstration; it rests on a number of cases and not simply one; these cases may be particulars grasped by perception or types or propositions; inductions may be successful or unsuccessful; inductions may demonstrate a positive or a negative; the epagǀgƝ may terminate in producing an indivisible concept, a definition, or the understanding of a 86

Although the work seems to be authentic, its place vis-à-vis the other two ethical works of Aristotle is still disputed. For a summary of the debate see Die Philosophie der Antike, Band 3: Ältere Akademie—Aristoteles—Peripatos, ed. by H. Flashar (Basel/Stuttgart: Schwabe, 1983), pp. 242-44. 87 Barnes’ translation.

Socrates and Induction

221

thing by reference to analogies; the number of instances or quality of their type to effect a good epagǀgƝ is undecided, although presumably greater diversity with respect to both is desirable; there is some ambiguity regarding the role of induction to verify or illustrate a concept/truth; induction argumentatively has broader appeal than deduction; induction is different from exemplification; inductions may be used to support hypotheses; and induction is useful in comprehending the nature of relationships. 3 Use of Induction in the Platonic Socrates. Aristotle’s development of formal logic (Prior Analytics), a theory of demonstration (Posterior Analytics), and an investigation of argumentative modes and fallacies (Topics, Rhetoric, Sophistical Refutations) give him a reflective edge over Socrates and even Plato. Aristotle clearly spends much time and energy in dealing with methodological issues while in the other two philosophers the remarks about method itself are comparatively few and far between. However, the Platonic dialogues are filled with numerous and varied modes of argument, and thus it is worth citing passages that effectively display at least some of the epagogic characteristics delineated by Aristotle. Plato is thought by some to have already prepared the way for the development of the syllogistic.88 Moreover, in a broader sense of the term syllogizesthai Socrates himself, according to Aristotle, was at work developing arguments, presumably of a type that technically went beyond the Sophists of his day. Since in the early dialogues we see no refined sense of demonstration and since the method of elenchus that is repeatedly used in the Socratic dialogues does not assume a syllogistic form and is not a mode of proving but rather a method of refutation, it would be difficult to apply the term apodeixis here, although the term does surface with a technical sense of Collection and Division in the Sophist and Statesman.89 Passages from any number of the so-called Socratic dialogues could be used to illustrate the use of epagǀgƝ in Socrates/Plato. Given the space limitations of this paper, however, a more protracted analysis of a single 88 See Paul Shorey, “The Origin of the Syllogism,” Classical Philology 19 (1924): 119. This was followed by E. de Strycker’s study, “Le Syllogisme chez Platon,” Revue Néoscolastique de Philosophie 34 (1932), pp. 42-56 and 34 (1932), pp. 218-39. Shorey’s response to de Strycker appears in “The Origin of the Syllogism Again,” Classical Philology 28 (1933): 199-204. Also see the later work by W.D. Ross, “The Discovery of the Syllogism,” Philosophical Review 48 (1939): 251-272. 89 For example, Statesman 277a2.

222

Joseph A. Novak

dialogue might well be the best approach to reveal the nature and role of induction in Socrates. The Hippias Minor is well suited for this purpose. One is led to think that this piece is especially appropriate for revealing something of the Socratic method since the opening of the piece reveals an invitation extended to Socrates to refute (elegchein) a demonstration (‘display’—epideixis) which the Sophist Hippias had given (endeixamenou), a display (epideixis 364b8) which Socrates himself notes that he was reluctant to interrupt by a question.90 The invitation is especially appropriate since the crowd present is constituted of those who pursue philosophy (tes en philosphia diatribes).91 The putatively dominant issue unfolding at the beginning of the dialogue is of the relative characters of Odysseus and Achilles. Socrates picks up the theme that as the Iliad is better than the Odyssey the chief character of the first, Achilles, is finer than the main character of the second, Odysseus. By a consideration of the possibility of one or both characters being wily (false), Socrates soon elevates the dialogical chatter beyond these particulars to the more general connections between the wily, the powerful, the intelligent, the knowledgeable, and the wise and the true. He then enunciates the principle that the good man who is true, is also (on account of his power and intelligence) the one who is also best able to be false, thereby making the true and the false man the same.92 In defense of this principle Socrates proffers what appears to be an induction supported by three instances. His first instance is Hippias himself in light of his mathematical skill. Socrates claims that he is best able to be false about numeric calculations since he is good at calculation and then claims that this ability will hold of any arithmetician. Socrates reasons similarly about Hippias’ skill with geometrical figures and then also claims that this will hold of any geometrician. Third, Socrates reasons in a similar way about Hippias’ skill in astronomy and that of any astronomer.93 Then he turns his attention to all the sciences (țĮIJ੹ ʌĮı૵Ȟ IJ૵Ȟ ਥʌȚıIJȘȝ૵Ȟ): metalwork, shoemaking, poetry, etc., and argues that the same principle applies in these.

90

Within the first two Stephanus pages 363a-364b, terms based on the root of ‘display’ (ਥʌȚįİȚț-) occur four times. 91 On the Sophistic epideixis see G. Kennedy, A New History of Classical Rhetoric (Princeton: Princeton University Press, 1994), p. 22. 92 Hippias Minor 365d-366b. 93 Socrates says here thirdly (IJȡ઀IJȠȞ) as though he were keeping account of the induction.

Socrates and Induction

223

Socrates then moves up to a much bolder principle, which is enunciated at 372d: “those who hurt or injure men, and do unjustly and deceive and cheat and err voluntarily, not involuntarily, are better than those who do wrong involuntarily,” and more succinctly in a question format 373c: “are those who err voluntarily or those who err involuntarily better?” In order to support this, Socrates employs first the superiority of the runner who voluntarily does badly, and then invokes the superiority of the wrestler who does badly. He then contends that he who assumes ungraceful bodily postures voluntarily is superior to one who does so involuntarily. He adds the case of singing and also of limping94 and visual malfunction. Hippias agrees reluctantly that the principle applies to such as these (IJ੹ ȖȠ૨Ȟ IJȠȚĮ૨IJĮ—374d) to which Socrates retorts that it applies to all (ʌ੺ȞIJĮ). The significance of the resistance to “go global” on Hippias part is met by Socrates’ response which seems to rest on the membership of the mentioned body parts with those others such as ears, nostrils, mouth and all the senses (374d). The strength in Socrates’ response rests on the similarity of all these bodily organs and their functions. On account of this, there should presumably not be any need to provide an endless enumeration of parts. However, Socrates does not stop the induction here. Very cleverly he then turns from natural organs to artificial organs (੕ȡȖĮȞĮ), i.e., instruments, of another sort—those external to the body, e.g., rudder, bow, lyre, flute, and “all other things” (IJਛȜȜĮ ı઄ȝʌĮȞIJĮ—374e) and shows how the principle applies in these instances. Next Socrates looks inward to the psyche of a living thing, first of two animals, a horse and dog, and then of man himself. With the former two he secures Hippias’ consent that the better of both animals would be ones whose soul could do vicious deeds voluntarily. In the case of man, Socrates selects as better the archer (IJȠȟંIJȘȢ) who voluntarily misses the mark. As an aside, this seeming irrelevant example (why choose an archer as an example?) does reveal Plato’s brilliance as a writer. The dialogue is now reaching its climax and approaching the very heart of moral action itself. The archer can miss the mark, i.e., hamartia which is precisely one of the basic terms in Greek moral vocabulary. It is no wonder that Socrates says: Is, then, the mind also which errs involuntarily worse than that which errs voluntarily?95 Hippias misses the point (the mark?) and simply responds, “Yes, in the case of archery (ਫȞ IJȠȟȚțૌ Ȗİ—in 94

It was this case that Aristotle focused on in his Metaphysics 1025a10 as noted above. The Greek is quite striking: ȀĮ੿ ȥȣȤ੽ ਙȡĮ ਕțȠȣıȓȦȢ ਖȝĮȡIJȐȞȠȣıĮ ʌȠȞȘȡȠIJȑȡĮ ਲ਼ ਦțȠȣıȓȦȢ; “Is then the soul which misses the mark involuntarily worse than one doing it voluntarily?” —375b. 95

224

Joseph A. Novak

the archer’s art).” Socrates then turns to the medical art, the art of lute playing, flute playing, and “all the arts and sciences” (IJ੹ țĮIJ੹ IJ੹Ȣ IJȑȤȞĮȢ IJİ țĮ੿ IJ੹Ȣ ਥʌȚıIJȒȝĮȢ - 375b). Socrates then raises the case of slaves who are probably representative of the lower part of the soul and gets agreement that they too fall under the principle. Finally, Socrates turns to the higher part of the soul and, much to his own horror, Hippias will have to respond positively to the question “Will not, then, the more powerful and better soul, when it does injustice, do it voluntarily, and the bad soul involuntarily?” He then moves the dialectic up from the component (soul) to the composite (man) and states: “It is, then, in the nature of the good man to do injustice voluntarily, and of the bad man to do it involuntarily, that is, if the good man has a good soul.” A review of this dialectic illustrates several aspects of epagǀgƝ which are noted characteristics of Aristotle’s analysis. The first issue to be addressed is the format of the epagǀgƝ. Socrates’ dialogues, in contrast to the Aristotelian schema, do not contain clearly formatted syllogisms. Likewise, the contrast between epagǀgƝ and deduction is not drawn as it is in Aristotle. Now it is important to note that Socrates is interested in establishing something by argument. Socrates clearly sees argument as directed to uncovering the truth,96 but the comprehension of the steps of a dialogical interchange cannot be formalized into the two premise-conclusion scheme of a deduction. So, although one might not be able to employ the same epagǀgƝsyllogismos contrast in the case of Socrates as in the case of Aristotle, Socrates is certainly engaged in the action of syllogizesthai. It almost goes without saying that a Socratic induction rests on a number of cases; a mere perusal of the dialogues makes one realize that Socrates is always drawing on a number of instances in his argumentation as Callicles remarks to him in the Gorgias, “I believe, on my soul, you absolutely cannot ever stop talking of cobblers and fullers, cooks and doctors, as though our discussion had to do with them” (491A). As one can see from a perusal of these instances, the particulars that are being used in the induction or, better put, “those upon which the universal is induced” are often themselves types or kinds. The Hippias above does show, however, as do other dialogues, that Socrates can even begin with a singular (Hippias himself as arithmetician, geometer, or astronomer; Euthyphro’s own legal action as an instance of judgment in the eponymous dialogue; the use of particulars in refutation as the Scythians and Aeneas in the Laches) and 96

As is obvious from such passages as Euthyphro 5a 9b, 14c15e, despite the patent irony that is at play.

Socrates and Induction

225

then move up to the type, then assembling types to yield the universal. Since so many of the early dialogues are involved with coming to know the “what is it?” or the ti esti of a certain characteristic or virtue, the conclusion is often drawn that an epagǀgƝ will terminate in a simple grasp or intellectual vision of a simple characteristic. This impression can be easily reinforced when one thinks of Plato’s middle theory of Forms as transcendent units comprehended by a noesis or essences grasped by an Aristotelian nous. Yet, Socrates is not engaged in a mystic enterprise to grasp a transcendent thing—as Aristotle himself says that he did not separate the universal—but in search of definitions which he ever tries as a intellectual midwife, albeit unsuccessfully, to extract from the pregnant minds of his interlocutors. Hence, it is not surprising to see that that the elements involved in his epagǀgƝ are propositions. Nor are these limited to being propositions that are simply definitional equalities but they may be of various sorts, as the Hippias Minor (374e) shows, as do other dialogues.97 However, one also wants to leave space that Socrates could pull under induction things that might be relational in structure, as in the case of Aristotle’s induction on analogies, such as all the bodily organs (feet, eyes, etc.) that are related to their respective activities (walking, seeing, etc.). The desired conclusion of an induction might at first blush seem to be a positive statement; this no doubt arises in part from the thought that what is being sought is a simple concept (intuition) or a well-formed definition. However, Aristotle’s own examples as well as those of Socrates show that the conclusion may be statement that is positive or negative in form, e.g., “The true man is not better than the false,” and may even be compound— Hippias Minor (367c).98 That an induction might be unsuccessful seems, of course, to be a real possibility. The fact that Hippias is prepared to halt the onward march to a generalization by stating, in so many words, “it’s true in this case [but not that]” seems to reckon with this possibility.99 It is something that seems—to invert the gadfly analogy—to spur Socrates on to provide more instances. The lack of success if one were not to bring in an adequate number of instances to support the universal claim would be due to incompleteness. 97

The Protagoras provides the argumentation that “Virtue is one,” “No one does evil willingly,” or the Meno, “Is virtue teachable?” 98 In this case it is conjunctive: ੖IJȚ ੒ Į੝IJઁȢ ȥİȣįȒȢ IJİ țĮ੿ ਕȜȘș੽Ȣ ʌİȡ੿ IJȠȪIJȦȞ, țĮ੿ Ƞ੝į੻Ȟ ਕȝİȓȞȦȞ ੒ ਕȜȘș੽Ȣ IJȠ૨ ȥİȣįȠ૨Ȣ; the same man is both true and false about these things and the true man is not better than the false. 99 Consider, for instance, 375b and 374d.

226

Joseph A. Novak

However, this incompleteness could enable not only an unsubstantiated claim but also facilitate a false claim. Clearly, if one picks randomly some instances of a type where all the ones chosen happen to agree in a character and then generalizes that all members of that type must possess that character, one could have concluded to a universal that very well may be false. Intriguingly it seems that in the case of this particular dialogue, the Hippias Minor, Socrates makes some moves that indicate he may be sensitive to this issue. As indicated a bit earlier, the progression of cases seems to provide a solid basis for the universality of the claim that those who err voluntarily are better than those who err involuntarily. He first raises the cases with regard physical limping, then visual impairment, then all the physical organs, then artificial organs, then living things (non-human and human), then to the principle of living things (the soul), then to parts of the soul (lower and higher), then to the whole composite of body and soul. Clearly here, one seems to be moving through all the groupings or types to which the principle might apply. In other words, Socrates is not taking into account each human individual—he would have realized this is impossible. However, by looking at groupings that are systematically linked to another and even where their relationships are governed by a certain conceptual ordering, i.e., some are subordinated to others, Socrates can feel secure that a general claim can be substantiated on their collective basis. One can see how an argument of this sort incorporates a diversity of instances not only in number but especially in type. A more difficult question in examining the nature of epagǀgƝ is the relationship of the instances to the general claim that is being enunciated. This issue is closely related to a famous debate launched by Peter Geach in 1966 in a piece entitled, “Plato’s Euthyphro.”100 In it Geach formulates what came to be known as the Socratic Fallacy: Let us rather concentrate on two assumptions that Socrates makes: (A) that if you know you are correctly predicating a given term “T” you must ‘know what it is to be T’ in the sense of being able to give a general criterion for a thing’s being T; (B) that it is no use to try to arrive at the meaning of “T” by giving examples of things that are in T. (B) follows from (A). If you can already give a general account of what “T” means, then you need no examples to arrive at the meaning of “T”; if on the other hand you lack such a general account, then, by

100

First appeared in the Monist 50 (1966) and reprinted in Logic Matters (Berkeley: University of California Press, 1980), pp. 31-44.

Socrates and Induction

227

assumption (A), you cannot know that any examples of things that are T are genuine ones, for you do not know when you a predicating “T” correctly.101

Although this problem, according to Geach, arises in the case of definitions and the particulars falling under them, it is easy to see that an analogous difficulty arises with regard to epagǀgƝ, one that is closely tied to the problem whether the instances in an epagǀgƝ are supportive of a universal claim or whether they are mere “examples” of that claim. One needs to keep in mind that, according to what Aristotle said above, an example seemed to be something that was singular and illustrative of the claim rather than an item to be invoked in support of it; that examples were appropriately found in rhetorical rather than in more dialectical reasoning. Of course it is quite likely that there is a certain circularity in the movement between the universal claim and the inductive instances. Surely the same particular could be used both as a basis to establish a general claim and later used to exemplify it. One might even suggest that the ‘later’ might be otiose, because it does appear at times in the Socratic dialectic or elenchic that an instance being proffered to an individual interlocutor in support of a claim is, in the very moment, also being used as illustrative of that claim. Thus, though one can admit the distinction of induction and exemplification, there can be a “dialectical” circle between the two. Conclusion An elucidation of the various applications of epagǀgƝ by Aristotle allows one to evaluate more precisely his claim that one of the major contributions of Socrates to philosophizing was the use of epaktikoi logoi. Likewise, an examination of passages in Plato which display Socrates using such types of reasoning renders concrete the Aristotelian claim. The greater the number of Platonic passages examined, the more accurate becomes the comprehension of what this method is. Nonetheless, in the end, one finds oneself confronting the problem raised at the beginning of this paper, namely, the problem of the “real” Socrates versus the “constructed” Socrates, the Socrates of history versus the Socrates of Platonic philosophy. If one uses the Platonic texts as an exemplification of the contribution of Socrates to philosophy, one is confronted with the challenge of demarcating the various methods employed in the dialogues and determining whether Plato’s own approaches affected the reporting of the Socratic method. Aristotle’s birth in 384 B.C. excludes him from real historical 101

Ibid., p. 33.

228

Joseph A. Novak

contact with Socrates who died in 399 B.C.; one presumes Aristotle is deriving much of his thinking about Socrates from what Plato had said and written. However, Plato’s own method seems to have undergone several shifts, as some would have it, from the elenchic and epagogic, to the hypothetical, the dialectical, and finally the method of Collection and Division.102 Although the divisions between these are not so hard and fast as might first appear, the reflective descriptions that Plato provides for the hypothetical method in the Republic103 as well as the “practice” model for Collection and Division at the beginning of the Sophist show far greater methodological sophistication than the epagogic in the early Socratic dialogues.104 The apparent simplicity of the early method of elenchus and epagǀgƝ conceals within itself some deeper methodological moves that more clearly reveal themselves in the later methods. One finds presages of dialectic and argumentative modes that only emerge more clearly as Plato continues his philosophical journey through life, his methods changing accordingly. A more thorough study of the early Socratic dialogues would show anticipations of these techniques to be as flashes of the Socratic/Platonic genius illuminating the dark night of Sophistic confusion. Further, there are characteristics that seemed shared by them all that can plausibly be related to the historical figure who seems to have been the “gadfly” of Athens. Let two brief remarks in this connection here suffice. First, the very term ‘epagǀgƝ’ contains within itself the notion of ‘leading,’ having as its root the Greek term ‘ago.’ One finds a parallel structure in the Latin equivalent ‘inductio.’ Any first-time reader of the Socratic dialogues tends to think that Socrates is rather deceptively asking “leading questions” of his interlocutor. However, there need not be anything perverse or illegitimate in this procedure. Socrates is seen as a teacher leading a student to see the truth rather than putting it somehow into that student’s soul. Thus, one can be lead by many instances to grasp a universal truth. This also seems to involve a movement through time, from one

102

See Richard Robinson’s groundbreaking work, Plato’s Earlier Dialectic, 2nd ed. (Oxford: Clarendon Press, 1953) and Kenneth Sayre’s Plato’s Analytic Method (Chicago: University of Chicago Press, 1969). 103 Note the elaborate discussion in famous section of Republic Book VI on the Divided Line and its correlatives in the Cave in Book VII. 104 See Sophist 218d but also see the Phaedrus 265d-266b description of Collection and Division as well as the method in the Philebus 16b-17a, which may or may not coincide with Collection and Division.

Socrates and Induction

229

instance to another, until the universal is achieved.105 In the dialectic as developed by Plato, there is an upward movement in the dialectical process to the Good (out of the Cave as in the Republic) or a gradual ascent to the Beautiful (as in the Symposium). In both of these latter images, one moves from many instances to the one (Form) and thereby engages in a process that parallels in manner the induction of the early dialogues. Second, in order to effect a good induction, one must keep a “record” of the things observed, an account of the instances that form the base of the generalization to emerge. This record involves the use of memory; its deliberate use in support of a universal involves “recollection.” Traditionally, recollection has been seen as a mental recall of a pre-natal experience of transcendent Forms. This-worldly experiences of material individuals, tokens of a given type, somehow provoke a recollection of transcendent reality functioning as their epistemological and ontological grounding. Plato adumbrates this view in the Meno and more clearly states it in the Phaedo. All this notwithstanding, a more obvious reading of the early dialogues shows recollection to have a more quotidian sense of keeping in mind the instances needed in order to generate a universal.106 This latter use of recollection, seen as a fundamental methodological device operative in the Socratic argument, is artistically alluded to in the Hippias Minor (368d-369b). The method of Socrates is intended to lead the student, i.e., the inquirer, to progress onward toward truth, once that the inquirer has been purified from false beliefs and from clinging to generalities that have no grounding in experience. Induction becomes one of the key elements in this purification process by forcing the inquirer to be attentive to experience and advance thereby to greater comprehension. By attending to particular passages in Aristotle and Plato, this paper can itself, it is to be hoped, furnish an inductive base for a better understanding of the notion of epagǀgƝ in Socrates.

105

One sees this temporal aspect present in Aristotle’s accounts of Metaph I and Post An II, 19, where in the former the move is from perception to experience to art and in the latter there is an assembling of particulars until there is a “rout.” 106 See J. Novak, “The Meno, Recollection, and the Role of Hypothesis,” Society for Ancient Greek Philosophy Newsletter 2004/5, p. 1-11.

The Problem of Example Paul Schollmeier The University of Nevada, Las Vegas

Abstract: According to Schollmeier, for Aristotle, there are two kinds of induction: a theoretical kind, i.e., induction, and a practical kind, i.e., example (see Pr An 2. 23 and 24). Schollmeier aims to show that theoretical induction is not susceptible to the problem of induction, but practical induction is. The reason for this problem lies in the different kinds of preexistent knowledge required for each kind of induction. Induction proper rests on preexistent knowledge of particular species; example rests on preexistent knowledge of individuals. Each kind of induction requires the convertibility of two terms for it to work: The conversion in induction can be perfect because the number of particular species is finite; but the conversion in example cannot be perfect since it concerns individuals, and their number can be infinitely large. Thus, the problem of induction is inescapable in the case of example but not in the case of induction. Schollmeier then draws several parallels between Aristotle’s problem of example and Hume’s problem of induction to further prove his point. He concludes that Aristotle’s logical analysis of induction (in Pr An 2. 23 and 24) shows that induction is empirical only in the sense that it concerns intelligible universals (particular species) acquired through sensation. It is not empirical in the sense that it concerns sensible individuals. Example does concern sensible individuals, hence, the problem of example.

Introduction The very opening sentence of the Posterior Analytics1 poses a problem for a contemporary theory of induction. This sentence is no doubt a puzzlement not only for most students but also for many professors. Recall what 1

The editions of Aristotle followed are Analytica Priora et Posteriora, ed. W.D. Ross (Clarendon Press, 1964); Ars Rhetorica, ed. W.D. Ross (Clarendon Press, 1959); Ethica Nicomachea, ed. I. Bywater (Clarendon Press, 1894); Topica et Sophistici Elenchi, ed. W.D. Ross (Clarendon Press, 1958); and The Basic Works of Aristotle, ed. Richard McKeon (Random House, 2001).

232

Paul Schollmeier

Aristotle says. “All knowledge acquired through instruction (didaskalia) or through reflection (mathƝsis dianoƝtikƝ),” he states, “comes to be from preexistent knowledge (ek prouparchousƝs … gnǀseǀs)”.2 We are today accustomed to think that knowledge can come to be through instruction. Indeed, philosophy professors occupy positions that depend on this very presumption. But we are not at all accustomed to think that any knowledge comes to be through reflection. We reflect merely on what we already know, do we not? Nor are we entirely comfortable with the thought that knowledge can arise from preexistent knowledge. Surely, all knowledge arises from sensation. What no doubt adds to our initial uneasiness are the proofs that Aristotle educes for his assertion. Among them we find the argument that both induction and deduction proceed in this way. That arguments of both kinds instruct us from what we already know, he asserts explicitly. Through syllogisms (dia sullogismǀn), apparently deductive, we grasp knowledge from what we understand, and through induction (di’ epagǀgƝs) we show a universal through a clear particular, presumably known.3 We can probably concede that deduction arises from knowledge that we already have. But we would likely contend that induction, and ultimately deduction, arise only from particulars that we sense. Nor are these sensed particulars entirely clear. Aristotle continues to imply, oddly enough, that rhetoric produces persuasion in a similar manner. Rhetorical arguments work through enthymemes (di’ enthumƝmatǀn), which are deductive, and through examples (dia paradeigmatǀn), which are inductive, he informs us.4 The implication is that an enthymeme arises from knowledge that we already have, and that an example establishes a universal through a known particular. But we might well wonder whether rhetoric could actually produce any knowledge worthy of the name. And, again, would not a rhetorical particular be one that we sense? 1 Our present interest in this opening assertion and its supplementary arguments concerns induction. I wish to pose the obvious question, What is induction? But other questions follow quickly on its heels. Does induction produce new knowledge from preexistent knowledge? Aristotle would 2

Posterior Analytics [Post An] 1. 1. 71a1-2. Post An 1. 1. 71a5-9. 4 Post An 1. 1. 71b9-11. 3

The Problem of Example

233

imply that it does. An induction somehow shows a universal through a known particular. Another question I wish to pose is, What is example? Aristotle implies that an example is an induction, too. But an example does not seem to be a philosophical argument. It is rarely analyzed outside of an introductory textbook on what we call critical thinking. Yet example is somehow philosophical. We frequently use examples in professional discourse. Today we have a particular penchant for contrary-to-fact counterexamples. Our question about induction is, therefore, complex. Its complexity rests on a presupposition. Knowledge for Aristotle, and for us if we deign to reflect on the matter, is of two kinds. “Knowledge” is a homonymic genus, in other words. The genus knowledge includes as its species what we might call knowledge proper, which is theoretical, and what we call belief or opinion, which is practical. Today we tend to think that knowledge proper is not really knowledge, and, curiously, we usually take opinion to be knowledge proper! Because knowledge is of two kinds, induction, I would think, is also of two kinds. If so, we may view “induction” as a homonymic genus. This genus would include both induction proper, which concerns knowledge, and example, which concerns opinion. Induction proper is a logical technique, but example, we shall see, is a rhetorical technique. These techniques for Aristotle have their similarities, but they also have their dissimilarities. Their dissimilarities are not insignificant. Of course, if we have knowledge of two kinds, we would also have preexistent knowledge of two kinds. If, that is, we may claim with Aristotle that we can actually acquire any knowledge through preexistent knowledge. If we do so acquire knowledge, then our inductions, theoretical or practical, would arise, presumably, from knowledge, theoretical or practical, that is somehow preexistent. With my analysis I shall show that problem of induction is actually a misnomer. My title is meant to suggest that it is. The problem of induction, so-called, is, I propose to argue, the problem of example. We have confused the logical technique with the rhetorical, and we have taken the rhetorical technique for the logical! The error, in modern times at least, would appear to have arisen, unfortunately, with the British empiricists. I shall take David Hume as paradigmatic though others would do as well.

234

Paul Schollmeier

2 I would now examine a presupposition. If we have knowledge of two kinds, do we not require intellectual faculties of two kinds? And do not our intellectual faculties concern objects of two kinds? That is to say, I shall assume with Aristotle that our different faculties have different objects, even our intellectual faculties. This assumption many other philosophers share though not all do so wittingly. In the Nicomachean Ethics Aristotle acknowledges that our intellect divides into two faculties. He explicitly does so on the grounds that our soul has different parts, and that these different parts concern different objects.5 The faculties into which he divides the intellectual part of our soul are, he argues, a scientific faculty and a calculative faculty.6 Our scientific faculty concerns “things of which the principles cannot be other than they are,” and our calculative faculty concerns “things that can be other than they are”.7 Our scientific faculty I take to concern knowledge, and our calculative faculty to concern opinion. Knowledge includes theoretical intuition and demonstration, Aristotle argues, and these intellectual virtues both concern objects that cannot be otherwise. That is, their objects are universal and necessary.8 Opinion includes practical intuition and deliberation, and these virtues concern what can be otherwise.9 Knowledge of the practical variety, he explicitly asserts, is opinion.10 This distinction, we might note, is not unknown to modern philosophers. David Hume, despite his differences, acknowledges the distinction, if implicitly, when he discusses human reasoning and its objects. The objects of human reasoning, he asserts, are relations of ideas and matters of fact. Our reasoning about relations of ideas, he implies, rests solely on the principle of contradiction, but reasoning about matters of fact requires another principle, which turns out to be association.11

5

Nicomachean Ethics [NE] 6. 1. 1139a8-11. NE 6. 1. 1139a11-12. 7 NE 6. 1. 1139a6-8. 8 NE 6. 3. 1139b18-24; 6. 6. 1140b33-1141a8. 9 NE 6. 5. 1140a24-1140b7; 6. 11. 1143b35-1144a5. 10 NE 6. 5. 1140b25-28. 11 Hume, David, Enquiries concerning Human Understanding and concerning the Principles of Morals, 2nd ed, eds. L.A. Selby-Bigge & P.H. Nidditch (Clarendon Press, 1978), 4. 1. 25-26; 5. 1. 41-42. 6

The Problem of Example

235

3 Our knowledge for Aristotle, then, is of two kinds. Or, at least, I shall so assume. That induction for Aristotle is also of two kinds, I shall now argue. The one kind, induction proper, leads us to logical principles, which are theoretical, and the other kind, example, takes us to rhetorical principles, which are practical. What is induction of the theoretical kind? Induction, Aristotle tells us, proves that one extreme term belongs to a middle term by means of another extreme term. More specifically he explains that induction shows that a major term belongs to a middle term by means of a minor term. His example is well known. If man, horse, and mule, say, are bileless, and if man, horse, and mule are long-lived, then induction shows that all bileless animals are long-lived.12 A theoretical induction turns on an assumption of convertibility. This convertibility is of the minor and the middle terms. Convertibility of these terms is possible, Aristotle explains, if the middle term is not wider than the minor, and if the minor term includes all the particulars.13 The resulting conversion in his example is that all the bileless animals are either man, horse, or mule. We thus have a deductive syllogism: All bileless animals are man, horse, and mule; man, horse, and mule all are long-lived; therefore, all bileless animals are long-lived. We now see what preexistent knowledge that induction requires. The preexistent knowledge required for an induction is our knowledge of the species under consideration. This knowledge, Aristotle states explicitly, must be of all the particulars.14 In his example the preexistent knowledge is that man, horse, and mule are long-lived, and that man, horse, and mule are bileless. These species are the most particular species within a genus. They are what we may handily call in scholastic parlance the infimae species. Please notice that knowledge of the infimae species is not knowledge of individuals. Our knowledge of any species is for Aristotle knowledge proper. If we know a species, we know that which cannot be other than it is. A species is a universal and necessary object. But we know an individual only in the sense that we have an opinion about it. An individual can obviously be other than it is. An individual is a contingent and particular object. 12

Prior Analytics [Pr An] 2. 23. 68b15-23. Pr An 2. 23. 68b23-27. 14 Pr An 2. 23. 68b26-28. 13

236

Paul Schollmeier

An induction for Aristotle arises not from the individual instances of a species, then, but from the species themselves. Induction goes from lower species to higher species, which are their genera. An induction, please note, does not require that we enumerate all the individuals. If I am right, induction does not require that we enumerate any individuals. Aristotle can thus argue, I think, that induction is about universals that we already know. He argues, after all, that induction, as does deduction, proceeds from preexistent knowledge. This preexistence knowledge, I am arguing, is knowledge of infimae species. 4 But a contemporary reader is bound to ask, Whence our knowledge of infimae species for an induction? Does our knowledge of species not arise from sensation? Aristotle rests his epistemology on psychology. He sets out his position in a passage no doubt familiar. Our mind is so constituted that from sense perceptions arise memories, and from memories arise experiences, which are universals within our soul. And our universals, he explains, furnish first principles for both art and science.15 But this psychology hardly seems sufficient. Our preexistent knowledge of universals would seem to be a less than adequate basis for a science. Where does our knowledge of this sort come from? It would appear simply to pop into our heads. Science for Aristotle does not even constitute an observational science, let alone an experimental science. It does not rest on any empirical observation at all, apparently. Aristotle would no doubt reply quite simply that he is analyzing science only of a kind acquired through instruction or through reflection. Remember the first puzzling sentence of the Posterior Analytics? This is armchair science at its finest! It is empirical science only in the sense that its objects are universals acquired through sensation. It is not empirical science in the sense that its objects are sensible individuals. 5 What, then, is practical induction for Aristotle? A practical induction is an example. An example, Aristotle argues, proves the major term to belong to the middle by means of a term resembling the minor term.16 To prove that a war against a neighbor is evil, we can show that a war, say, against the 15 16

Post An 2. 19. 99b34-100a9. Pr An 2. 24. 68b38-39.

The Problem of Example

237

Phocians was a war against a neighbor and was evil.17 The resembling term is the Phocian war, war against a neighbor is the middle, and evil is the major. We may, he observes, use several instances to show that a war against a neighbor is evil.18 Why does Aristotle say that we prove the major to belong to the middle term by a term resembling the minor? Do we not do so by means of the minor itself? The fact is that we often use an example to apply its inductive conclusion to a new particular. If we know that a war against Thebans, say, is a war against a neighbor, we may wish to know whether it would be a good thing or a bad thing to undertake. By taking the Phocian war as an example, we can establish our major premise, that a war against a neighbor is bad, and then easily apply the major term to the minor.19 Aristotle briefly discusses convertibility and example. He remarks explicitly that example, unlike induction, does not draw its proof from all the particulars.20 Yet we can see that the minor and middle terms must be convertible. Otherwise, we would have not a deductive syllogism. The minor premise resulting from the conversion is that a war against a neighbor was the Phocian war. The syllogism resulting from the conversion would be: A war against a neighbor was the Phocian war; the Phocian war was evil; therefore, a war with a neighbor is evil. What is the preexistent knowledge that example requires? Example requires knowledge of individuals that are sensible. Or, more precisely, it requires opinion about sensible individuals. We must have an opinion, to continue with our example, about one or more past wars against neighbors, and our opinion must be that these wars turned out badly. Otherwise, we would have no minor terms upon which to base our proof that a war against a neighbor is evil. Notice, too, that example yields not a theoretical but a practical principle. A general occupied with military affairs, for example, does not have the leisure to work out a theory of warfare. His concern is with present exigencies. Should he go to war with his neighbor? He obviously does not concern himself about universals but about individuals. No one, Aristotle remarks, deliberates about that which cannot be other than it is.21

17

Pr An 2. 24. 69a4-7. Pr An 2. 24. 69a11-13. 19 Pr An 2. 24. 68b41-69a4, 69a7-11. 20 Pr An 2. 24. 69a19. 21 NE 6. 2. 1139a13-14. 18

238

Paul Schollmeier

We can now see what the problem of example is. The conversion in induction and the conversion in example differ significantly. The conversion in induction can be perfect. Why? The number of infimae species is finite. The number in some genera may be large, but their number is a definite one. The conversion in example cannot be perfect. Example concerns individuals, after all. Their number can be and often is very large indeed. It would be indefinitely large if not infinitely large. But you may object, does not an example lead us to a universal? In our present example, the universal would be that to wage war against a neighbor is a bad thing. My response is that this proposition is not a universal proper, but that it is what we ought rather to call an empirical generalization. A universal of this kind constitutes not knowledge but opinion. It concerns individuals in innumerable number. Aristotle recognizes this philosophical difference. He explicitly argues that we may either know or opine a general proposition. If we have knowledge, we grasp a truth as not capable of being other than it is, but we grasp a truth as capable of being other than it is if we have opinion.22 We may, he explains, view our humanity either as incapable of being other than animal or as capable of being other than animal.23 6 One might wonder, does Aristotle offer any psychology to account for example? He does, we have seen, take up the epistemological psychology of induction in the Posterior Analytics. Unfortunately, he does not, as far as I know, in his logical treatises or in his rhetorical treatise discuss an epistemological psychology for example. He does, however, extend his analysis of example in the Rhetoric, and his extended analysis points the way toward an implicit psychology. I would note that rhetoric clearly concerns the same ontology that example concerns. Rhetoric, Aristotle argues, concerns things that we deliberate about.24 But we do not deliberate about things that cannot be otherwise. We deliberate, he states literally, about things that “can turn out either way”.25 He argues that rhetoric offers arguments of two kinds about these contingent things. These arguments we have already encountered. They are 22

Post An 1. 33. 89a16-21. Post An 1. 33. 89a33-37. 24 Rhetoric [Rhet], 1. 2. 1357a1- 2. 25 Rhet 1. 2. 1357a4-7. 23

The Problem of Example

239

enthymeme, which is deductive, and example, which is inductive.26 Both enthymeme and example, he asserts more explicitly, concern “things that can be other than they are,” though some of these are necessary. These contingent things, he explains, are both probabilities and signs, and some signs are necessary.27 In the Rhetoric Aristotle also recognizes examples of three kinds. He divides these kinds into examples of things that have happened before or examples that are made up.28 Examples of things that have happened are the more pertinent for our purpose. These examples must clearly rest on preexistent knowledge, or rather opinion, about the past.29 These examples are the more useful, he observes, because the future for the most part resembles the past.30 Made up examples he subdivides into fables and parables. Fables, he explains, would include animal stories, such as those of Aesop.31 Parables include the arguments of Socrates.32 I would presume that fables and parables also require preexistent opinion on which to base their inferences. He argues only that we can easily invent parables and fables if we can see the similarities between things, which we learn from philosophy.33 7 We can now see what psychology Aristotle has to offer for example. He appears, at least, to discuss a psychology appropriate to historical examples in the short treatise On Memory and Recollection. What we shall discover is that Aristotle has a theory of association, and that his theory can explain how we form inferences with examples taken from the past.34

26

Rhet 1. 2. 1356a35-1356b6. Rhet 1. 2. 1357a22-1357b10. 28 Rhet 2. 20. 1393a28-30. 29 Rhet 2. 20. 1393a32-1393b4. 30 Rhet 2. 20. 1394a6-8. 31 Rhet 2. 20. 1393a30-31, 1393b8-1394a1. 32 Rhet 2. 20. 1393b4-8. 33 Rhet 2. 20. 1394a3-5. 34 Samuel Taylor Coleridge drew my attention to this little treatise. But Coleridge does not see a connection to rhetoric or to example (Samuel Taylor Coleridge, Biographia Literaria, ed. George Watson (E.P. Dutton & Co., 1975), 5. 60; cited recently by White and Macierowski, Commentaries on Aristotle’s On Sense and What is Sensed and on Memory and Recollection, eds. Kevin White & Edward M. Macierowski (The Catholic University of America Press, 2005), v). 27

240

Paul Schollmeier

Our concern is not with memory but with recollection. Aristotle states that, when we recollect, one psychological motion naturally comes to be after another.35 Recollection, he continues, can proceed either by necessity or by habit! By necessity one motion will, presumably always, lead to another. By habit one motion will lead to another “for the most part”.36 That we recollect knowledge proper by necessity, and by habit we recollect opinion, I shall assume.37 We are concerned with recollection of opinion, of course. What happens, Aristotle explains, is that one psychological motion leads to another motion, and these motions become a habit.38 When we recollect, we first feel one mental motion, and then we fell another motion after it. We can in this way recollect by thinking now from one motion similar to, contrary to, or contiguous with the motion sought!39 Aristotle explains further that our mental habits can become natural. We remember more quickly that which we more frequently think about. This psychological process rests on an assumption that motions in our mind and motions in nature follow similar paths.40 But he points out that, as an extraneous thing can divert the usual course of nature, so an extraneous thing can also divert our mind can from its recollection.41 Similarity would obviously be the most important quality for the recollection of an example. Recall that an example proves a major term to belong to a middle term by a term resembling the minor. Consider Aristotle’s example again. If we wish to know whether a war with our neighbor is good or bad, we ought to recall other past wars with neighbors, and recall whether they were good or bad. That fables and parables also rest on similarity, we can without difficulty see. We can, Aristotle argues, better make up fables if we see the similarities between things.42 Fables about animals, for example, rest on similarities between animals and their situations and ourselves and our

35

On Memory and Recollection [Memory] 2. 451b10-11; 451b22-25. Memory 2. 51b10-14. 37 But see Memory 2. 452a2-4. 38 Memory 2. 451b14-16, 451b28-29. 39 Memory 2. 451b16-22. 40 Memory 2. 452a26-30; 451b31-452a1. 41 Memory 2. 452a30-452b7. 42 Rhet 2. 20. 1394a3-5. 36

The Problem of Example

241

situations.43 Parables turn on more general similarities between different subject areas.44 8 Aristotle briefly discusses a method for recollection. His method lends itself to an analysis similar to example. He argues that we ought to start with a universal principle that is a middle term.45 From a middle term we can proceed to its minor terms or to its major term, he implies. His argument is schematic. From the middle term C one might recollect the minor terms F or G. Or from the middle H one might recollect the minors D or E. One might also recollect from the middle terms C or H the major term A.46 His analysis of example in the Prior Analytics can serve to illustrate his schematic argument. We might, for example, recollect from the middle term to a minor term. From war against a neighbor we can recollect the Phocian war or the Theban war. Or we might recollect from the middle term to the major. From a war against a neighbor we can recollect evil. Aristotle explicitly concludes that recollection is not memory because recollection is a syllogism of a certain kind. One who recollects, he states, is syllogizing and inquiring.47 Might he not have in mind a syllogism of the kind that rhetoric employs, especially argument by example? He adds that animals that can recollect have a faculty of deliberation because deliberation is a syllogism of a certain kind.48 I would add that animals with a deliberative faculty can employ rhetoric in their deliberations.49 We have, then, confirmed our inference that we can acquire knowledge of more than one kind from preexistent knowledge of more than one kind. Our preexistent knowledge can be either knowledge proper or opinion. That is, it can be either theoretical or practical knowledge. 43

see Rhet 2. 20. 1393b8-1394a1. see Rhet 2. 20. 1393b4-8. 45 Memory 2. 452a17-19; also 451b29-452a2; 452a12. 46 Memory 2. 452a19-24. Aquinas suggests this interpretation with a diagram of recollection (Commentaries 6. 220). But he does not see a connection with the middle term of example. He appears to view the middle term as useful for an association less disciplined (219-220). Unfortunately, David Ross in his commentary makes a number of emendations to the text, and these emendations would undermine this interpretation. He would make recollection rest primarily on association not by similarity but by contiguity (Naturalia 241, 247-248). 47 Memory 2. 453a6-10. 48 Memory 2. 453a12-14. 49 Rhet 1. 2. 1357a1-7, e.g. 44

242

Paul Schollmeier

Induction rests on preexistence knowledge of infimae species, but example rests on preexistent opinion about individuals. Our preexistent knowledge depends on objects of different epistemological and ontological status. Induction, recall, concerns knowledge about universals, which are eternal and necessary. They are principles that cannot be other than they are. Example concerns opinion about individuals, which are decidedly contingent and temporary. They are what can be other than they are. 9 ǿ can now show you, if you have not already divined it, why the so-called problem of induction is actually the problem of example. The conventional wisdom is that the problem of induction originated with David Hume. Let us see what Hume tells us about induction. Unfortunately, we immediately find ourselves somewhat disadvantaged by his discussion. Hume fails to use the term induction in any philosophical sense, and he does not offer a logical analysis of the technique.50 We can see, nonetheless, that for Hume any problem of induction clearly could not be a problem concerned with knowledge but a problem concerned with opinion. Recall how Hume divides the objects of human reason into relations of ideas and matters of fact. His concern is not with relations of ideas but with matters of fact. Relations of ideas, he all but explicitly asserts, we can discover by reflection or instruction! Explicitly he asserts that they are discoverable “by the mere operation of thought”.51 He also indicates that relations of ideas rest on the principle of contradiction. Their contraries, he implies, would be self-contradictory. Our mind cannot conceive them with any clarity.52 Nor are these relations dependent on any existent object. Euclidean geometry would remain certain even if no circle or triangle ever existed in nature, he explains.53 50

Electronic searches of online editions show that Hume does not use the term “induction” even once in the Enquiry concerning Human Understanding. He uses the term only twice in A Treatise of Human Nature, but he uses it in an ordinary, not a philosophical, sense (Treatise 1. 2. 1. 26-27; App. 628-629). Nor does Hume use the term “example” in the Enquiry. He does use the term seven times in the Treatise, but he, again, uses it always in an ordinary, pedestrian, sense (e.g., Treatise 1. 4. 7. 273274; 3. 2. 2. 497-498; or 3. 2. 5. 519-521). 51 Enquiry 4. 1. 24. 52 Enquiry 4. 1. 25-26. 53 Enquiry 4. 1. 25.

The Problem of Example

243

But matters of fact we can never discover by the operation of thought alone. We know matters of fact by cause and effect, and cause and effect we know by experience only.54 Matters of fact also have contraries that are not self-contradictory, and the mind can clearly conceive them. That the sun will not rise tomorrow, is a proposition quite intelligible.55 That the sun exits in nature, Hume does not bother to assert. We find, then, an echo in our modern philosopher of the ancient distinction between knowledge and opinion. Human reason according to Hume has two distinct objects. Relations of ideas cannot be other than they are, we might say. Their contraries imply a contradiction, and they are inconceivable. Matters of fact can be other than they are. Their contraries are quite conceivable and imply no contradiction. 10 What is the so-called problem of induction, then? The problem for Hume, if he thought it the problem of induction, obviously does not concern knowledge proper and its object but rather opinion and its object. Hume explicitly inquires not after a principle for relations of ideas but after a principle for matters of fact. Relations of ideas rest on the principle of contradiction, he assumes. But on what principle do matters of fact rest? he asks.56 Hume, indeed, shows why our beliefs about factual matters, and our inductive beliefs in particular, cannot constitute knowledge. We can have no intuitions with which to construct demonstrations, he argues. He denies in effect that universals can exist in nature. Or, rather, that we can know them to exist in nature. Nature withholds “all her secrets” from us, and keeps her powers concealed, he explains. She reveals to us only “a few superficial qualities of objects.” These qualities we are aware of through sensation only.57 We consequently cannot discover a middle term, which Hume calls a medium, for a demonstration.58 If we could discover a middle term, we would be able to form a demonstrative syllogism. But we cannot know by what secret power bread nourishes, for example.59 If we did, we would know a connection between the observed qualities of bread and the enjoyed 54

Enquiry 4. 1. 26-30. Enquiry 4. 1. 24-25. 56 Enquiry 4. 1. 26; 5. 1. 41-42. 57 Enquiry 4. 2. 32-33. 58 Enquiry 4. 2. 34, 36-37. 59 Enquiry 4. 2. 33, 37. 55

244

Paul Schollmeier

qualities of nourishment. Our demonstration would be: bread has this power, this power nourishes, therefore, bread nourishes. We again see that the problem of induction, so-called, must concern matters of fact. Should you still harbor a doubt, Hume reminds us that without any contradiction the course of nature can change. May I not conceive, he asks, that a body resembling snow in all other respects might yet have the feeling of fire or the taste of salt?60 Matters of fact, in other words, can be other than they are. 11 We might now ask, Does Hume show that our reasoning concerned with matters of fact takes a form similar to example? Unfortunately, Hume does not present a syllogistic analysis for his solution to what he calls his skeptical doubts. But from what he does say about his doubts we can with little difficulty construct a formal analysis of his solution, and the analysis so constructed turns out to be identical to the formal analysis of example. Hume asks in effect how we can show that a major term belongs to a middle term by means of a term resembling the minor! To continue with his example, How do we know that bread nourishes? We can show that this loaf was bread, and that this loaf nourished us.61 The resembling term is this loaf; the middle term is bread; the major is nourished us. He tacitly assumes that we may use several instances to show that bread nourished. He is particularly concerned to show that we may apply our major premise to a new minor term. How, he asks, can we show that bread will nourish us in the future? He shows that we can apply the major term to a new minor term by means of the middle term. By taking this loaf as our example, and perhaps other loaves as well, we can establish a major premise, that bread nourishes us, and we can apply the major term to the new minor. We conclude that the loaf in question will also nourish us. What many philosophers take to be the problem of induction concerns the convertibility of the minor and middle terms. Without their convertibility we cannot apply the major term to the new minor. The minor premise resulting from the conversion would be that bread included these loaves. The requisite syllogism resulting from the conversion would be: Bread included these loaves; these loaves nourished; therefore, bread nourishes. 60 61

Enquiry 4. 2. 35. Enquiry 4. 2. 33, 37.

The Problem of Example

245

But the minor terms and the middle term are not perfectly convertible. Hume is at pains to point out that we cannot know the minor term in all its instances. We have experience only of the past instances, and we do not know all the past instances. Nor are the past instances, even if we knew them all, exhaustive. The presumed instances of the future also remain unknown.62 What is more, Hume kindly reminds us that the past instances need not resemble the future instances.63 12 Hume, then, is concerned with what I call the problem of example. He is concerned with opinion and its object. Or, he himself would say, with belief and matters of fact. His question, then, is, How can we come to a conclusion about a future particular if our awareness of past particulars is not exhaustive? Put in other terms, How can we induce a general proposition and apply our proposition to a new particular if matters of fact can be other than they are? He famously finds his answer in his epistemological psychology. He argues that habit carries us from past particulars to a future particular! The observation of past particulars occasions a mental habit, and this habit impels our thought toward a new particular. The repetition of an activity produces a propensity to renew the activity, and this propensity is the result of custom, he argues.64 After observing, for example, loaf after loaf to be bread and to nourish, we cannot but expect a future loaf to be bread and to nourish. Hume offers a psychology uncannily similar to the Aristotelian. His psychology would even appear to allow, albeit implicitly, for matter of fact reasoning by example of three kinds. He clearly admits of historical reasoning by example. He calls reasoning of this kind probability of cause. When events are not entirely uniform, we favor those past events found to be the most usual, he argues.65 His example of bread concerns memories about past instances of eating bread and of being nourished. But he also allows for matter of fact reasoning that we make up. Reasoning of this kind he calls probability of chance. He does not give any examples of animal fables. But consider his example of a die. If a six-sided die has one number on four sides and another number on two sides, we can 62

Enquiry 4. 2. 33-34. Enquiry 4. 2. 37-38. 64 Enquiry 5. 1. 43-45. 65 Enquiry 6. 57-59. 63

246

Paul Schollmeier

infer that the number on four sides is twice as likely to turn up. Why? We imagine the various outcomes of casting the die, and to those outcomes more frequent we give our assent.66 We might even say that he allows for parables. He acknowledges that reasoning about matters of fact can concern general as well as particular facts. Reasoning concerned with general facts includes the empirical sciences, among them politics, chemistry, and physics. These sciences concern “whole species of objects”.67 I would add that Hume and Aristotle share two similar presuppositions. Hume observes that what I call historical instances rest on the supposition that the future resembles the past.68 He also marvels at the harmony, apparently pre-established, between the course of our ideas and the course of nature.69 13 My reader may agree that there is a general similarity between the Humeian and the Aristotelian epistemological psychology concerning matters of fact or opined things. But you might yet object that Aristotle does not mention causation when he discusses mental habit and association. He lists only resemblance, contrariety, and contiguity.70 Nor does Hume mention association by contrariety. He lists resemblance, contiguity, and cause and effect.71 I would answer that Hume does allow for association by contrariety. He argues explicitly that one can derive contrariety from resemblance and cause and effect. His argument is terse. But its conclusion appears to be that the idea of an effect we associate by similarity with the idea of an effect not yet realized. Obviously, an effected object and an object not effected are contraries. What he states is that the cause of the annihilation of an object and the idea of its annihilation imply the idea of the object not yet annihilated.72 Could Aristotle not argue, conversely, that we can derive association by cause and effect from resemblance and contrariety? The idea of an 66

Enquiry 6. 56-57. Enquiry 12. 3. 164-165. 68 Enquiry 4. 2. 35-36, 37. 69 Enquiry 5. 2. 54-54. Coleridge goes so far as to claim that Hume acquired his concept of association from the commentary of Thomas Aquinas on the Parva Naturalia. He asserts that Hume owned a copy of the commentary, and that his copy had marginalia in his hand (Biographia 5. 60). 70 Memory 2. 451b18-20. 71 Enquiry 3. 24. 72 Enquiry 3. 24. n. 4; also see Treatise 1. 1. 5. 15. 67

The Problem of Example

247

object and the idea of the annihilation of an object imply an idea of a cause. Assume an object, say a human being, to remain similar to itself and yet to undergo change. Allow this object to lose one contrary and to gain another, changing, say, from alive to dead or from hungry to fed. The new contrary would be an effect, obviously, and would imply a cause. I would point out, nonetheless, that association by resemblance is sufficient for my purpose. An example concerning wars with neighbors rests on a similarity among the minor terms. A war with the Phocians and a war with the Thebans are similar in that they were wars with neighbors, and they ended badly. And so a loaf yesterday and a loaf the day before are similar in that both are bread, and both nourished. 14 I now conclude. With Aristotle I recognize a logical technique that we can use to form universal propositions by going from lower to higher species, and I also recognize a rhetorical technique that we can use to form empirical generalizations by going from individuals to lower and higher generalizations. With Hume I agree that we can induce a general proposition from individual particulars. But I would argue that we can do so not by induction proper but by example, and I would claim that we can use example to arrive not at a genuine universal but only at an empirical generalization. I concede, however, that we can take an empirical generalization for a genuine universal. That is, we can induce a major premise through example, and we can view our major premise as concerned with what cannot be otherwise and not with what can be otherwise. Aristotle recognizes explicitly this philosophical fact. We may, recall, view our humanity either as incapable of being other than animal or as capable of being other than animal.73 But how do we know whether our major premise is a universal or a generalization? This question is one for dialectic and not for logic or rhetoric, Aristotle argues. Dialectic is an art that enables us to discover universal propositions. This art is useful for discovering the principles of the sciences, he explains.74 But only through opinions we can discover these principles, he explicitly states.75 Aristotle also asserts that rhetoric concerns propositions that do not belong to a science or an art. He cautions us that the better we select our 73

see Post An 1. 33. 89a33-37. Aristotle, Topics 1. 2. 101a36-37, 101b3-4. 75 Topics 1. 2. 101a37-101b2. 74

248

Paul Schollmeier

premises the closer we come to some other discipline.76 He in fact observes that, if we select our premises too well, we might stumble upon a premise that is a first principle of a science. We are then engaged in science and not in rhetoric.77 Yet I cannot myself but wonder whether these universal principles might not be empirical generalizations that we happen to think unexceptional. Hume offers, perhaps, an insight into our knowledge proper or, he would say, into our relations of ideas. Necessity Hume reduces to a psychological phenomenon. A necessary connection of cause and effect is one that in our experience admits of no exceptions.78 Fire always burns, and water always suffocates.79 Can we truly know any universal, then? I must admit that I have my doubts. We can enjoy when at our leisure, perhaps as a respite from our empirical travails, what might prove to be eternal and necessary truths in all their divine splendor. We do so when we indulge in instruction or in reflection on our acquired universal concepts. But we must inexorably awaken from our divine slumbers. When we arise from our armchair or from our professorial chair, we are obliged to employ truths decidedly contingent and temporal. We do so whenever we might wish to wend our way back to the office after class, perhaps, or, if we are at home, to the fridge for a frosty beer. Conclusion We ought, then, to keep in mind that induction is a homonymic genus. It includes what I would call induction proper and example. Aristotle speaks of induction proper when he discussions induction, but the British empiricists speak of what Aristotle would call example when they discuss induction. Though he does not use the term, Hume clearly discusses not induction but example. We have, further, two distinct inductive techniques, one logical and one rhetorical, and they concern objects of two kinds, one necessary and one contingent. I would suggest that we may wish to keep these two techniques and their two objects separate, and that we may find them of use for philosophical or practical purposes, which are obviously distinct.

76

Rhet 1. 2. 1358a2-9. Rhet 1. 2. 1358a10-26. 78 Enquiry 7. 2. 73-76. 79 see Enquiry 6. 57. 77

The Problem of Example

249

But let us not forgot preexistent knowledge. We can see that these two techniques rest on preexistent knowledge of two kinds. Induction rests on known universals, which, presumably, cannot be other than they are. These universals are the infimae species arising in our soul. Example rests on opined particulars, which, obviously, can be other than they are. These particulars are memories resting in our soul. I end with a humbling question, Could we possibly know or opine anything other than the meagre furnishings of our own mind?

The Object of Aristotelian Induction: Formal Cause or Composite Individual? Christopher Byrne St. Francis Xavier University

Abstract: According to a long interpretative tradition, Aristotle holds that the formal cause is the ultimate object of induction when investigating perceptible substances. For, the task of induction is to find the essential nature common to a set of individuals, and that nature is captured solely by their shared formal cause. Against this view, Byrne argues that Aristotle understands perceptible individuals as irreducibly composite objects whose nature is constituted by both their formal and their material cause. As a result, when investigating perceptible objects, the task of induction is to discover their composite, formal and material nature. The process by which universal claims about this composite nature are justified, Byrne argues, is similar to what we now know as mathematical induction. In particular, such claims are grounded in a nonenumerative, but replicable process in which things are resolved into their simplest components. As a result, the observation of past uniformities has, at most, a heuristic function in scientific inquiry.

Introduction According to a long interpretative tradition, Aristotle holds that the formal cause is the ultimate object of induction when investigating perceptible substances. The task of induction here is to take the step from empirical observation to scientific knowledge by finding what is essential and invariable in the objects under investigation. On the traditional view, this process proceeds by way of abstracting the formal cause from the set of perceptible individuals in which it is found. For, it is argued, the formal cause is the only part of individual perceptible substances that is both essential to them and invariable. The material cause has a role to play in that it individuates different members of the same species. It does not, however, contribute to their essential nature because it is only responsible for their idiosyncratic, transitory properties. Understanding perceptible substances,

252

Christopher Byrne

then, requires analyzing them into their material and formal causes and then setting aside their material cause in favour of their common, formal nature. Against this view, I argue that Aristotle understands perceptible individuals as irreducibly composite objects whose nature is constituted by both their formal and their material cause. Indeed, given that the job of induction is to discover what is necessary and invariable in perceptible individuals, it must look at their material causes. For necessity in perceptible objects always involves their material causes. To make this case, in section I below, I set out Aristotle’s account of the goal of induction, namely the discovery of the first principles of any given science; in section II, I consider the traditional account of how we reach these first principles through induction, as well as two problems with this account; in section III, I argue that Aristotelian induction is, instead, similar to what we now know as mathematical induction. Finally, in response to the traditional account of induction, I consider the role of formal causes in defining perceptible objects. 1 Historically, inductive arguments have been characterized in two ways: 1) inductive arguments take the step from the particular to the universal inasmuch as they conclude with a claim about all of the members of a given set of things on the basis of information about just a finite sub-set of those things; and 2) they are not deductively valid arguments in that their conclusion does not necessarily follow from their premises.1 Both of these features are anticipated by Aristotle. In his Posterior Analytics, Aristotle argues that induction is the process by which we move from the perception of individuals to the knowledge of universals.2 In addition, he argues that the job of induction is primarily to find the first principles that serve as the basis for scientific knowledge.3 There are several criteria that these scientific first principles must fulfill; one is that they must be indemonstrable, or, as Aristotle puts it, first in the order of demonstration.4 In other words, 1

Modern accounts tend to use just the second, non-deductive characteristic. See, for example, Merrilee Salmon, Introduction to Logic and Critical Thinking, 3rd ed. (Fort Worth, TX: Harcourt Brace & Co., 1995), pp. 69-70. Howard Kahane calls an inductive argument that draws a universal conclusion from premises concerning particular cases a ‘categorical inductive generalization.’ Logic and Philosophy: A Modern Introduction (Belmont, CA: Wadsworth, 5th ed., 1986), p. 289. 2 Posterior Analytics [Anal. post.] I 1, 71a1-11; 18, 81a38-b9; II 19, 100b3-4; see also Topica I 12, 105a11-19. 3 Anal. post. II 19, 100a15-b15. 4 Anal. post. I 2, 71b21 & 26-29; 72a5-8 & 14-15; 10, 76a31-32.

The Object of Aristotelian Induction

253

these first principles cannot be derived from any other propositions. Given that these first principles are discovered by induction, induction cannot itself be a deductive process; if it were, the propositions discovered by induction would be derivable from other propositions and, hence, not themselves indemonstrable. Aristotle’s account of induction, however, is more restrictive than the modern account, because he sets further requirements on the principles that induction is expected to discover. Given that the job of induction is primarily to find the first principles of any given science, the restrictions on what kinds of proposition can act as these first principles impose requirements on the kinds of proposition induction is expected to yield. Thus, in addition to being universal and indemonstrable, the principles discovered by induction must also be explanatory.5 For, among other things, scientific knowledge provides the reasons or causes for things being as they are.6 This requirement explains why, on Aristotle’s account, induction cannot just be a matter of empirical generalization. For, such generalizations only state that something is the case, not why it is the case.7 Instead, the first principles of any science must explain the phenomena in question. As a result, these first principles must also take the form of one of the four types of explanatory principle that Aristotle recognizes, namely the formal, material, efficient, and final causes.8 Finally, the first principles of a science must be necessary in the sense of stating what is invariable and cannot be otherwise with respect to the subject matter of that science.9 Here again, empirical generalizations fall short, for, in the absence of knowledge of what is necessary, observations of past uniformities remain idiosyncratic and unreliable. In sum, Aristotle sets the bar for scientific knowledge very high. To know, in the strict sense of the term, is to know what is the same everywhere and always with respect to a certain subject matter. That universal knowledge, in turn, is grounded in the knowledge of the first principles of the relevant science; in addition to being indemonstrable, these first principles must also be explanatory and necessary. The goal of induction is 5 Anal. post. I 2, 71b19-22; II 2, 90a5-7. These criteria are nicely discussed by P. Biondi in his translation and commentary on Aristotle’s Posterior Analytics II.19 (Québec: Les Presses de l’Université Laval, 2004), pp. 80-107. 6 Anal. post. I 2, 71b9-12. 7 Metaphysics [Meta.] I 1, 981a28-b2, 10-13. 8 Anal. post. II 11, 94a20-24. 9 Anal. post. I 2, 71b12-16; 6, 74b5-21.

254

Christopher Byrne

to discover these first principles. In the case of perceptible objects, induction seeks to discover the unchanging causes of their characteristic forms of behaviour, the ways in which they either always or typically move or change.10 2 If the goal of induction is to grasp the unchanging principles of explanation with respect to a given subject matter, the traditional account of Aristotelian induction collapses the object of induction into just the formal cause by collapsing Aristotle’s four explanatory principles into just the formal cause. In effect, all induction leads to just the formal cause because all explanation proceeds by way of just the formal cause; scientific demonstration only deals with the essential properties of the objects under consideration, and all of the essential properties of perceptible substances, on the traditional account, are contained in their formal cause. Aquinas, for instance, argues that induction abstracts from the individual matter of a perceptible object, for example, the flesh and bones in a particular animal, but not from its common matter, for example, flesh and bones in animals taken generally. On Aquinas’s account, even the common material cause derives its nature from its formal cause because the latter gives all actuality to the material cause and to the resulting composite substance. Thus, a perceptible object derives its nature entirely from its formal cause.11 Perceptible substances are still understood as composite beings, but their formal cause ends up doing all of the explanatory work.12 10

Physics [Phys.] I 1, 184a10-16; II 2, 193b22-194a12. See his Summa theologiae I, q. 85, a. 1, response; Questiones disputatae de potentia, q. 4, a. 1, response; Questiones disputatae de anima, q. 1, a. 9, response; Summa theologiae I, q. 66, a. 1, response. This question is nicely discussed by Eleonore Stump, “Aquinas on the Foundations of Knowledge,” Canadian Journal of Philosophy, Suppl. vol. 17 (1991), pp. 125-158. 12 Some contemporary commentators who argue that the nature of natural substances is exhausted by their formal cause include: J. Owens, ‘Matter and Predication,’ in The Concept of Matter, ed. E. McMullin (Notre Dame: University of Notre Dame Press 1963), pp. 99-115, esp. p. 112, reprinted in Owens, Aristotle: The Collected Papers of Joseph Owens, ed. J. Catan (Albany: SUNY Press 1981); W. Charlton, Aristotle’s Physics I & II (Oxford: Clarendon 1970), pp. 75-77; J. L. Ackrill, ‘Aristotle’s Definitions of psuche,’ in Articles on Aristotle, vol. IV, ed. J. Barnes, et al. (London: Duckworth 1979), pp. 65-75; L. Gerson, ‘Artifacts, Substances, and Essences,’ Apeiron 18 (1984), pp. 50-58; L. A. Kosman, ‘Animals and Other Beings in Aristotle,’ in Philosophical Issues in Aristotle’s Biology, eds. A. Gotthelf & J. Lennox (Cambridge: Cambridge University Press 1987), pp. 360-p. 391; S. Cohen, ‘Aristotle on Heat, Cold, and Teleological Explanation,’ Ancient Philosophy 9 (1989), pp. 255-270; M. L. Gill, 11

The Object of Aristotelian Induction

255

This reduction of the nature of perceptible substances to just their formal cause proceeds in two steps. The first step consists in relegating all of the properties of perceptible substances that are due to their material cause to the status of accidental properties. The claim here is not just that the material cause is responsible for the accidental properties of perceptible substances, but also the converse, namely that the material cause is only responsible for accidental properties; not only are all accidental properties material ones, but all material properties are accidental. The material cause is not simply eliminated from perceptible substances, because it is still required to account for their accidental properties and also to individuate spatially discrete perceptible objects that are the same in kind, that is, that have the same formal cause. Nevertheless, because the material properties are transitory and idiosyncratic, they are left behind when it comes to discerning the permanent nature of perceptible substances. The second step in reducing all explanation of perceptible substances to their formal cause lies in collapsing the distinction between their formal, efficient, and final causes. To be sure, Aristotle sees these three types of explanation as closely related; he even says that they are, in some sense, one and the same.13 In the case of the efficient cause, for example, the agent producing the change must be, at some level, the same in kind as the object being moved, because the agent and patient must have a common substratum in order to be able to interact at all.14 Moreover, the agent must in some way already contain the effect it produces in the object on which it acts. In the case of self-motion, where the causal power by which something is moved is found in the object itself, here again there is a close connection between formal and efficient causes. For, perceptible objects are typically defined in terms of the causal powers by which they either move themselves or are moved by other objects. Animate beings are a good example of this connection because their formal causes, their souls, consist precisely in a particular set of causal powers.15 The same holds for inanimate natural substances, which, like all natural substances, are defined in terms of their Aristotle on Substance: The Paradox of Unity (Princeton: Princeton University Press 1989), pp. 146-167; E. Katayama, Aristotle on Artifacts: a Metaphysical Puzzle (Albany: SUNY Press 1999); C. Frey, ‘Organic Unity and the Matter of Man,’ Oxford Studies in Ancient Philosophy 32 (2007), pp. 167-204; M. Scharle, ‘Material and Efficient Causes in Aristotle’s Natural Teleology,’ in Aristotle on Life, ed. J. Mouracade, Apeiron 41 (2008) Suppl. vol., pp. 27-45. 13 Phys. II 7, 198a24-27. 14 De Generatione et Corruptione [GC] I 6, 322b11-21; 10, 328a19-22. 15 De Anima [DA] II 2, 413a26-28; 4, 415a19.

256

Christopher Byrne

capacity to move or change themselves. Non-natural physical artifacts such as houses and statues lack the ability to move themselves, but they too are defined in terms of certain causal capacities inasmuch as their primary function is to be useful to us in various ways. In general, then, the formal causes of perceptible objects always include their distinctive causal powers, and the latter are among their most important features. The efficient cause, in turn, is connected to the final cause inasmuch as causal powers are defined in terms of the effect that they produce.16 Where the effect is some end or good for the sake of which a perceptible substance acts, the efficient cause is defined in terms of that end or good, traditionally called the final cause. Hence, if perceptible substances are what they are by virtue of their causal powers, and these causal powers, in turn, are understood in terms of the end for the sake of which they are exercised, perceptible substances have only one nature: their formal cause consists in their ability to produce a certain effect. Their material cause is excluded from their nature because it is held to be only accidental to exercising their distinctive causal capacities. The upshot is that every explanation proceeds by way of the formal cause, which, in turn, consists of the ultimate goal for the sake of which all of an object’s causal powers are exercised. The job of induction is to discover this one goal. There are, however, at least two problems with this account. The first is that it makes explanations of the behaviour of perceptible objects tautological. For, if the formal cause is defined in terms of a set of causal capacities, and those causal capacities, in turn, are defined simply as whatever produces the effect to be explained, the nature that is supposed to explain the behaviour of perceptible objects simply offers a description of that behaviour. In other words, this approach quickly leads to the type of empty causal explanations so nicely parodied by Molière in his Le malade imaginaire, where the ‘dormitive’ power of opium is explained by means of its virtus dormitiva. The problem is not that the cause cannot be specified in relation to the effect that it produces; if one is using a transmission theory of causality, as Aristotle seems to be doing, then the cause and effect have to be connected inasmuch as whatever is transmitted to the patient must originally have been contained in some way in the agent. Rather, the explanation becomes vacuous if it does not also specify the mechanisms by which the agent is able to transmit the relevant attributes to the patient and the patient is able to receive them. 16

Meta. IX 8, 1049b10-17.

The Object of Aristotelian Induction

257

Aristotle is aware of the need to avoid such vacuous explanations. When discussing the explanatory role of the formal cause, he points out that everything is identical to itself and that explaining the nature of a perceptible substance by appealing to its formal cause can lead to just such an empty identity statement: a human being is a human being by virtue of having the formal cause of a human being.17 The problem is not that formal causes are causally irrelevant; on the contrary, when specifying the formal cause of a perceptible individual, Aristotle typically looks for the distinctive causal capacities that belong to that kind of object, and these distinctive causal capacities are typically the ones that those objects gain by virtue of the addition of their formal cause. The problem, rather, is that when it comes to specifying just how those causal capacities work, it is insufficient simply to refer to the effects that they produce. When explaining what makes a human being to be a human being, it is not enough simply to refer to the fact that it engages in human activities. Instead, what makes scientific explanations non-tautological, on Aristotle’s account, is that the causal powers to which such explanations refer are grounded in the particular structure and parts of both the agent producing the change and the object on which it is acting. In general, Aristotle has an agent account of causality, in that he thinks that it is typically a thing that causes a change to take place.18 It is the builder, he says, that moves bricks and builds a house, not the art of building.19 Nevertheless, because individual perceptible objects typically have many causal capacities, a correct scientific explanation has not been reached until we have specified not only the agent causing the change, but also the particular capacities by virtue of which it produces the change in question and the parts of the agent to which those capacities belong. Thus, not only do real effects require real causes, but the agent must also have the right kind of causal powers to produce the effect in question, and those causal powers can only be found in certain kinds of parts.20 The same holds of the object on which the agent is acting; it too must possess the correct passive powers, in the right kinds of parts, in order for the agent to be able to act on it. In sum, it is not the case that just any cause can produce just any effect; the agent and the 17

Meta. VII 17, 1041a6-22. Phys. III 2, 202a9-12; GC I 7, 324a8-l4; DA II 5, 417a19-21; De Generatione Animalium [GA] II 1, 734a30-33; Meta. VII 9, 1034a21-25, 1034b16-19. 19 DA I 4, 408b11-15; GC II 9, 335b20-29. 20 Phys. II 3, 195b16-21; DA II 5, 417a17-18; III 7, 431a3; GA II 1, 734a30-33; Meta. VII 9, 1034b17; IX 8, 1049b24-27; XII 6, 1071b12-17. 18

258

Christopher Byrne

patient must be the right kinds of thing, with the right kinds of capacities, found in the right kinds of parts.21 The second problem with the traditional account of perceptible substances is that the latter cease to be truly composite beings. Perceptible substances may have both a formal and a material nature, but their material nature is held to contribute nothing to explaining their characteristic behaviour. Aristotle, however, repeatedly argues that perceptible objects are composite beings, composed of both a material and a formal principle, and he regularly uses the material causes of perceptible objects to explain nonaccidental aspects of their behaviour.22 This composite character is true not only of physical human artifacts such as bronze spheres, wooden chairs, and iron saws, where the raw materials and the formal characteristics are readily distinguishable; it is also found in natural substances, everything from plants and animals to metals, flesh, bone, and, ultimately, the physical elements out of which all perceptible objects are made. Natural substances, he says, have two natures, one by virtue of their formal cause and another by virtue of their material cause.23 From the simplest elements to the cosmos itself, nature consists of raw materials organized in distinctive ways. In fact, the number of natures that perceptible objects possess can be multiplied beyond that of their immediate formal and material causes. Aristotle allows for multiple layers of material causes in one and the same object: something can both act as a material cause for something else and have a material cause of its own.24 Bronze, for example, can both act as the material cause for statues and, at the same time, have a material cause of its own, the basic physical elements. This layering of material causes is seen most easily in the case of physical artifacts such as bronze statues and wooden houses, but it is also found in natural substances. The crucial point here is that the lower-level raw materials possess causal powers in their own right; their causal powers are proprietary and cannot be explained by the formal cause of the objects made from these raw materials. Just as the formal cause of a statue does not explain the distinctive 21

De Caelo [DC] IV 3, 310a27-32; GA II 6, 743a18-27. Phys. II 1, 193a28-31; 2, 194a12-27; 8, 199a30-32; GC I 5, 321b19-22; DA II 2, 414a17; III 4, 429b13-14; PA I 1, 641a25-28; GA I 18, 724a20-b1; Meta. V 4, 1015a611; VI 1, 1025b28-1026a6; VII 7, 1032a12-22; 8, 1033b12-26; 10, 1035b27-32; 11, 1037a5-7, 10-20. 23 Phys. II 2, 194a16; 8, 199a30-32. 24 Meta. V 4, 1015a7-10; VIII 4, 1044a15-25; IX 7, 1049a18-27; Phys. II 1, 193a9-21. If, working from the top down, an object can have several material causes, it follows that, working from the bottom up, it can also have several formal causes. 22

The Object of Aristotelian Induction

259

features of bronze, so too the formal cause of living organisms, their soul, does not explain the nature of the compounds and physical elements from which living organisms are made. In fact, far from explaining the causal capacities of their raw materials, formal causes typically presuppose and are dependent upon the causal capacities of their raw materials.25 The upshot is that some aspects of the behaviour of perceptible objects must be explained by the lower-level raw materials from which they are made and the causal capacities that these raw materials possess in their own right. By failing to recognize the independent nature of the material cause, the traditional account of induction misunderstands the role of physical necessity in perceptible objects. According to Aristotle, the primary meaning of the term ‘necessity’ (anagkƝ) is that which cannot be otherwise.26 He further distinguishes between what is necessary simply or unconditionally, and what is necessary hypothetically or conditionally.27 All perceptible objects, both natural substances and physical human artifacts, are subject to both of these types of necessity. The simple physical necessity to which perceptible objects are subject is seen most clearly in the material elements. Of necessity, Aristotle says, all of the elements move naturally to or within a certain place in the cosmos.28 (Even though the sublunary elements can be prevented from moving to their natural place by an external obstacle, the tendency to move in that direction is always present in them.) This necessity is unconditional in that the elements always move this way, whether they exist by themselves or as part of a composite object. Thus, all perceptible objects have a natural motion to a place in the universe due to the material element from which they are predominantly made.29 In addition, the elements are responsible for the basic ways in which bodies physically interact with one another. Indeed, in the case of the sublunary elements, the causal powers 25 Phys. II 9, 199b34ff.; De Partibus Animalium [PA] I 1, 639b21-640a10, 642a2-b4; Meta. VIII 4, 1044a25-29; DA I 1, 403b17-18. 26 Meta. V 5, 1015a34-36, b11-15; XII 7, 1072b7-13; Anal. post. I 6, 74b5-7; 33, 88b32-33; GC II 11, 337b35-338a2; Nicomachean Ethics [Eth. Nico.] VI 3, 1139b1924. These passages also suggest that Aristotle thinks that the concept of eternity is grounded in that of necessity. 27 Meta. V 5, 1015a20-26, b2-9; Phys. II 9, 199b34-35, 200a5-30; PA I 1, 639b21640a1; GC II 11, 337b14-33, 388b6-11. 28 Phys. VIII 1, 252a17-19; II 8, 198b19-20; 9, 199b34-200a5, 30-32; DC IV 2, 308b12-15; 4, 311b14-19; GC II 11, 338a17-b11; PA I 1, 642a33-b4; Anal. post. II 12, 96a2-5; Eth. Nico. II 1, 1103a18-23. 29 GC II 8, 334b31-34; DC I 2, 268b27-269a2; IV 4, 311a30-b3.

260

Christopher Byrne

that govern their physical interactions are more fundamental than their natural motions to or within a certain place in the universe.30 For the properties that define the sublunary elements have to be able to explain how these elements interact and are generated from one another, and these processes take place only by means of physical contact. The basic physical powers of the sublunary elements, in turn, are grounded in two pairs of contrary properties: heat and cold, and fluidity and solidity.31 Heat and cold are the active powers in the elements that cause bodies in contact with them to separate or congregate in certain ways, and fluidity and solidity are the passive powers that determine the ease or difficulty with which the elements change their shape when they come into contact with other bodies.32 In fact, these powers even underlie the natural motions of the elements and all other perceptible bodies to their natural place in the universe. These natural motions and the heaviness or lightness of perceptible objects arise from their relative density and rarity, and the latter is determined by the mixture of the four sublunary elements from which heavy and light bodies are made.33 There are many other examples in Aristotle’s works where he explains natural processes in terms of the simple physical necessity that governs the interaction of the elements. Some of these processes involve the interaction of all five of the basic elements, that is, ether as well as the four sublunary elements, indicating that, contrary to what is often claimed, Aristotle does apply certain principles of his natural science to both the celestial and terrestrial realms. These processes include the way in which heat is produced in the sublunary world by the sun;34 the transmission of light from the celestial bodies to the sublunary realm;35 and why it is that 30

GC II 2, 329b7-24; I 6, 322b21-29; 323a10-12. GC II 1, 329a24-b3; 3, 330a30-331a6; Meteorologica [Meteor.] IV 1, 378b10-14; PA II 2, 648b9-11. 32 GC II 2, 329b24-32. 33 Aristotle connects density and rarity with natural motion down and up, respectively: DC III 1, 299b7-9; Phys. IV 5, 212b2-3; 9, 217b11-12, 24-26; VIII 7, 260b7-10. Heat and cold cause things to become rare and dense, respectively: Meteor. I 4, 341b36342a1 & 19-20; Phys. VIII 7, 260b7-10; GC II 5, 332a21-22 (here he indicates that the two upper sublunary elements, fire and air, are rarer than the two lower elements, water and earth; this is also the division between the hot and the cold elements). As a result, hot things are light and move naturally upward, and cold things are heavy and move naturally downward: Meteor. I 4, 341b7-13 & 342a16-17; PA II 7, 653a3-8. 34 DC II 7, 289a20-35; Meteor. I 3, 341a13-32; 4, 341b18-24. 35 DA II 7, 418b4-13. 31

The Object of Aristotelian Induction

261

the motions of the planets and stars produce no sound.36 These examples all involve physical interaction between the elements, or between bodies made out of the elements, and in all of them the physical interactions involved are explained by Aristotle in a purely mechanical way, that is, without reference to a soul, mind, or agent acting for the sake of an end.37 The same is true of the fundamental attributes of the four sublunary elements, their heat and cold, and fluidity and solidity. The motions and physical interactions of the five material elements, then, are governed by a simple physical necessity, which, in turn, governs all other perceptible objects because the latter are all ultimately made out of these elements. In addition, all perceptible objects are subject to a kind of hypothetical necessity. This necessity governs the relation between perceptible objects and their material causes. For, a particular sort of material cause is typically required if a certain kind of formal cause is to be actualized and the resulting composite object is to function properly; saws have to be made out of something hard, such as iron, if they are to cut wood.38 (This kind of necessity does not apply just to artifacts; Aristotle says that the passions of the soul are inseparable from “natural matter” (phusikƝ hulƝ).)39 These relations of hypothetical necessity reveal the ways in which the functional parts of perceptible objects are dependent upon the material causes from which they are made; without the hardness of the iron, the saw blade could not do its job of cutting wood. The simple physical necessity found in the material elements and the compounds made from them is put to use by the objects made from these elements and compounds in order to perform their own, distinctive functions; without the former, the latter would not work. Thus, the formal nature of a perceptible object always presupposes a material nature of a certain kind. In sum, if induction is to yield explanations and not just similarities, the kinds according to which individuals are classified must be explanatory kinds. Identifying the correct explanatory kind, in turn, requires identifying the right set of features in the objects under consideration. Perceptible individuals have indefinitely many properties and attributes; a correct explanation identifies the ones that are causally relevant to the effect to be explained. It is here, in their multiple causal capacities, that the composite 36

DC II 9, 290b30-291a28. For a more extensive discussion of this topic, see my “Aristotle on Physical Necessity and the Limits of Teleological Explanation,” Apeiron 35 (2002), pp. 19-46. 38 Phys. II 9, 200a7-13; PA I 1, 642a9-14; Meta. VIII 4, 1044a27-29. 39 See DA I 1, 403b17-18. 37

262

Christopher Byrne

character of perceptible objects manifests itself most clearly. Perceptible objects are composites of a formal and a material cause, and the functional capacities of perceptible objects as a whole are systematically dependent upon the causal powers of the raw materials from which they are made. 3 If the job of induction is to reach explanatory principles of the sort described above, the question remains of how universal claims about such explanatory principles are to be reached. In a well-known passage in his Posterior Analytics, Aristotle describes this process as analogous to the one by which ancient Greek soldiers lined up on the field of battle: first, one soldier takes his place, and then another next to him, and so on, each successive soldier taking his place next to the ones already in line.40 The process Aristotle has in mind here, I argue, is similar to what we now know as mathematical induction. In mathematical induction, all of the members of a well-ordered set of entities are shown to have a certain property by virtue of the first member of that set having the property in question (the so-called basis clause), and that property being such that if any arbitrarilyselected member of the set has that property, the next member in the series has to have it as well (the so-called inductive step). In other words, all of the members of a set have a certain property because the first member of the set has it and that property has to be passed along to all of the other members as well. Mathematical induction is often compared to falling dominoes: if the dominoes are lined up correctly, once the first one is tipped over, all of the other ones will fall as well. With respect to Aristotle’s example of the soldiers lining up in battle, the first premise, the basis clause, corresponds to the first soldier making his stand, and the inductive step corresponds to the other soldiers lining up next to the previous ones. On this analysis of Aristotelian induction, a universal claim about some set of objects is based on two prior claims. The first claim, the basis clause, states that some particular individual necessarily has some feature or other. The second claim, the inductive step, states that things that are the same in kind must have the same basic properties. Taken together, these two premises claim that once a property has been found to be necessary to some individual, that property will also be found in every other individual that is the same in kind as the first. The problem of induction, then, lies not so much in taking the step from the particular to the universal, but in determining what is necessary and invariable in the individuals under 40

Anal. post. II 19, 100a12-13.

The Object of Aristotelian Induction

263

consideration. More specifically, induction of this kind will work only if it is possible to determine that a given property is necessary to an individual without having to look at all or most of the other members of the set to which that individual belongs. Indeed, the first premise presupposes that it is possible to determine such a necessary connection on the basis of observing just one individual. Once this necessary connection in an individual has been set out in the first premise, the job of the second premise is to extend this necessary connection to anything else that is the same in kind. The implicit claim here is that whatever is the same in kind must also have the same basic properties. This claim is perhaps not so controversial; indeed, it can be construed as a version of the principle of the indiscernibility of identicals. It does presuppose, however, that we already know what kind of thing the objects under consideration are. Thus, both premises presuppose knowledge of the invariable features of the objects under consideration. On this account of induction, then, we know that something is universally the case because we know that it is necessarily and invariably the case. Something is universal because it is necessary, not necessary because it is universal. It may be that a true claim about what is necessarily the case will be true in all possible worlds, but that is not what makes such a claim true in the first place. The universal claim made in the conclusion of an inductive argument—that all things of a certain kind have a certain property—is warranted because the premises have established that things of that kind necessarily have the property in question. The primary job of induction, then, is to discover what is necessary about the individuals in question. This discovery proceeds by means of an analysis of the things under consideration so as to reveal what is necessary and invariable about them, i.e., what is actually the case and cannot be otherwise. Aristotle’s four causes provide the method by which this analysis is performed; the four causes show us how to take things apart so that we can see what is unchanging in them. As we saw in the previous section, one part of this method is the analysis of things into their material components. In effect, this step is based on the view that part of the behaviour of complex objects is to be explained in terms of their simpler and, therefore, less variable components. The final stage of this step is reached when things are analyzed into their simplest material components, the elements. These components are the atomic, indivisible parts of the things made out of them

264

Christopher Byrne

because they cannot be further divided into something different in kind.41 While the four sublunary elements are subject to generation and destruction, the results of those changes are always other elements; material objects are always one or the other of the elements or something made out of them. The material elements, then, are the simplest components of all perceptible objects. Because they are the simplest components of perceptible objects, the elements always behave in the same way; their behaviour is invariable because they cannot be decomposed into a simpler, independently-existing kind of matter. All of the interactions of material bodies are governed by their nature, but their behaviour is not governed by anything more primitive than they are. The second part of the method by which complex objects are understood looks at the way in which their components have been put together. This is the job of the formal cause, the principle of composition.42 The type of necessity that applies here is the hypothetical necessity also discussed in the previous section; in order to function properly, a complex object requires material components of a certain kind, and these components must be put together in a certain way. These two types of necessity, the simple necessity of the material elements and the hypothetical necessity that governs their composition, determine the nature of perceptible objects; they also belong to the two fundamental parts of perceptible objects, their material and formal causes. Perceptible objects, then, are composite objects, with a material and a formal nature. Perceptible objects are the same in kind just in case they have the same material components and the same principle of formal composition. 4 The above account of perceptible objects as composite beings also has implications for Aristotle’s account of definitions, for the job of a definition is to state the nature of the thing being defined. The traditional account argues that the material cause is not part of the nature of perceptible objects because it is not part of their essence. The essence of a perceptible object is captured by its definition, and the definition of a perceptible substance is, in the first instance, a statement of what its formal cause is. 43 Perceptible 41

Aristotle’s definition of an element as something indivisible in kind is found at Meta. V 3, 1014a26-31. 42 Phys. II 3, 195a20-21. 43 Meta. V 2, 1013a26-29; VII 7, 1032b1-2, 14; 8, 1033b5-8; 10, 1035a1-23; 1035b416, 32; 1036a22-23; 11, 1036a26-1037a20; VIII 3, 1043b1-2.

The Object of Aristotelian Induction

265

substances are defined in this way because they are named and known, in the first instance, by virtue of their formal cause.44 The material cause appears in the secondary role of that which is added to the formal cause to make up the composite substance. As a result, the material cause is knowable only in relation to its formal cause.45 Perceptible substances may be composite wholes that can be destroyed by taking away their material parts, but, at least initially, these material parts are not themselves included in the definition of these substances. The whole is not indifferent to its material parts, but is not defined by them. The trouble with this account is that, despite this definitional priority, Aristotle does not reduce perceptible objects to just their formal cause. In fact, when he describes more precisely the way in which the formal cause defines a composite object, it becomes clear that the material cause must have a discrete nature of its own.46 The formal cause tells us what something is by telling us what has been added to the material cause of the object in question.47 Rather, it tells us how the elements of a composite object have been put together to form something of that kind. In effect, in asking what kind of thing a perceptible object is, we are really asking why it has certain features over and above what already belongs to it by virtue of its material cause. Such an inquiry clearly presupposes the existence of a distinct material cause. Indeed, Aristotle argues that asking why something is what it is presupposes that we are inquiring about a composite entity.48 Aristotle calls the formal cause the ‘first cause of being’ for perceptible objects, but it is not their only cause of being.49 The formal cause defines a natural substance, but it does this by specifying what must be added to the material cause of that substance.50 Thus, the formal cause does not make whatever acts as the material cause to be the kind of thing it is. Aristotle’s claim, then, that the formal cause defines a composite substance does not mean that whatever acts as a material cause is without any intelligible content of its own. Aristotle does say that the material cause is unknowable.51 This attribute, however, applies to the material cause only in a restricted or qualified way. The material cause is unknowable inasmuch 44

Meta. I 7, 988a34-b5; VII 7, 1032b1-2; 10, 1035b14-16; 11, 1037a25-30. Meta. VII 10, 1035a6-9; 11, 1037a27. 46 Meta. VII 17, 1041a6ff., esp. a32-b4. 47 Meta. VII 17, 1041b31. 48 Meta. VII 17, 1041a9-26. 49 Meta. VII 17, 1041b28. 50 Meta. VII 17, 1041a32-b11. 51 Meta. VIII 2, 1043a12; IX 6, 1048a35-b6; Phys. I 7, 191a7-12; II 2, 194b9. 45

266

Christopher Byrne

as something is a material cause only in relation to something else that is or can be made from it. In this respect, the term ‘material cause’ acts more like a job description than the name of a particular kind of thing. Thus, when Aristotle considers the material cause of something, what he has in mind are the raw materials from which it is made, and the term ‘raw materials’ does not refer to any one kind of thing. Something is a material cause simply by virtue of its role in the construction of something else. Despite this functional definition, it does not follow that whatever acts as a material cause is unknowable in its own right. To be sure, as a material cause, it lacks a certain formal cause. In order to fulfill the functions that fall to it as a material cause, however, whatever acts as a material cause must also have a nature of its own. The same is true of the potentiality, passivity, and indeterminacy of the material cause. These attributes all refer to its ability to acquire a certain formal cause. This ability entails a certain privation inasmuch as the formal cause in question is something that the material cause by itself lacks; it also entails, however, that the material cause has whatever features are required to acquire that formal cause. Not every subject can acquire just any formal cause. This requirement becomes clear when Aristotle explains the potentiality of the material cause in Book IX of the Metaphysics. When he comes to explain the second, metaphysically more important meanings of ‘potentiality’ and ‘actuality’, he says that they cannot be defined directly, but must be generalized from certain examples.52 The examples of potentiality that he then gives are the raw materials from which statues, houses, and other finished products can be made. In all of them, the raw materials have a prior and determinate nature of their own, which must be adequate to receive the formal cause added to them. The potentiality of a material cause, then, is not the absence of any determination whatsoever. The privation found in the material cause is a qualified non-being, indicating the lack of something in particular. To be a material cause is to stand in an extrinsic relation to something else; something is a material cause because something else can be made out of it. This extrinsic relation does not entail that whatever acts as a material cause has no intrinsic attributes of its own. In fact, given all of the demands on the material cause as the persisting substratum of generation and change, whatever acts as a material cause must have an independent, determinate nature of its own. The result is that not everything necessary to a composite object is part of its formal cause. As we saw above, certain attributes are necessary 52

Meta. IX 6, 1048a35-37.

The Object of Aristotelian Induction

267

to a composite object, in that they are required for the actualization of its formal cause, but are not part of that thing’s formal cause. Thus, the interpretation of Aristotle according to which all necessary attributes belong to a composite object by virtue of its formal cause misinterprets the relation of hypothetical necessity. The formal cause does not define whatever it presupposes.53 Given the independent nature of the material causes of perceptible objects, it is misleading to incorporate into the formal causes of perceptible objects all of the properties required for their actualization. This attribution is incorrect not only because some of these properties belong, in the first instance, to the material causes of perceptible objects, but also because these same attributes are found in perceptible objects with different formal causes. In order to be actualized, the formal cause of a perceptible object requires a very precise combination of raw materials, but there is much about these raw materials that can be known independent of that formal cause. Perceptible objects remain irreducibly composite objects. With respect to Aristotle’s account of induction, the composite nature of perceptible objects helps to explain why making correct inductive generalizations is so difficult. For, given their composite nature, perceptible objects belong to more than one natural kind. Indeed, given the multiple layers of composition that can be found in perceptible objects, one and the same object can belong to a large number of different kinds. Every human being, for example, has certain, unvarying properties qua physical object, qua chemical object, qua biological object, qua perceiving object, and qua reasoning object. The difficulty, Aristotle says, is that our sense experience presents these many different properties to us all jumbled together.54 In order to understand them, the first thing we have to do is sort them out and 53

J. Cooper in his ‘Hypothetical Necessity,’ Aristotle on Nature and Living Things, ed. A. Gotthelf (Pittsburgh & Bristol: Mathesis Publications 1985), 151-67, esp. p. 158, argues that Aristotle’s account of hypothetical necessity presupposes that the material elements and their powers are simply given. Other commentators who hold that the nature of perceptible substances is not exhausted by their formal cause include R. Boehm, Das Grundlegende und das Wesentliche (Den Haag: Nijhoff 1965), esp. pp. 826, 40-54; R. E. Allen, ‘Substance & Predication in Aristotle’s Categories,’ in Exegesis and Argument, ed. E. N. Lee et al., Phronesis Suppl. 1 (1973): 362-73; S. Mansion, ‘The Ontological Composition of Sensible Substances in Aristotle (Metaphysics Z 79),’ in Articles on Aristotle, vol. III, ed. J. Barnes, et al. (London: Duckworth 1979), 80-87; M. Wedin, Aristotle’s Theory of Substance (Oxford: Oxford University Press 2002), esp. pp. 427-441. 54 Phys. I 1, 184a21-22.

268

Christopher Byrne

separate them from one another. The problem with Aristotelian induction is not that it presupposes an illegitimate notion of natural kinds.55 The problem is that there are so many different natural kinds to which each thing belongs simultaneously. In sum, Aristotle’s scientific method is grounded in the method of analysis incorporated in his doctrine of the four types of explanatory principle, traditionally known as the four causes. This method of analysis is a replicable process, but it can be applied to just a single object or to a population that is relatively small when compared to the total population under consideration. Thus, the observation of past uniformities has, at most, a heuristic function in scientific inquiry, helping us to analyze the objects under investigation. Empirical generalizations, however, are neither necessary nor sufficient for scientific knowledge. Instead, the analysis of perceptible objects seeks the causes of their behaviour. When it comes to finding these causes, their material causes must be included. This approach to Aristotle’s account of induction and scientific explanation does not deny that formal causes are crucial. It simply claims that material causes have an important role to play as well. In particular, to the extent that induction seeks the invariable principles that explain the behaviour of perceptible objects, it must consider their material causes. For the two kinds of necessity discussed above are both connected to their material causes. If induction were just about discovering the ways in which perceptible objects resemble one another, it would not yield scientific knowledge, for there is an indefinite number of ways in which perceptible objects resemble one another, and most are scientifically irrelevant. These similarities are scientifically relevant only to the extent that they are invariable. Any account of what is invariable in perceptible objects must include their material causes.

55

For a defense of Aristotelian natural kinds, see L. Groarke, An Aristotelian Account of Induction: Creating Something from Nothing (Montreal: McGill-Queen’s University Press, 2009), chapter 9.

From Particular to Universal: Drawing upon the Intellectual Milieu to Understand Aristotle and Euclid Dwayne Raymond Texas A&M University

Abstract: In an effort to understand Aristotle’s account of induction, which involves a movement from particulars (either species or individuals) to a universal, and which involves certain “properties which can be treated as separate even though they do not exist in isolation,” Raymond presents an alternative method of generalization, one that does not directly involve the enumeration of individuals. This technique is used by Euclid to draw a general conclusion from a particular diagram. The discussions of Euclid are not intended to suggest that Aristotle’s main influence is geometry, as opposed to biology. The purpose is to establish, within the ancient Greek milieu, the presence of a method of generalization that does not rely upon the enumeration of individuals. With this in hand, Raymond is able to argue that Aristotle’s “properties which can be treated as separate even though they do not exist in isolation” is an elliptical reference to this method of generalization, one that has a greater affinity with the diagrammatic/textbased approach found in Euclid’s Elements than the approach to generalization found in classical logic (Predicate Logic). Raymond contends that this chapter explicates, but does not defend Aristotle’s views on induction.

Introduction: Something More The present anthology collects together alternatives accounts and commentaries to the standard, Humean view of induction—induction involving the enumeration of individuals. On the standard view, induction is, by definition, not a form of deduction. It covers all cases of non-deductive reasoning in which the truth of the conclusion is not entailed by the truth of the premises. Instead, the premises provide good reason to believe the conclusion’s truth. Aristotle gives an alternative account. While induction (epagoge) is a movement from particulars (either species or individuals) to

270

Dwayne Raymond

universals, Aristotle’s account violates the standard view. First, in the Prior Analytics,1 he identifies a form of induction (i.e. perfect induction) as a form of deduction. Second, induction provides, not just a probable view of reality; for Aristotle it provides a true picture of reality. In one case (the case of perfect induction), inductively knowing the universal requires complete enumeration of particulars.2 In other cases, we come to know the universal through the perception of many particulars,3 or through a single particular.4 The differences between Aristotle’s view and the standard view are stark. How do we understand Aristotle’s view? Typically, commentators have taken Aristotle to be confused about induction. He does not seem to notice the difference between treating induction as the means by which concepts are discerned from that which is perceived and treating induction as the means by which one infers a general claim from claims about particulars. Is Aristotle deeply confused about these two senses of induction? Why does he hold that induction provides actual knowledge and not a lesser form of probable knowledge? And, how can induction from a single instance provide the same standard of knowledge as complete enumeration? The standard view would never admit such a claim, given that it takes induction to involve the enumeration of instances and a determination of likelihood based on that enumeration. May the appearance of oddness and the appearance of confusion lay with us? Are we having difficulty understanding Aristotle’s view because the framework into which we are attempting to fit it does not support his concepts, nor his methods without distortion? If so, what framework should we be using? This limited treatment will focus attention on the case of obtaining knowledge by reasoning from a single instance to a universal result. If ever there was a case that challenged the enumeration account of induction (a Humean account), this is it. The task before us is to explain it. In keeping with the anthology’s theme, it is reasonable to expect that this chapter on Aristotle’s epagǀgƝ be about Aristotle’s views per se— possibly his views on deduction and induction, or his views about the role of perception in concept formation. It is not. While it is true that the contrast between deduction and induction and the role of sense perception are fundamental to Aristotle’s view, there is something more. This something more is required to fully understand Aristotle’s view of induction. 1

Prior Analytics [Anal. pr.] II 23. Anal. pr. II 23. 3 Posterior Analytics [Anal. post.] II 19. 4 Anal. post. I 3, 88a10-18. 2

From Particular to Universal

271

It is this something more that separates Aristotle’s account from the standard account where induction involves the enumeration of individuals. The something more is part of the intellectual milieu within which deductive reasoning began in ancient Greece. The something more is not part of our modern framework. As we will see, it underwrites both conceptual and methodological differences, including induction. Allow me to briefly explain this last point. It is worth observing the broader significance of studies such as this study to our intellectual history. A supposed property of a logical system, called ‘topic neutrality’ (involving the fact that logical relations hold independently of the content (or the topic at hand)), appears to justify the use of modern logic in historical argument reconstruction and evaluation. Topic-neutrality alone, however, does not licence this use. Even if a logic is neutral with respect to content, it need not be neutral with respect to method. The concepts and the methods that one development of logic supports need not be supported by an alternative development. Methodological differences may be part of semantic differences, which contribute to different rules of inference being identified as sound. The result will be two systems, both of which are sound with respect to their own semantics, but that are incommensurable with respect to their derivation systems and their ability to support various concepts and methods. Importantly, the difference may go deeper than those differences countenanced within philosophical logic. That is, the systems may not simply be variations of classically based logics, as suggested by Burgess.5 There is no requirement that, at its core, a system of semantics involves the collection of individuals into groups. What is required is that the semantics be able to account for logical relations. As we will see later, there are at least three developments of the intuitions which are basic to reasoning. Systems may operate with a particular development or with a combination of these developments. With a broader array of options comes the possibility for interesting and alternative foundations for sound systems of logic. These alternatives bring with them the possibility for alternative methods. I believe that history shows us that this possibility is an actuality. For this reason topic neutrality alone is not sufficient; methodological neutrality is also required to justify a logic’s use in argument reconstruction and evaluation. This long unnoticed fact bears on the current scholarship. If the logic used by the commentator does not support the concepts and the 5 See J. Burgess, Philosophical Logic (Princeton: Princeton University Press, 2009): Ch. 1, esp. pp. 1-3.

272

Dwayne Raymond

methods of the original author, then the exegetical errors that are suspected by the commentator may be little more than artefacts of analysis. They may be created by the methodological incompatibility between the logic used in the reconstruction and evaluation and the logic used by the original author. Both the fact that we can, at times, use modern logics without any difficulties and the fact that modern logic does not always fit the text reflect the prior fact that modern logic is but one development of a pair of insights informing the development of logic in ancient Greece. With these remarks on conceptual and methodological differences in different systems of logic in mind, let us return to Aristotle. To see what the something more is in his case, consider Anal. post. I, 81a40-b5: ...demonstration develops from universals, induction from particulars; but since it is possible to familiarize the pupil with even the so-called mathematical abstractions only through induction - i.e. only because each subject genus possesses, in virtue of a determinate mathematical character, certain properties which can be treated as separate even though they do not exist in isolation - it is consequently impossible to come to grasp universals except through induction. But induction is impossible for those who have not sense-perception. For it is senseperception alone which is adequate for grasping the particulars: they cannot be objects of scientific knowledge, because neither can universals give us knowledge of them without induction, nor can we get it through induction without sense-perception.6

To be sure, both sense perception and the contrast between deduction and induction factor prominently in the text. The text also mentions both an example (mathematical abstractions) and a method associated with that example (treating things as separate even though they do not exist in isolation). This seemingly innocuous example and the reference to a method of abstraction point to that something more. What is it? In drawing attention to the role of abstraction in induction, I am not suggesting, as do others, “that Aristotelian induction originates in abstraction.”7 That is, I am not equating induction with abstraction by taking the intellectual insight (noesis) by which we understand a new universal to be abstraction. Groarke appears to equate noesis with abstraction. However, in so doing, he equivocates between two different characterizations. Immediately 6

Trans. G. R. G. Mure in The Works of Aristotle, ed. W. D. Ross (Oxford: Oxford University Press, 1946). 7 L. Groarke, An Aristotelian Account of Induction: Creating Something from Nothing (Montreal: McGill-Queens University Press, 2009), p. 163; P. Biondi, Aristotle: Posterior Analytics II.19 (St. Foy, PQ: Laval University Press. 2004): pp. 266-70.

From Particular to Universal

273

after describing abstraction as peeling away that in which we are not interested, Groarke quotes Richard Clarke as describing the same thing. However, Clarke’s treatment involves the peeling away of that in which we are interested.8 The latter is required to equate abstraction with the ‘bare flash of intelligence’ by which concepts are formed, noesis. In fact, the type of item being peeled away (disinterested vs. interested) is one basis for the difference between the abstractive test (peeling away that in which we are not interested) and a mental act of discernment (peeling away that in which we are interested). Why does this matter? The difference has implications for both Aristotle’s system of deduction and his treatment of induction. Consider deduction. By beginning with an existing thing and abstracting that in which we are not interested, the end result remains in the world. That is, there is always an existential commitment. Unlike modern scientists, Aristotle does not theorize by means of hypothetical deduction. As a result, he does not require a system of deduction that supports hypothetical reasoning without existential commitments or a means of introducing existential commitments. I have argued elsewhere that Aristotle’s deductive system (unlike classical logic) requires a means of removing the existential commitment. I have argued that this is the purpose behind the problematic portion of his syllogistic, where the modal operator ‘contingent’ modifies the copula: A contingently belongs to all B. By this means, there is no existential commitment being made about the belonging of A to B. As it pertains to induction, the distinction between peeling away that in which we are not interested and that in which we are interested allows for a more incremental account of induction than Groarke seems to suggest.9 It is more incremental, not at the point of intellectual insight, but prior to it. On this account, noesis need only be the insight into which of the attributes define the thing. Following Biondi, Groarke identifies two stages in induction: the enumeration of individuals and the subsequent act/process of leading from particulars to universal.10 By keeping abstraction, the peeling away of that in which we are not interested, as a distinct test (as I will do), we can allow for an incremental process to be operative in the second stage (when much background knowledge already exists) and still 8

Groarke, p. 162. This point is noted by McCaskey. See J. P. McCaskey, “Review of Louis Groarke An Aristotelian Account of Induction: Creating Something from Nothing,” Notre Dame Philosophy Reviews (2010). 10 Groarke, p. 115. 9

274

Dwayne Raymond

allow noesis to operate as the final act. The final act is not itself incremental; what leads up to that act can be incremental. That is, for those who need it, the abstraction test will, in an incremental fashion, produce an increasingly Spartan subject. Very bright individuals may be able to quickly grasp the new universal; those who are less gifted may only arrive at the insight after distractions have been removed.11 By keeping the intellectual act of noesis as distinct from abstraction, I am not simply emphasising Cleary’s excellent point that, for Aristotle, abstraction is not an automatic mental act; it is part of a logical test by which one identifies various dependency relations between entities. Cleary calls the test, the ‘subtraction-abstraction test’ and he has it identify the proper subject of predication.12 I will slightly diverge from Cleary. Since a dependency relation is nothing more than the relation that is picked out by a process called co-demolition, I will refer to the logical test as the ‘codemolition test’, emphasizing its more basic task of determining the presence of dependency relations. The proper subject of predication is derivative, requiring that we unpack the dependency relations. (Section 1 contains a general discussion of the test.) In addition to agreeing with Cleary in seeing abstraction as part of a logical test, I will draw attention to something more—an important fact that has not been fully appreciated in the literature. The logical test I refer to as the co-demolition test is the tip of an iceberg, which includes, as we will see, the fact that the test is connected to one of the three different developments from which logic originated in ancient Greece. Logic, like ancient Greek philosophy, developed from thinking about things that combine and things that separate. The extreme ranges of things that never combine (polarity) and things that never separate (inseparability) were used in early arguments by means of pairs of opposites. The difference between polar opposites and inseparable opposites, as well as variations among polar opposites (contraries and contradictories) and the variations among inseparable opposites (reciprocal and non11

I am grateful to the editors for pressing upon me the need for an account about the logical importance of the two methods of abstraction and for the need to more clearly explain what I mean by an incremental process. 12 See J. Cleary, “On the Terminology of ‘Abstraction’ in Aristotle,” Phronesis 30 (1985): 13-47; Aristotle on the Many Senses of Priority (Carbondale: Southern Illinois University Press, 1988); and Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics (Leiden, NY: E. J. Brill, 1995). In other works, Priority and Mathematics, he points to the test’s role in determining the presence of dependency relations between two attributes.

From Particular to Universal

275

reciprocal) are run together, and problems ensued. The Pythagorean Table of Opposites, for example, runs together polar opposites such as ‘limit’/‘unlimited’ (which do not admit an intermediate term); and ‘square’/‘oblong’ (which do admit intermediate terms, and each of which can exist without the other); and inseparable opposites ‘right’/‘left’ (which are relative terms, or more properly, they are co-relatives in the sense that right cannot co-exist without left and left cannot co-exist without right).13 Logic develops from the attempts to clarify things and to provide a solid epistemological foundation. As part of these various efforts, logic eventually emerges as a discipline with Aristotle. It arises as a result of thinking about polarity and inseparability that begins long before Aristotle.14 For our purposes, there are three developments of these extreme ranges polarity and inseparability (see Section 1). Of the three developments, two inform standard predicate logic (a truth-functional development and a collections development); the third development (the co-demolition development) is wholly absent from modern logic. The standard account of induction draws upon the first two developments. Aristotle’s induction includes the third. The third development underwrites a very different intellectual milieu when it comes to reasoning. It is the something more that underwrites both conceptual and methodological differences in logic briefly explained above. In this chapter, I will limit discussion of this something more to those which bear upon our topic, including: i) the fact that the co-demolition test peels away that in which we have no interest (by contrast, modern abstraction abstracts from all else that in which the theorist is concerned);15 and ii) the fact that the co-demolition test uncovers whether a dependency relation holds. There are two such relations: non-reciprocal and reciprocal. A number of uses of these relations are derivative. The non-reciprocal dependency relations are used to specify relations of priority: e.g. point, line, figure, solid. The reciprocal dependency relations are used to identify within one thing its essence (genus plus differentia, as with man and rational animal) or its unique properties (man and risible).16 Between 13

For the Greeks, opposite are not synonymous with contraries and contradictories; it has to do with two extremes, such as The Hot and The Cold. See Aristotle’s Categories [Cat.] 7; Metaphysics [Meta.] V, 15 for a discussion. 14 I call this ‘the polarity and inseparability thesis’. The details are being woven into a book length study. Early efforts include, but are not limited to, Hesiod’s use of night and day, Heraclitus’ unity of opposites, and Parmenides’ heart of unshakeable truth. 15 John Thorp points to this difference in the conceptions of abstraction. 16 Topics I, 5.

276

Dwayne Raymond

distinct things, it identifies co-relatives (the ancient Greek notion of a relation), such as half of and double of. 17 I will show how the co-demolition test provides the means by which Euclid argues from a particular diagram to a universal result. Euclid employs i, ii, and that which is derivative from ii. I will show that co-relatives, especially, play an important role in generalization in Euclid. I will show that Aristotle avails himself of the same conceptual tools when he moves from a particular to a universal. The tools provide for his inductive syllogism, and they supplement his process of induction, explaining how it is possible to arrive at universal knowledge from one particular. I will argue that the co-demolition test (the abstractive test) allows the process leading to the spark of insight, which Aristotle calls noesis, to be incremental. The spark in insight itself is not incremental, and it is something different from the subtractive-abstractive test that I call codemolition. The purpose of this chapter is to reveal the key aspects of a very different intellectual milieu and to sketch their relevance for Aristotle’s puzzling treatment of induction. Specifically, I begin by sketching the origins of logic, and I outline the three developments that were noted above. I show how the third development provides for a different notion of abstraction, which is part of a test for both reciprocal and non-reciprocal dependency relations and how it pertains to an alternative method of generalization. I will show that reciprocal dependency relations identify, among other things, co-relatives, and that non-reciprocal dependency relations identify priority (the order of things) and aid in limiting consideration to the most universal attributes.18 17

Cat. 7. Predicate logic’s broad use of multiple quantifiers (something that Aristotle rejected) required the replacement of an ancient view of relations (co-relatives) with that of n-place predicates. While commentators (famously, J. R.Weinberg in Abstraction, Relation and Induction: Three Essays in the History of Thought (Madison, University of Wisconsin Press, 1965), are quick to point out the benefits of n-place predicates, there is a paucity of discussion on the kinds of uses to which co-relatives were put prior to Galen’s efforts to develop a relational syllogism. 18 An odd pronouncement by Empedocles can be understood within this approach. In Purifications, Empedocles lists the opposite of Truth as Obscure, as opposed to False. On this reading, truth is discerned; it is separated from all that is present, but with no requirement to belong or not belong. That truth resides beneath a layer of appearances is also suggested by Parmenides’ discussion in the Proem (to his Poem On Nature) of the unshakable heart of a well-rounded truth, and his division of this poem into that which deals with truth (being) and that which deals with appearances (becoming). Not only is the distinction between appearances (realm of becoming) and reality (realm of

From Particular to Universal

277

Next, I turn to a key problem from Euclid: given that Euclid reasons with a specific diagram, what justifies his general conclusion? Even though Euclid does not enumerate alternative diagrams, his results are general. He is very successful at it. What makes his results general? To answer this question, I draw upon Ken Manders and his two distinctions.19 The first concerns the difference between text and diagrams and the combined role that they have in a diagrammatic system; the second concerns a distinction between exact and co-exact attributes: exact attributes, such as a given length, specify an exact property of a particular figure, whereas co-exact attributes are those that are shared by all figures of a given kind. When Manders makes the notion of a co-exact property more precise, he characterizes it in terms of topology. Exact properties can vary, but co-exact properties are topologically invariant. This second distinction (exact and co-exact) explains the division of labour between text and diagram. Exact properties are supplied by text, and co-exact attributes come from the diagram. According to Manders, Euclid succeeds in reasoning from a particular diagram to a universal result because he only relies on co-exact properties in his diagrammatic inferences. Manders’s thesis has been demonstrated by successful approaches taken by Miller and Mumma.20 I briefly outline these systems. Next, I turn to Euclid. I argue that he is not doing topology, as conjectured by Manders et al. While I argue that Euclid is not doing topology, I show that he does employ something like the distinction between exact (properties that are specific to a given case) and co-exact properties (properties that are invariant across all transformations). By drawing upon the above noted conceptual tools (i, ii and those that are derivative from being) retained by Plato, but the basic insight is equally retained in modern idioms such as, ‘the heart of the matter is …’ or ‘it all boils down to ….’. 19 K. Manders, “The Euclidean Diagram (1995)” in The Philosophy of Mathematical Practice, ed. P. Mancuso (Oxford: Oxford University Press, 2008). 20 N. Miller, “Case Analysis in Euclidean Geometry: An Overview” Diagrams (2000): 490-493; N. Miller, “A Diagrammatic Formal System for Euclidean Geometry,” (PhD diss., Cornell University, 2001); N. Miller, Euclid and his Twentieth Century Rivals. Diagram in the logic of Euclidean Geometry (Stanford: CSLI Publications, 2007); J. Mumma, “Intuition Formalized: Ancient and Modern Methods of Proof in Elementary Euclidean Geometry,” (PhD diss., Carnegie Mellon University, 2001); J. Mumma, Review of Euclid and his Twentieth Century Rivals. Diagram in the logic of Euclidean Geometry. Philosophia Mathematica 16 (2008): 256-281; J. Mumma, “Ensuring Generality in Euclid’s Diagrammatic Arguments” Diagrams (2008): 222-235; J. Mumma, “Proof, Pictures and Euclid” Synthese 175 (2010): 255-287.

278

Dwayne Raymond

two, especially the ancient Greek notion of a relation, the co-relative), I show how Euclid is able to reason via something akin to ‘co-exact’ properties (properties which are shared by all figures of a given kind) without having recourse to topology. That is, like Aristotle, Euclid reasons with “properties which can be treated as separate even though they do not exist in isolation.” Euclid obtains this with a combination of text and diagram. Finally, I return to Aristotle and his treatment of induction. I sketch how these results provide for that which distinguishes between the standard account and Aristotle’s account of induction. Unlike the standard account, Aristotle held that a form of induction is a type of syllogism, and he maintained that induction provides knowledge of a universal, from cases ranging from complete enumeration, to a single case. I will argue that Aristotle’s approach draws upon what we see in geometry. Most significantly, it draws upon the practice of carving up the individual to isolate universals in a bid to consider the dependencies between them, that is, between the universals. The actual individual is incidental to the study of these dependency relations. It is because of this practice that Aristotle is able to countenance the possibility of obtaining knowledge from a single case, provided the required background knowledge is known. By focusing on a single case, I attempt to draw these observations back to the collection’s theme: alternatives to Humean induction. 1 The Greek origins of logic and formal thinking: Three developments As with Greek philosophical views, formal reasoning in ancient Greece originates in thinking about things that combine and things that separate. Individuals were initially taken to be aggregates of components. What Aristotle calls attributes were initially understood to be things in their own right. Rather than ‘hot’ as an adjective, it was ‘the hot’. The early view of character-powers was that they were things, or thing-like, in their own right. That is, they were concrete entities. This contrasts with thinking of them as qualities of a single thing. Individuals were seen to be complexes or aggregates of thing-like components. For example, a “human being might be thought of as the complex of and locus of several (indeed a large number) of such character powers: a person’s body texture, colour, gait, warmth, courage, fears, passions, and many others.”21 Mourelatos characterizes this 21 A. P. D. Mourelatos, The Route of Parmenides: Revised and Expanded Edition (Las Vegas: Parmenides Press, 2008), p. 301.

From Particular to Universal

279

stage of thought along these lines: “[e]ach thing will be complete by itself, and the plurality of things will form a whole (harmonious nevertheless) in which all relations are external and explicit.”22 As the early Greeks became aware of the various affinities and polarities amongst these powers, such as the day and the night, or the hot and the cold, the wet and the dry, they began to recognize that not all such relations are explicit. Some of the components were self-contained, while others were seen to constitute pairs of opposites, involving affinities (such as three and odd, or up and down) or polarities (such as night and day, square and oblong, or odd and even).23 The affinities and polarities were put to use, framing early views24 and some arguments.25 Hesiod’s Theogony 748-54 famously illustrates the opposition between night and day: …where Night and Day come close to each other and speak a word of greeting, and cross on the great threshold of bronze; for the one is coming back in and the other going outdoors, and the house never at once contains both of them, but at every time, while one of them is out of the house, faring over the length of the earth, the other remaining indoors waits for the time of her own journey, when the other one comes back.26

While such views are often cast under the rubric of metaphysics, there is an important proto-logical dimension to them. (A very real and substantial possibility that is not pursued here is the prospect that all three of the developments accord with the way that our minds reason abstractly. In this way, the development of logic is not seen as a distillation, where pure logical content is distilled from metaphysical considerations. It is seen as a progression that is shaped in part by the mechanisms enabling abstract thinking. All three developments are explicable with the same basic mechanisms and yet yield different systems of logic.) As with the early Greek views on the cosmos and other matters, logic too originates with thinking about things that combine and things that separate. In fact, my 22

Mourelatos, p. 316. I do not endorse Mourelatos’ tendency to frame this change in thinking about character powers as being a linguistic enterprise. 24 E.g., “A road up down one and the same ” Heraclitus, Heraclitus: Fragments, trans. T. M. Robinson (Toronto: University of Toronto Press, 1987), Fragment 60. 25 Cf. or Plato’s Phaedo, esp. 96a-107b, or Dissoi Logoi. 26 Hesiod, Hesiod: The Works and Days, Theogony, the Shield of Herakles, trans. R. Lattimore (Ann Arbor: University of Michigan Press, 1959). 23

280

Dwayne Raymond

thesis is that logic as a discipline, and Greek formal thinking in general, developed from insights about things that combine and things that separate. What makes the Greeks unique is not so much how they conceived of the extreme ranges of combining and separating. Others cultures before the Greeks dealt with inseparability and polarity in very similar ways to those of the Greeks. What makes the Greeks unique is how their conception of the extreme relations of combining and separating informs the deductive techniques they used, and how these developments shaped their inquiry into deduction.27 The extreme ranges—things that never separate (inseparability) contain the seeds for logical consequence, and things that never combine (polarity) contain the seeds for inconsistency, contradictories and contraries. Formal reasoning began with the use of loose frameworks, framed by primitive versions of inseparable and polar interconnections, to draw conclusions.28 An early form of this is seen in both the Sophistical use and the Socratic use of opposites in arguments.29 For the Greeks, opposites include both things that never combine (e.g. contraries or contradictories) and things that never separate (e.g. co-relatives).30 To see how logic’s most basic insights develop from inseparability and polarity, we need to know how the Greeks understood the notions. There are at least three distinct ways of conceptualizing the extreme ranges of combining and separating: two of which inform the standard textbook treatment of logic as a natural deductive system (NDS), known as first-order relational predicate logic with identity, and one development of inseparability and polarity that is no longer part of the text-book treatment.

27

This development is in large part driven by the fact that the Greeks, unlike the ancient Hindus, looked to mathematics as a model for epistemology. With the exception of the Carvaka (a.k.a. Lokatata, a materialist movement in Hinduism during the Epic period), the Hindus sought an epistemic foundation in direct apprehension, which is only attainable via meditation. Their account of meditation is informed by codemolition, producing a levels view of reality. Meditation gives access to the deepest level. In the end, meditation, and not mathematics, became the primary source for knowledge in Hindu thought. 28 For a discussion see G. Lloyd, Polarity and Analogy: Two Types of Argumentation in Early Greek Thought. (Cambridge: Cambridge University Press, 1966). 29 One/many problems and other errors in reasoning arise from the fact that different versions of polarity and inseparability were not distinguished. It took some time to work out the precise difference between contraries and contradictories (see Lloyd). 30 E. Babin, “The Theory of Opposition in Aristotle,” (PhD diss., University of Notre Dame, 1940).

From Particular to Universal

281

To understand the differences, consider the example of cold and snow. Whereas we are tempted to conceptualize the relationship as either a truth-functional relationship (the truth of the assertion ‘This entity is cold.’ is a necessary condition for the truth of the assertion ‘This entity is snow.’), or as a relationship expressed in terms of how collections of entities fit together (the collection of all snowy things is fully contained in the collection of all cold things), the ancient Greeks also talked about codemolition (the demolition of cold brings about the co-demolition of snow, but the demolition of snow will not co-demolish cold). The co-demolition development was explicitly used to determine relations of priority among geometrical objects such as point, line, plane and, solid.31 It was also used to determine the existence of (and frame the concept) of co-relatives such as master and slave, or half of and double of.32 The demolition of slave brings the co-demolition of master and vice versa. The same holds for half of and double of, and even, for Heraclitus, up and down. It goes without saying that modern mathematical logic, predicate logic for example, employs the first two conceptualizations, whereas the third way of thinking about the extreme range (i.e. co-demolition) has all but disappeared. Indeed, predicate logic even replaces co-relatives with n-place predicates. There is a temptation to think that co-demolition reduces to either a truth-functional treatment (e.g. propositional logic), a collection of entities treatment (e.g. classes, or set theory), or a combination of the two (e.g. relational predicate logic with or without identity). That there are differences among the treatments is made clear by considering such well-known problems as the paradox of material implication. On the standard truthfunctional treatment, a conditional is true if and only if either the antecedent is false or the consequent is true. The following conditional is true: if I like chicken, then two plus two equals four. The conditional is true (in fact, it is always true), given that the consequent is always true. Thus, ‘two plus two equals four’ is a necessary condition for the truth of the claim ‘I like chicken’. It is a necessary condition even though the antecedent and the consequent are unrelated. This situation arises precisely because there is no requirement that the necessary condition be relevant to the sufficient condition; the relation is merely truth-functional. The co-demolition development builds relevance into its treatment. It does so in a way that is stronger than a collections version. Co-demolition is concerned with necessary belonging, not just belonging. The difference is not expressible 31 32

Topics VI, 4. See Cat. 7 and Meta. V, 15.

282

Dwayne Raymond

with, for example, the standard Venn diagrams. Moreover, a strictly extensional view cannot distinguish between co-extensive sets such as the set of equilateral things and the set of equiangular things. Not being limited to extensions, co-demotion provides for the distinction. The different developments lead to different stages and approaches in the history of logic, including: arguments that are structured by crude notions of opposites; deductive-axiomatic reasoning, such as that found in elementary Greek mathematics; what look like truth-functional notions found in the Megarians and later in the Stoics; and Aristotle’s Syllogistic, where he rejects the conditional treatment by the Megarians, and offers a terms logic. This chapter will show how the third development informs both some rudimentary versions of ancient Greek geometry (plane geometry) and Aristotle’s treatment of induction. My discussions of diagrammatic reasoning and Euclid (in the following section) are not intended to suggest that Aristotle’s main influence is geometry, as opposed to biology. The purpose is to establish the presence within the ancient Greek milieu of a method of generalization that does not rely upon the enumeration of individuals. In fact, of the three developments, co-demolition is the most natural offshoot, within a milieu which takes individuals as aggregates, that makes generalization from one particular case possible. 2 Reasoning from a particular diagram to a universal result For over two millennia, Euclid’s Elements was the paragon of rigorous proof. This changed in the nineteenth century. In the nineteenth century a desire to work with alternative geometries and understand their interrelationships, combined with the general shift towards algebraic formulation of general principles, brought with it not only the recasting of Euclid’s Elements, but also close scrutiny.33 Concerns pertaining to diagrammatic reasoning ranged from the expressive power of diagrams to the potential to be lead astray with features that were accidental to the diagram and to the fact that universal results are often drawn from particular diagrams. These concerns remained largely un-rebuffed until the end of the twentieth

33

For a discussion of the transition, see I. Grattan-Guinness, “Numbers, Magnitudes, Ratios, and Proportions in Euclid’s Elements: How did He Handle Them?” Historia Mathematica 23 (1996): 355-375.

From Particular to Universal

283

century, when logicians, including Sun-Joo Shin, began rebuilding our understanding of reasoning with diagrams.34 In a work that more directly bears on Euclid’s use of diagrams (a paper that circulated for 13 years prior to its publication in 2008, where it attained the status of being an underground classic), Ken Manders drew two important distinctions. The first is between components in a demonstration; and the second, between types of information conveyed by these components. Manders distinguished between the discursive text and a graphical part, the diagram.35 The text and diagrams work together; each provides different information. As Manders notes, “the key to reconstructing standards for producing and reading diagrams is the realization that the diagram and the text contribute differently, so as to make up for each other’s weaknesses.”36 The second distinction provides a way of distinguishing between their roles. It is the distinction between exact attributes and co-exact attributes of a diagram. Exact attributes, such as a given length, specify an exact property of a particular figure; co-exact attributes are those that are shared by all figures of a given kind such. “Co-exact attributes express the topology of the diagram”; they are “those conditions which are unaffected by some range of every continuous variation of a specified diagram.”37 Exact and co-exact attributes explain the division of labour between text and diagram. Exact properties are supplied by text and co-exact attributes come from the diagram.38 As Mumma notes, “If Manders’s analysis is correct, Euclid’s proofs ought to go through with diagrams which are equivalent in a co-exact 34

S. Shin, The Logical Status of Diagrams (New York: Cambridge University Press, 1994). 35 Manders. 36 Manders, p. 88. R. Netz uses this basic framework to inform his study of Euclid and a varied assortment of other Greek mathematicians in The Shaping of Deduction in Greek Mathematics (Cambridge: Cambridge University Press, 1999). 37 Manders, pp. 91-92. 38 A reviewer questioned the wisdom of adopting Manders’s terminology instead of using ‘accidental’ for ‘exact’ and ‘necessary’ for ‘co-exact’, which are found in Aristotle. While the mapping between vocabularies is plausible, the terms ‘exact’ and ‘co-exact’ carry with them an added specification; exact properties are supplied by text and co-exact attributes are supplied by the diagram. Manders’s terminology fits well with Euclid; it is less clear how this terminology maps onto Aristotle’s terms. I have decided to retain the terminology of ‘exact’ and ‘co-exact’ properties rather than accidental and necessary because the notion of necessity in Aristotle is neither de re nor de dicto. There is much that needs to be sorted out, more than I can do within the scope of this paper.

284

Dwayne Raymond

sense, but differ with respect to their exact properties. This turns out to be the case.”39 Consider Euclid’s proof for proposition 1, book 1. I have included two diagrams. The first diagram is accurate. The second is distorted. Euclid’s proof works with either diagram. Consider Euclid’s proof: [Protasis (enunciation)] On a given finite straight line to construct an equilateral triangle. [Ekthesis (setting out)] Let AB be the given finite straight line. [Diorismos (definition of goal)] Thus it is required to construct an equilateral triangle on the straight line AB. [KataskeuƝ (construction)] With centre A and distance AB let the circle BCD be described; again with the centre B and the distance BA let the circle ACE be described; and from the point C, in which the circles cut one another, to the points A, B let straight lines CA, CB be joined. [Apodeixis (proof)] Now, since the point A is the centre of circle CDB, AC is equal to AB. Again, since B is the centre of circle CAE, BC is equal to BA. But CA was also proved equal to AB; therefore each of the straight lines CA, CB is equal to AB. And things which are equal to the same thing are also equal to one another; therefore CA is also equal to CB. Therefore the three straight lines CA, AB, BC are equal to one another. [Sumperasma (conclusion)] Therefore the triangle, ABC is equilateral; and it has been constructed on the given finite straight line AB. (Being) what is required to do.40 The proof works for both the accurate diagram and the distorted diagram. Even with the distortions, the two diagrams are equivalent in terms of their co-exact attributes. Keep in mind that the co-exact attributes express the topology of the diagram; they are those conditions which are unaffected by some range of every continuous variation of a specified diagram. What exactly are those conditions? In both diagrams there are two circles: D is a circle with A as its centre and E is a circle with centre point B. The two circles intersect at point C. A straight line connects point A with point B. A 39

Mumma, “Generality,” p. 224. Euclid. Euclid: The Thirteen Books of the Elements vol. I trans. T. L. Heath (New York: Dover, 1956), p. 241. Both diagrams are from Mumma, “Review”.

40

From Particular to Universal

285

straight line connects point B with point C. A straight line connects point C with point A. Even though line segments AB and AC appear to be different lengths in the distorted diagram, we know from the co-exact properties that they are not. AB and AC both line on the centre of circle D and fall onto Circle D’s circumference. We know from the co-exact property of a circle that there is a topological relationship between the centre of a circle and its circumference. Straight lines, which start from the centre and end on the circumference, are the same length. The same holds for straight lines AB, BC, and the circle E with centre B. “The diagram’s burden is to reveal how certain co-exact relationships lead to others. It is not used to show exact relationships. This is the job of the text.”41 While Euclid successfully limits his attention to co-exact properties, Miller42 and Mumma43contend that Euclid does not provide “any explicit criteria for how the separation of the general from the particular is to be made.”44 The problem of how to do this formally has been tackled successfully by Miller and Mumma.45 Both produced systems based on Manders’s distinction between exact and co-exact properties. Miller’s system is a diagrammatic system that runs on a computer. The computer begins by producing all possible diagrams for co-exact properties that are expressed at each step of Euclid’s proof. To avoid the obvious explosion of diagrams, Miller employs heuristics, limiting the consideration to viable diagrams. Within his purely diagrammatic system, he employs hash marks to denote equivalent line segments. His computer-generated diagrammatic proof for Proposition 1, Book 1 looks a lot like Euclid’s proof. His set-wise diagrammatic proofs is this:46

41

Mumma, ”Generality,” p. 225. Miller, “Diagrammatic”; Miller, Euclid. 43 Mumma, “Intuition”; Mumma, “Generality.” 44 Mumma, ”Generality,” p. 228. 45 Miller, Euclid; Mumma, “Review”; Mumma, “Generality.” 46 Diagram from Miller, “Case Analysis.”. 42

286

Dwayne Raymond

Mumma47 develops a heterogeneous system. A heterogeneous system integrates both text and diagrams. His approach includes syntax and rules of well-formed diagrams and metric assertions. The text and diagrams interact in a precise way. Mumma outlines rules for constructing diagrams and reasoning with the diagrams and text. The role of the text is limited to expressing relations of equality or greater than between magnitudes: lines, angles and areas. As with Miller’s system, Mumma’s system substantiates Manders’s analysis: Euclid obtains a universal result by only relying on coexact attributes in his reasoning.48 Basing a system of reasoning on co-exact properties (understood as topology) works mathematically, but is it Euclid? What is crucial about coexact attributes is that they are “those conditions which are unaffected by some range of every continuous variation of a specified diagram.” Manders’s focus on topology is certainly one possible rendering. Is there another way to obtain co-exact properties, one which is more consistent with Euclid and his intellectual milieu? The answer to this is yes. In fact, it is exactly this kind of use for which the co-demolition test is best suited. (Note that I do not intent to contrast topology with logic; instead, I intend to contrast systems of logic that preclude alternative methods and concepts.49) As noted above, the co-demolition test is a test for inseparability. It works by removing, in a step-wise fashion, the accidental attributes of a particular. An accidental attribute is, according to Aristotle, “one that has no requirement to belong or not belong.” Indeed, Aristotle’s definition is exactly the range of combination lying between the extremes of polarity (a requirement to not belong) and inseparability (a requirement to belong). The test distinguishes between the required from the non-required properties. If a 47

Mumma, “Intuition”; Mumma, “Proof.” Avigad, Dean, and Mumma provide a third system in J. Avigad, E. Dean, and J. Mumma, “A Formal System for Euclid’s Elements” Review of Symbolic Logic 2, no. 4 (2009): 700-768. 49 That concepts and methods are altered when we recast them in different logics must be admitted by those who think that the development of n-place predicates was a grand achievement over the old treatment of relations as co-relatives. My foray into ancient reasoning reclaims the older notion, showing the role that dependency relations, in the form of co-relatives and relations of priority, had in these systems. These results are only obtainable with the former notion that was replaced by nplace predicates. Indeed, the property that generates so-called Cambridge changes (co-existence) also plays a key role in structuring the system. We could recast the system using n-place predicates, but the recasting would not be the ancient system of logic. 48

From Particular to Universal

287

non-accidental attribute is destroyed, the underlying subject is codestroyed. What remains is highly abstract. Just like the definitions with which Euclid begins the Elements: 1.1 A point is that which has no parts. 1.2 A line is breadthless length.50 Commentators commonly held that these definitions play no role in Euclid’s proofs; further, that these definitions are in all likelihood dressing which pays homage to his predecessors. This widely held view errs. The definitions do not just identify elements called lines; they serve to exclude from consideration all accidental features. A line is just breadthless length. Consider two lines running from A to B. Case 1 A

Case 2 B

A

B

If the line is part of a proof, the fact that the line in case 1 is thin compared to the thick line in case 2 is of no concern to the proof. What matters is length, and not just length, but breadthless length. When we look at a diagram, if we abstract (peel away) from the line all that is accidental to it (everything but breadless length), we end up with that which is universal to all lines: length and only length. The diagram merely helps to make visible that which must truly be understood in the mind. This too is a common theme, distinguishing the ideal from the perceptible. The perceptible helps us to understand the ideal; it is not itself ideal. The Greek method of abstraction limits our attention to the ideal aspects. In an important respect, the definition for line identifies “those conditions which are unaffected by some range of every continuous variation of a specified diagram.” Euclid is doing this without having recourse to topology. But we are not out of the woods yet. The topological version of co-exact properties is able to treat straight and less than straight lines as equivalent in terms of their co-exact properties. This allows poorly drawn lines to count as straight. How does Euclid achieve this result? The answer is threefold. Let us begin with, what seems to be, an unrelated pair of definitions, definitions 1.13 and 1.14: 50

Euclid, p. 153.

288

Dwayne Raymond

1.13 A boundary is that which is an extremity of anything. 1.14 A figure is that which is contained by any boundary or boundaries.51 This very important pairing is a pairing of co-relatives, like half of and double of. In this case, the pairing is between figure and boundary. Destroy the boundary or boundaries and the figure is co-destroyed. Destroy the figure and the boundary (or boundaries) is (are) co-destroyed. Now consider definitions 1.3 and 1.4: 1.3 The extremities of a line are points. 1.4 A straight line is a line which lies evenly with the points on itself.52 Given that points are the boundaries of a line and that a figure is contained by a boundary, the line is a figure contained by two boundaries, called points. Whenever there is a line, there are two end points, and whenever there are two points, there is a line between them. While there is a line between two points, there is no requirement that it be a straight line. A

B

A

B

Definition 1.4 only tells what is meant by a straight line, it does not limit the line between two points to a straight line. Euclid achieves this by introducing postulates. Consider the first two postulates: 1.1 To draw a straight line from any point to any point. 1.2 To produce a finite straight line continuously in a straight line.53 The first postulate limits our consideration to only straight lines. In this way, Euclid limits consideration of the lines between two points to lines that are straight. This is not a topological constraint. If the squiggly line in case 4 is part of a proof, it is so as a straight line. Again, the abstractive procedure is operative here, but it does not do all the work. In considering line AB, one peels away from it all but the breadthless length between A 51

Euclid, p. 153 Euclid, p. 153. 53 Euclid, p. 153. 52

From Particular to Universal

289

and B. The breadthless length is normalized not by definition 1.2, but by the constraint in postulate 1.1. The second postulate removes any limit on a straight line’s length, all the while retaining the reciprocal figure-boundary structure. The addition of finite lengths can be carried out indefinitely. Without this postulate, the figure-boundary framework would collapse in the face of an infinite line, one without two extremities. This is an early instance of the syncategorematic notion of infinity. As we can see, the definition, along with the co-demolition test, limit consideration to “those conditions which are unaffected by some range of every continuous variation of a specified diagram.” This leaves open the question of how Euclid reasons with his diagrams and text. I will show one proof here. I will repeat the proof for proposition 1, showing how in it Euclid relies both on definitions and on a framework of co-relatives so as to limit consideration to highly abstract features of a diagram. En route to this, we need one more set of notions. Let us begin by considering how this reciprocal structure of co-relatives informs Euclid’s treatment of the circle: 1.15 A circle is a plane figure contained by one line in such a way that all straight lines falling upon it from one point among those lying within the figure are equal to one another.54

Not only does this provide a way to define a circle, it equally provides the means by which lines (breadthless lengths) can be compared for equality. The plane figure ‘circle’ is simultaneous with its boundary, which is “contained by one line in such a way that all straight lines falling upon it from one point among those lying within the figure are equal to one another.” In this case, the boundary is stated in such a way as to provide a context to compare lines. Reed has called this a context for comparison.55 There is only one kind of circle. But there are different sizes of circles. Postulate 1.3 rules out the possibility that there may be limitations on a circle’s size. It provides for the existence of any circle of any size: “To describe a circle with any centre and distance.”56 The figure-boundary reciprocity holds for any circle of any size and it uniquely holds; for each size of circle there is exactly one boundary. Change the boundary, and the 54

Euclid, p. 153. D. Reed, Figures of Thought: Mathematics and Mathematical Texts (London: Routledge, 1995). 56 Euclid, p. 153. 55

290

Dwayne Raymond

size of the figure changes. Without having recourse to topology, Euclid has woven into a structure of reciprocal dependency “those conditions which are unaffected by some range of every continuous variation of a specified diagram.” He made this particular context avail whenever he needs it by means of Postulate 1.3. With this approach, Euclid is able to limit consideration to and only to co-exact properties, not the topological co-exact properties but those which are invariant across transformations. Recall Euclid’s proof from above. The task is to construct an equilateral triangle on a given line. As noted above, the protasis states a very general task. At the second stage of setting out, a specific line, line AB, is given. The proof proceeds in relation to this specific line. At the diorismos, the task is stated, “to construct an equilateral triangle on the straight line AB.” The definitions do not aid in the selection of a diagram; they inform its construction, not in terms of a topographical nature, but in terms of the part-whole relations that were established. The austere definitions keep the proof at the level of universal features, and the contexts for comparison limit focus to co-exact attributes that are informed by reciprocal dependency relations. The ekthesis sets out a straight line AB. A line (breadthless length) is simultaneous with two points as its extremes. Each point can serve as the centre for a circle whose distance is the length AB. In the kataskeuƝ stage, two circles are described. The drawing of each circle with the distance AB and one with a centre at A and one at B is justified by postulate 1.3. The two circles cut across each other.57 One of these points is labelled C. Given the pair of points AC and the pair of points CB, the boundary condition for the respective lines, line AC and line CB, exists. Since breadthless length (the figure) co-exists with its boundaries (two points), the drawing of a line only renders it explicit to us. Given Postulate 1.1, the only line that we consider is a straight line, two straight lines are added for the respective pairs of points AC and BC. In effect, the drawing of the lines makes visible that which simultaneously exists when two points exist: a breadthless length between them. With the diagram set out, only the mathematically relevant features factor into the proof. In Proposition 1.1, the mathematically relevant features of the diagram are those which are specified by the following pairings. 57

I do not question whether the circles intersect. My purpose here is not to defend Euclid, but to illustrate the role that reciprocal and non-reciprocal dependency relations have in the Elements.

From Particular to Universal

Boundary Two points A boundary line such that all straight lines falling upon it from one point among those lying within the figure are equal to one another

291

Figure Line (breadthless length) Circle

The austere definitions of a point (no parts) and a line (breadthless length) further limit the relevance of various visual aspects to the proof. That is, the austere definitions function to exclude all but the most universalized features from the demonstration. The circle CDB reciprocates with a context to compare any straight line that has one point at its centre point A and the other on its circumference. Lines AC and AB are thus equal. The circle CAE reciprocates with a context to compare any straight line that has one point at its centre point B and the other on its circumference. Lines AB and BC are thus equal. Common notion 1.1, according to which things that are equal to the same thing are equal to one another, equates line BC with line AC. Thus, lines AB, AC, BC are equal and the triangle ABC is an equilateral triangle. The proof is repeatable for any size of line AB, with each proof being invariant, precisely because each proof turns on and only on those features that are invariant across transformations. Euclid achieves this not by identifying the topology, but with the aid of the co-demolition test. The co-demolition test not only limits consideration to those attributes which are invariant but also serves to structure by means of co-relative pairs, contexts for the comparison of previously defined geometric objects, which are themselves only the most universal attributes, such a breadthless length. The diagrammatic proof for proposition 1.1 is such that is allows us to go in the reverse from an equilateral triangle to a given finite straight line. The claim here is not that the written proof is exactly reversible, but that order of sequence can be reversed in the diagram. That is, it is reversible in the sense described by Pappus in his controversial discussion of the ancient Greek geometrical methods of analysis and synthesis. Pappus held that: in analysis we suppose that which is sought to be already done, and we inquire from what it results, and again what is antecedent of the latter, until we on our backward way light upon something already known and being first in order…. In synthesis, on the other hand, we suppose that which was reached last in anal-

292

Dwayne Raymond

ysis to be already done, and arranging in their natural order as consequents the former antecedents and linking one with another, we in the end arrive at the construction of the thing sought.58

Starting with the ABC triangle, draw a circle CDB with point A at the centre and distance AB. Draw a second circle CAE with point B at its centre and distance AB. The circle CDB reciprocates with a context to compare any straight line that has as one of its points the circle’s centre point A and its other point on the circle’s circumference. Lines AC and AB are equal. The circle CAE reciprocates with a context to compare any straight line that has one point at its centre point B and the other on its circumference. Lines BA and BC are equal. The entire process can begin with the common line AB. Line AB is an element that is prior to triangle ABC. We can reason forwards and backwards in a diagram because the contexts for comparison are structured by co-relatives—two things bound by a reciprocal dependency relation. What makes something prior or posterior is the non-reciprocal dependency relation that runs through the basic definitions. A point can exist without a line, but a line requires two points. Destroy one point, and the line is co-destroyed, but the other point remains. Aristotle reports that geometers relied upon co-demolition to determine the priority among points, lines, planes, figures, and solids.59

58 Translated in J. Hintikka and U. Remes The Method of Analysis: Its Geometrical Origin and its General Significance (Dordrecht, Netherlands: D. Reidel Publishing Company, 1974), pp. 8-9. 59 With the exception of Hintikka and Remes, Method, the literature has generally focused on reasoning depicted in lists of propositions, where each entry is either an assumption or justified by a rule of inference. Since rules of inference work in one direction, a strict account of analysis has seemed to be a pipe dream. By limiting the reasoning to chains of bi-conditionals, one is able to reason from the conclusion to the assumptions and from the assumptions to the conclusion. With such an approach, there is no way to determine which is prior. I propose that the practice is part of reasoning with diagrams in the way that Euclid reasons. The co-relative relation licenses reasoning from a given to a result and from the result to a given. The non-reciprocal dependency relations among the definitions establish priority. Given that his approach draws upon both text and diagram, his method has more resources available to him than a purely linguistic account of logic proof. For a recent survey of ancient and early modern notions, see K. Smith, Matter Matters: Metaphysics and Methodology in the Early Modern Period (Oxford: Oxford University Press, 2010). For a recent alternative

From Particular to Universal

293

For the present purposes, two things are important. The first concerns the fact that Euclid’s Elements work with a co-demolition development and not a collections development. Second, the fact that the co-demolition development peels away that in which we are not concerned, leaving behind that in which we are interested, provides a way of reasoning from particulars to universal results. In fact, the co-demolition test plays a key role in both arriving at the universal, such as the definition for point, and it plays a role in obtaining a universal result. Both of these are relevant to Aristotle’s account of induction, which involves a movement from particulars (either species or individuals) to universals. Induction was used in two ways. First, in the Prior Analytics60 he identifies a form of induction (i.e. perfect induction) as a form of deduction. Second, for Aristotle, induction provides not just a probable view of reality, but also a true picture of reality. In one case (the case of perfect induction), inductively knowing the universal requires complete enumeration of particulars.61 In other cases, we come to know the universal through the perception of many particulars,62 or through a single particular.63 As we will see, the ability to move from one individual to a universal draws upon co-demolition and the ability to divide an individual into a number of universal attributes. For this reason, individuals are more than mere counters determining membership in sets. Let us turn to Aristotle’s treatment of induction and sketch how these results pertain to his views. 3 Aristotle reasoning from particulars to a universal Aristotle’s induction begins with a process of enumeration from senseperception. While sense-perception provided the raw material, the enumeration of individuals does not instil scientific knowledge. At most, it provides a numerical understanding, as Aristotle himself notes at Anal. post. I 5, 74a25-74a32: Even if one should prove, with reference to each triangle, the equilateral, scalene and the isosceles, separately, that each has its angles equal to two right angles, either by one proof or by different proofs, he does not yet know that the triangle in general, has its angles equal to two right angles, except in a sophistito my view, see J. Hintikka, “Method of Analysics: A Paradigm of Mathematical Reasoning?” History and Philosophy of Logic 33 (2012): 49-62. 60 Anal. pr. II 23. 61 Anal. pr. II 23. 62 Anal. post. II 19. 63 Anal. post. I 31, 88a10-18.

294

Dwayne Raymond

cal sense, even though there exists no triangle other than triangles of the kinds mentioned. For he knows it not qua triangle, nor of every triangle, except in a numerical sense; he does not know it notionally of every triangle, even though there be actually no triangle which he does not know.64

Reasoning from particular diagrams to universal results in Greek geometry provides insights into Aristotle’s practice. That is, it sheds light on how he proposes to obtain knowledge either after complete enumeration of cases is considered, or once a single case is perceived. In response to a worry that it is impossible to go through all particulars, Biondi observes that, an induction can be held to have gone through all particular instances, not because it has actually enumerated every single particular instance … but because it has done so potentially by having acquired the cognition of the universal essence of the particulars being enumerated.65

If Biondi is right and Aristotle was thinking along theses lines, then, by grounding Biondi’s reading within the proper intellectual milieu, we end up with a more charitable understanding of Aristotle’s account; this, of course, is independent of any judgment that we make about its veracity. The co-demolition test and the discussion of reasoning from a particular diagram to a universal result are part of the intellectual milieu that grounds Aristotle’s approach. Like a geometer who does not enumerate all diagrams but reasons from an individual geometrical diagram to a universal result, Aristotle carves up the individual to determine if the various combinations of things that are present in the individual are inseparable from one another. In fact, the assertion that “he knows it not qua triangle” is a reference to the product of the co-demolition test. To know something qua triangle is to take an equilateral triangle and demolish from it all but the attributes that are triangle. If something belongs qua triangle, it will belong to each of the (specific or particular) triangles. In this way, the codemolition test aids us in arriving at universal knowledge. (Complete universal knowledge requires that we prove it for an arbitrary instance of triangle. The full criteria include: all (enumeration), per se (makes use of co-demolition), and universal (proven for an arbitrary instance).) The final gap is bridged by noesis, a spark of intellectual insight, that is, an act of discernment. Reference to the test illustrates a more incremental practice 64

Translated by J. Barnes, Aristotle’s Posterior Analytics (Oxford: Clarendon Press, 1984), slightly emended. 65 Biondi, p. 207.

From Particular to Universal

295

(in the steps leading to noesis) in Aristotle’s conception of induction, in which the individual (or a group of enumerated individuals) is (are) not considered as individual, but as things composed of universals, some of which are inseparable in terms of reciprocal dependency relations, some of which are inseparable in terms of non-reciprocal dependency relations, and some of which have no requirement to belong or not belong. As with Euclid, the shift in Aristotle’s account of scientific thinking is away from all that is accidental to the individual. He reasons at the same level of abstraction seen in Euclid about the universals (secondary substances) that are grounded in the individual (primary substance). This move, towards a more incremental view of induction, is exactly what Aristotle considers at Anal. post. I 31, 88a10-18: “grasp something universal from seeing. E.g. if we saw the glass to be perforated and light coming through it …. [we would understand] at one time that it is thus in every case.”66 Aristotle arrives at the induction, not by counting instances, but by looking for the cause. The cause is arrived at with the aid of codemolition as seen in Anal. post. I 5. We learn that having the internal angles equal to two right angles (2R) belongs to bronze isosceles triangle qua triangle and not qua bronze or qua isosceles. Aristotle uses the test to establish that triangle is the cause of 2R belonging to a bronze isosceles triangle. (More needs to be said here; it suffices to point out that Aristotle uses this test and ‘qua’ to arrive at his conclusion.) With induction, Aristotle’s focus is not on the individuals per se, even if it begins with the perception of a particular. In fact, in his explicit discussion of perception, he tells us that the perception of the individual is accidental to the universals that are perceived. His analysis is about the universals that are combined or separated within the individual. This suggests a different account of truth, one that we see explicitly in Aristotle’s writing. Truth and falsity is not (exclusively or even primarily) about a correspondence between collections of individuals and the grouping described in an assertion. For Aristotle, truth and falsity is about combination and separation. Combining and separating occur in thought and in the world: “a true judgement affirms where the subject and predicate really are combined, and denies where they are separated” according to the Metaphysics.67 And, the De Anima records the following observation:

66 67

Trans. J. Barnes. VI 4, 1027b20-21.

296

Dwayne Raymond

[W]here the alternative of true or false applies, there we always find a putting together of objects of thought in a quasi-unity. [..] For falsehood always involves a synthesis; for even if you assert that what is white is not white you have included not white in a synthesis. It is possible also to call all these cases separation as well as combination.68

This is a slightly different view than that which informs our standard logic. It is only because, unlike the standard view in logic, Aristotle does not view an individual as an indivisible atom whose only role is to be aggregated into various collections of individuals (classes or sets) that he is able to countenance the possibility of arriving at knowledge through the induction of a single case. As with geometry, sometimes that which holds universally comes from investigating many different instances, or, given the right prior knowledge, that which holds universally can be obtained by analysing the dependency relations that hold between the universals comprising the particular. Aristotle’s discussion of an Inductive Syllogism is part of his attempt to adapt that which informs geometrical reasoning into a system that can also accommodate dialectic. Unlike mathematics, dialectic includes accidental connections. He tells us that: If it were impossible to prove truth from falsehood, it would be easy to make an analysis; for they would convert from necessity. Reciprocity occurs more in mathematics, because mathematics assumes no accidental connections (differing in this from dialectic) but only definitions.69

As shown above, the reciprocity in geometry is the result of contexts structured by co-relatives (e.g. half of and double of co-exist). However, to accommodate accidental connections, Aristotle drops the use of co-relatives and adds a layer that includes a collections treatment of individuals. That is to say, Aristotle adds a collections treatment of inseparability and polarity to accommodate accidental connections. His assertoric syllogistic involves the collections treatment; his necessary logic involves the co-demolition treatment; neither treatment involves the truth-functional development. Moreover, he develops a system whose rules—and whose primitive concept (follows of necessity) —allow for the fact that truth can follow falsity, but falsity cannot follow truth.

68 69

III 6, 430b1-4. Anal. post. I 12, 78a6-13.

From Particular to Universal

297

On the surface, it appears that his system does not accommodate an important type of reciprocal reasoning known as counter-predication. Counter-predication involves the conversion of terms where the subject belongs to all of the predicate before and after the conversion. This is a problem for his discussion of inductive syllogisms. The inductive syllogism requires that two terms counter-predicate. Specifically, an inductive syllogism purportedly proves the relation between the major term P and the middle term M by means of the minor term, S. By contrast, the first-figure universal affirmative syllogism (Barbara) proves the relation between the major term P and the minor term S by means of the middle, M. Barbara Major Premise: Minor Premise: Conclusion:

Inductive Syllogism

P belongs to all M

P belongs to all S

M belongs to all S

S belongs to all M

P belongs to all S

P belongs to all M

To do this, the inductive syllogism requires that the minor S and the middle term M counter-predicate. In his discussion of an inductive syllogism, Aristotle enumerates a list of species in place of the subject term S. It is true that Aristotle’s syllogistic does not appear to accommodate counter-predication; there is, at least, no rule by which one can switch the counter-predicating terms in an assertion. However, in his discussion of reciprocal proofs in the Anal. pr. II 5-7, Aristotle does, in fact, accommodate counter-predication, not with a rule of inference, but simply with an assertion. If two terms counter-predicate S and M, then he writes out two sentences in the beginning: ‘M belongs to all S’ and ‘S belongs to all M’. His reasoning proceeds accordingly. While this is not elegant, it is enough to accommodate counter-predication within the syllogistic. This is sufficient for his treatment of an inductive syllogism. This is the direction towards which Biondi was moving, but, without a broader conception of the milieu from which reasoning develops in ancient Greece, he was likely condemned to fit Aristotle into a Procrustean bed. That is, when a complete picture is required, attempts will be made to reconcile Aristotle’s view with some version of a purely extensional logic. Groarke does this with his reworking of Hamilton’s logic. While quite interesting, it obscures what I argue to be the most important feature of

298

Dwayne Raymond

Aristotle’s approach—the ability to mentally peel away attributes from individuals in considering the combinations of universals that are grounded within each individual. This is very much part of a set of conceptual and methodological differences which are underwritten by some but not all of the developments whence logic springs. A full discussion of Aristotle’s views on induction is beyond the scope of this chapter. It would require a discussion of the Posterior Analytics. It is for this reason that I merely sketch out the approach I think must be taken. The point of this chapter is not to detail induction in Aristotle, but to explain the intellectual milieu from which it comes. It suffices to point to Aristotle’s famous discussion of ‘every case’, ‘in itself’, and ‘universal’ in Anal. post. I 4. In this chapter, Aristotle provides the means by which one obtains universal knowledge by carving up a particular case. The approach explicitly makes use of qua-locutions, which, as Cleary has shown,70 are part of Aristotle’s use of co-demolition. Indeed, his concept of truth more naturally fits the view that Aristotle thinks of individuals as divisible. As explained above, for Aristotle, truth and falsity depend on combination and separation. Furthermore, Aristotle’s induction must be understood within his entire system of logic. I have argued elsewhere in print that Aristotle’s apodictic syllogistic is in fact sound and quite interesting. For Aristotle, the modal term modifies the copula: necessary belonging. Rather than being concerned with necessary truth or necessary being, necessary belonging concerns inseparable terms. Once again, the test for this is the codemolition test. By making an allowance for the product of the codemolition test, long-standing problems dissolve.71 The point here is that the method underwrites an alternative concept of necessity, necessary belonging. The practice of induction is part of this set of concepts and methods. To better understand Aristotle, we need a better understanding of that which informs his concepts and his approach to reasoning, both be it inductive, syllogistic, apodictic, and so on. For this reason, I have turned to questions about the origins of logic in Greece.

70

See “Terminology.” See D. Raymond, “Polarity and Inseparability: The Foundation of the Apodictic Portion of Aristotle’s Modal Logic” History and Philosophy of Logic 31, no. 3 (2010): 193-218.

71

From Particular to Universal

299

Conclusion Returning to the theme of this anthology, the standard view would never admit that we can obtain knowledge and not just true belief from the induction of a single case. After all, the modern account of induction involves the enumeration of instances, and a determination of likelihood based on that enumeration. This treatment of induction falls within our intellectual milieu, which treats individuals as indivisible atoms whose only role is to be aggregated into various collections. We reason solely based on the inclusion, the overlap, and the exclusion of these collections. Indeed, our standard logic is informed by a system of semantics that fully embraces the treatment of individuals as indivisible. As interesting and as powerful as our modern systems are, they are not part of Aristotle’s treatment. His treatment draws upon a test of inseparability that is entirely absent from our standard approach. The test violates the assumption that individuals are indivisible. But as we saw in Euclid, the test proves to be exactly what is needed for the construction of general results from particular cases. Given that Aristotle is working within this milieu and that he continues to explicitly use the co-demolition test, his methods and his concepts need to be understood accordingly. We saw how prior, posterior, and simultaneity (the co-existence of co-relatives) played a key role in Euclid. It is not a coincidence that Aristotle’s discussion of scientific knowledge includes various requirements of priority: true, primary (prota), immediate (amesa, “without a middle”), better known or more familiar (gnôrimôtera) than the conclusion, prior to the conclusion, causes (aitia) of the conclusion. By trying to understand the milieu, we will be in a better position to understand Aristotle. His odd treatment of induction is but one example of how his concepts and methods differ from ours in interesting and important ways. Aristotle’s treatment of induction presents a challenge to the Humean enumeration account of induction. Aristotle does not treat individuals as indivisible wholes; he peels away aspects, looking for reciprocal and nonreciprocal dependencies among universals that are grounded in the individuals. In this way necessary knowledge is acquired by considering a single instance. Indeed, by considering a single instance (be it a diagram or a representative example), one is considering a matter of fact, but because of the method of generalization, the instance being considered constitutes necessary knowledge (relations of ideas). In this way, the mutual exclusivity of the tines on Hume’s fork is equally challenged.72 72

I am indebted to the editors and anonymous commentators for this point of analysis.

Not Induction’s Problem: Aquinas on Induction, Simple Apprehension, and Their Metaphysical Suppositions Matthew Kostelecky University of Alberta

Abstract: This chapter argues that “the problem of induction” is not really induction’s problem, at least not according to Thomas Aquinas. While Thomas believes that induction is an important feature of how humans arrive at the first principles of particular sciences, it does not sit at the center of his theory of human cognition. Kostelecky tries to identify precisely the role induction plays in Thomas’ larger theory of cognition and to determine the relative importance of induction vis-à-vis other basic features of his account of human knowledge, including simple apprehension, judgment, and noninductive ratiocination. Kostelecky shows that the problems that are often associated with induction are more properly laid at the feet of simple intellectual apprehension. As the fundamental lynchpin to Thomas’ theory of cognition, this simple apprehension provides more resources to deal with these problems. Aquinas’ resolution provides a metaphysical account of the intellect’s relation to things rather than an epistemological justification of knowledge. Although this solution may yet deepen the problem (a question beyond the scope of the essay), Kostelecky concludes that it does properly situate where the problems lie.

Introduction St. Thomas Aquinas has a theory of human cognition, though I am not sure that he has an ‘epistemology’. To be sure, one can find similarities between aspects of his thought and contemporary accounts of epistemology and argue, moreover, that Thomas is (or isn’t) a foundationalist,1 or an internal1

Alvin Plantinga is a well-known proponent of this interpretation of Aquinas. For a critical treatment, replete with references across Plantinga’s writings and others who interpret Thomas as a foundationalist, see A.N. Williams, “Is Aquinas a Foundationalist?” New Blackfriars, 91 (2010): 20-45.

302

Matthew Kostelecky

ist,2 or an externalist,3 or reliabilist,4 and so forth—and such arguments have sometimes been made in the past decades. Of course, the extent to which it is proper to cast either the entirety or an aspect of his account of how humans know as ‘epistemology’ will depend on how the term is used. If what one means by ‘epistemology’ is a rigorous and thoroughgoing justification of knowledge in light of dogged skeptical concerns, then Thomas’ account of human cognition is not, I think, properly called an ‘epistemology’. However, if one defines epistemology in a different sense, as eschewing primarily justificatory aims and oriented toward providing a) an account of what constitutes knowledge and b) describing the processes that humans go through to produce knowledge, then it seems to me correct to call an aspect of Thomas’ thought ‘epistemological’, namely, that part of his account of the human being that describes how human cognition occurs. In this essay I will try to show why Thomas’ account of cognition does not fit into the first conception of epistemology above, not only because I think it would be false to say otherwise, but because I think it is wrongheaded to make Thomas’ cognitive theory respond to skeptical concerns that are foreign to it, at least if that cognitive theory is shoehorned into the same vocabulary or directed to the same concerns and standards as a more skeptically driven epistemology. Moreover, I do not think a contemporary student of Thomas needs to cede the terms of the debate to the skeptical concerns that gave a particular character to much modern philosophy and epistemology, not because those currents arose well after Thomas died (though they did since these concerns are usually associated with ‘modern’ currents, like Cartesian and Humean skepticism; however, a more refined casting of the issues sees aspects of these skeptical currents arising a good deal earlier than Descartes, as, for example, in Nicholas of Autrecourt and the anti-skeptical response by Jean Buridan in the 14th century). Rather, it is because whether one concedes to one of the modern forms of skepticism or, by contrast, looks at human cognition as basically reliable depends upon a prior decision regarding the desirability or 2

Scott Macdonald, “Theory of Knowledge,” in The Cambridge Companion to Aquinas, ed. Norman Kretzmann and Eleonore Stump (Cambridge: Cambridge University Press, 1993), 160-195. 3 John I. Jenkins, Knowledge and Faith in Thomas Aquinas (Cambridge: Cambridge University Press, 1997). See especially pp. 215-218. 4 Eleonore Stump, “Aquinas on the Foundations of Knowledge,” Canadian Journal of Philosophy, Supplement 17 (1991): 125–158. Stump’s argument is more nuanced than asserting that Thomas is a reliabilist. She is arguing, in the mains, against Plantinga’s interpretation.

Not Induction’s Problem

303

even the reasonability of placing absolute certainty as a basic criterion for knowledge. Instead of trying to justify Thomas’ account of knowledge on inhospitable terrain and trying to make it do something that it is not designed to do (i.e., justify knowledge against persistent skeptical concerns), it is perhaps better to show why it is at least as reasonable, though admittedly less than apodictically certain, to begin where Thomas and a host of other pre-modern thinkers begin: with a descriptive account of how humans know. (This is also where much of what today operates under the aegis of ‘naturalized epistemology’ begins.) My lodestone for this endeavour will be to explain what Thomas means by ‘induction’, a term that means different things to different people and which has been an essential focus for many modern skeptical critiques. The problem of induction as traditionally conceived is not really induction’s problem, at least not for how St. Thomas construes the relevant issues. Instead, the problems that are often associated with induction (e.g., that induction is not certain or that a complete enumeration of all instances is required for an induction to be certain) are more properly laid at the feet of other, more fundamental aspects to his account of the human being that have more and different resources to deal with the purported problems. This essay is split into three basic parts. First I present Thomas’ construal of induction in broad outlines and then distinguish between different sorts of induction. Second, I argue that Thomas holds that some inductions are indeed ‘necessary’, in spite of several comments he makes that might indicate otherwise. This includes distinguishing the role of inductions in dialectics and scientia. Third, I present the various ways in which induction relies on the abstractive capacity of the agent intellect, which itself rests upon a host of metaphysical assumptions that those who level the critiques associated with the problem of induction likely do not share. I briefly discuss what some of these assumptions are in order to stress that Thomas’ approach to cognition is not an epistemological justification of knowledge, but a metaphysical account of the intellect’s relation to things, which substantially shifts basic features to the discussion of how one deals with induction. I do not think this repositioning of the issue completely dissolves the force of the traditional critiques of induction (in fact, it may deepen the problem in unwelcome ways), but it does properly situate where the relevant issues lie.

304

Matthew Kostelecky

1 The Contours and Kinds of Induction There is no self-standing or systematic account of ‘induction’ in Thomas’ writings. Of the various uses of the term, I would point out three relevant uses. First, Thomas uses it as a cognate of ‘introduction’. For example, Thomas says that a student is slower mentally if he requires more ‘inductiones’ to grasp a given subject matter.5 Second, Thomas uses ‘inductio’ in explicitly causal contexts. One example is that a fire might be said to ‘induce’ its form onto properly disposed matter, thereby setting the matter alight,6 but this causal sense of the term is far more widespread than merely talking about fires making fires. Third, and most importantly for what I will be discussing, is the use of the term that is inspired by Aristotle’s use of ‘epagǀgƝ’, especially as contained, for example, in the Posterior Analytics II, 19. I believe that there is some overlap between the second (causal) and third (cognitive) sense of how Thomas uses the term, as I discuss below. Unsurprisingly, Thomas gives the greatest explanation of the cognitive sort of induction7 in his commentary on Aristotle’s Posterior Analytics, wherein induction is primarily explained in terms of its role in providing the principles upon which a particular form of argument, the demonstrative syllogism, relies.8 He also treats the issue in some detail in his commentary on the Metaphysics and touches on it in Commentary on the Nicomachean Ethics VI (hereafter, In Ethica). Thomas did not write a commentary on either the Topics or the Prior Analytics, both of which contain vital resources for approaching Aristotle’s use of epagǀgƝ. We can find the term induction fairly frequently outside of his commentaries on Aristotle (e.g., in both the Summa Theologiae and the Summa contra Gentiles and the various disputed questions), but Thomas does not provide robust accounts of what he means by the term in these contexts. Instead, he usually uses the term 5

Quaestiones Disputatae de Veritate, q.8, a.10: “A person with higher intelligence is ready, from a few principles he has within himself, to proceed to various conclusions which those with a less acute intelligence cannot reach without diverse inductions [nisi per varias inductiones] and without knowing the proximate principles of these conclusions.” 6 Quaestiones Disputatae de Potentia, q. 6, a.3, arg. 12 : “The power to induce a form into matter, and the power to prevent its induction are in the same genus: thus the form of fire is induced into matter by the power of a body, and it is also the power of a body that prevents the induction of that form.” See also Summa contra Gentiles II, 43. 7 Henceforth, when I use the term ‘induction’, it refers to the cognitive sort, unless otherwise specified. 8 See Robert Schmidt, The Domain of Logic According to St. Thomas Aquinas (The Hauge: Martinus Nijhof, 1966), pp. 270-272.

Not Induction’s Problem

305

with minimal explanation (often merely distinguishing syllogisms and inductions as different ways of reasoning9) and moves on to making the points he wants to make, seeming to take for granted that the meaning of the term is fairly clear. Thomas tends to use ‘syllogize’ for a deductive demonstration and contrasts that with induction, at least with respect to one way of construing induction, as I explain below. (I will follow Thomas’ word choice and use ‘syllogize’ as a way of reasoning that shares some properties with induction, but differs from it in others.) Disambiguating the term ‘induction’ is then not a particularly easy task to accomplish, because Thomas does not directly state in any one place how he conceives of induction tout court. The fact that Thomas does not treat the issue systematically is perhaps a hint that he looks at induction as rather unproblematic. It is best, I think, to start by explaining some general commonalities among different instances of induction and then present the character of the different notions of induction that Thomas employs. At its broadest level, induction refers to a distinctly human process (for Thomas neither angels and God nor non-human animals cognize inductively) by which humans move from sensed particulars to generalized statements about those particulars, which then serve as the general principles upon which syllogisms rely as their beginning point. An excellent example of this general use of induction is the following: But it is impossible to grasp universals without induction. This is more obvious in the case of sensible things, because we acquire universal knowledge through our experience of sensible singulars, as Aristotle explains in the beginning of his Metaphysics. But it seems to present a difficulty, especially in the case of things which we consider abstractly, i.e., mathematical things. For experience begins from sense knowledge, as Aristotle states in the text just cited. But there seems to be no place for sense knowledge in the case of things abstracted from sensible matter. Responding to this difficulty, Aristotle states that even those things which are considered abstractly can be made known through induction. For in any genus of abstract things, there are some particulars which are not separable from sensible matter insofar as each of them is such. The line, for example, is considered abstractly, but the principles of abstract things, the principles from which we demonstrate about these things, are revealed to us only through the sense perception of particulars. By seeing a singular sensible whole, for example, we are led to an understanding of what a whole and a part are, and, by ob9

At Prior Analytics II, 23-4, Aristotle is clear that inductive reasoning can be formalized syllogistically, that we can have inductive syllogisms. As Aristotle cleanly summarizes the issue, there is a “syllogism which springs from induction.” Thomas clearly knows this text well, but does not comment upon it.

306

Matthew Kostelecky

serving this in many cases, we come to understand that every whole is greater than its part. Only through induction, therefore, do the universals from which demonstrations proceed become known to us.10

In this sense, induction includes within it abstraction and provides the propositions upon which syllogisms depend. It is a synecdoche of the whole process of human knowing—including within it sensation and experience of singular particulars, simple apprehension, and judgment—up to (but not including) the point of making syllogistic inferences. Note that the explanation here includes an explicit reference to the first chapter of the Metaphysics, which sets out the basic schematic for human knowing according to Aristotle. It is noteworthy, I think, that this more general usage of the term nearly always occurs when Thomas is commenting upon Aristotle’s use of the term, which itself has been taken often to refer to concept formation generally speaking, rather than dealing strictly with propositional inferences.11 Thomas also uses the term in a stricter sense. In its stricter application, induction is solely a form of reasoning. For Thomas there are three basic actions of the human intellect, namely simple apprehension (which produces a concept), composition and division (which produces a sentential judgment), and reasoning. When operating across these basic human intellectual actions, Thomas construes induction such that it falls into the last of these three sorts of intellectual action. As such, induction is fundamentally intertwined with the other form of reasoning, the syllogism, such that an explanation of this sort of induction requires some discussion of syllogism, as well as an understanding of the sorts of argument in which they are jointly used. Indeed, both of these forms of reasoning share a basic characteristic: there is a motion of sorts in both induction and syllogism whereby the knower moves from knowledge that she already has and, by a process of discursive reasoning, arrives at knowledge that she did not previously have. The new knowledge of both a syllogism and an induction are had by way of deriving a conclusion, which has the form of a proposition, from premises of the right sort. In spite of this similarity, induction in the strict sense generally moves from the (more) particular to the (more) general, while syllogism generally moves in the other direction, from the 10

Commentary on the Posterior Analytics [In Po An] I, lectio 30. See Louis Groarke, An Aristotelian Account of Induction: Creating Something from Nothing (Montreal: McGill Queens, 2009), pp. 156-225 for an interpretation of different uses of induction in Aristotle.

11

Not Induction’s Problem

307

(more) general to the (more) particular.12 In this strict sense of the term, although induction and abstraction (i.e., the first operation of the intellect) share an orientation or direction of going from the particular to the general, Thomas does not conflate the two: induction in the strict sense generates a sometimes fallible propositional conclusion, whereas the product of abstraction is an always ‘infallible’ non-propositional concept. Induction in the strict sense occurs because of our ability to pick out similarities across instances of propositions that we already know and, through a process of reasoning wherein differences are dropped off and likeness are held on to, we make a generalized statement about those instances regarding those similarities. This generalized statement can then serve as a premise from which a syllogism of whatever sort can begin. So far as I can find, when Thomas explicitly talks about induction and then provides an example of a proposition so induced, he always provides causal examples of how human reasoning filters out differences and picks up on similarities inductively.13 The classic example is provided in In Po An II, lectio 20, when Thomas describes how a physician is able to alight upon the healing properties of an herb in treating a particular fever.14 From the instances in which the physician sees the herb cure Socrates and Plato of a given fever (such that the following propositions are held in the physician’s mind: ‘This herb cured Socrates’ and ‘This herb cured Plato’), he induces something causal about the herb, that it can effect a cure of that fever in humans generally, given the right conditions (the induced proposition would be something like ‘This herb cures that fever’). The causality here is twofold: first a recognition of the causal properties of the herb in this and 12

Many examples could be provided. For one see Quaestiones Disputatae de Veritate, q.8, a.15, s.c. 1: “All discursive knowledge is had by reasoning either from the universal to particulars or from particulars to the universal, for all reasoning is reduced to syllogizing and induction.” 13 For a good account of the role of causal interaction in Thomas’ account of induction see chapter 4 of Ariane Economos, “Intellectus and Induction: Three Aristotelian Commentators on the Cognition of First Principles” (PhD diss., Fordham University, 2009). Economos argues that the causal sort of induction that Thomas presents does not match up with the sort of first principles that Aristotle provides at Posterior Analytics I, 2 and that Thomas is expanding his notion of induction beyond that of Aristotle. 14 See also In Ethica VI, lectio 9: “It is obvious that singulars have the nature of principles because the universal is drawn from singulars. From the fact that this herb cured this man, we gather that this kind of herb has power to cure. Because singulars are properly known by the senses, it is necessary that man should have experience of these singulars which we say are principles and ultimates….”

308

Matthew Kostelecky

that instance which is then generalized as pertaining to the herb, but also in the reasoning process. There is a sort of causality in the mind of the knower such that the propositions cause the physician to induce a given conclusion. The force of this conclusion, the certitudo, that is had depends upon the sort of reasoning or argument in which an induction occurs (say, scientia or dialectics, or rhetoric) while the certitudo of a science varies in part according to the sort of subject matter that the science treats (i.e., being as being, mathematical entities, or things that undergo generation and corruption, and so on).15 Thomas states that the mathematical sciences are the most certain, in comparison to both natural and divine science (i.e., metaphysics). Natural science focuses on matter and motion and relies upon many factors (e.g., understanding ‘form’, material dispositions, ‘matter’ and so forth), which combine to make natural science less stable. Divine science is less certain than mathematics because “the objects of divine science are further removed from sensible things, from which our knowledge takes it origin.”16 These distinctions among inductions with respect to the sort of argument in which they are found are seen neatly in the first part of Thomas’ In Po An I. Thomas is commenting upon the opening words of the Posterior Analytics, namely, Aristotle’s argument for the necessity of pre-existent knowledge in “all intellectual teaching and learning.” In order to establish that pre-existent knowledge is necessary for any and all learning, Thomas says that Aristotle proceeds ‘inductively’. Upon doing so, Thomas is careful to distinguish two things that warrant immediate mention: first, that pre-existent knowledge is not required for all ‘knowledge’ (cognitio), but that pre-existent knowledge is only required for ‘learning’ (doctrina) or ‘learned knowledge’ (disciplina); and, second, that it is pre-existent knowledge, not pre-existent science (scientia) or understanding (intellectus) that must pre-exist learning. Then Thomas proceeds to show how three different sorts of argumentation necessarily employ pre-existent knowledge. These three kinds of argumentation, which as argumentative involve ratiocination, are: 1) scientia, resulting in a demonstrated knowledge; 2) dialectic, resulting in opinion or probable knowledge; and 3) rhetoric, resulting in belief or suspicion. 15

See In de Trinitate, q. 6, a.1, (b) co. & ad 1-3. Here is a summary statement, ibid.: “It is clear, then, that mathematical inquiry is easier and more certain than physical and theological, and much more so than that of the other sciences that are practical, and for this reason it is said especially to proceed according to the mode of learning.” 16

Not Induction’s Problem

309

Regarding the first Thomas states, First, [Aristotle] shows that [pre-existent knowledge] holds for the demonstrative arguments by which we acquire science. Among the sciences, the mathematical disciplines have first place, because their way of demonstrating is the most certain. After these come the other arts, each of which has a way of demonstrating—otherwise it would not be a science.17

The pre-existent knowledge Thomas mentions here is had in demonstrative arguments by way of induction, as he says multiple times throughout the commentary.18 Importantly, here Thomas explicitly recognizes the greater certitudo that attaches to demonstrations in mathematics in comparison to other sciences, for example, in the natural sciences. As I discuss in more detail in section 3 below, there are various reasons why some sciences are certior than others. First, some sciences borrow their principles from socalled higher sciences and accordingly do not know the ‘reason why’. Second, some sciences proceed from fewer principles than others and are certior on account of that. Third, and most important for what I am discussing, is the notion that the sciences whose subject matters are of mobile matter are less ‘certain’ because of that mobility.19 The propositions that are induced for science are taken as or, as he says at times, ‘supposed’ (supponere) as to be necessary. Regarding the second kind of reasoning, dialectic, Thomas states, Second, [Aristotle] shows that his thesis also holds for disputative or dialectical arguments. These make use of syllogisms and inductions, both of which proceed from something previously known. In syllogisms, the knowledge of a universal conclusion follows from known universal propositions, and, in inductions, the universal is shown from evident singulars.20

Thomas states here that both syllogisms and inductions occur in dialectics, as Aristotle too obviously holds.21 Dialectics, however, does not achieve the 17

In Po An I, lectio 1. For instance, in In Po An I, lectio 30: “But it is impossible that universals be known scientifically without induction.” 19 See In Po An I, lectio 41: “This is why Aristotle says that arithmetic is more certain than and prior to music; it is prior because music makes use of arithmetical principles, and more certain because the cause of uncertainty lies in the changeability of sensible matter. Hence, the more closely a science approaches matter, the less certain it is.” 20 In Po An I, lectio 1. 21 See Topics I. 18

310

Matthew Kostelecky

certitudo of science, but more restrictedly, achieves ‘probable knowledge’ and ‘opinion’. The inductions of dialectic are taken to be not necessary though quite possibly true, given that dialectic begins and ends in probable knowledge. Regarding the third kind of reasoning, Thomas says that preexistent knowledge is required for rhetorical arguments, which relies on singular human actions, for which “we cannot presume premises which are truly universal.” As such, “rhetorical persuasion is effected not by syllogisms or complete inductions, but by enthymemes and examples.” Thomas then provides further details about the kinds of pre-existent knowledge that rhetoric requires: Similarly, [in rhetoric] in place of the induction, which concludes to a universal, we use the argument by example, which proceeds not from singulars to a universal, but from singular to singular. Just as the enthymeme is a kind of truncated syllogism, so the example is a kind of imperfect induction.22

The kind of pre-existent knowledge used by rhetoric is, then, not achieved by way of an induction properly so called, because it does not proceed from singular propositions to universal propositions, but only from singular to singular. A peculiar feature of this explanation is Thomas’ contrast between a ‘complete induction’ and that of an ‘imperfect induction’, and it is not clear what Thomas means by the former term, nor does Thomas, to my knowledge, use the term anywhere else in his oeuvre. The latter term, while not exhaustively explained, obviously attains to the sort of pre-existent knowledge required by rhetoric because rhetoric has induction only in a manner of speaking, or by way of comparison to the sort of ‘truncated syllogism’ found in the enthymemes through which rhetoric ‘syllogises’, as it were, a conclusion. What counts as a ‘complete induction’, what its criteria are, what sorts of things are induced and in what sorts of arguments complete inductions are found is left open, though it is safe to conclude that scientia will require complete inductions given that it is inconceivable that scientia be grounded by an imperfect induction. Perhaps Thomas specifies that a rhetorical induction is ‘imperfect’ because it goes from the particular to the particular. By contrast, a ‘complete induction’ would be complete because it achieves the end of an induction, which is to acquire a universal. Thomas is not explicit on the matter, and it would go beyond the scope of this essay to argue for this reading further. It is clear, though, that Thomas 22

In Po An I, lectio 1.

Not Induction’s Problem

311

does not take ‘complete induction’ to mean a complete enumeration of instances because that is simply not how he ever conceives of induction. What we have, then, is the use of the term induction in two ways with some subdivisions then among the more strict application of the term. In the strict sense, Thomas uses induction to describe how an argument is able to arrive at the pre-existent knowledge that it requires, and he distinguishes between inductions in scientia, dialectics, and rhetoric. Within scientia itself, some deductions are certior (i.e., more ‘certain’) than others, because of the stability of the subject matter that the science is working on and the surety of the principles from which they proceed. (Recall that some sciences might be more certain than others for other reasons as well.) The deductions occurring in dialectics and rhetoric will be less certain than in any science (and presumably rhetoric less certain than dialectics), and their inductions will likewise be affected. In the more general sense, induction describes the intellective process as a whole up until we reach the point of making syllogistic inferences. What remains to be addressed is whether Thomas thinks that at least some of these inductions, i.e., those that provide the principles upon which scientia depends, are certain and necessary and, if he does, where that confidence comes from. 2 The Certainty of Induction Of the various modern or contemporary criticisms of induction probably the most trenchant and fundamental underlying feature is the assertion that we cannot induce with certainty: the past is no a priori guarantor of the future, and instances—no matter how many experienced—cannot provide a basis upon which to know securely that other instances will be similar in the relevant ways. Regarding the issue of how Thomas construes the certainty of induction, the simplest way to proceed would perhaps be to state simply that the inductions of the demonstrative sciences are certain since scientia proceeds to necessary conclusions from necessary principles and these necessary principles are (at some point) attained through induction, whereas the inductions of dialectical arguments are not certain since those arguments result only in probable knowledge.23 This tidy manner of procedure, however, is complicated by several features which problematize the issue a 23

See In Po An I, lectio 14: “Since a demonstration causes scientific knowing, it must be about necessary conclusions and proceed from necessary principles.” Dialectics requires different sorts of principles. See In Po An I, lectio 31: “Such are the propositions from which the demonstrator proceeds [i.e., propositions known per se]. The dialectician, however, does not require them.”

312

Matthew Kostelecky

bit and, I think, make the issue more interesting philosophically. For example, Thomas has a couple of statements that are, prima facie at least, out of joint with this simple manner of procedure. I will begin by discussing these instances and then move on to discuss the relationship between dialectical and scientific inductions wherein the different sorts of or levels of certitudo said to occur in those arguments play a decisive role in accounting for the inductions of those disciplines. In Posterior Analytics II, 5, Aristotle argues that we cannot prove or demonstrate what a thing is by way of division alone. In expounding on this text Thomas attempts to clarify Aristotle’s argument about division by comparing division to induction, and he does so three times in such a way that brings the simple approach described above into question. Note that all three of the following quotations are taken from the same lectio, and they occur in the order presented below. Quotation 1: [Aristotle] proves that nothing can be syllogized by way of division from the fact that a conclusion obtained through division does not follow necessarily, even when the premises are true, as would be required for a syllogism. The way of division is like the way of induction; when we argue inductively from singulars to a universal, we neither demonstrate nor syllogise with necessity.

Quotation 2: Note that division is appropriately compared to induction. In both cases we must assume [supponere] that we have taken everything contained in something common. Otherwise, we could neither conclude the universal from the enumerated singulars when making an induction, nor conclude one part of a division from the rejection of the other parts when making a division.

Quotation 3: Although something indivisible must result on these assumptions (as just explained), the way of division is, nevertheless, not syllogistic. It brings about an understanding of what a thing is in a different way. This is not impossible, i.e., it is not impossible that something be manifested without a syllogism. For when we use an induction, we do not prove anything syllogistically; yet we do manifest something.24

These striking statements (especially the parts I put into italics) seem to conflict with an account that induction of any sort can produce a necessary 24 As noted, all three block quotations are taken from In Po An II, lectio 4. Italics added.

Not Induction’s Problem

313

conclusion, and Thomas is clearly not operating here across the divide of scientific and dialectical arguments. Indeed, at this juncture he is concerned only with scientific arguments. Some have read Thomas here to be acknowledging that inductions are a “notoriously uncertain mode of inference.”25 We will have to look at the quotations in more detail with a particular attention to their context to be able to discern just what Thomas is getting at here. In quotation 1, Thomas attempts to clarify why a conclusion derived through division is not necessary by way of comparing it to what he seems to take as the more obvious case of induction, through which, he says, “we neither demonstrate nor syllogise with necessity.” Quotation 3 is thematically similar to this in asserting that “we do not prove anything syllogistically” in an induction. Quotation 2 is problematic because Thomas says that we have to “assume [again, supponere] that we have taken everything contained in something common,” which is hardly the lockstep certainty that would seem to come along with the principles of a science being necessary. In spite of these arresting comments, I think that the simple manner of procedure that I outlined at the beginning of this section still holds for Thomas: the principles of scientia are necessary. That being said, these comments do nuance how Thomas conceives of induction. To my mind the most striking feature of all three quotations is found at the end of the first, wherein Thomas says that when we argue inductively we “neither demonstrate nor syllogise with necessity,” and I think it is easy to focus on the “syllogise with necessity” (syllogizat ex necessitate) part and conclude that Thomas countenances the fallibility of all inductions, since it seems to indicate that they do not operate with necessity. Instead, if one puts the emphasis on what immediately precedes those words, Thomas says, more restrictedly, that when we argue inductively from singulars to universals we do not demonstrate, which is true. Inductions do not demonstrate. Keeping this in mind will help in treating what the third quotation says the italicized part, namely, “For when we use an induction, we do not prove anything syllogistically.” Again, this is unproblematic for exactly the same reason: inductions do not prove (or demonstrate) syllogistically. Instead, induction provides the principle(s) upon which a syllogism relies. Looking at the text of Aristotle that Thomas had before him, Aristotle says, “For in no way does it become necessary that a thing be such and such when the premises are true, just as someone making an induction does not 25

Stump, “Aquinas on the Foundations of Knowledge,” p. 141.

314

Matthew Kostelecky

demonstrate.”26 Aristotle’s text is not particularly problematic and Thomas is recapitulating that, though appending the simple fact that in inducing we do not demonstrate with the phrase “nor syllogise with necessity.” Moreover, the greater context of the quotations provide more detail on just what an induction does in comparison to what a demonstrative syllogism does and how both are grounded by a more fundamental intellectual operation. Immediately after quotation 1 Thomas says, “For when something is proved syllogistically, it is not necessary that the one syllogizing ask about the conclusion or that the one responding concede, because the conclusion must be true, if the premises are true.” Immediately after quotation 3 Thomas says, To show that we do not syllogize when we arrive at a definition by way of division, Aristotle takes a similar case. If we infer a conclusion from a major proposition without middle terms, and then maintain that this conclusion follows necessarily from the premises, the responder can ask is why it follows necessarily. But this does not occur in syllogistic proof.

Both of these indicate that a questioner can ask, in reviewing a proposed induction (or division), why it is the case that such and such holds, which is simply not possible with respect to a demonstration. One’s reason is forced, as it were, upon the conclusion of a demonstrative syllogism. The reason why is evident if the premises are properly ordered and taken as true. The real issue here is that even though an induction is taken as or assumed to be true that there is still room for a question as to whether the minor term is in fact convertible with the middle term, which is how a valid inductive syllogism is constructed, because that issue cannot be resolved by logic alone.27 It is useful at this point to employ the distinction between induction in the broad sense and in the strict sense that I discussed above. In this 26

The quotation from Aristotle here is the English translation of the Latin text that Thomas had before him. Jonathan Barnes translates the same passage as follows: “For it nowhere becomes necessary for the object to be that if these are the case—just as someone who is giving an induction does not demonstrate.” Posterior Analytics II, 5 (92b14-15). 27 For a good explanation of how inductive arguments require the conversion of minor terms with the middle term, see Richard Berquist, translator’s commentary, Commentary on Aristotle’s Posterior Analytics, trans. Richard Berquist (Notre Dame: Dumb Ox Books, 2007), pp. 345-6 and Groarke, An Aristotelian Account of Induction, pp. 124130.

Not Induction’s Problem

315

section of the In Po An, Thomas is clearly talking about induction in the strict sense, as a form of reasoning. As strictly a form of reasoning, induction does not provide one with the quiddity of the thing. This becomes particularly apparent in the subsequent lectio, which continues the basic project of this part of the commentary, namely, of accounting for Aristotle’s argument for the impossibility of demonstrating what a thing is. More particularly, Thomas is treating Aristotle’s argument that the quiddity of a thing cannot be demonstrated by ‘supposition’ (In Po An II, lectio 5, commenting on Posterior Analytics II, 6). Toward the end of the lectio, having accounted for three ways that Aristotle argues against the notion that we can prove what a thing is, Thomas says, In addition to these ways, there is a fourth, the way of induction. However, we cannot prove what a thing is from what is plainly the case in singulars, by showing that something belongs to all the singulars and that there are no exceptions. For by making an induction in this way, we will not demonstrate what something is; we will merely demonstrate the fact that something is or is not the case, e.g., that every man is an animal, or that no man is a stone.

Thomas clearly believes that the abstractive capacity of the intellect is able to move from sensed particulars to determine what a thing is, its quiddity or essence. Yet, if we were to take the second sentence from this quote out of its context, it would seem as though for Thomas we cannot have quidditative knowledge—which is plainly false. He must be talking about something else here, as he is talking about something else in the earlier quotations about not syllogizing with necessity. This ‘something else’ is induction construed in a tightly logical way, as indicated at the beginning of the third sentence: “For by making an induction in this way….” This sort of induction does not have the capacity to deliver the right sort of content. It does, as he says in the 3rd problematic quotation, manifest something, but it does not demonstrate nor produce the ‘what it is’. The examples at the end of the quotation directly above are plainly not quidditative statements, because there are many things other than humans that are animals and that are not stones (one can see here just how similar inductive reasoning is to division). Thomas concludes that to demonstrate what a thing is, all that is left is to refer to the senses, as when one points to something with his finger, which is obviously inadequate because the quiddity of a thing is not a matter of sensation, but of intellect. The result is that the logic of terms, by itself, cannot provide access to the quiddity of a thing. The knowledge of the quiddity cannot be delivered by way of logic, whether inductive or

316

Matthew Kostelecky

syllogistic, because the logic presumes it. This also helps us make sense of the second problematic quotation above, which states that we must assume (supponere) that we have taken everything contained in something common. The inductive inference by itself does not safeguard this supposition because it is not adequate to do so. The supposition will be underwritten by an act that precedes discursive ratiocination. However, if we take induction in the broader sense, as indicating the whole process of knowing from sensed particulars to abstraction and judgment, then indeed induction can be construed as to deliver the quid est of the thing. But this construal of induction is not strictly logical and includes within it a myriad of separate acts, especially that of simple apprehension, by which humans are said to know the quiddity of the thing. It is in this sense that induction is not only required for syllogisms, but what gives the propositions so ‘induced’ their necessity. It provides the intellect with content about which it can judge, i.e., form sentential judgements about things actually existing, which then roll over into the propositional inferences of logic. These propositional inferences, however, are entirely incapable of determining what a thing is, though the distinctly human capacity to see or read into things (interlegere, as Thomas likes to parse intellectus) is what will provide the confidence that an induction is necessary. As I noted at the outset of this paper, the problem of induction is not really induction’s problem. Induction in the strict sense relies upon something that Thomas takes to be trustworthy: the capacity of the agent intellect to abstract concepts from sense experience of particulars, which results in an understanding (intellectus) of the nature of the thing. Understanding is then taken to cognize all instances of the nature of the thing, regardless of when or where it occurs, without having sensed all of those instances. Understanding is an in principle28 or virtual cognition of all instances because of the human capacity to see what is essential and necessary in those instances. Ratiocination is dependent upon understanding, so much so that Thomas states that understanding is an action that is at rest, whereas ratiocination moves out from that rest and returns to it through its discursive motion.29 28

Groarke, An Aristotelian Account of Induction, p. 130. See Summa Theologiae, Ia, q. 79, a.8: “Reasoning, therefore, is compared to understanding, as movement is to rest, or acquisition to possession; of which one belongs to the perfect, the other to the imperfect.” For much more detail about understanding being at rest and reasoning being in motion away from and back to understanding see In de Trinitate, q.6, a.1 (b) co.

29

Not Induction’s Problem

317

It should be apparent that Thomas’ construal of induction does not immediately map onto how induction is often defined, at least not those inductions that serve as the principle of the arts and sciences, which have to be concerned with what is necessary and essential. Take the textbook example of ‘All crows are black.’ In scientific inductions, Thomas is clearly not talking about this sort of induction. There is, to be sure, an induction being made in “All crows are black,” but it not a scientific induction, because there is nothing necessary nor essential about crows posited. There is nothing in the concept of ‘crow’ that causes blackness (as opposed, say, to crows having a beak or feathers, both of which are necessary and ‘flow from’ the nature of the crow). This well-worn example is only the result of an enumeration of instances, which may well be worth something in terms of coming to know crows in the initial stages of inquiry, but could be jettisoned without problem upon the discovery of the first nonblack crow. The induction ‘All crows are black’ would likely be an induction of dialectical inquiry. Now, the divide between dialectics, which trucks in probable knowledge, and science, which deals only in necessary knowledge, is not one of complete divorce. Dialectics is often a necessary step toward science,30 and much of our cognition—especially of material things—stays at this level. I would note, in passing, that Thomas’ notion of dialectics likely has a good deal of overlap with the scientific method as currently practiced: it is probable, open to revision, requiring further experiment and inquiry, and the inductions of this form of inquiry can be overruled by several or even just one example that does not fall into line.31 The differ30

For a telling remark on the relationship between dialectics and scientia see Summa Theologiae, III, q.9, a.3, ad 3: “So, too, opinion caused by a dialectical syllogism is a way to knowledge, which is acquired by demonstration, yet, when this has been acquired, there may still remain the knowledge gained by the dialectical syllogism, following, so to say, the demonstrative knowledge, which is based on the cause, since he who knows the cause is thereby enabled the better to understand the probable signs from which dialectical syllogisms proceed.” 31 An excellent example of Thomas throwing out a non-scientific induction is found in his argument for the incorruptibility of the soul in Summa contra Gentiles II, 80-81. The objection says that we know by induction that all operations of all things with souls are materially conditioned. In his reply to this objection, Thomas states simply that human understanding and willing cannot be accounted for corporeally. The human being is then taken as an example that rules out the propriety of the induction. Note: the point is not how convincing one finds the argument for incorruptibility, but how Thomas disposes of an induction because of an instance which runs contrary to it.

318

Matthew Kostelecky

ence between Thomas’ approach to dialectics and contemporary scientific method, especially as elucidated by, say, Karl Popper, is that Thomas is confident that we can, in principle, get to the point of understanding the causal interactions between agents and patients to know with certainty what will happen if the agent is introduced to the patient (given the right material conditions). Necessary knowledge is possible, even of things that are only conceptualized as material. The distinction here is, for Thomas, between the objects of mathematics which only exist in matter but can be conceptualized apart from matter and those of the natural sciences which not only can only exist in matter but can only be thought of materially. An example here is of moving from examining this flesh and these bones to thinking about ‘flesh and bones’ generally. I can think of mathematical objects, for example numbers, without any such reference to materiality, while it is impossible to do so for the objects of natural science.32 It also bears mentioning that the physical sciences are difficult precisely because of their necessary relation to matter, which does not have the stability of the objects of either mathematics or first philosophy. In sum, for Thomas, scientific inductions are indeed ‘necessary’. That interpretive matter, however, is unlikely to be met with unmitigated approval by the dogged skeptic. I turn now to discuss the suppositions that underwrite Thomas’ confidence that are likely not shared by the skeptic. 3 Some Metaphysical Suppositions Underlying Inductive Inferences Are inductions certain? I have argued that for Thomas some inductions are. But this term, ‘certain’, means something different for us today than it did for Thomas as is plain if we examine how he uses the term certitudo. For us ‘certainty’ is an absolute qualification and a property that is (or is not) attributed to cognitive states—either something known is certain or it is not. For Thomas, however, the term certitudo occurs on a sliding scale of more and less, and he sometimes uses an analogy of causality to describe certitudo. This causal use of certitudo clearly does not map onto our use of ‘certainty’. See, for example, Thomas’ introduction to In Po An. There Thomas contrasts the different sorts of certitudo that fall to different sorts of intellectual inquiry and he explicitly sets up the contrast by way of comparing the different ways that ‘natural acts’ (i.e., causes in nature) cause their proper effects. Some natural acts cause without fail, as occurs in the certitudo of scientia; others are usually or sometimes causally efficacious, like in dialectics and rhetoric, both of which he says admit of 32

See In de Trinitate, q. 5, a.2.

Not Induction’s Problem

319

different degrees of certitudo; while some natural acts utterly fail in their causal power as when there is a defect in the generative process that results in an birth defect, as occurs in sophistics in which there is no certitudo. Elsewhere, Thomas says that a cause is certior (i.e., more certain) than its effect and that a form is certior than its matter. Whatever Thomas means by certitudo, it cannot be unambiguously transliterated into what we mean by certainty, if for no other reason than that it makes no sense for us to say that a cause is more certain than its effect or that a form is more certain than its matter.33 Today certainty is taken as a cognitive property, whereas it is a causal/cognitive property for Thomas. Here we can see a wide gulf between Thomas and much of what occurs in modern and contemporary philosophy, especially in their more skeptical currents. For Thomas the human intellect is a basically reliable feature of human beings, just as nature is basically reliable. The causes that occur in nature, while not always perfect (Thomas is well aware of birth defects, for instance), occur with a basic and fundamental reliability, and so too does the human intellect. Humans are able to pick up on the regularity of nature and make generalized statements because we are able to discern the necessary and essential properties of things as they manifest themselves regularly in nature. This is not to say that doing so is easy, indeed Thomas does not hesitate to say at times that it is quite difficult to know the essences of things.34 Moreover, Thomas uses his basic physical categories in order to explain what the human intellect does. For example, at the end of Summa contra Gentiles II, Thomas is contrasting angelic knowledge and human knowledge. The possible and agent intellects, viz. the basic features he uses to describe how humans are both receptive to and causative of intellectual cognition, cannot really be applied to the angelic intellect (for reasons that do not immediately concern us). In this explanation he compares the human possible intellect to prime matter, insofar as both are completely undetermined and open to any act. Obviously, the possible intellect is open to the act of the agent intellect, whereas prime matter is receptive of any natural agent.35 They are both, however, a blank slate, as it 33

In Po An I, lectio 41. Stump, “Aquinas on the Foundations of Knowledge,” pp. 142143 has a good discussion that contrasts ‘certainty’ and certitudo. 34 Summa contra Gentiles I, 3: “The same thing, moreover, appears quite clearly from the defect that we experience every day in our knowledge of things. We do not know a great many of the properties of sensible things, and in most cases we are not able to discover fully the natures of those properties that we apprehend by the sense.” 35 Summa contra Gentiles II, 96: “Again, just as prime matter ranks lowest in the order of sensible things, and is, therefore, purely potential with respect to all sensible forms,

320

Matthew Kostelecky

were, upon which nothing has been written. The cognitive realm, in which we have access to ens rationis, is reflective of the real world, the world of real things. Both are reliable, though admittedly our access to truth is limited and fraught with error in a way that does not occur in natural causes. This fallibility, though, does not betoken or require a skeptical response, because Thomas is not trying to justify our knowledge. He is trying, instead, to describe it.36 Given Thomas’ general categories, i.e., that God made the world and the human being to be in his likeness and image (which Thomas construes in terms of limited cognitive similarities), it is hardly surprising that he would find such a supposition about the regularity of nature unproblematic. There is a remarkable passage in his Super Boethium de Trinitate q.3, a.1, ad 4 (hereafter, In de Trinitate) that shows in stark lines just what Thomas’ suppositions are. Thomas is comparing the mode of assent to things that are naturally known by reduction to first principles—which is how certitudo is achieved in scientia—and the mode of assent that occurs by way of the habit of faith. He says, remarkably, that the habit of faith, as it is divinely infused into the human mind … is more sufficient for inducing belief than any demonstration, for though from the latter no false conclusions are reached, still man frequently errs in this: that he thinks something is a demonstration which is not. The light of faith is also more sufficient than the natural light of reason by which we assent to the first principles, since this natural light is often impeded by bodily infirmity, as is evident in the case of the insane. But the light of faith, which is, as it were, a kind of impression of the First Truth in our minds, cannot fail, any more than God can deceive us or lie.

This is remarkable for several reasons. First, the notion that faith is more certain than any demonstration is rather surprising and deserving of further explanation (which Thomas provides subsequent to the quotation above), but that is aside to my current point. Second and more relevant to my so the possible intellect, being the lowest in the order of intelligible things, is in potentiality to all intelligibles, as we have already seen.” Ibid, II, 98: “For the possible intellect exists as in potency in intelligible being, and becomes in act through the intelligible species, just as prime matter is actualized in sensible being by a natural form.” 36 Economos concludes her treatment of Aquinas’ notion of induction with a similar point and sees John Haldane making a similar appeal to the descriptive rather than justificatory aim of Thomas’ cognitive theory. See Economos, “Intellectus and Induction,” p. 134.

Not Induction’s Problem

321

current concerns, this quotation shows that Thomas is clearly attentive to the problematic aspects of human knowledge, in a way beyond what one finds in modern forms of skepticism. For example, he states that even in demonstrations, which are what one gets out of scientific syllogisms, does the human being frequently err. Thomas is explicitly underlining the notion that even in demonstrations (which are had by way of deduction) are humans fallible, which, in a sense, goes well beyond what one finds in traditional criticisms of induction. These criticisms point at the problematic side of induction without as much attention to the fallibility that can still occur in deduction. Then there is Thomas’ invocation of ‘the insane’ and the possibility of a liar God—both of which feature so prominently at the outset of Descartes’ Meditations and, thereby, at the outset of the modern problem of skepticism. Thomas presents both and simply dismisses both as real problems. His construal of the insane person would be deeply problematic for Descartes, because Thomas goes further than Descartes before stepping back from the ledge. Descartes’ imaginary insane person introduced at the beginning of the First Meditation is able to make recourse to the natural light of reason through which he is able to deduce any number of things. In Thomas’ construal, the insane person may not even be able to access that. Thomas is well aware that our cognitive capacities have limitations, that some people are sometimes deceived because of physical infirmity (even to the point of being incapable of assenting to absolutely first principles), and that our knowledge is often or even usually mixed with error, but those are not sufficient reasons to cast the whole endeavour of explaining cognition into doubt and skepticism. It is, for him, more rational to get on with the project of describing the rather remarkable phenomena of what it is to know the essential and necessary properties of things even though our experience is only of contingent particulars. Conclusion I do not think that modern skepticism, especially skepticism about induction, is defeated merely by understanding what Thomas means by induction. Indeed, by forcing the issue, the skeptic is likely to be just as firm, if not more resolute, in his or her criticism that inductions are not justified. At most, the result of such a discussion would be that at least everyone is talking about the same thing (i.e., necessary and essential attributes, rather than the shop-worn examples like ‘All crows are black’). Turning to the metaphysical suppositions that underlie Thomas’ account is likely to be

322

Matthew Kostelecky

taken as so much hand waving and pleading, because it is so much more complicated (and thereby likely taken to be betraying Ockham’s Razor) and requires, seemingly, a previous assertion about the regularity of nature and how the human intellect functions as a part of that nature. And yet, if Thomas’ account of induction does not blunt the force of the skeptic’s critique, I think that is due in part to the very tight requirements for knowledge that gave a particular shape and character to much modern philosophy and epistemology, which is just as historically constituted and blind to its own presuppositions as any other philosophical endeavour. If Thomas’ thought does not meet those requirements, well, then it does not meet those requirements. Their thought would not meet his, either. As shown in the extended quotation with which I concluded the previous section, Thomas clearly thinks about skeptical issues but does not take the problems particularly seriously. Instead, it seems that he just gets on with describing the processes of and criteria for human cognition. If that is less rational than requiring justificatory epistemology, the explanation of why will have to come from something beyond the demand for requiring justification. Thomas is not an epistemologist and does not have an epistemology, if that term is taken to be a defence or justification of knowledge in light of persistent skeptical concerns. Whether that is a fatal flaw in his robust theory of knowledge, appropriated from Aristotle and his commentators and filtered through a particular reading of the neo-Platonic tradition, seems to me to be a decision that does not necessarily fall to epistemology in the skeptical sense.

Grounding Necessary Truth in the Nature of Things: A Redux Douglas B. Rasmussen St. John’s University, NY

Abstract: In this essay Rasmussen challenges an argumentative technique often employed (by Hume and Analytic philosophers who use the method of conceptual analysis) to deny the existence of natural necessities and indeed the claim that like things in like circumstances behave in like ways (i.e., the uniformity of nature). This technique proceeds as follows: Consider some state of affairs, for example, a solid iron bar weighing 20 pounds sinking when placed unsupported in a tub of water on earth. According to deniers, if one can imagine/conceive/suppose such a bar in such a situation floating, then such a state of affairs is possible and one has proof positive that there is no natural necessity in the bar sinking. Rasmussen not only challenges this inference but also the truth of the antecedent. His argument involves a detailed discussion of the nature of abstraction, conception, and logic and their relation to the world. In other words, this essay provides an Aristotelian essentialist critique of logical possibility and necessary truth.

“‘Tis an established maxim of metaphysics, That whatever the mind clearly conceives includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible.” —David Hume, A Treatise of Human Nature “In showing that there is no rational ground for believing in the uniformity of nature and in universal causation, Hume used … this method: If P were a necessary truth, then the supposition of P’s falsehood would imply a contradiction; but not-P does not imply a contradiction; therefore P is not a necessary truth.” —Arthur Pap, Semantics and Necessary Truth

324

Douglas B. Rasmussen

Introduction It might seem at first that the method Pap describes is not really the same as Hume’s “established maxim of metaphysics,” for the supposition of P’s falsehood must “imply a contradiction” in order for P to be a necessary truth, while Hume’s principle only stresses that P cannot be a necessary truth if its falsehood can be clearly conceived or imagined.1 (P stands for a proposition or a statement.) In other words, the method Pap describes for discerning that P is not a necessary truth seems to require that the falsehood of P is not only conceivable or imaginable, but also does not “imply a contradiction.” Yet this difference is more apparent than real, for how is “imply a contradiction” to be determined? This determination cannot be made in terms of the principle of non-contradiction (PNC), because this would be circular; so “imply a contradiction” must be explicated some other way. But what way is this? One way is the method of conceptual analysis. One examines the content of a concept to determine whether not-P implies a contradiction, and this is revealed by whether not-P is conceivable or imaginable. If one can conceive or imagine not-P, then the supposition of not-P is not selfcontradictory, and P is not a necessary truth. For example, since one can conceive or imagine fire without heat, the contradictory of the proposition “Where there is fire there is heat” is possible, and hence this proposition is not a necessary truth. So, for all intents and purposes, the method Pap describes and Hume’s “established maxim of metaphysics” amount to the same thing—certainly, they have been used that way by practitioners of conceptual analysis. They are part and parcel of the same argumentative technique or method that has been used to reject the possibility of there being any necessary truths that pertain to the natural order. Whether the method of conceptual analysis can determine whether P is a necessary truth or not is based, in large part, on what is meant by “conceptual.” This will be considered in detail later, but it also needs to be appreciated that this method has a long history. It originates in a concern among modern philosophers of both rationalistic and empiricist stripes with examining ideas so as to determine what is or is not possible (or what is or is not necessary)—as we see, for example, in ’Descartes’ claim to ground truth in clear and distinct ideas of the intellect and in Locke’s view of 1

This essay has benefited from the suggestions and comments of two anonymous referees, the editors of this volume, Roger E. Bissell, Douglas J. Den Uyl, and Jared Meyer.

Grounding Necessary Truth in the Nature of Things

325

knowledge as the perception of agreement or disagreement of ideas. Norman J. Brown explains that according to the classical view of analyticity … a concept can only be necessarily related to what it contains. A concept is thought of as analogous to a chemical compound, a complex capable of resolution into (comparative) simples; indeed, the notion of simple ideas which we find in Locke, with their successors the simple unanalyzable qualities of Moore, the atomic facts of logical atomism and the protocol sentences of some positivists (merely the linguistic version of the old conceptual doctrine) have been cast very much in the chemical-analysis mould. Necessary statements, on this view, simply unpack the implications—the contents—of a given concept. Above all, they cannot extend to “matters of fact and existence.”2

In view of these considerations, the method of conceptual analysis might be better portrayed as inspectio mentis. This portrayal highlights two things: the provenance of conceptual analysis and the aim of this essay to return to a fork in the philosophical road regarding the nature of concepts, abstraction, and necessary truth in order to reconsider whether there might not be a better path—indeed, one that leads away from Hume and to the conclusion that necessary truth is grounded in the nature of things. Consequently, inspectio mentis is the central concern of this essay. Two questions are asked: (I) Is what is conceivable or imaginable determined through inspectio mentis? And (II) even if not-P is conceivable in some sense or other, does that show that P is not a necessary truth or that to which it pertains in the natural order is not necessary—that in effect, there is no natural necessity? Before offering answers to these two questions, however, the full force of the Humean argument against natural necessity needs to be examined carefully, and this requires the consideration of other matters as well. To begin with, the notion of logical possibility that has been used in analytic philosophy (and which owes much of its inspiration to Hume) needs to be explained, especially the role it plays in the argument on behalf of the claims that no proposition about beings in rerum natura3 can be a necessary truth and that there is no rational ground for believing in the uniformity of nature or the principle of causality. There is, for example, no 2

Norman J. Brown, “A Kind of Necessary Truth,” Philosophy 50, no. 191 (1975): 3754, p. 49. 3 As traditionally understood, these are beings that exist and are what they are apart from being the object of human cognition.

326

Douglas B. Rasmussen

justification for believing that because one burned one’s hand the first time one put it in a fire that it will be burned the next time or indeed that its being burned the next time is even probable. Second, the question to which Hume assumes he knows the answer—namely, What is it that makes P a necessary truth?—needs to be re-examined so as to consider whether necessary truth can be explained by logical or linguistic features alone or whether such truth might not be due to the nature of things. Third, the difference between the forms or relations that pertain to the logical order and those that pertain to the natural order needs be understood so as to determine whether the difference between the two orders precludes the necessity exhibited in the PNC and other logical truths from being ultimately grounded in the nature of things or whether it is possible that the necessity exhibited in logical truths is itself but an expression of the necessity found in things. These considerations will bring us to a point where questions I and II can be answered. The answers offered to questions I and II will depend on the foregoing considerations, as well as on an account of two ways of abstracting that will be presented in the examination of question II. Overall, it will be argued that Hume was mistaken—or very confused—when he claimed that “the contrary of every matter of fact is … possible; because it can never imply a contradiction.”4 1 Logical Possibility and the Rejection of Natural Necessity A state of affairs asserted to exist by propositions (or that which is described by a statement) is what is said to be logically possible or impossible. The determination of whether a state of affairs is logically possible is accomplished by recourse to an analysis of the meaning of the terms involved and by the PNC. What is logically possible is set up by exclusion. If a state of affairs does not contradict the meaning of the terms involved, then it is logically possible. Whether a state of affairs does not contradict the meaning of the terms is determined by whether it is conceivable or imaginable. Note, however, that the standards for determining what is logically possible and logically impossible are not parallel, for if a state of affairs is inconceivable (or unimaginable), this might merely reflect an incapacity of a human mind to grasp something. Hence, it is not the standard for what is logically impossible. Nonetheless, conceivability or imaginability remains the benchmark for logical possibility. No one can 4

David Hume, Enquiries Concerning the Human Understanding and Concerning the Principles of Morals, ed. L. A. Selby-Bigge (Oxford: Clarendon Press, 1902), Section 5, Part 1, p. 25.

Grounding Necessary Truth in the Nature of Things

327

conceive or imagine a contradiction.5 This is what has been called inspectio mentis. Thus, if a state of affairs is conceivable or imaginable, then it is logically possible. Consequently, if necessary truths have logically impossible denials, then any P whose denial is logically possible is not a necessary truth, and the state of affairs asserted to exist cannot be a matter of logical necessity. For example, there would be no logical necessity in fire burning with a bright hot flame as opposed to a cold black one, in a solid iron bar sinking when placed unsupported in water as opposed to floating, in a cat giving birth to kittens as opposed to pups, or in rabbits being herbivorous as opposed to carnivorous. Two demonstrations of this reasoning are as follows. The first concerns the logical possibility of a solid iron bar floating. It is a law of physics that objects with a greater specific gravity than water (i.e., weighing more than an equal volume of water) do not float on water (with certain exceptions such as the phenomenon of “surface tension.”). There is no logical necessity about this—that is to say, it is logically possible for it to be otherwise. You can imagine it now (remember, if you can really imagine it, it is logically possible, but if you can’t, it may only mean that your powers of imagination are limited): you take a piece of iron (a chemist has verified that it really is iron), you weigh it, then you plunge it into a vessel of water, and behold, it floats. You have also verified that it is a solid iron bar, not hollow inside with large air-filled spaces like a battleship; indeed, you have weighed it and measured it so as to make sure that its weight is really greater than that of an equal volume of water. This is a logically possible state-of-affairs; it does not actually occur, but there is nothing logically impossible about it.6 Another demonstration of this reasoning is that of a cat giving birth to pups. It is claimed that no contradiction is involved, and though it may be a fact of nature that like produces like, there is no logical necessity about it. “But isn’t anything that a cat gives birth to, by definition, a cat?” You need only think this through for a moment to see that it is false. Suppose that what the cat gave birth to 5

For an examination and critique of conceivability or imaginability as a benchmark for logical possibility, see Douglas B. Rasmussen, “Logical Possibility: An Aristotelian Essentialist Critique,” The Thomist 47, no. 4 (1983): 513-540. For a list of articles that discuss the problematic character of “logical possibility” as used in analytic philosophy, see p. 513n2. Some material from this article is adapted for use in this essay. 6 John Hospers, An Introduction to Philosophical Analysis, 2nd ed. (Englewood Cliffs, NJ: Prentice-Hall, 1967), p. 173.

328

Douglas B. Rasmussen

barked, wagged its tail, had all the contours of a dog, exhibited typical dogbehavior, and was unhesitatingly identified by everyone as a dog. Would you still call it a cat? In such a situation no-one would say that the offspring was a cat—rather, they would be astonished by the unusual phenomenon that a cat had produced, not another cat, but a dog. “But if a pup was the offspring, the mother must not have been a cat!” Not even if it looked like one, meowed, purred, and had all the other characteristics which cause us to call it a cat? Would you have hesitated to call it a cat before the strange birth took place? Must you wait to see what the creature’s offspring look like (if it has any) before being able to identify it as a cat? Once again, cats are distinguished from dogs and other creatures … by their general appearance, and it is logically possible for something with all the feline appearances to give birth to something with all the canine appearances. That nature does not operate in this way, that like produces like, is a fact of nature, not a logical necessity.7

As far as logic is concerned, there exists a possibility that a cat may give birth to pups. Nature does not operate that way. However logic cannot guarantee that it might not. There is no logical necessity about it, for there is no self-contradiction in conceiving, supposing, imagining the occurrence of such a situation. Accompanying such reasoning is also an account of empirical possibility. Empirical possibility is determined by reference to the laws of nature, and any state of affairs not contrary to such laws is an empirical possibility. A solid iron bar floating on water would be an empirical impossibility, for that would be contrary to the laws of nature. The relationship between logical possibility/impossibility and empirical possibility/impossibility is as follows: If something is logically impossible, then it is empirically impossible, but if something is empirically impossible, it need not be logically impossible. If something is logically possible, then it need not be empirically possible, and if it is empirically possible, it certainly is logically possible. It is held that logical possibility is determined from the philosopher’s armchair, by an appeal to the meaning of terms and the laws of logic (that is, by inspectio mentis), while an empirical possibility is determined by an investigation of the facts, by the research of the empirical sciences. It is concerned with more than logic and the meaning of terms. No one expects a solid iron bar to float or a cat to give birth to pups. There is not the least empirical possibility that they will happen, but the basic point is simply that the assertion they did happen, or

7

Ibid., pp. 173-174.

Grounding Necessary Truth in the Nature of Things

329

would happen—even though false—would not be self-contradictory. The socalled laws of nature are not necessary truths. Of course, David Hume has framed these matters more generally and with greater notoriety: The separation … of the idea of a cause from that of a beginning of existence, is plainly possible for the imagination; and consequently the actual separation of these objects is so far possible, that it implies no contradiction nor absurdity.8

And: Were a man to abstract from everything which he knows or has seen, he would be altogether incapable, merely from his own ideas, to determine what kind of scene the universe must be. … For as nothing which he clearly conceives could be esteemed impossible or implying a contradiction, every chimera of his fancy would be upon an equal footing; nor could he assign any just reason why he adheres to one idea or system, and rejects the others which are equally possible.9

And: That there are no demonstrative arguments in the case seems evident; since it implies no contradictions that the course of nature may change, and that an object, seemingly like those we have experienced, may be attended with different or contrary effects. May I not clearly and distinctly conceive that a body, falling from the clouds, and which, in all other respects, resembles snow, has yet the taste of salt or the feeling of fire?10

Hence, the principle of causality— “Whatever begins to exist has a cause”—and the principle of the uniformity of nature—“Like things in like circumstances behave in like ways”—are not necessary truths. We can clearly conceive of a beginning to exist without conceiving of a cause, and we can do the same with regard to like things in like circumstances not behaving in like ways. There is no rational justification for either believing in the principle of causality or the uniformity of nature, and further there is no basis for attributing necessity to the relationships found in nature. Natural necessity is banned from the world.

8

David Hume, A Treatise of Human Nature, ed. L. A. Selby-Bigge (Oxford: Clarendon Press, 1888), Book I, Part III, Section III, pp. 79-80. 9 David Hume, Dialogues Concerning Natural Religion, ed. Henry D. Aiken (New York: Hafner Publishing Co., 1948), Part II, p. 19. 10 David Hume, Enquiries, Section IV, Part II, p. 35.

330

Douglas B. Rasmussen

However, what seems to be the essential point11 behind Hume’s rejection of there being a rational ground for believing in universal causation or the uniformity of nature has not as yet been spelled out. It is one thing to talk about logical necessity and quite another to talk about natural necessity. We have a pretty good idea of what it is that makes P a necessary truth, at least Hume thought so, but do we have an equally good idea of what is involved in a natural necessity? What grounds do we have for saying that the solid iron bar must sink? What justifies this claim? Hume’s basic point seems to be that the basic principles of logic (that is to say: the PNC, the Law of Identity, and the Principle of Excluded Middle) explain the necessity exhibited in a proposition (a statement) or an argument (a demonstration), but matters of fact—beings in rerum natura—are neither propositions nor arguments, and so these principles will not explain the necessity we attribute to the natural order. Indeed, when we try by appealing to such principles, as the examples noted above illustrate, we find no basis for attributing any necessity to how things behave. (The problem here is fundamental: How can one attribute necessity to the behavior of things and nonetheless admit that there is nothing self-contradictory in supposing them to behave differently?12) In sum: Logic alone cannot determine how things will behave, and since the logical order is not the same thing as the natural order, the necessities of logic have nothing to do with how things in nature work. There is no basis for propositions or statements about the natural order being necessarily true. Unless one wants to endorse a rationalist or idealist metaphysics and treat the natural order and the logical order as one and the same, then 11

It could also be argued that the essential point behind Hume’s conclusion that we have no idea of natural necessity is a phenomenalist ontology in which things are constructed out of sense-data that are treated as the primary entities. This is generally regarded as the result of his sensationalist epistemology. Yet, as Milton Fisk has noted, Hume’s conclusion could be inverted to show that such an ontology is impoverished. See Fisk, Nature and Necessity: An Essay in Physical Ontology (Bloomington and London: Indiana University Press, 1973), p. 4. This work is still important for understanding and defending natural necessity, as are: Baruch Brody, Identity and Essence (Princeton: Princeton University Press, 1980); and Rom Harré and E. H. Madden, Causal Powers: A Theory of Natural Necessity (Totowa, NJ: Rowman and Littlefield, 1975). For a careful analysis and critique of sensationalist epistemology, see chapter two of David Kelley, The Evidence of the Senses (Baton Rouge and London: Louisiana State University Press, 1986), pp. 44-80. 12 Of course, Kant does this with his “transcendental turn,” but he does so at the price of precluding necessity from, or indeed having any knowledge of, beings in rerum natura.

Grounding Necessary Truth in the Nature of Things

331

certainly it seems correct to note that a necessity found in logical forms or relationships is not the same as any purported necessity found in the forms or relationships of nature. Implication, a logical relation, is, for example, not a connection found among things; and there would seem to be relationships found among things: cause and effect, part and whole, and many others, but these are not logical relationships. But are we as clear just as to what it is that makes P (for example, the PNC) a necessary truth? Can logic alone explain necessary truth? And though logic is not the same thing as the natural order, does that mean that logic cannot be an organon that grasps, and ultimately reflects, the necessities of that order’s basic what’s and why’s? Indeed, has the door really been closed on there being natural necessity? These queries will be considered now, and then questions I and II, which were noted earlier, will be addressed. 2 Searching for the Basis of Necessary Truth If P is necessarily true, then the supposition of its falsehood is contradictory. So, P is necessarily true only if its denial requires asserting P and not-P. This we might call the test for determining whether P is necessarily true, but that does not by itself explain or ground the necessity of P. For certainly, to say that P is necessarily true because its denial is self-contradictory not only presupposes that P’s being self-contradictory is necessarily false but also that P’s being an instance of the Law of Identity is necessarily true. But what is it that explains the necessity of the PNC or the Law of Identity? Of course, to note this lack of explanation or grounding is not to question that P’s having an A-is-A form (or its denial having the A-is-not-A form) is the test for determining if P is a necessary truth. Nor is it to question that the Law of Identity (or the PNC) is a self-evident truth, but it is to ask what it is that grounds or explains either’s necessary truth. This is a question that has not often been addressed in contemporary accounts of necessary truth, and if one responds that being a necessary truth is just for P to have the Ais-A form (or for its denial to have the A-is-not-A form), then nothing is clarified and the circle is only enlarged. Hence, showing that either P or its denial is a substitution-instance of such basic logical principles does not advance the explanation of what it is that constitutes13 the necessary truth of P. 13

See Arthur Pap, Semantics and Necessary Truth: An Inquiry into the Foundations of Analytical Philosophy (New Haven: Yale University Press, 1958), pp. 7-8; and Panayot Butchvarov, The Concept of Knowledge (Evanston, IL: Northwestern University Press, 1970), pp. 105-52. Butchvarov argues that most of the debate in twentieth century among Anglo-American philosophers over whether all necessary truths are analytic

332

Douglas B. Rasmussen

However, it might be argued that having a self-contradictory denial is just what it is that makes the PNC a necessary truth, because such a denial destroys itself. In other words, since the very possibility of language, thought, and argument depend on the PNC,14 the denial of this principle is meaningless. The PNC’s necessary truth is based on the fact that without it one is simply making noises when one speaks, or marks when one writes, and as long as one seeks to communicate or understand anything, then one must accept it. And this is what makes it a matter of convention—but, of course, a highly useful one. Naturally, the issues here are whether such a basic logical principle is merely a convention and in what does its “usefulness” consist. Yet, more important is the issue as to why its denial is immediately dismissed: Is a self-contradiction dismissed because it is meaningless or because it is necessarily and obviously false? It would seem not to be literally true that when someone contradicts himself, he has said nothing or just uttered noises. Meaningless sounds and marks are not capable of being true or false, but a self-contradiction is most certainly considered false. When one says Socrates is sitting and he is not sitting, one is saying something necessarily and obviously false, but it is not the case that one is just making arbitrary sounds. What leads listeners and readers to treat a self-contradictory statement as if nothing has been said or as if only noises have been made is the obvious falsehood of the statement, but this does not make the statement meaningless. Therefore, this proposed account of the necessary truth of the PNC fails, because it ignores: (1) the difference between a statement being treated as if it were meaningless, and it literally being so; and (2) the difference between a statement being immediately rejected because it is obviously false and because it is meaningless. What grounds the necessary truth of the basic principles of logic remains unanswered.

failed to determine in what the necessary truth of such basic logical propositions consists and thus was in large measure beside the point when it came to understanding necessary truth. 14 See Douglas B. Rasmussen, “Aristotle and the Defense of the Law of Contradiction,” The Personalist 54, no. 2 (1973): 149-162; and for a recent discussion of whether the very possibility of all language, thought, and argument do indeed depend on the PNC, see Graham Priest, JC Beall, and Bradley Armour-Garb, eds., The Law of NonContradiction: New Philosophical Essays (Oxford and New York: Oxford University Press, 2004), especially Greg Littmann and Keith Simmons, “A Critique of Dialetheism,” 314-335; Alan Weir, “There Are No True Contradictions,” 385-417; and Edward N. Zalta, “In Defense of the Law of Non-Contradiction,” 418-436.

Grounding Necessary Truth in the Nature of Things

333

The attempts to provide an answer in terms of a truth-tabular definition of logical connectives or in terms of logical form also do not succeed. The former is circular, because the very construction of such truth tables is done in accordance with these logical principles,15 and the latter leads, if continually applied, to an infinite regress. The claim that it is the form of such statements as “If Tabby is a black cat, then Tabby is a black cat” or “It is not the case that Tabby is a black cat and not a black cat” that guarantees their truth is not itself true in virtue of its form. To wit: “All P’s with the form ‘If ____then _____’ or the form ‘Not the case that ___ and not ____’ are true” is not itself a claim true in virtue of its form. And so, what is it that grounds or explains the necessary truth of this claim? The problem is just pushed back another step. Not surprisingly, there have been other attempts to explain necessary truths in terms of logic and language. A more powerful maneuver on behalf of a linguistic theory of necessary truth is the claim that language is more like a game than anything else and that necessary truth is to be understood in terms of following the rules of a game. But these have fared no better than the foregoing ones.16 There has been also the general rejection of necessary truth by certain forms of pragmatism, particularly that espoused by Quine.17 Quine claims that Hume “was right in discrediting metaphysical necessity” and that the “air of necessity” that surrounds mathematical and logical truth can be accounted for by “our prudence in not excessively rocking the boat.”18 Quine famously holds that the truth value of a statement is not determined apart from the conceptual scheme to which it belongs, and accordingly one decides whether to give up or stand by a statement according to where that statement is located in the reigning conceptual scheme. Among the questions one is to consider in deciding to 15

“The three Laws of Thought [identity, non-contradiction, and excluded middle] can be regarded as the basic principle governing the construction of truth tables.” Irving M. Copi, Introduction to Logic, 4th ed. (New York: MacMillan; London: CollierMacMillan, 1972), p. 286. 16 See Butchvarov, The Concept of Knowledge, pp. 105-152. For a criticism of the language is a game gambit, see: Douglas B. Rasmussen “Necessary Truth, The Game Analogy, and the Meaning-Is-Use Thesis,” The Thomist 46, no. 3 (1982): 423-440; as well as Butchvarov, pp. 124-140. 17 The classic example of this is W. V. O. Quine, “Two Dogmas of Empiricism,” From a Logical Point of View: Nine Logico-Philosophical Essays, 2nd ed., rev., (Cambridge, Massachusetts and London, England: Harvard University Press, 1980), pp. 20-46. 18 W. V. O. Quine, Quiddities: An Intermittently Philosophical Dictionary (London: Penguin Press, 1990), p. 140.

334

Douglas B. Rasmussen

stand by or give up a statement is: What havoc would it create for the truth values of the rest of statements within the scheme if this statement were abandoned? When faced with this decision, Quine suggests that the maxim to be followed is one of “minimum mutilation” to the conceptual scheme constituted by scientific practice. Whether a statement is upheld or overthrown is determined by how central it is to the conceptual scheme and ultimately how “efficacious” that scheme is. For Quine, the necessary truth of P is explained by its role in a conceptual scheme. It would seem, then, that Quine’s approach amounts to saying that theory or practice determines in the last analysis what is real.19 However, in the preface to the second, revised edition of From A Logical Point of View, Quine suggests that his commitment to so-called ontological relativity has been misunderstood. He states that “Posited objects can be real” and notes that he elsewhere wrote that “to call a posit a posit is not to patronize it”20 Yet if one consults places where he said that one should not look down on posits, it is evident that he nonetheless understands a posit’s existence to be a function of a theory. For example: Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.21

In other words, the reason that one should not look down on posits is because that is all with which we have to work and for a posit to be real is for it be part of a conceptual scheme that has been adopted. It thus seems that for Quine the only difference between posits (myths) and reality is the difference between something which is regarded as existing when we are creating a theory and something which is regarded as existing by the theory 19

“It makes no sense to say what the objects of a theory are, beyond saying how to interpret or reinterpret that theory in another.” W. V. O. Quine, “Ontological Relativity” in Ontological Relativity and Other Essays (New York and London: Columbia University Press, 1960), p. 50. 20 From A Logical Point of View, p. viii. 21 W. V. O. Quine, Word and Object (Cambridge, Massachusetts: The MIT Press, 1960), p. 22. For a criticism of the claim that existence is a function of theory, see Douglas B. Rasmussen, “Ideology, Objectivity, and Political Theory” in John K. Roth and Robert C. Whittemore, eds., Ideology and the American Experience: Essays on Theory and Practice in the United States (Washington, DC: Washington Institute for Values in Public Policy, 1986), pp. 45-71.

Grounding Necessary Truth in the Nature of Things

335

that is being created. Ultimately, there is a refusal to accept any ontological distinction between posits and reality.22 Quine’s ontological relativism is based on the view that it is senseless to think that things have a nature apart from a conceptual scheme, but this claim is not well supported. Moreover, it supposes that if we use a conceptual scheme we are therefore imposing our concepts on reality and are unable to say what things really are. But this is a non sequitur.23 Such ontological relativism is in fact dubious in that it seems incompatible with the existence of human knowledge. However, further discussion of these issues is beyond the scope of this essay. Nor is it necessary. It is sufficient simply to note that Quine’s view remains highly controversial and is by no means the only game in town, especially when it comes to necessary truth. So, if one is not quite ready to follow this pragmatist course, and if logico-linguistic considerations seem inadequate to the task of explaining the necessary truth of P, then might not the door be open to considering the idea that the necessity exhibited in a necessary truth is a reflection of necessity observed in the natural order? Put directly, since the impossibility of a contradiction being true does not consist in its being contradictory, might not its necessary falsity just be due to it being a fact about reality that contradictions do not exist?24 “We cannot think contradictory propositions because we see that a thing cannot have at once and not have the same character; the socalled necessity of thought is really the apprehension of the necessity in the

22

What Richard Cartwright noted nearly sixty years ago about Quine’s approach to ontology remains on target. “To enquire into ontological commitments of a theory is not to ask what there is, but only to ask what the theory says it is.” “Ontology and the Theory of Meaning,” Philosophy of Science 21, no. 4 (1954): 316-325, p. 316. See also Douglas B. Rasmussen, “The Importance of Metaphysical Realism for Ethical Knowledge,” Social Philosophy & Policy 25, no. 1 (2008): 56-99, especially Section IV, “Reconsidering the Demise of Metaphysical Realism,” pp. 90-98. 23 See David S. Oderberg, Real Essentialism (New York and London: Routledge, 2007), pp. 21-61; and Douglas B. Rasmussen, “Quine and Aristotelian Essentialism,” The New Scholasticism 58, no. 3 (1984): 316-335. Some material from the latter article is adapted for use in this essay. 24 For discussion of whether developments in quantum physics have overthrown the PNC, see: Tuomas E. Tahko, “The Law of Non-Contradiction as a Metaphysical Principle,” Australasian Journal of Logic 7 (2009): 32–47; and Roger Trigg, Reality At Risk: A Defense of Realism in Philosophy and the Sciences (Sussex, England: The Harvester Press and Totowa, New Jersey: Barnes & Noble Books, 1980), pp. 153-182.

336

Douglas B. Rasmussen

being of things …”25 To be is to be something, and something cannot be what it is not. This is the ultimate ground of necessary truth. Whether this proposal is itself susceptible to the charge of circularity depends in large measure on (1) whether logical forms or relations are in their very nature of or about something other than themselves and (2) whether reality or existence is primary and thus the point where explanation ends. More will be said about the first point shortly, but something should be said about the second point at this time. What can be said, however, can be only a point of emphasis, for this essay is not an essay in metaphysics or ontology. Perhaps, then, the best thing to be said is that that there is no problem in deriving a “must” from an “is.” A thing is what it is and it cannot be what it is not. The very fact that a being is always a determinate thing precludes it from being something else. Such a limitation of possibilities results not from any extrinsic source but instead from the very nature of the thing. As we shall see later, none of this entails the denial of change or the manifestation of variety in the natural order, but it is to note a basic ontological fact: existence must be in some form or other. Determining what these forms are cannot be accomplished from one’s philosophical armchair, and here we find another reason for not collapsing the distinction between the logical order and the real order. Yet we do nonetheless know that whatever exists must exist in some way.26 All entities are what they are by virtue of their identity. To exist is to exist by identity, and to exist by identity is to exist by necessity. This need not destroy the distinction between the metaphysical and man-made or imply that human beings are not responsible for their actions, but again this essay cannot take up these issues.27 Suffice to say, the fundamental claim is that it is the identity of things that provides the ground for necessary truth. Yet with this proposal to ground necessary truth in the being of things, the well-founded point behind Hume’s skepticism regarding natural necessity—namely, that logical forms or relations are not the same as those forms or relations found among beings in rerum natura—needs to be 25

H. W. B. Joseph, An Introduction to Logic, 2nd ed., rev. (Oxford: Clarendon Press, 1916), p. 13. See note 75 below. 26 See Henry B. Veatch, “A Non-Cartesian Meditation upon the Doctrine of Being in Aristotelian Metaphysics,” Graceful Reason: Essays in Ancient and Medieval Philosophy Presented to Joseph Owens CSSR, ed. Lloyd P. Gerson (Toronto: Pontifical Institute for Mediaeval Studies, 1983), pp. 75-100. 27 But see: Edward Pols, “Rational Action and the Complexity of Causality,” Journal of Theoretical and Philosophical Psychology 22, no. 1 (2002): 1-18; and idem, Mind Regained (Ithaca, New York: Cornell University Press, 1998).

Grounding Necessary Truth in the Nature of Things

337

addressed now more than ever. Can one ground the necessity of logic in the nature of things without collapsing the distinction between logic and reality? Just what is it that fundamentally differentiates logical forms or relations from those found in nature? 3 Logical Forms or Relations as Tools for Knowledge: Their Character There are various ways of understanding logic, but if we are interested in seeing how it is possible for the necessary truth exhibited in the basic principles of logic to be explained in terms of the nature of things, then logic needs to be understood as a tool—indeed, the human tool, an organon—for the acquisition of knowledge. So understood, the tools of logic— specifically, the concept, the proposition, and the argument—have a certain character, and it is this character that differentiates them from physical things we perceive in that natural order. The fundamental character of these tools of logic consists in their being of or about something other than themselves. Their nature is not merely explained by reference to something else; their nature is a reference, a respect, an ordination to something else. They are inherently relational or intentional and cannot be known first, before it is known what they are of or about. They are formal signs because they do not need some tertium quid to make them of or about something.28 On the other hand, physical beings that we perceptually encounter in the natural order do not exhibit this ontological character.29 They must be known first, before it can be determined what, if anything, they are of or about.30 For example, smoke may be a sign in the sense of being a signal of fire, but it does not signify fire as “fire” does. Smoke has to be recognized—just as the marks or sounds that are transformed into “fire” do— before one knows what it is signifying. Smoke, just like marks or sounds, is not inherently of or about something. Any significatory character physical beings might have is extrinsic to their nature and must come from some 28

See Francis H. Parker and Henry B. Veatch, Logic as a Human Instrument (New York and Evanston: Harper & Row Publishers, 1959), pp. 13-29 for a discussion of formal and other types of signs. 29 For a discussion of this and related points, see Douglas B. Rasmussen, “The Significance for Cognitive Realism of the Thought of John Poinsot,” American Catholic Philosophical Quarterly 68, no. 3 (1994): 409-424 as well as idem, “Realism, Intentionality, and the Nature of Logical Relations,” Proceedings of the American Catholic Philosophical Association 66 (1992): 267-277. 30 See Mortimer J. Adler, Some Questions About Language: A Theory of Human Discourse and Its Objects (La Salle, Illinois: Open Court, 1976), pp. 22-24 as well as Parker and Veatch, Logic as a Human Instrument.

338

Douglas B. Rasmussen

other source. Indeed, it is only in the cognitive activities of living things that we find this intrinsically relational or intentional character. It is distinctive of awareness.31 Awareness is and must be ultimately an awareness of something other than itself,32 and for human awareness this means that concepts, propositions, and arguments can be best described as logical forms or relations that are intentional in character. Though concepts, propositions, and arguments do not exist apart from psychological activities of conceiving, judging, and reasoning—and thus can be termed “relations of reason” —psychological states do not constitute these unique tools of logic. Further, though the activities of conceiving, judging, and reasoning generally have some form of linguistic or symbolic expression, marks and sounds do not constitute these unique tools of logic either. Rather, these tools are found in the significatory character of the activities of conceiving, judging, and reasoning and in the significatory character of marks and sounds when they are transformed into linguistic and symbolic expressions.33 Put differently, language cannot be language until physical notation (marks or sounds) acquire meaning, and this it cannot do on its own. (Moreover, to say that we endow such marks or sounds with meaning is not an explanation but just a statement of what needs to be explained.) As logical forms or relations, concepts, propositions, and arguments are distinct from and not reducible to either psychological states or the marks and sounds of linguistic and symbolic expression. In the main, then, concepts, propositions, and arguments are intentions, and psychological states and linguistic marks and sounds are respectively their cognitive and symbolic infrastructure. The term “intention” carries with it an important ambiguity. It may be used to indicate the operation of intending or the object which is intended. 31

See Douglas B. Rasmussen, “Rorty, Wittgenstein, and the Nature of Intentionality,” Proceedings of the American Catholic Philosophical Association 57 (1983): 152-162, and idem, “Deely, Wittgenstein, and Mental Events,” The New Scholasticism 54, no. 1 (1980): 60-67. 32 As Sir Anthony Kenny interprets him, this is the ultimate point behind Wittgenstein’s so-called private language argument. See the following works by Kenny: The Legacy of Wittgenstein (Oxford: Blackwell, 1984), chap. 5; The Metaphysics of Mind (Oxford: Clarendon Press, 1989); The Unknown God: Agnostic Essays (London and New York: Continuum, 2004), chap. 11; and Wittgenstein, rev. ed. (Oxford: Blackwell, 2006), chap. 10. 33 See notes 29, 30, and 31 as well as Jacques Maritain, “Language and the Theory of Sign,” in Language: An Enquiry into Its Meaning and Function, ed. Ruth Nanda Ashen (New York: Harper and Brothers, 1957), pp. 86-101.

Grounding Necessary Truth in the Nature of Things

339

Thus an intention involves an object intended in an intending. Suppose, for example, that the object intended is a horse and that the operation of intending is one of conceptualization. We may say, then, that a horse is the first intended (a first intention) of a first intending. We may note that what is formed by this act of conceptualization is the concept of a horse. The first intending, however, can become the object of a second intending (an act of reflection). Thus, the concept of a horse becomes the second intended (a second intention), and it has features that its object, the first intended, a horse, does not have. The concept of a horse has, for example, such features as predicability, extension, and intension, while horses do not. A horse can, however, run in a race, but the concept of a horse cannot. In the case of an argument, we can note that there is an implication in knowing that Old Dobbin is a horse and horses are mortal—namely, that Old Dobbin is mortal—but that is not a relationship in which Old Dobbin stands as a being in rerum natura. To be sure, it is the nature of Old Dobbin that provides the basis for this implication,34 but the implication exists only insofar as Old Dobbin stands in the relationship of being a thing known. Implication is a form of thinking about things, not a form of things. It is a second intention. As Aquinas succinctly states: “Although it is necessary for the truth of a cognition that the cognition answer to the thing known, still it is not necessary that the mode of the thing known be the same as the mode of its cognition.”35 A concept of a horse is of a horse, but it is not a horse. And the implication of mortality is a result of being about Old Dobbin’s nature; but the implication is not a feature of Old Dobbin’s nature. On the whole, it is not things that exist in rerum natura but things as they exist qua known that are the proper objects of study for logic. Logic studies second intentions, not first intentions. Concepts, propositions, and arguments as logical forms or relations are second intentions. Further, and to state in a slightly different manner what was noted previously, there is an overall character that all logical forms or relations (that is, second intentions) have that first intended objects do not have. This is intentionality. Thus, second intentions are formal signs, because they are simply that in and through which first intendings intend their objects and carry out acts of cognition.36 34

For a defense of this claim, see Henry B. Veatch, “A Modest Word in Defense of Aristotle’s Logic,” The Monist 52, no. 2 (1968): 210-228. 35 Aquinas, Summa contra gentiles, II, 75. 36 See Henry B. Veatch, Intentional Logic: A Logic Based on Philosophical Realism (New Haven: Yale University Press 1952; reprinted by Archon Books, 1970); and John

340

Douglas B. Rasmussen

Since logical forms or relations so understood are formal signs and thus intentional in character, they cannot be considered or examined without considering, at least to some extent, the nature of the reality they disclose. It is thus a serious mistake to “abstract entirely from and disregard all questions as to what [one] thinks about, and still find that there are certain principles in accordance with which, if [one] is to think about anything, [one] will think.”37 Logic, at least if it is to be an organon,38 cannot be done in a “wholly a priori manner and in complete indifference to what the nature and character of reality may be…”39 Thus, the PNC is, for example, not formal in the sense of being totally independent of the nature of what is thought of. Rather, it is formal in the sense of pertaining to the form of logical relations—that is, in being of or about what it is we think—and in the sense of not varying when the particular subject-matter of which we think does vary, for it notes what is common to any and every being that exists. Accordingly, the rules of logic are formed only by reflexively considering our acts of apprehending, judging, and reasoning and coming to grasp the intentional character of concepts, propositions, and arguments. We become aware of our cognitive operations, and we learn how to properly connect our thoughts by making sure we do so in ways that follow the fundamental character of reality. For example, the fundamental character of reality is reflected in logic by the rules concerning the proper use of the “logical words” (traditionally called syncategorematic terms). The elemental meaning of such terms as “and,” “or,” and “not” is expressed in the rules on how to construct propositions and relate them to others. One may not construct propositions with the form “P and not-P,” but one may construct propositions with the form “P or not-P.” The PNC and Principle of Excluded Middle are powerful rules, and they allow for the development of even more logical rules. This can become a highly complex process, but Deely, “The Ontological Status of Intentionality,” The New Scholasticism 46, no. 2 (1972): 220-233, pp. 232-233 n34. 37 Joseph, An Introduction to Logic, p. 5. 38 Of course, it could be argued that logic need not be an organon, but then the basic question would be why bother with logic in the first place? For a defense of logic as an organon and a critique of views of logic that do not treat it as a tool for human knowledge, see Henry B. Veatch, “A Logic That Can’t Say What Anything Is” and “Alternative Logics: A What Logic and a Relating-Logic,” in Two Logics: The Conflict Between Classical and Neo-Analytic Philosophy (Evanston, Illinois: Northwestern University Press, 1969), chapters 1 and 2, pp. 26-62. 39 Henry B. Veatch, “Concerning the Ontological Status of Logical Forms,” The Review of Metaphysics 2, no. 6 (1948): 40-64, p. 46.

Grounding Necessary Truth in the Nature of Things

341

all our knowledge of the rules of logic is based on this reflexive awareness of the proper syntactical use of these logical words. The upshot of all these considerations, then, is this: though it certainly true that logical forms or relations are not the same as those forms or relations found among the physical beings encountered in the natural order, it does not follow that the necessity exhibited in the basic principles of logic, such as the PNC, the Law of Identity, or the Principle of Excluded Middle, must be different in kind from any necessity that might be found in nature. It is only by failing to distinguish between the objects to which necessity might apply—that is, first and second intentions—and the very modality of necessity that such an inference could be drawn. Furthermore, given that the nature and structure of logical forms or relations are determined wholly on the basis of their being adapted to disclose or signify the nature and structure of reality, it is certainly not beyond the pale to hold that necessary truths have their ultimate ground in the necessities found in beings in rerum natura. This is, of course, a much larger claim that requires more development—part of which involves considering questions I and II. 4 Inspectio Mentis and the Uniformity of Nature Question I asks: Is what is conceivable or imaginable determined through inspectio mentis? For a logic that regards its basic forms or relations as intentional in character, the answer to this question is negative. It is so in part, because “meaning,” like “intention,” has an important ambiguity. It can signify either the activity of meaning or that which is thereby meant. Likewise, “concept” can signify the logical instrument of conceiving or the object itself which has been consequently conceived. Thus, a concept qua instrument of conceiving does not itself have a meaning, but rather is a meaning. A concept so understood is not a mental “container” that “holds” meaning that can be unpacked from one’s philosophical armchair. Rather, it signifies something, something that is of—something that is meant—but it does not itself have a meaning or content apart from the object meant. Of course, it is perfectly possible to make a concept or a meaning an object for analysis, and this is just what logic does when it examines a concept or meaning as a second intention. But it is certainly not legitimate to make a concept or meaning the object of one’s analysis and from that analysis attempt to make a determination about what is the case, or possibly the case, or necessarily the case for beings in rerum natura. Such a move confuses second intentions with first intentions—it confuses logic with reality.

342

Douglas B. Rasmussen

This ambiguity can be illustrated in the claim it is conceivable that a solid iron bar floats when placed unsupported in a vessel of water. Are we talking about the concept of such an iron bar or are we talking about an actual iron bar? It is one thing to talk about what is conceivable with respect to the concept of something (and the relationships among concepts such as genus to species40) and quite another thing to talk about what is conceivable with respect to what the concept is of, with the object that is meant. If we are talking about the latter, then it is generally speaking what the thing in question is that tells us what is conceivable in regard to it. In this particular case, it is what it is to be iron and what it is for a mineral to float that are pertinent in determining whether one can conceive of such a bar floating. The specific gravities of each—in the range of 7.3/7.8 (iron) and less than one (it floats)—leads us to realize that the denial of the claim that a solid iron bar sinks when placed in a vessel of water amounts to saying that a mineral with a specific gravity in the range of 7.3/7.8 (i.e., it is iron) is a mineral with a specific gravity of less than one (i.e., it floats). What we know of the nature of iron and floating works against conceiving such a purported event.41 And so denying the claim that it sinks is selfcontradictory and thus logically impossible in the sense that it is shown by logic to be so in virtue of what it is to be iron and what it is to float. But what is shown pertains to beings in rerum natura, not to objects logic examines. Another illustration of this ambiguity is the claim it is conceivable that a cat gives birth to pups, but this time the nature of the ambiguity pertains to a failure to distinguish between a definition of a cat and a cat. It is argued that since a definition of a cat says nothing about the nature of its offspring, there is nothing inconceivable about an actual cat giving birth to pups. In other words, it is assumed that if one holds that what a cat is precludes its being able to give birth to pups, then one also holds that this incapacity is part of a cat’s definition. But this does not follow. What a cat is, or for that matter what anything else is, involves much more than what its definition requires. A definition represents a condensation of a vast amount of knowledge regarding a thing and is a formula-like statement of those basic features, characteristic, properties, etc. that make a thing what it 40

There are others relationships to a species such as: difference, definition, property and accident, but none of these relationships characterize the way a species term signifies its object. See Rasmussen, “Quine and Aristotelian Essentialism,” on how the species term signifies the entire nature of its objects, not just a part. 41 See George Seddon, “Logical Possibility,” Mind 81, no. 324 (1972): 481-494.

Grounding Necessary Truth in the Nature of Things

343

is and thus allows it to be distinguished from every other sort of thing in reality. Such definitions are traditionally called real definitions. They are not determined in some a priori manner. The defining characteristics are those that not only distinguish X—for there may be many distinguishing characteristics—but do so fundamentally. Fundamental characteristics are those distinguishing characteristics on which all the other characteristics (or greatest number of others) depend.42 If a definition were to provide a description of all the features or characteristics of a thing, then it would defeat its very purpose. Therefore, a definition of a thing is not immediately given but is the result of a cognitive process. Overall, the accuracy of definitions help concepts “map” the world, and they are vital to human knowledge. But in no sense can it be said that a definition, which is tool of human cognition and thus a second intention, is the same as the very nature of the reality a concept signifies. What is happening, therefore, with the claim it is conceivable that a cat give birth to pups is the following: There is a shifting of focus from things to definitions and back again, and this creates the confusion. (There is also the assumption that the ability to visualize or form a picture of tiny baby dogs emerging from a cat’s womb constitutes a conception of such a state of affairs, and if not that, there is the assumption that a picture is sufficient in itself to determine what can be conceived.43) When asked to determine whether it is conceivable (and hence logically possible) for a cat to give birth to pups, one is asked to consider an actual entity, a cat, and to ponder whether logically it could give birth to pups. It is at this point that the focus of the question shifts from beings in rerum natura to the definitions of such beings. The question now becomes whether the definition of a cat precludes the cat’s offspring being baby dogs. Since a definition is not a description (and should not be so), we discover that a cat’s definition says nothing about the nature of its offspring. Thus, the definition does not preclude, show the falsity of, the claim that a cat could give birth to pups. Then the focus of the question shifts back to the actual entity, and prestochango, one notes that despite everything we know about the nature of a cat it is conceivable and thus logically possible for a cat to give birth to pups!

42

Also, there is no more reason for thinking real definitions face some insuperable difficulty and instead must be ultimately about language, or be true in virtue of language, than there is for so regarding necessary truths. 43 For a critique of these assumptions, see Rasmussen, “Logical Possibility: Aristotelian Essentialist Critique,” pp. 529-531. See also note 65 below.

344

Douglas B. Rasmussen

This entire argument confuses logic’s objects with those of science and metaphysics. What is conceivable or logically possible can be understood as pertaining to the objects that logic studies (that is, second intentions), but this means that while logic is not a purely formal enterprise, neither is a logical consideration the same as an ontological or scientific one. In other words, an examination of the relationship between the concept of cat and the concept of dog does not require that logic become zoology or biology; rather, all that is required for logic is the definitions of the realities involved. This establishes a tie between logic and beings in rerum natura but not an identification. It allows logic’s objects not to be purely formal, but it does not confuse second with first intentions. Logic uses definitions in making conceptual comparisons, but it does not discover definitions. In this context, what is conceivable or logically possible is determined by the concepts themselves, which is generally the definition,44 not the objects these concepts signify. Hence, what is conceivable or logically possible with respect to the concepts themselves is not a basis for determining if the denial of a proposition about beings in rerum natura is self-contradictory, because a definition is (as noted above) about the nature of a thing but is not itself a thing’s very nature. (Even if it should prove true that a full biological definition of a cat does preclude it from giving birth to pups, the basic issue here is that definitions are not ontologically ultimate but are tools of human cognition. It is not the definition, but the nature of a thing that, so to speak, wears the trousers. To treat the definition as the starting point for determining what is necessary or possible for a being in rerum natura is similar to an error found in Porphyry’s jumbling of Aristotle’s doctrine of the predicables where he assumes that what a term signifies is determined by the ways it can be predicated of other terms. In effect,

44

It is also possible to determine what is conceivable by considering only the minimal meaning necessary to employ a word. For example, one can for the sake of convenience in regard to “triangle” mentally hold apart certain features from others—for example, think only of being three-sided and not think of being isosceles, equilateral, or scalene. Or, one can for the sake of entertainment mentally isolate certain features of a thing from other features as one does in engaging in fantasy—for example, the notions of mermaids or centaurs. There is nothing wrong with such activities but, as already said, they should not be used as a basis for determining whether the denial of a proposition about beings in rerum natura is self-contradictory.

Grounding Necessary Truth in the Nature of Things

345

starting with definitions lets logical relations, and not the nature of a thing, determine what is essential and necessary to a thing.45) By ignoring the foregoing distinctions, inspectio mentis treats concepts as having meaning but apart from any consideration of what concepts are about. Accordingly, a concept’s meaning is not an object meant, but its (the concept’s) meaning, yet in such a way that this meaning is not something meant at all. To illustrate, consider the claim: “The truth of ‘men are animals’ is due solely to the meaning of ‘men’ and not to anything meant by ‘men,’ but at the same time ‘men’ is not being mentioned because ‘men are animals’ is not about the term ‘men.’” This claim obliterates the distinction between use and mention. It is as if the concept is not being used, so much as considered in its use, and yet still not being mentioned— that is to say, it is as if a concept is made into an object of consideration without it thereby being made into an object of still another concept.46 The issue is how can a statement be true in virtue of the meaning of its terms without the terms being about something (using them) or without making the truth pertain to the terms themselves (mentioning them). The answer is: it can’t. (This problem pertains to the very description Hume gives to propositions that are intuitively or demonstratively certain, that is, “relations of ideas.” “Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe.”47) This conflation of use and mention provides the illusion that there is a non-empirical path to a closed, a-contextual repository of knowledge.48 It results from the unnoticed shifting of focus from first 45

See Rasmussen, “Quine and Aristotelian Essentialism.” See also Joseph, An Introduction to Logic, pp. 66-110 for a thorough discussion of Aristotle’s doctrine of the predicables as well as E. A. Moody, The Logic of William of Ockham (New York: Russell & Russell, 1965), pp. 66-117. 46 See Henry B. Veatch, Two Logics, pp. 88-89, 106-125. 47 Enquiries, Section IV, Part I, p. 25. 48 This point cannot be developed within the confines of this essay, but an endorsement of the following two claims can be made: (1) “The terms ‘necessary’ and ‘a priori’ … as applied to statements are not obvious synonyms. There may be a philosophical argument connecting them; but an argument is required, not simply the observation that the two terms are clearly interchangeable.” Saul Kripke, “Naming and Necessity,” Semantics of Natural Languages ed. Donald Davidson and Gilbert Harman (Dordrecht, Holland: D. Reidel Co., 1979), p. 263. (2) “Fallibilism and necessity are perfectly compatible. … Fallibilism is a thesis about our liability to error, and not a thesis about the modal status (possible falsity) of what we believe.” Susan Haack, “Epistemology with a Knowing Subject,” The Review of Metaphysics 33, no. 2 (1979): 309-335, p. 309.

346

Douglas B. Rasmussen

intention to second intention and then back again. Yet, there is no justification for treating concepts in this manner. Additionally, this procedure assumes that concepts are what one knows rather than that by which one knows. It treats concepts as direct objects of our knowledge and thus makes them “intermediaries” that in turn require some tertium quid to relate them to the world “outside” of awareness. The entire approach to concepts is more or less what Thomas Reid called the “way of ideas” that Descartes and Locke are often charged with introducing into modern philosophy, which had some currency in the seventeenth and eighteenth centuries. Yet, even then, it was challenged by such thinkers as John Poinsot (whose religious name was “John of St. Thomas” and who was a contemporary of Hobbes and Descartes) and later by Reid. The view quickly degenerated into skepticism regarding the world “outside” of awareness, as Hume most aptly illustrates.49 It is only one way of understanding concepts, however, and not a very good one. Without a doubt, it is not a way for determining whether P is a necessary truth or explaining why it is a necessary truth (if it is). But what of the Humean claim that there is no rational basis for believing the uniformity of nature, how is this judged in light of the foregoing considerations? H. W. B. Joseph has set out the classic reply to this claim, and it bears full quotation: Uniformity of action is not indeed the fundamental element in the causal relation, for it depends on repetition of the action; the causal relation has nothing to do with number of instances, so far as its existence—though much so far as its detection—is concerned; it is bound up altogether with the nature or character of things, and the nature of anything is not a question of the number of such things that may be or have been fashioned. Yet if a thing is to have any determinate nature and character at all, there must be uniformity of action in different things of that character, or of the same thing on different like occasions. If a thing a under conditions c produces a change x in a subject s—if, for example, light of certain wave-lengths, passing through the lens of a camera, produces a certain chemical change (which we call the taking of a photograph of Mount Everest) upon a photographic film—the way in which it acts must be regarded as a partial expression of what it is. It could only act differently, if it were different. As long therefore as it is a, and stands related under conditions c to a subject that is s, no other effect than x can be produced; and to say that the same thing acting on the same thing under the same conditions may yet produce a different effect, is to say that a thing need not be what it is. But this is in flat conflict with the Law of Identity. A thing, to be at all, must be something, and can 49

Treatise, Book I, Part II, Section VI, pp. 67-68.

Grounding Necessary Truth in the Nature of Things

347

only be what it is. To assert a causal connexion between a and x implies that a acts as it does because it is what it is; because, in fact, it is a. So long therefore as it is a, it must act thus; and to assert that it may act otherwise on a subsequent occasion is to assert that what is a is something else than the a which it is declared to be.50

Though there are certainly practical difficulties in ensuring that the ceteris paribus proviso is met, there is no way, to continue with Joseph’s example, a thing A (light of a certain wave-length) can be what it is under condition C (passing through the lens of a camera) and not produce X (a certain chemical change) in subject S (photographic film). To deny the uniformity of nature is to say that a thing both is what it is and is not what it is. The Humean claim to conceive of it being otherwise is just plain false. The uniformity of nature is a necessary truth. It is crucial in appreciating Joseph’s reply to understand that he is not suggesting that difficulties a scientist might encounter in determining just what A is might be overcome by his account of the uniformity of nature. This account involves only a general type of knowledge—“if A causes X, it does so in virtue of its nature”—and it does not guarantee that consequences or further determinations of A’s nature can be deduced from the definition of A, or from the concept of A in a Leibnizian-like manner. This must be an empirical process. Further, there is nothing in Joseph’s account that prohibits A from changing. Nature can change its course. The hesitation that one has regarding whether this A has changed (or is changing into something different) or the hesitation that one may have regarding whether one knows enough to make accurate predictions do not pertain to the principle of uniformity of nature. Each of these is a real concern for the scientist, but neither of them casts any uncertainty on the relationship between an entity’s nature and its actions. This relationship holds. Hume has not succeeded in showing that there is no rational ground for believing in the uniformity of nature. Nonetheless, it might be objected that Joseph can only maintain his defense of the uniformity of nature by widening his definition of A to include its effects, and if this is so, then he makes it more and more problematic whether we do indeed have an instance of A or not. Furthermore, on Joseph’s account it would seem that one never abandons a particular causal law, but only redefines the terms in which it is expressed. His account, then, would not only provide no help to scientists about their 50

Joseph, An Introduction to Logic, pp. 407-408.

348

Douglas B. Rasmussen

inductions but also only succeed at defending the uniformity of nature at the price of trivializing it. Joseph simply stipulates that any A that does not produce effect X is not A. And if this is so, then he has not provided an explanation of why the events in nature really operate in a uniform manner. He has not shown that they must be so. Yet, in spite of appearances, it is not the case that widening of the definition of A is always required by Joseph’s defense of the uniformity of nature, because not all expressions of A’s identity—in this case the actions that produce effect X—need to be included in the definition of A. At their very best—and to develop a point noted above—definitions record what is fundamental and essential to a thing, but the very process of determining what is fundamental and essential requires that there be more to the nature of a thing than just what its definition states. It is as if every definition has the following introduction: “After full consideration of all the acknowledged facts concerning the thing in question, the following has been settled on as the fundamental and essential, therefore defining, characteristic(s) or feature(s) …”51 Thus, to note that certain effects follow from A’s identity does not require including those effects in the very definition.52 What is more, the claim that a widening of the definition of A is always required rests on a confusion that results from failing to appreciate an ambiguity found in “definition.” This ambiguity is similar to that found in “intention.” “Definition” can signify that act of defining or it can signify that which is defined, and a definition qua instrument of defining can be made the object of analysis, and this is just what logic does when it considers what is included in a definition. But it does not follow from this that the definition of A determines whether A produces effect X for subject S under conditions C. The same confusion that was noted earlier in regard to both “concept” and “meaning” is also found in the charge that a widening of a definition is always required to defend the uniformity of nature. By assuming that a necessary connection must be an expression of a definition, this charge confuses second intentions with first intentions. Neither is it the case that Joseph’s account requires that particular causal laws never be abandoned but only redefined. This would be required 51

For an account of the basis for such a preamble, see Rasmussen, “Quine and Aristotelian Essentialism,” p. 328. 52 The process of discovering whether something is an instance of A may require looking to see if it produces X in circumstances C on subject S. Indeed, scientific accounts of A at times involve tests of this sort. But this admission does not in itself make Joseph’s defense of the uniformity of nature trivial or unhelpful.

Grounding Necessary Truth in the Nature of Things

349

only if causal behavior was included in the very definition of A, and this, as has been shown, need not always be. Thus, when confronted with an A that fails to produce X in subject S in certain cases, then this can be dealt with by simply noting that A caused X in subject S only under certain conditions and that A did not cause such an effect X under the conditions previously thought. No redefinition need occur, and thus it is possible for a causal law to be abandoned. In this regard, the following statement by Henry B. Veatch is worthy of note: It is indeed odd to what extent it is generally supposed that any recognition of essences in things, coupled as it is with a logic of what-statements and necessary truths about the world, etc., must inevitably bring in its train an extreme dogmatism, claiming an absolute certainty for is pronouncements on what is necessarily the case. However … neither essentialism in philosophy, nor the what-logic that is associated with it, necessarily involves any such pretensions to infallibility in knowledge.53

Finally, Joseph’s account of the uniformity of nature does indeed show why the uniformity of nature must be so, because it is based on the fact that things, whatever they may be, are what they are. This is both informative and a necessary truth.54 It lies behind everything that happens and any attempt to understand what happens. For a view such as Joseph’s, the natural order is full of changing things, but change is orderly and not sheer “flux.” Things can, and do, develop and evolve, but there is always something that does the developing or evolving. And while we can, and do, discover things changing in ways never dreamt of, such a discovery is itself 53

Two Logics, pp. 153-154. But also consider Haack’s statement in note 48 above as well as the following observation by J. L. Austin: “Being aware that you may be mistaken doesn’t mean that you are aware that you are a fallible human being; it means that you have a concrete reason to suppose that you may be mistaken in this case.” Philosophical Papers, 2nd ed., ed. J. O. Urmson and G. J. Warnock (Oxford: Oxford University Press, 1970), p. 98. 54 In response to the claim that P cannot be a necessary truth and informative, because every P that is informative is empirically disconfirmable, it can be asked: On what is this claim based? Is “Informative propositions are empirically disconfirmable” a necessary truth or not? If it is a necessary truth, is it informative or not? If it is informative, then it is an instance of what it purports to deny, and if it is not informative, then nothing has been said about what it is for P to be informative. Finally, if the claim is not a necessary truth, then it does not preclude the possibility of there being a P that is informative and not empirically disconfirmable. On logical truths being informative, see Butchvarov, The Concept of Knowledge, op cit., pp. 118-119. See also notes 48 and 75.

350

Douglas B. Rasmussen

based on discovering what is involved in the changing. We note the powers and capacities that make a thing what it is and from that basis begin an explanation of what is happening. Though Hume speaks of “nature changing its course,” it is more like one thing being suddenly and instantaneously replaced by another thing. The vase that becomes a woman is either a case of the rearrangement of molecules (sword to ploughshares) in which case it does not support the Humean line, or it is a case of the replacement of one entity which has been annihilated by another newly created, in which case it is a Humean event pair, but is a fortiori incapable of being given a rational account, and so its logic is irrelevant to the understanding of science, which is precisely the set of rational accounts of change.55 In other words, there is once again a shifting of focus in the Humean analysis, but this time it starts from a speaking of change and shifts to instantaneous replacement and then back to change. We are presented with an alleged example of nature changing it course when in fact all we are presented with is a consideration of one feature of a thing associated with a feature of another. And while there is nothing wrong in their own right with such mental gymnastics or imaginary exploits, they carry no weight when it comes to casting doubt on the uniformity of nature—that is, of course, unless one seeks to replace ontology with Walt Disney or change with flux. 5 Thinking Something is Thus-and-so and Its Being Thus-and-so Question II asks: Even if not-P is conceivable in some sense or other, does that show that P is not a necessary truth or that to which it pertains in the natural order is not necessary—that in effect, there is no natural necessity? The answer to this question is negative, and this is not only because of the confusion of second with first intentions that was discussed in the previous section but also because of a failure to consider the ways in which something might be considered or abstracted. To begin with, consider (as Hume would allow) a putative example of a necessary connection between cause and effect: fire and heat. It is certainly possible to consider the particular features and characteristic of the cause just 55

Harré and Madden, Causal Powers, p. 107. Of course, Hume’s challenge to the uniformity of nature may be nothing more than an expression of an underlying ontology of events. And while a critique of such a view is far beyond the scope of this essay, it seems that if such an ontology works against the possibility of being able to provide an intelligible account of change, then that would itself constitute a prima facie reason to look elsewhere for an ontology.

Grounding Necessary Truth in the Nature of Things

351

in itself without considering how it brings about an effect. Now in this case, thinking of fire that is still fire when heat is gone is most certainly an example of fanciful thinking that proves nothing in regards to what logic shows is possible for fire56 (or the necessary truth of the propositions pertaining to it), but the point here is that even if no objection is made to this alleged conception of there being fire without heat, the fact that one can be considered without considering the other is irrelevant to the question of whether there is a necessary connection between heat and fire. It does not show such an effect is not in fact necessarily dependent on its cause or recognizable when our consideration involves the whole relationship. To think of fire without thinking of heat is not the same as thinking that fire can exist without heat. Abstractio non est mendacium: to abstract is not to falsify.57 Aquinas distinguishes between two ways of abstracting or considering the form or character of an existent. The first way, which is called “nonprecisive” abstraction (that is, abstraction without precision), considers the form or character of an existent as a whole and thus makes it possible to affirm an identification between an individual and its form or character. For example, we say that Socrates is a human being, that Socrates is an animal, and that Socrates is a physical thing. Each of these predicates characterizes Socrates in a distinctive way, but each applies to Socrates taken as a whole, in his entirety, and not as some part. Further, each of these propositions asserts a union in reality between these respective forms or characters and Socrates. The second way of abstracting or considering the form or character of an existent, which is called “precisive” abstraction (that is, abstraction with precision), is not concerned with making possible the identification of an individual with its form or character. This type of abstraction occurs when we seek to focus on the form itself and not the form as fully embodied and individualized. It is by means of precisive abstraction that such abstract notions as, for example, humanity, animality, and corporeality are fashioned. “These different aspects are precisively represented as the forms that 56

E. H. Madden, “Hume and the Fiery Furnace,” Philosophy of Science 38, no. 1 (1971): 64-78, no. 68. 57 G. E. M. Anscombe has observed, “I can imagine or think of a sprig of leaves existing without there being a definite number of leaves that I think of it as having. Naturally, this does not mean that I can think of it as existing without having a definite number of leaves.” “Whatever has a Beginning of Existence must have a Cause: Hume’s Argument Exposed,” in G. E. M. Anscombe, The Collected Philosophical Papers of G. E. M. Anscombe: From Parmenides to Wittgenstein, Volume One (Minneapolis: University of Minnesota Press, 1981), p. 99.

352

Douglas B. Rasmussen

constitute the nature of the subject. … Each is represented as something just in itself.”58 In precisive abstraction, therefore, the focus is on the form or character of an existent as not related to its individual differences and manner of existence—that is to say, the form or character is considered as excluded or “cut off” from its individual differences and manner of existence. The form so considered is but a logical or conceptual “part” of the whole reality from which it is abstracted. (The abstract nouns noted in the previous paragraph do not refer to any physical distinction between the form and the subject in which they inhere. This distinction is made within cognition. Moreover, this distinction does not even show that a material thing is composed of two physical principles, namely, form and matter. That claim must come from an investigation of the things, not from merely our ability to abstract.) As a result, it is improper to predicate a form so abstracted of the subject in which it exists, for example, humanity of Socrates. It is false to affirm that Socrates is humanity. Humanity is the form of Socrates’s form or nature, but it is not Socrates’s very form or nature. There is nothing wrong with this type of abstraction, however. Indeed, it is important for understanding and analyzing the features of any existent’s form or character. It is this type of abstraction that is involved in logicians or mathematicians considering the so-called formal nature of something.59 Yet such a consideration does not mean that a formal nature exists just as such or constitutes the very nature of something that exists in rerum natura. Nor does it mean that such a consideration is to be used in determining what is necessary or impossible for any existent in the natural order. By contrast, nonprecisive abstraction occurs by focusing on the entire form or character of an existent in an indeterminate manner so that its individual differences are not specified but are nonetheless regarded as requiring specific determination. The form must—within a range—be specified or determined. The form or character is thus regarded merely not as related to its individual differences and manner of existence. In other words, the form or character is not excluded or “cut off” from its individual 58

Joseph Owens, C. Ss. R., Cognition: An Epistemological Inquiry (Houston, Texas: Center for Thomistic Studies, 1992), p. 149. The expressions “nonprecisive” and “precisive” are taken from Owens’s discussion of abstraction, pp. 139-165. See also note 61 below. 59 For a logician, this generally is expressed in the definition and for the mathematician it is expressed by quantity. However, none of this is to say that forms or relationships logic considers are the same as those of mathematics. See Veatch, Intentional Logic, pp. 29-78.

Grounding Necessary Truth in the Nature of Things

353

differences (including manner of existence). Instead, these differences are not expressed but treated as implicit. Aquinas illustrates this way of abstracting when he states that the “genus signifies some form, though not determinately this or that (form) which difference expresses determinately, which is none other than that (form) which is signified indeterminately through genus.”60 Thus, when we consider in similar manner the forms or characters of, for example, human beings, we are considering their forms or characters indeterminately (that is, without regard to their determination) but we know nonetheless that it must have some determination. This type of consideration allows us to predicate human being not only of Socrates in his entirety, but of Aristotle, and any other individual humans as well.61 This is so because the concept of human being does not positively exclude individual differences of these men and treats these differences as implicit. These differences only become explicit when each instance of the concept of a human being is considered. What is common to the respective natures of these individuals must be expressed determinately in the concrete forms or characters of these individuals.62 Such determinations are part of the meaning or signification of the concept of a human being. It was nonprecisive abstraction that was employed in the preceding section’s discussion of what it is to conceive of “iron,” “water,” and “floating” or “cat,” “pups,” and “gives birth to.” Nonprecisive abstraction makes it clear how a concept’s meaning or signification involves an intension (or comprehension), which is not limited to what is only explicitly considered or stated in a definition, and an extension that applies over a 60

Aquinas, Concerning Being and Essence, trans. George C. Leckie (New York: Appleton-Century Crofts, 1937), p. 13. 61 “It is clear, then, that the essence of man is signified by the two terms ‘man’ and ‘humanity’, but in different ways, as we have said. The term ‘man’ expresses it as a whole, because it does not prescind from the designation of matter but contains it implicitly and indistinctly, as we said genus contains the difference. This is why the term ‘man’ can be predicated of individuals. But the term ‘humanity’ signifies the essence as a part, because it includes only what belongs to man as man, prescinding from all designation of matter. As a result, it cannot be predicated of individual men.” Aquinas, On Being and Essence, 2nd rev. ed., trans. Armand Mauer, C.S.B. (Toronto: The Pontifical Institute of Mediaeval Studies, 1968), p. 44. See also translator’s note 15, p. 39 as well as Rasmussen, “The Significance for Cognitive Realism of the Thought of John Poinsot,” op. cit. For an excellent account of Aquinas’s “moderate realism,” see Joseph Owens, “Common Nature: A Point of Comparison Between Thomistic and Scotistic Metaphysics” Mediaeval Studies 19 (1957): 1-14. 62 On Being and Essence, p. 42. On this point, see also Joseph, An Introduction to Logic, pp. 85-86; and Veatch, Intentional Logic, p. 115.

354

Douglas B. Rasmussen

wide range of individuals.63 For this type of abstraction, a concept’s meaning or signification is not the formal nature of something.64 When considering, then, the entire relationship between something coming into existence and a cause—or, more particularly, a rabbit coming into existence and a parent rabbit—the issue is not whether engaging in a process of abstraction with precision is possible.65 Indeed, it is, but rather whether it is relevant and appropriate to what is supposed to be considered—in this case, something coming into existence. If we are concerned with understanding the actual change that is the activity or process of coming into existence, if we are concerned with grasping what it is, then we need to consider the whole character of this change, not just a part. The type of abstraction to be employed is abstraction without precision, and this requires understanding the nature of the realities involved. In the case of a rabbit’s coming into existence, this change cannot be understood without a parent rabbit, since a rabbit cannot bring itself into existence. But in the case of matter or energy—or whatever might be the basic “stuff” of the universe—that might never cease to exist but only change its form, the new forms of existence it takes would have to be accounted for in terms of its own powers. But in either case, a change has occurred and to understand a change requires conceiving of what brings it about. It is to conceive of a cause. Yet if this is so, then it is indeed not possible to conceive of something coming into existence without a cause. The basic reason the contradictory nature of Hume’s claim to conceive a beginning to exist without a cause is not immediately realized is that there is, once again, an unnoticed shifting of focus in the Humean argument. It starts with a consideration of the activity of beginning to exist as it is in rerum natura and moves to a 63

See Veatch, Intentional Logic, pp. 112-113. See also Rasmussen, “Quine and Aristotelian Essentialism,” p. 320 n10. Further, this is not to say that only concepts are needed for human knowledge. There are important roles for propositions and arguments as well, but this point cannot be developed here. But it should be noted that Hume tries in effect to reduce the function of propositions and arguments to that of concepts. See Treatise, Book I, Part III, Section VII, pp. 96 n1. 64 Of course, Hume has no use for distinctions such as these. See Treatise, Book I, Part 1, Sections I and VII, pp. 1-7 and pp. 17-25 respectively. 65 Nor is it a question of imagination. “That this is the imagination of a rabbit coming into being, and without a cause is nothing but, as it were the title of the picture. Indeed I can form an image and give my picture that title. But from being able to do that, nothing whatever follows about what is possible to suppose ‘without contradiction or absurdity’ as holding in reality.” Anscombe, “Whatever has a Beginning of Existence Must Have a Cause,” p. 98. See also note 43 above.

Grounding Necessary Truth in the Nature of Things

355

consideration of its formal nature, and then it returns to the activity as a reality. But by now it should be evident that this sort of argumentative move does not work. Overall, lurking behind Hume’s claim that “Whatever begins to exist has a cause” and “Like things in like circumstances behave in like ways” are not necessary truths is an assumption. This assumption, which was implied by our earlier discussion in this section, needs to be explicitly stated: namely, thinking something thus-and-so is the same as something being thus-and-so. But this assumption simply is not true, and it is by no means required to uphold cognitive realism. Reality is intelligible and can be known, but this does entail that ultimately what is thought determines what exists, can exist, or must exit. Moreover, this assumption seems to have its source in a rationalist or idealist metaphysics, but if so, there needs to be an argument on behalf of such a viewpoint. It cannot be merely accepted without debate. Finally, it should not go unnoticed, as Jose A. Benardete once suggested, that Hume’s “established maxim of metaphysics” might have its ultimate source in scholastic metaphysics where everything that is not explicitly contradictory—that is, contrary to the formal natures of things which are but reflections of divine ideas—is possible and thus this world is but one of a host of possible worlds that God could create. There could be, for example, one such possible world which is exactly the same as our present world but with one exception—a solid iron bar, which has properties identical to those of iron in our present world, floats on water. God could will this possible world, or some other one in the future, to be the actual world. Whether Benardete’s suggested origin of Hume’s “established maxim of metaphysics” is correct cannot be this essay’s concern,66 but his comment about modern ontology expresses well this essay’s principal foil: Modern ontology, following Hume, models itself on scholastic metaphysics … , [but] having lost confidence in the arguments for the existence of God, the modern philosopher cannot find any application for the concept of necessary being. This is not to say that its correlative, the concept of contingent being, is also abandoned. By no means! Everything that exists now is seen as contingent: to 66

Of course, the influence of Malebranche on Hume is a possible source for this maxim. But also, since Aristotelian ontology makes no provisions for supernatural exceptions to the natural order, the maxim might be fundamentally the result of replacing Aristotle’s natural order with a created and contingent order that is compatible with the Christian faith. See E. A. Moody, “Ockham, Buridan, and Nicholas of Autrecourt,” Franciscan Studies 7, no. 2 (1947): 113-146, p. 142.

356

Douglas B. Rasmussen

be is to be contingent, but contingent on nothing. Hence, “nothing we imagine is absolutely impossible.”67

The alternative to this modern ontology, then, would require rejecting consciousness or mind as ultimate—be it God’s or man’s—and instead accepting as the point where explanation ends the world of existing things that are what they are and cannot be what they are not. Conclusion Hume claims that “all beings in the universe, considered in themselves, appear entirely loose and independent of each other. ‘Tis only by experience we learn their influence and connexion; and this influence we ought never to extend beyond experience.”68 And when we go beyond this experience, he claims that we do so without justification, because it is impossible … that any arguments from experience can prove this resemblance of the past with the future; since all these arguments are founded on the supposition of the resemblance. Let the course of things be allowed hitherto ever so regular; that alone, without some new argument or inference, proves not that for the future it will continue so.69

Though what has been argued in previous sections of this essay is at odds with many of these claims, there is one respect in which there is agreement—namely, we first learn of the connections between things through sense experience. We do not know, for example, that fire is hot until our first encounter with it. Indeed, all our knowledge of the world must come from our sensory experience, but the question of course is: What do our senses know?70 This question cannot be answered in any detail at this time, but a basic feature of an alternate and older empiricist view of sense knowledge to that of the standard Humean view needs to be indicated briefly so as to provide a better understanding of the context surrounding

67

José A. Benardete, “Is There a Problem About Logical Possibility?” Mind 71, no. 283 (1962): 342-352, pp. 349-350. See also Wallace Matson, “Against Induction and Empiricism,” Proceedings of the Aristotelian Society 62 (1961-1962): 143-158, and idem, Grand Theories and Everyday Beliefs (Oxford: Oxford University Press, 2011), pp. 135-138. 68 Hume, Treatise, Book III, Part I, Section I, p. 466. 69 Hume, Enquiries, Section IV, Part II, p.38. 70 See David Kelley, The Evidence of the Senses, op cit.

Grounding Necessary Truth in the Nature of Things

357

the proposal that the ground for necessary truth is found in the being of things. According to this alternative, more or less “Aristotelian” view, the core empiricist claim, “Nothing is in the intellect that is not first in the senses,” is interpreted to mean that all objects of knowledge are without exception presented in sense experience, but this does not mean that they are thereby recognized by the senses. This view stands in contrast to the standard Humean view (or at least what is here called the standard view) of this matter: namely, that the objects that are presented in sense experience are also and necessarily recognized by the senses themselves such that if an object is not explicitly recognized by the senses, then it is not presented in sense experience. But as Étienne Gilson once noted, “The senses carry a message which they cannot interpret.”71 There is, then, more to sensory experience than what appears on the surface, so to speak, and it takes human rationality to discover and integrate what the senses present.72 In the Aristotelian tradition, there is no bifurcation of human knowledge into two kinds—the rational/conceptual and the empirical/sensory. Rather, human knowledge is rational and empirical, conceptual and sensory, and though they can be distinguished, they are not separable. Moreover, what is crucial to understand is that an awareness of the nature of something is already implicit in sensory knowledge, and though conceptual knowledge of the nature of a thing is seldom achieved all at once, the process is never simply one of looking at what might be called “bare particulars” and trying to determine (assuming even this activity to be possible in such a putative context) what they might be. Rather, the individual beings one encounters are something or other. They have natures such that whatever pertains to the nature of one individual being will also be true of another individual being of the same kind. Thus, when trying to determine whether the next solid iron bar one encounters must sink when placed unsupported in water, it should be realized that one is not making an inference from “some” to “all,” but rather one is moving from a conceptual awareness of the nature of one thing to other instances of that same nature. There is nothing easy about this process, and much more explanation of

71

Étienne Gilson, Thomist Realism and the Critique of Knowledge, trans. Mark A. Wauck (San Francisco: Ignatius Press, 1986), p. 173. 72 For an account of perceiving the action of causal power, see Harré and Madden, Causal Powers, pp. 49-68.

358

Douglas B. Rasmussen

conceptualization is required.73 Yet there is in principle no difficulty talking about the what’s and why’s of different individuals that can be seen through a process of abstraction to have a common nature.74 There are natural necessities. But as said, there is much more to this story.75

73

See Parker and Veatch, Logic As A Human Instrument, pp. 270-275, and Louis Groarke, An Aristotelian Account of Induction: Creating Something from Nothing (Montreal and Kingston, London, and Ithaca: McGill University Press, 2009), pp. 156225. 74 For an account of abstraction that is similar in certain respects to that of Aquinas’s, see Ayn Rand, Introduction to Objectivist Epistemology: Expanded Second Edition, ed. Harry Binswanger and Leonard Peikoff (New York: Meridian, 1990). 75 For related discussions, see: E. J. Lowe, “What is the Source of Our Knowledge of Modal Truths?” Mind 121, no. 484 (2012): 919-950, especially p. 947; Kit Fine, “Essence and Modality” in Philosophical Perspectives 8: Logic and Language ed. James E. Tomberlin (Atascadero, California: Ridgeview Publishing Co., 1994), pp. 116; and Sydney Shoemaker, “Causal and Metaphysical Necessity,” Pacific Philosophical Quarterly 79, no.1 (1998): 59–77. But most importantly, see Oderberg’s Real Essentialism, op cit., particularly chapter 1, pp. 1-20.

Narrative and Direct Experience: A Dialogue on Metaphysical Realism Ernest John McCullough Saint Mary’s University College

Abstract: In this Platonic/Socratic dialogue, an imagined conversation takes place between Sophia (Wisdom personified), a recent philosophy graduate teaching in a university on contract, and a young student of philosophy. In this conversation Ernie McCullough guides the reader through the thoughts of the Greek philosophers Plato and Aristotle, of the Scholastic thinkers Boethius, Aquinas, and Suarez, and finally, of Descartes, the father of modern philosophy. McCullough believes the two Greek philosophers espouse similar doctrines regarding sense perception and intellect and their respective roles in the inductive process. This similar doctrine is then reworked and reshaped by Suarez and Descartes. McCullough’s main message is that induction is a cognitive process that works well within the metaphysical and epistemological context provided in the perennial philosophical tradition rooted in Plato and Aristotle. It only becomes problematic after this context has been radically altered by Suarez and Descartes, who provide a new direction for subsequent philosophical reflections. The narrative form of the dialogue invites the reader to reconsider contemporary forms of philosophical expression, which often emphasize argument, symbolic logic, and scientific method.

Characters N: Narrator, a recent philosophy graduate who specialized in Ancient Greek philosophy and is teaching on contract S: Sophia (Wisdom personified), a woman with both philosophical and historical insight Y: A young student of philosophy

360

Ernest John McCullough

Introduction Narrator: To what do we owe this visit, Sophia? Sophia: Oh, you recognize me? N: Of course. I have studied Ancient Greek philosophy and the classics. I recognize your fair countenance. What are doing in my classroom? S: Well, I fear that philosophy in the 21st century is in a sorry state. I have come to see whether anything can be done about it. N: What a happy coincidence to hear you say that! I was just talking here with my student and saying how philosophy, especially in the Englishspeaking world, has become more like a science. Young student: Yes, I decided to study philosophy in the hopes of gaining a better understanding of our very complex world today. But so far, I am finding that philosophy, at least as it is practiced in our philosophy department, does not seem to speak about the serious ethical and social issues facing us today. S: And that is why you are taking a course in Ancient Greek philosophy from a sessional lecturer in the Classics department: to see whether the first philosophers can still speak to us today. Y: I see that you are indeed wise and capable of sizing up a situation with meagre information. S: Well, I am called Sophia for good reason. But to answer your professor’s question, I have come because I am quite worried about the current state of philosophy. The vituperative treatment present-day philosophers reserved for Thomas Nagel, when he questioned the adequacy of evolution as a way of fully accounting for mind and consciousness, seems to me to be analogous to the treatment of heretics in the late Middle Ages. I would have thought that we had left such attitudes far behind. Instead, the response of many academics to Nagel’s latest book Mind and Cosmos has been dogmatic rather than reasonable. If the model for reasonable inquiry must restrict itself to reductionist “objective” discourse, and if one excludes the “subjective” and the historical, as is so often the case in so much of academic philosophy today, philosophic wisdom is threatened, I fear. Philosophy runs the danger of becoming peripheral to ordinary life, a pale image of what it once was as a rich source of insight and wisdom. Not only is reason threatened by such a narrow approach; the content of direct sense experience is lost in the emphasis on the quantitative as opposed to the qualitative. Y: Yes, as a newcomer to philosophy, I must admit that the angry treatment of Nagel seems rather unbecoming for philosophers. In my brief exposure

Narrative and Direct Experience: A Dialogue

361

to academic philosophy I have noticed that the scientific paradigm and the rationality of abstract symbolic logic seem to have blinded philosophers to their own un-philosophical behaviour. That is why I decided to learn about the wisdom of the Ancient Greek philosophers; but courses like this, sadly, are not offered through the philosophy program. S: For a neophyte you are already quite perceptive, and courageous. Look how you are carrying on without shame with Sophia in your presence. [Y blushes.] S: You are quite right, the scientific nature of much contemporary philosophy and its emphasis on abstract forms of reasoning and rational argument makes discourse in fields such as ethics and political philosophy, and even metaphysics, impossible. There is so much about human life that is not captured once you banish the subjective aspect of things and direct sense experience. Y: Excuse me, Sophia, but I cannot help but think of this passage from Aristotle’s Nicomachean Ethics, which I just came across recently: “There is a difference between arguments from and those to the first principles. For Plato, too, was right in raising this question and asking, as he used to do, ‘are we on the way from or to the first principles?’” (I.4.1095a30-34). There is a difference, as there is in a race-course between the way from the starting point to the finish line and the way back to the starting point again. S: And your point is…? Y: What Nagel is doing is walking along the path to first principles. In fact, he is inviting his fellow philosophers who have accepted a materialist and reductionist starting point to reconsider this limiting conception as a first principle when it comes to explanations of mind and consciousness and the emergence of life. This is the task of the philosopher, it seems to me, not the task of the scientist who merely accepts the respective first principles of his or her field and then deduces the logical consequences that follow from them. That is the path from principles to understanding. But we can also travel backwards from our experience or our explanations to the first principles we started with again. S: Hmm. That is quite insightful. Go on, you seem to have more to say. Y: Thank you. Those who criticize Nagel do not seem to realize this. They forget that materialism and reductionism are first principles, assumptions or presuppositions they have made about what is real. Their investigations, scientific or philosophical, follow from these presuppositions, but why shouldn’t we question them, especially if they seem to be unable to explain certain basic phenomena of nature? Contemporary philosophers seem to

362

Ernest John McCullough

have forgotten that there are two paths: the road to and the road from first principles; and that philosophy is especially concerned with the path to these principles. S: Yes, indeed. The passage you cite points to a common ancient distinction between two modes of reasoned discourse. The first is commonly referred to as induction and is usually conceived of as a “mode of discovery.” In inductive argument, as this is construed by most philosophers today, the truth of the premises does not guarantee the truth of the conclusion. However, traditionally, induction has often been characterized as a process of going from particulars to universal first principles. The second mode of argument, usually characterized as a “mode of proof,” is the deductive argument in which valid inference together with the prior truth of the premises guarantee the truth of the conclusion. Traditionally, the deductive mode of argument has been characterized as going from universals to particulars. There is a relation between these two modes which allows each to share in discovery and proof. Induction refers to the way we discover first principles; deduction refers to a process of the justification of claims based on those previously discovered principles. Y: And Nagel is inviting us to discover first principles that will better explain mind, consciousness, and the emergence of life than through the currently accepted principles of materialist reductionism. S: That is right. Now if you will bear with me, I would like to discuss something with your professor, who happens, after all, to be the narrator of this dialogue. Narrator, please come here. Let me pull you out of your usual background role in this text so that you can be a participant in this dialogue as well. N: Why would you want me to do that? S: Because I don’t think philosophers today appreciate your role and the role of narration. They want to be empirical or scientific or logical in an abstract, mathematical way. They equate reason with the deductive path from principles. N: Sophia, if you don’t mind, I think we should simply end the conversation and allow you to write your thoughts in essay form. After all, this is an academic publication, and that is the accepted form of writing today. S: To write an academic essay which explores the value of narrative in philosophy is precisely what I refuse to do. What is wrong with using the narrative form to explore the role of narration in philosophy? You seem to have forgotten that Plato, and even the early Aristotle, wrote dialogues to explore ideas philosophically. Even Berkeley and David Hume did so many

Narrative and Direct Experience: A Dialogue

363

centuries later. Surely, one of the motivations for that form of expression, at least in the cases of Plato and Hume, seems to have been to avoid reprisal and any negative repercussions from those in authority and who disagreed with the views expressed by these philosophers. To this day Hume scholars are still debating over which of the characters in his Dialogues Concerning Natural Religion speak for the philosopher. Given the reaction to Nagel, I think it is safer to present my own views in dialogue form. But, really, we should discuss the value of narration in philosophy and the role it should and could play in that discipline. 1 The Narrative Approach N: I am not quite sure where to begin. Perhaps we could start by noting that the root of the cognate terms narrate, narrator, narration, and narrative lies in words for knowledge, in Latin, gnarus, gnosco, and nosco, and point to the giving of an account by one who knows or is informed. S: So the narrator is the one who knows what is happening in the dialogue or, more generally, who knows the story being narrated. N: Yes, but I am not quite certain how narrative would work in philosophy today. Perhaps we could say that the narrator in a philosophical narrative could play three roles. To begin with, the narrator could introduce and conclude each section and help the reader discern the conceptual focus. Second, he or she could indicate which of the two processes of proceeding to principles and of proceeding from principles is underway in the dialogue. And thirdly, the narrator should perhaps supply a perspective on the relationship of reason to the senses in human cognition. This would shift the focus to the nature of consciousness itself as unifying principle behind all cognition. But I would think you already know this, Sophia. S: This conversation is not for my benefit. Do not forget that there is a young student here. Together we can all seek to understand and explain the value of the narrative approach in philosophy. N: One of values of narrative in philosophy is that it can offer a different notion of reason and rationality. This is particularly the case in discourse about ethics, which is of concern to my student here. S: Can you enlarge upon this point? How does all this pertain to our discussion about induction and its application to larger questions of social life and ethics? N: Contemporary academic philosophers are often skeptical about applying reason to areas other than empirical science. But the scientific method, which relies on direct physical observation, cannot cope with ethics, with

364

Ernest John McCullough

history, with evolutionary biology (which requires historical knowledge), or even with any cosmology in which possible worlds and reconstructions of the past are provided. An exclusive scientism overlooks the reasonableness of ethical and even other orders of discourse such as the aesthetic, metaphysical, historical, or theological. It also misconstrues the way in which deduction and induction apply in these areas. S: Yes, I see. N: Contemporary philosophers find it difficult to explain the relationship between different areas of philosophy. Thomas Nagel, for example, points out how difficult integrating neurophysiology and philosophy of mind with evolutionary theory is, particularly when it comes to consciousness of objects. In present-day biology, we have the rejection of essentialist notions of logic, as biologist Ernst Mayr would have it, and in physics, we encounter an essentialist and “platonic” endorsement of essentialism, as mathematician Roger Penrose has it. This disjointed theoretical anarchy, an inability to pull all the pieces together into one unified whole, marks intellectual disagreement in this age of specialization. We have made remarkable progress in different disciplines, but we have no way of adding all this knowledge up so as to produce one big picture. Y: Is this phenomenon widespread? N: There are important contemporary publications pointing to very different notions of reason which limit or expand different orders of discourse. Consider Alasdair MacIntyre who, in his text Whose Justice? Which Rationality?, points to a wider view of reason rooted in practices and tradition, and which may include a metaphysical viewpoint. He contrasts this with various notions of reason which exclude metaphysical explanation or which point to ethical reflections as rooted in emotion or rooted even in evolutionary biology. And it does not end there. Y: Go on. N: Well, look at the way in which different historical schools treat logic and philosophy. We have continental, Anglo-American, analytic, empirical, and eastern logical traditions. These varied approaches are too rich to ignore. Those who only accept the methods of empirical science as epistemologically valid uncritically and dogmatically exclude many of these approaches from consideration. S: Can you explain to the young student here why this matters so much? N: Well, how we understand logic affects the way we do philosophy in every field. We can distinguish between a non-historical, non-interpretative, and non-narrative approach to logic, on the one hand, and, on the other hand, an

Narrative and Direct Experience: A Dialogue

365

historical, interpretative, and narrative approach to logic. Contemporary philosophers, like the ones who attacked Nagel, only accept the first approach as valid and worthwhile. This makes it impossible to reason about larger issues like metaphysics and morality. S: So you think that if philosophy is going to contribute to the common good and to a wide range of important issues we need to recognize the importance of a narrative approach to logic. N: Yes, I think so. Narrative deals with concrete, lived experience, with immediate sense experience, with the historical, the interpretative, and the personal. It is particularly well suited for the exploration of ethical and political ideas and positions. S: How so? N: The narrative approach to philosophy presents lived and living experience of behaviour, actions, character, and cultural norms. These are all important elements in ethical considerations, and which a non-narrative approach cannot present. We can use narration to introduce and summarize an experience, to identify the cultural and historical context, to point out how we might apply a moral or political doctrine and discover its strengths and weaknesses today. S: Why is that? Why is a narrative better than a non-narrative approach? N: The formal, non-narrative approach deals with the systematic, the conceptual, the ahistorical, and the non-interpretative. It seeks to be literalist and “objective,” that is, impersonal. It deliberately excludes authorities and opinions, depending instead on abstract and numerical data and equations. It favours analysis, focusing on isolated ideas and propositions or on conceptual systems and their relationships to one another. It aims at “objectivity” to the exclusion of the subject. It ignores the role of interpretation or context. When it considers moral and ethical questions, it is non-situational, rigid, abstract, and universally prescriptive. S: So it is not suited for discourse on ethics? N: No, it isn’t. In ethics, providing the historical context helps in understanding the meaning and significance of social realities such as love and friendship. There is an element of the subject or subjective introduced as well. We can better access all this using narration as our philosophical method. S: Understanding human behaviour ethically, means more than linking together a mere sequence of discrete un-interpreted events? N: Of course! It requires a direct encounter with the habits and personal histories of individuals and the cultural norms of a community. In teaching

366

Ernest John McCullough

Ancient Greek philosophy, for instance, knowledge of 4th and 5th century Greek culture grounds our discussions on ethics and politics. We cannot properly understand and assess the arguments found in the writings of Plato and Aristotle without some familiarity with the social practices and institutions through which ethical notions such as love, friendship, or justice were expressed in the Greek world. Y: And the same applies today, I suppose. N: Indeed, one always has to consider the wider social and cultural context. It provides an indispensible framework from within which human actions are to be understood. This applies to all historical periods. S: Alright, but let’s stay on topic. You suggested that there are other important qualities of the narrative approach. N: A narrative method begins in lived experience. In Plato’s Symposium, for example, each speaker makes a speech that dovetails with the known qualities, the character, personality, and past behaviour of that participant. They do not speak like academics writing papers! They speak like living individuals would speak, out of the specificity of their lives. In his Philebus Plato speaks about the balance between the reasonable and the emotional in a fulfilling human life. Life is about experienced and expressed emotions as well as about concepts. This is part of the living experience communicated in a narration. Aristotle’s Nicomachean Ethics, although not in dialogue form, follows a similar form with examples and references to Greek ideas of how good and bad people act. S: But if this is what makes narration different, doesn’t this require historical accuracy? N: Yes, but old actions, habits, and cultural norms can be made present, even if only partially or incompletely, through the magic of skilful writing. Unlike bare argument, narration can identify and communicate qualities of soul, that is, mind and character, to be shared by readers living in different historical periods. It can achieve a kind of direct disclosure that is otherwise unavailable. Of course, the writer must possess a gift for a certain descriptive and poetic intuition, but the universality of the experience of love and friendship is such that it deeply touches people in all historical periods. A direct retelling of a philosophical conversation between friends can secure the credibility of the account. It can even communicate the meaning of ancient friendships in a contemporary medium. S: But Aristotle’s extant writings are not dialogues in narrative form. N: He did write dialogues that are now lost to us. But it still does not matter in his extant writings. His writings on ethics and politics presuppose a

Narrative and Direct Experience: A Dialogue

367

specific historical and cultural context. As a professor teaching these works, I must act as a narrator telling stories of persons living within that context. The narrator is both a story teller and as well, a descriptive expositor. My role is to put primary emphasis on the story of people living in a specific historical period and the experience which the story illustrates. I see my role as narrator as one of placing the direct experiences related by the stories at the forefront of the process of discovery, hence, primary. S: You seem to be referring again to the path of discovering principles. N: Yes, the principles of ethics must be acquired from the direct experience of human beings living in a specific social setting. S: I take it from this, then, that for you the ultimate ethical ‘principles’ are actions, habits, and cultural norms all accessible through immediate sense experience? N: Yes, but I would see this experience enriched by the powers of imagination and memory as integral to consciousness. Without contact with direct experience all argument suffers from a lack of principled ground. In the Symposium, the Philebus and the Nicomachean Ethics, to only refer to the works mentioned above, the sensible ground lies in the practices and experiences of the individuals that composed Greek society at the time. Aristotle’s own approach integrates the intellect and emotion as much as Plato’s Philebus. (Cf. Nicomachean Ethics VII.3.1147a27-31.) S: So the narrative approach has the advantage over the non-narrative by offering us a direct description of the recounted experience with emotional content and a reliable description of particularity? N: That’s it exactly. Reason must be anchored in the reality of lived experience. In narration, the senses—what one observes and hears and then reports—can become the crucial starting point for an inductive dialogue that goes back and reconsiders first principles. Without the initial direct experience and the final probative experience, our philosophical explanations are circular. They are isolated, insulated from the world. Because narration is closer to what we immediately experience and feel, it is closer to the ground of our beliefs. 2 Direct Experience S: Direct experience becomes crucial then in acquiring principles of ethics? N: Yes, it is unavoidable. Sense perception and experience are the starting point for the path to the first principles. Induction cannot occur without recourse to sense perception. S: Aristotle definitely acknowledges this.

368

Ernest John McCullough

N: True; however, there is some ambiguity in the Aristotelian account of sense perception when he distinguishes between proper sensible objects and common sensible objects. Clearly, the senses cannot err in their approach to the sensibles that are proper to one of the five senses. Sight, for instance, cannot err about seeing light and colours. But sensation can err with respect to sensibles common to more than one sense; that is, sensations involved in attributes of objects such as motion and magnitude can lead to problems with accuracy (De Anima III.3.428b22-24). In addition the senses can only accidentally or indirectly lead us to conclusions about the substance or nature of things: that Socrates is a human being, say. One could be mistaken here, too. The example Aristotle uses is that one is not deceived about the fact that there is white; we can, however, be deceived about whether this instance of whiteness is this thing or that thing (De Anima III.3.428b19-22). This Aristotelian account follows a similar account to the Philebus, which contains the same example of whiteness (Philebus 53a-c). S: So the senses, then, are not entirely reliable? N: Later commentators such as Thomas Aquinas and Albertus Magnus take the notions of imagination, memory, and judgment as subject to error but not the senses as passive receptors in themselves. Since the five senses are passive receptors, and are not active in judgment, they are reliable. However, confusion may arise when common sensible objects such as magnitude and motion form a large part in cognition. The difficulty becomes epistemological if cognitional being (the “being” we apprehend with our mind) and real being (being as it actually exists out in the world) are confused. The Platonic distinction between the existence (an est) of whiteness and the nature of the object (quid est) becomes central to the realism/anti-realism debate. S: But consider the many ways in which the senses deceive us. We do have mistaken impressions such as the judgment that there is an imagined lake in the distance or that the oar in the water is broken. In addition, deceptions multiply when we take into account other experiences which involve pleasure and pain. We may be mistaken in believing a particular pleasure is also a good, something good for us. N: It does seem that we have reliable and unreliable impressions, and genuine and counterfeit pleasures, but these are matters of interpreted judgments based on the exercise of reason and not on the senses themselves or the action themselves (Philebus 40a-d). S: Yes, but how can we distinguish between “reliable” and “unreliable” in sensations or “genuine” from “counterfeit” in pleasures?

Narrative and Direct Experience: A Dialogue

369

N: We can distinguish by the use of intelligence or reason in both cases. If we follow Plato’s thoughts in the Philebus, in understanding pleasure and pain in sense experience, there is a balance; some kind of a continuum in both pleasure and pain is discerned through the application of intelligence and reason. S: Can we distinguish between a sensation which involves judgment and one which does not? N: The distinction lies in the act of the intellect. The sensation is passively received and cannot be in error. Judgments are active and often in error. S: Doesn’t judgment involve both reason and interpretation? N: Reason and interpretation are involved in judgment. S: What is the relation between reason and interpretation? N: Reason is a faculty which exercises a power to understand. Interpretation is a reflective act which supports and advances reason. Reason need not check all of the immediate experience, but it can achieve greater clarity by paying close attention to its content. S: But we were just talking about Aristotle’s views. What does this have to do with Aristotle? Are you suggesting that Plato’s views in the Philebus are identical to Aristotle’s on this matter? N: Yes, I do see a resemblance in their views when it comes to understanding the relationship between the senses as passive receptors and the intellect as active judge. S: Suppose we assume that the senses are reliable, that we can trust the content of our perceptions, how then is the universal principle induced from experience? Gadamer thinks that “Aristotle ingeniously left open the question of how universal concepts are formed.” He simply assumed “that the natural process of concept formation by language [was] always already going on.” In this sense, nothing is decided by prior epistemological commitments. “Concepts by language possess a perfectly undogmatic freedom” (Truth and Method, p. 430). N: In the passage to which Gadamer refers, that is, Posterior Analytics II.19, Aristotle provides a metaphor of the retreating army in which the army ultimately takes a stand much as one might take a stand with sense experiences. This particular example of a retreat is ambiguous, for the notion of induction has multiple meanings in Aristotle. It does appear, in fact, that we can use the term “induction” in several different ways. It may refer to: (1) the mental movement from particular to general, (2) the inductive syllogism (which is really a kind of abduction that reveals an

370

Ernest John McCullough

essence as in Peirce), or (3) an exercise of intuition (the epagogic type of induction) which only incompletely reveals an essence or nature. S: Given this ambiguity, Gadamer’s skepticism about a clear explanation would make sense. Further exegesis is needed. Often, as in epagoge (3), the essence of the thing is only revealed partially and gradually, not instantaneously and completely. So concept formation can be a mysterious process. Are there other instances in Aristotle of more specific focus on the formation of universal concepts? N: Aristotle certainly noted the contributions of Socrates and Plato to the question. In Metaphysics XIII, he attributes two things to Socrates: “inductive (epagoge) arguments and universal definition,” which he says, “are both concerned with the starting point of science.” Although Socrates was, first and foremost, a moral philosopher, he was, according to Aristotle, “seeking the essence, for he was seeking to syllogize, and ‘what a thing is’ is the starting point of syllogisms” (Metaphysics XIII.4.1078b18-34). S: So induction from direct experience can lead to a universal definition of a character trait or a moral excellence? N: Possibly. But let’s stick with the example of whiteness to better make the point. The observation of an object as “something” is the first apprehension. Both Plato and Aristotle recognize this in the “whiteness” of a white object apprehended as an object of perception. Even if there has been a deliberate attempt to deceive, then, despite this, the white object is still known as a white object. We could be confused, of course, about the “nature” of the object. Perhaps that white bit of snow is really white sand, or a bit of white cloth, or the glare of the sun. If it becomes clear under further inspection, then a modification of “what it is” in the mind of knower is required (if cognition is to genuinely occur). S: But this is confusing. How can the universal be integrated in the individual? How can, for example, the universal “whiteness” be joined to, say, this handful of white sand in the manner in which Plato seems to endorse in the Philebus? N: Well, this is a difficult point. I admit it. Universality and particularity have a difficult and seemingly contradictory status in the concrete individual substance. It is precisely at this point that the special role of epagoge becomes crucial to understanding the role of partially disclosed essence in the concrete individual substance. We can confidently know that the substance is (an est) if the senses are reliable, and we can know that there are essential qualities that compose the substance itself (quid est). The inductive process involves a mental illumination that grasps an intelligible

Narrative and Direct Experience: A Dialogue

371

form such as whiteness in our immediate experience. What is lacking is the complete disclosure of the essence itself, even though its existence is a necessary condition for successful cognition. S: Would you then maintain that the an est of existence, and the quid est of apprehension are complementary but distinguishable aspects of the sensible object itself? And do you think that Plato’s position on this is complementary to Aristotle’s stance? N: Yes, I do. That something is and what something is are complementary cognitional principles for Plato, just as for Aristotle matter and form are principles in real existence. This distinction of an est and quid est is recognized and endorsed by Plato as being part of the epagogic process. The function of epagoge is to bring these two aspects together; this is how knowledge originates. S: There is a particularly puzzling part of the first book of Aristotle’s Physics that refers to universals as first in the order of cognition and to the particular as last in the order of cognition. According to this disputed passage, “what is to us plain and obvious at first is rather confused masses, the elements and principles of which become known to us by later analysis. We must advance then from generalities to particulars; for it is a whole that is best known to sense perception and a generality is a kind of whole, comprehending many things within it like parts” (Physics I.1.184a23-26). But this seems backwards! Wouldn’t this text reverse the usual view of induction as moving from particular to general and replace it with a process of moving in the opposite direction from the general to the particular? N: In fact, this sort of thing would be possible in an epagogic process in which we start with the universal concept. Aristotle’s meaning here is that it is the concrete sensible whole that is more cognizable by the senses, but it is also known by the intellect vaguely through very general properties. He goes on to make it clear that the general properties which are initially unclear come to be understood in terms of more specific principles. We initially see, for instance, that this shape is a human being. But what is a human being precisely? We need to analyze the whole set of properties attributable to human beings to come to see which organization of principles explains it. The universal “whole” in epagoge is the first step in discovery. S: So this is like Plato’s example from the Philebus, where the existence of the object resting under the tree can be reliably sensed but the character of the object, or what it is, remains a discovery ahead for the knower. N: Yes, so what it is, precisely, becomes clear after considered epagogic judgment.

372

Ernest John McCullough

S: But this also seems to lead us to a serious difficulty, since the initial “universal” is experienced as confused and obscure. This hardly supports the notion that the senses are reliable. N: In fact, Aristotle makes a twofold distinction. He maintains that the universal is more knowable in the order of explanation, and the particular is more knowable in the order of perception. He points to the passivity of the sense organ which is activated in response to a sensible object. The senses cannot err since they do not ‘act’ but are acted upon. The receptivity cannot be in error, although what the receptivity reveals (what it is) can be falsely judged (De Anima III.3.428b1-20). Plato could easily endorse this account. S: So there is no deception in what the senses receive? N: Again, this is not the right way to describe it. “Deception” always involves the misuse of an active power. The senses are passive receptors. Truth and error lie in judgment, not in the senses; hence, the senses cannot truly “deceive.” They operate passively and receptively. The senses do not create but receive, much as a radio receiver receives messages but does not itself create responses. Again, the senses make present the image to the knower. S: Hmmm, the senses cannot deceive. We can take that as a universal principle. N- The imagination plays a role here, for it creates an image based on the initial sensation, say, of something visible under a tree. The first judgment based on the initial sense perception could be that the object is a human being, but the observer might be misled. Suppose shepherds made a humanlike figure out of rocks on a ridge as a landmark. The observer thinks: there is a human being. Maybe he “remembers” (through an image called to mind) that he saw a human being over on the ridge. There is a conflict here between the reality and what he “remembers.” But the problem lies with the judgment that what he saw was a human being. It is still true to say that he saw something that looked like a human being. S: Can this not lead to skepticism about the first, initial experience? N: Indeed yes, but the skepticism also has to do with the act of judgment as to the nature of the object. Error lies in judgment and not in the sense. Aristotle confirms the source of the error when he speaks of the sources of “sense illusion.” The senses are never, strictly speaking, in error in their making what they perceive present to the observer or in the actualization of a potentiality of the senses. Only the judgment of the nature of the object,

Narrative and Direct Experience: A Dialogue

373

or of what it is, can be in error. The distinction between an est (that it is) and quid est (what it is) in knowing is crucial to this clarification. S: So would the false empirical claims that Aristotle makes as the Physics proceeds through books VII and VIII be errors in judgment? N: These well-known mistakes about projectiles and free fall of bodies arise from Aristotle’s reliance on everyday experience. Unfortunately, he was wrong about these gravity or projectile related cases. Plato, in thinking that anti peristalsis or of peristaltic action was analogous to digestion, also had it wrong; but his attempt at explanation is still important. The interesting point, which arises from the mistaken notions of both Plato and Aristotle, is that they both tried to provide empirical explanations. They looked, at least, for cogent demonstrations and explanations out of a sense of critical responsibility. They realized that knowledge must be able to answer conundrums and resolve difficulties. S: So, you are absolutely convinced that the primary senses are always reliable and not, as so many observers contend, a source of uncertainty and subjectivity. N: The senses provide, in fact, the very ground for objectivity. Knowledge arises out of sense perception, “for although the act of sense perception is of the particular, its content is universal” (PosteriorAnalytics II.19.100a16b1). The actualization of the universal arises from the epagogic process. S: We have now returned to the passage from Posterior Analytics. N: Only a consideration of Aristotle’s metaphor of the retreat of the army can provide an understanding of induction as a function of the intuitive presence of the universal in the soul. This presence can account for the universal concept of standing firm. What matters is not so much a summation of a group of experiences, but the single stop of one retreating individual which brings the whole army to a halt. The rest of the army recognizes the noble concept of standing firm. The source of the army’s stand is not a syllogism about the general concept of bravery. It lies in the direct experience of a comrade who stops and provides an instance of individual bravery in the midst of general cowardice. It is the general intuition of bravery which inspires all to stop and stand. Plato would be equally supportive of such a brave stand. I think that everything I have said with regard to Aristotle is also valid with regard to Plato. Y: What? Just a minute! I have been listening patiently all this time; I know I am only a student but how can you say such a thing! I have noticed that on a number of occasions you mention Plato while presenting Aristotle’s position. Are you really suggesting that there is a harmony about their

374

Ernest John McCullough

philosophical positions on induction? Do you really think that Plato and Aristotle are in agreement about the relation between the senses and reason or about how reason requires sense experience to acquire principles? This does not seem to be what I have read in Plato’s dialogues. Surely, Plato opposes the senses and reason, viewing the senses as an obstacle to knowledge sought by the soul, which alone can acquire knowledge. The difference between Plato and Aristotle is strikingly portrayed in Raphael’s famous painting “The School of Athens,” which I saw when I visited the Vatican once. On the one hand, we see Plato pointing upwards, professing the reality of transcendent forms and, on the other hand, we see Aristotle with his palm facing downward, indicating the presence of the forms in matter. You obviously see a harmony where I do not. S: Young man, you have raised a large and contentious issue that many philosophers have argued about. We cannot delve into it in detail now. But perhaps you can briefly say something about it to allay the young student’s concerns. 3 Digression: Harmony of the Late Plato and Aristotle N: My own conviction is that not only do Plato and Aristotle agree on the dependence on sensation but also on the importance of narrative in recognizing this dependence. Sensation plays the role of the ground from which the narrative develops. It provides the ground from which both physical reality and intentional acts can be established. In the Symposium, for example, the account of Diotima tells us that the instructor begins with one beautiful body “so that his passion may give rise to noble discourse” (210ac). The dialectic leads us to a higher level of understanding. The combination of intellect and bodily sensation is counter to current views regarding the unreliability of the senses. Y: But even in the Symposium, Plato insists that we must move away from the senses and towards non-sensible manifestations of the Form of Beauty. This does not seem to show any dependence on sensation. N: Neglect of the senses in Plato constitutes an unbalanced account which needs to be reviewed carefully. This is particularly the case today with the growing power of a post-modernist tendency to see realism in the forms of claims of truth as misguided. The harmony between Plato and Aristotle is most clearly shown by focusing on Plato’s late dialogues. A case must be made for a substantial change in meaning or a more principled shift in the later dialogues. Plato does provide a shift in method involving different

Narrative and Direct Experience: A Dialogue

375

characters and a far different model of reasoning. This shift in dramatic personae is not accidental. Y: I have heard that the character of Socrates almost disappears entirely from these dialogues. N: For those Plato scholars, like Gregory Vlastos, who believe he is a systematic thinker, a difficulty arises when openness to change and development become part of the virtue of the thinker. Plato shows this openness very explicitly in the Philebus when he admits: “I must have weapons different from those of my previous arguments” (23b). This statement constitutes notice that there is an evolving consciousness in the late Plato. Y: So you are suggesting that Plato’s initial position, in the early and middle dialogues, which presents the senses as an obstacle to knowledge changes in the late dialogues where he has come round to viewing the senses as an aid to knowledge? N: Almost. The middle dialogues show that Plato is already starting to rethink his philosophical positions. The shift in the role of the senses is closely tied to a related change in attitudes towards the Socratic elenchic and the introduction of Forms, as demonstrated in the Republic and the Symposium. Plato’s understanding of reason and its methods is simultaneously being rethought. Finally, when Plato reports on logical method in the Philebus (15-17), he promotes a change in the mode of argument from excessive focus on the elenchic concern with contradiction and disputation, which involves refutation, to a more positive mode of argument involving an epagogic approach rooted in discovery, “the parent of all disclosure in the arts” (Philebus 16-18; cf. Republic 556c and 472a). The ultimate reliance on the senses is recognized in the way Plato divides up knowledge and wisdom in the later dialogues, the Sophist, the Statesman and the Laws. Y: Can you provide any other evidence to substantiate your claim about the harmony between the late Plato and Aristotle? N: The Philebus points to three possible logical methods: the eristic which deals with the disputes over words, the elenchic which deals with instances of contradiction, and the epagogic which deals with principles of discovery. All accord well with the Aristotelian accounts of logical process in the Organon. Y: Anything else? N: There is even a literary connection between the Philebus (38e) in which the soul is like a book to be written in and MetaphysicsIII (4.29b30-430a2) where the tabula rasa or empty tablet appears as model for the mind. Recall

376

Ernest John McCullough

the example of whiteness already mentioned earlier: Aristotle borrows it from the Philebus. Y: Yes. N: When commentators refuse to see the role of direct experience in the late Platonic works, it is evident that the Laws, a very late work, does not form a significant part of their interpretation. The doctrine of Book X provides all the evidence that one needs that Plato has moved physical experience and the direct experience to the order of much more than complementarity if not identity with Aristotle’s doctrine of Physics. Can one explain this away without recognizing that the doctrine of the Laws is a radical acceptance of direct sense experience as essential to the mature Platonic doctrine? Y: So there are many similarities? N: Yes, many! For example, Book X of Plato’s Laws provides a short form of the argument which Aristotle advances in Book XII of the Metaphysics and Book VIII of the Physics for a Primary Cause. Aristotle argues that there is a primary cause of motion and being. It is as if he is following in the footsteps of Plato. Y: And what should we make of all this? N: Well, Socrates provides the key to the Philebus (64b) when he associates a blended notion of the good as both the intellectual and the pleasurable with the idea that there is a non-corporeal order or form that governs the individual from within. This order does not come from outside the individual. (Do not be distracted by the use of the word “kosmos” in the text!) The general argument of the Philebus makes it clear that the “disembodied order that will govern well an ensouled body” is an internal order and a matter of spirit. In late Plato then, the forms have become internalized in the individual, which explains how the real can be directly experienced inside the mind. But this is Aristotle’s position! Y: So you believe that the Philebus establishes that Plato had exchanged, by that point in his career, his original view of the Forms as paradigmatically external to the individual for a realism based on direct apprehension of forms within things. N: Yes, that is correct. This new account is carried through in the Sophist and the Statesman, where classification and ultimate insight into reality are the result of a refined division and separation. Much here hangs on the interpretations of these late dialogues and the feasibility of holding on the more developmental view of Plato which I endorse.

Narrative and Direct Experience: A Dialogue

377

Y: I am in no position to know whether you have sufficiently proven your point; however, it does seem more plausible to me now than a moment ago. S: Your position would certainly make of both Aristotle and Plato the founders of the tradition of metaphysical realism. It certainly illuminates your views on narrative and direct experience. N: Yes, and the tradition of metaphysical realism continued, for the most part, throughout the Scholastic period. Granted Plato’s realism was not understood as I have argued. Most Scholastic thinkers, because of their Christian worldview and limited access to Plato’s corpus, understood the Platonic Forms as exterior exemplars existing in the mind of God. Yet, the element of direct experience with an objective reality still remained, for knowledge of the Forms required knowledge of the mind of God on the part of the knower. So the Forms inside the mind of God had to somehow enter into the mind of the individual knower. 4 Loss of Metaphysical Realism: The Transition in the Late Scholastic Period S: If your case is that direct experience is the most reliable source of understanding, and that this philosophical tradition lasted through to the Scholastic period, you need to explain to our young student here why science shifted its focus so dramatically away from the sense experience to the hypothetical and the deductive in the 16th and 17th centuries? I know the answer, but our student can’t be expected to resolve such complex historical problems on his own. N: Indeed, this question requires more than a cursory answer since the notion of disengaged reason and the ultimate independence from sense becomes the common understanding and part of the Enlightenment program. But I will limit myself to providing a cursory answer for now. Simon Blackburn suggests that the starting point for any answer must be with Descartes, since he is our immediate source for modern philosophy. We tend to associate Descartes with the notion of innate ideas, but he himself is rather modest about this aspect of his view. He affirms, for example, “I never wrote or concluded that the mind required innate ideas which [are] in some sort different from its faculty of thinking, but when I observed the existence in me of certain thoughts which proceeded not from extrinsic objects nor from distinctions of my will but solely from the faculty of thinking which is within me, then that I might distinguish the ideas or notions which are the forms of these thoughts from other thoughts adventi-

378

Ernest John McCullough

tious or factitious, I term[ed] the former innate” (Descartes, “Notes Against a Programme”, in Haldane and Ross, Descartes, p.442). Y: So why is this notion so important? N: We have considered engaged reason as one related to induction and epagogic sense experience, as developed in Greek and Scholastic thought. A paradigm of disengaged reason, a reason disengaged from either extrinsic or transcendent objects, appears in Descartes’ notion of innate ideas. Because Descartes places the ideas-forms in the human intellect, this obviates the need to refer either to transcendent forms in the mind of God or to forms intrinsic in sensible objects. Y: Is this the first time that the forms of Greek Platonic and Aristotelian origin had been given an intrinsic, independent reality in human thought? N: I am not sure, but as Blackburn notes, Descartes provides the pivotal point for modern philosophic thought about methods, objects, and even about notions of objectivity; yet, Descartes’ sources lie deeply in Scholastic and post-Scholastic thinking. S: Yet many philosophers today believe that references to precursors of Descartes are extremely complex and unnecessary for understanding our own time and our own philosophic world. N: Such an attitude seems entirely out of sympathy with my references to the Greek tradition with respect to induction and epagoge, as I have developed it thus far. But this has not been an arcane and valueless conversation. Recent scholarship has shown how much Descartes and 16th century thought is indebted to its predecessors. There was an obvious opening for philosophers who could provide the program to meet the demands of the time. Suarez, the Jesuit commentator, and Bacon were such thinkers. Y: But is it possible to discuss this pre-modern period without getting bogged down in historical and linguistic problems beyond the limits of our discussion? Do we really need to go back to pre-Cartesian thinkers to understand the position of Descartes? N: That historical background can be quickly examined with benefit. We can show the origins of the non-representational doctrine of ideas focused on consciousness itself which Descartes promotes, a view still championed today by authors such as Rorty. The implications for our understanding of science are enormous as they undermine traditional notions of truth and realism. Y: Go ahead; I am listening.

Narrative and Direct Experience: A Dialogue

379

N: We must discuss at least three important thinkers prior to Descartes in order to see the shift in notions of induction which underpin our own time. These thinkers are Boethius, Thomas Aquinas, and Francisco Suarez. Y: Why begin with Boethius? He is not a figure of the Scholastic period, is he? N: Boethius is a key transitional figure in the development of a Scholastic account of logic. Beyond that, he is one of the notable thinkers who saw a harmony between Plato and Aristotle. It was his ambition to make them accessible to his own time. His work the De Hebdomadibus, one of his theological tractates, is the best place to start. Y: A theological tractate seems an unlikely place to gain a philosophical understanding. N: We need to go back to our earlier discussion and differentiate between the existence and the nature of the thing. Boethius mentions the distinction between esse and id quod est in this work (De Hebdomadibus Regula 1-2). As I have argued, both Plato in the Philebus and Aristotle in the Posterior Analytics make the same underlying distinction. For example, in the Posterior Analytics Aristotle distinguishes between existence and essence: the fact that a man exists and what human nature is, are not the same things (Posterior Analytics II.7.92b10-12). Boethius notes that the distinction applies to accidental predicates as well, making use of our previous example of “whiteness” to show this point (De Hebdomadibus Quaestio). S: But there also other thinkers commenting on Boethius’s text who point to the same distinction. N: Of course, that’s true. Thomas Aquinas, in his commentary, endorses a similar account of the realism of entities and provides a further focus on the reality of “whiteness” (Expositio super librum Boetii De Hebdomadibus II A 1 a). He also takes the word hebdomadibus to be based on the Greek word hebdomado, which means edere, which in turn refers to “editions” or “conceptions” (Expositio super librum Boetii I B 2). In Thomas’s account, there is a faithful interpretation of Boethius that follows the Platonic tradition in viewing participation in an essence as participation in an extrinsic form, an interpretation which accords well with the common understanding of Plato in Thomas’s time. S: The tradition seems to be intact up to Aquinas. Y: But how do we get to Descartes from Aquinas? N: Descartes took pride in avoiding authority as a source of his ideas and refrains from citing authorities in his key works. He does, however, mention Suarez in several places. Given his studies at the Jesuit school at La Flèche

380

Ernest John McCullough

(Hume studied there, too), he was bound to be well aware of Suarez and the role he played in 16th century thought. Durandus, a Dominican, and Francisco Suarez, a Jesuit, are of particular interest in determining the sources for Descartes’ doctrine of innate ideas. Y: So, please, let’s focus on their pivotal contribution and leave aside Aquinas, who must have seemed very old-fashioned by that time. N: Indeed, let’s focus on the notion of “innate ideas” and how it develops from Durandus and then Suarez and see how all this relates to epagoge or induction. Durandus was a 13th century Dominican who did not follow the teachings of Thomas with respect to objects of knowledge, to which he refused entitative status in consciousness. In his sympathies, he was Augustinian with respect to the “inner word” and Scotistic with respect to the possible and the modal. But the details are not so important. What is important is that his work marks the beginning of a slide away from understanding cognition either as a participation in Divine Ideas or as the abstraction of forms from physical bodies, as in the interpretations of Plato and Aristotle current in his time. S: But Durandus of Saint-Porcain is a minor figure. N: Yes, but Suarez often uses Durandus as a foil in his influential discussions with opponents. Y: So, what did he argue? N: To begin with, Durandus argued, like Augustine, that Divine Ideas are exemplars and common notions determinative of things arriving at essence through their participation in the Divine Essence (In Petri Lombardi Sententias theologicas commentariorium I, D. 36, Q. 3, 6). The essence of a rose, say, is the “objective idea” first present in the Divine Essence (In Petri I, D. 36, Q. 3, 12). Outside of God, this objective idea is then the nature of the thing, of the rose, in this case. Finally, within the intellect of a human knower, the nature is given an intentional mode of existence (In Petri I, D. 36, Q. 3, 13). Y: Now what is wrong with that? N: Well, Durandus is not clear on the details. When it comes to describing human knowledge, firstly, it appears Durandus does not rely upon the objective idea present in the Divine Essence. Secondly, if there were an intentional form in the human mind, he says it would be known first; but he also claims such an intermediary is not immediately grasped (In Petri II, D. 3, Q. 6, 84). Truth, he says, is to be seen as the mental thing as understood in conformity to itself as it is in nature. True and certain knowledge turns out to lie in reflection on our mental operations, the acts of intending

Narrative and Direct Experience: A Dialogue

381

natures; it is not seen in some likeness or representation either in sense or in intellect. Durandus does not explain clearly what the relation between the “subjective” character of the idea in the human mind and the “objective” character in nature is. S: Of course, this problem had already been examined in detail in Plato’s Parmenides. Y: Let’s not get off track, please. So you believe that Durandus’ view is not a “representational view”? N: Well, it does seem a little more complicated than that. It does appear that he provides a direct relation between the natural object we call the rose and sensation, in a manner that might be similar to that of Ockham. The senses are affected by the rose, the prickly, pink, beautiful thing out there. Durandus believes that, somehow, there is a simple and direct cognitive relationship between the extrinsic object, the rose, and the senses. Y: And how does the more famous Suarez provide a different account? N: Suarez provides a different explanation of Divine Ideas, objective ideas, and truth. In the Disputationes metaphysicae XXV, he maintains that the idea or exemplar or form is not an intrinsic form that constitutes the thing’s essence in the Divine Essence, as in Durandus, but the form simultaneously conceived in the human intellect and extrinsic to it as a pink and a prickly object. As in Plato, the experience of knowing is both subjective as involving an aptitude and objective as revealing a pink, prickly thing out there. Note, however, that it is not one form alone that establishes judgment as to the nature of the object. The rose is prickly and pink, each of which are forms. The rose, or any other thing, is conceived as a number of different forms somehow combined together in the one thing. Y: I don’t understand. N: Suarez had earlier identified a distinction in the human mind between the formal and objective concept. The formal concept is the act of the mind in knowing the rose; the objective concept is that which is known or represented through the act of knowing of the mind. This activity-idea (form-content) distinction only applies to the human mind. In the Divine Mind, the exemplar or idea is known directly, without intermediary. There is no divide between activity and idea (form and content). God’s ideas are known by God as implicit tendencies to themselves. They exist as modal alternatives or possible realities, not as something external, an act which is a mere function of reason (Disputationes metaphysicae XXXI, s. 2, 10). Y: How then do ideas exist in the human mind?

382

Ernest John McCullough

N: Against Durandus who argued for an act of the mind without any intelligible form, Suarez argues that the verbum or “inner word” of “rose” is distinguished modally from the act of the intellect (Disputationes metaphysicae XXV, s. 4, 2). It is as a disposition rather than as a thing that the idea of a rose has existence in the human mind. This verbum is not a representative entity because its reality is based on a logical aptitude involving non-repugnance or non-contradiction in understanding or knowing the rose as pink or prickly. According to Suarez, truth refers to real dispositions or habits of the intellect which express a real union in the aptitude between one thing and another. Y: Can you elaborate a little more fully? N: The rose as conceived is not a third thing between the mind and the actual rose. The rose as conceived is a quo, or that “by which,” the actual rose is understood. Suarez identifies this “by which” with a tendency in the mind, or as a modal object, a possibility, a really possible rose. There could be room for a non-prickly or non-red rose as a possibility (Disputationes metaphysicae, XXV, s. 1, 4). The doctrine provides a gloss on the Thomistic position that there is no mediating quod, or “thing” (which is known in the mind), between the mind of the knower and the external object. In other words, for Suarez, the conceived rose is recognized in the tendency but not as a representative object or a quod. In this way, Suarez provides a sophisticated and attenuated understanding of intentionality. Y: How do these doctrines of Suarez with respect to Divine Ideas, and formal or objective concepts, play out in Descartes’s interpretation? N: It is clear that Descartes’s training at La Flèche brought him in touch with the Scholastic controversies over Divine Ideas, intentional objects, and representative and non-representative notions of truth. It is clear that he takes one notion of eternal ideas as indefensible, namely, the notion that there are eternal truths that exist, such as those of three-sided triangles even if, per impossible, God does not exist. Y: Is this notion of per impossibile truths from Suarez? N: This idea might be associated with Suarez, but it is not clear that Suarez held such a notion of eternal truths or that Suarez is Descartes’s adversary. Descartes, however, is thought to have accepted some notion of possible truths in the Divine Mind with connections going back to Suarez and eventually to Scotus. His doctrine of formal and objective reality seems to have Suarezian elements in the dispositional and modal account of ideas in the human mind. Y: Where does Descartes express these ideas most clearly?

Narrative and Direct Experience: A Dialogue

383

N: Descartes, in “Notes against a Programme” (which I have already mentioned) does provide such a dispositional account of human cognition similar to that provided by Suarez. This is a doctrine of an aptitude or disposition in the human mind. S: It does seem you have sufficiently shown the background to Descartes’ views on the matter. N: So I will make my point, then. Boethius and Thomas argue for a direct realism, while Suarez provides a modal explanation based in dispositions of the human mind. Descartes, following after Suarez, assumes that knowing is primarily a mental disposition. Having given up on the immediate, epagogic experience through the senses, reason seeks an explanation drawn from consciousness itself. This constitutes a conceptual revolution in itself: knowledge comes about through introspection rather than through direct contact with the world. Y: What you are suggesting is that Descartes replaced notions of inductive understanding or epagoge in sense experience with the notion of innate ideas, ideas within the human mind, known through introspection. N: According to the Suarezian account, truth accrues to the human mind insofar as the acts of the will applied in judgment depend on God. For Descartes, truth is revealed in clear and distinct ideas (including that of God). In both cases, reason is disengaged from immediate experience. Y: And this eventually led to the modern Humean skepticism about induction? N: Yes, it all begins with Descartes; and even his approach has historical antecedents. As I have tried to briefly show, his mentalist account is rooted in Scholastic and Jesuit speculations insofar as they put reason and truth at a distance from the real. The reality of the world beyond our minds is pushed out of reach, and contact with our own mental dispositions and the logical relations between our ideas becomes the ground of truth and metaphysics. The doctrine that logical distinctions correspond to real distinctions provides a further rationale for this disengagement. Y: But how did the Suarezian and Cartesian account enhance modern scientific explanation? Science is said to be empirical, and yet, you are suggesting that reason has become disengaged with empirical reality. This is a real paradox! N: This new approach shifted the sources of explanation to orders of hypotheticals and to direct and repeatable quantifiable observations made under controlled empirical circumstances. The more narrow focus on quantitative considerations and on necessary empirical validation based on

384

Ernest John McCullough

frequency of observation was of immense value to experimental science. But it was disastrous for ethics and metaphysics in which actions, virtues, the cultural and historical background and ‘being’ itself are key principles. We urgently need to recover the epagogic approach to induction if we hope to return to a more plausible approach to ethics and metaphysics. S: It always helps to see matters in their historical context. The contemporary understanding of induction is indebted to analogy, and to statistical, quantitative and logical analysis for its general acceptance. The possibility of a mode of induction derived from direct experience that is at once particular and universal introduces a mode that is foreign to most contemporary thinkers. And yet, induction in the Greek and mediaeval mode allows the phenomenological access to the essential properties, even if this access is only partial. Recognition of a broadened concept of induction might give modern thinkers grounds for reconciling continental and AngloAmerican traditions. N: Indeed, a deeper understanding of the 16th and 17th centuries in terms of the Suarezian / Cartesian revolution would be helpful in explaining the origins of our current limited grasp of induction. In an odd way, Descartes distanced himself from the physical world, under the influence of his later Scholastic forbears, to produce a powerful, new scientific vision that disqualified the inductive or epagogic mode of reasoning in favor of a deductive, mathematical approach that ultimately opens the door to skepticism; hence the prevailing non-representational approach to epistemology. Y: I don’t think I can absorb any more ideas today. Thank you both for a stimulating conversation.

Goethe and Intuitive Induction Jakob Ziguras The University of Notre Dame, Sydney

Abstract: This chapter presents an account of induction that can be found in the scientific writings of Johann Wolfgang von Goethe. It begins with a brief examination of two central metaphysical and epistemological assumptions of the Humean theory of induction. The Humean account is then contrasted to Goethe’s rival views on knowledge. Ziguras first gives us a general account of Goethe’s epistemology and argues that it involves a conception of ‘intuitive induction’ much like Aristotle’s, namely, a method which, starting from sensible examples, leads to the intuitive grasp of necessary structures discernible within, and explanatory of, the phenomena of nature. He then considers the question of the specific type of necessity characterising the Goethean archetypal phenomenon (Urphänomen) and argues that the archetypal phenomenon represents an example of a posteriori necessity. The necessity of the Goethean archetypal phenomena is a posteriori because it is discoverable only through experience. As such, the Goethean archetypal phenomenon is characterised by a form of necessity not recognised by Hume and thus contradicts the still widely accepted view that a posteriori truths are contingent. Ziguras concludes that, as an alternative to the still dominant Humean conception of induction, Goethe’s approach merits a closer consideration by philosophers than it has received up till now.

Introduction Although as a poet he stands with Homer, Dante and Shakespeare, the scientific writings of Johann Wolfgang von Goethe are still rarely discussed by philosophers.1 While his scientific ideas found some favour with contemporaries, Hegel being one of the most prominent thereof, to many readers, both then and since, they have seemed a puzzling anomaly, out of step with the mainstream of philosophical thinking about the nature of 1

In what follows I refer to the existing English translations of Goethe’s writings. The original German sources are cited in brackets.

386

Jakob Ziguras

scientific knowledge. However, Goethe’s epistemology is deeply consistent with an older tradition that goes back to Aristotle. In this essay, I will argue that Goethe offers a distinctive account of what, in the Aristotelian literature, is sometimes referred to as ‘intuitive induction,’ as an alternative to the still dominant Humean conception of induction. First, a cautionary note: To my knowledge, Goethe never speaks of his own method as “inductive,” and his very few references to induction are critical. However, when these statements are considered together with his substantive epistemological views, it becomes clear that Goethe is critical only of the narrow, empiricist conception of induction. It seems that Goethe was not familiar with the Aristotelian conception of induction and that his objection to using the word to characterise his own approach, stemmed from his association of induction with empiricism. Modern discussions of induction have, for the most part, moved within the parameters set down by Hume. As J. R. Milton puts it: David Hume appears as perhaps the first and certainly the greatest of all inductive skeptics, as a philosopher who bequeathed to his successors a Problem of Induction, which might be solved, or dissolved, or by-passed, but which could not legitimately or honestly be ignored.2

Hume’s arguments against induction are so widely known that I will not repeat them here. Instead, I want to draw attention to two central assumptions underlying Hume’s approach, assumptions which have had a widespread influence. One of the reasons Goethe’s scientific writings have often been misunderstood is precisely that he rejects these assumptions; hence, a brief consideration of them will bring the alternative, Goethean perspective into sharper relief. These assumptions are as follows: firstly, the rejection of the “ancient distinction”3 between sense and intellect4 and the related 2 J. R. Milton, “Induction Before Hume,” The British Journal for the Philosophy of Science 38, no. 1 (1987): 49-74, p. 49. 3 Frank J. Leavitt, “Hume Against Spinoza and Aristotle,” Hume Studies, 17, no. 2 (1991): 203-208, p. 204. 4 Peter Millican, Introduction, in David Hume, An Enquiry Concerning Human Understanding, ed. Peter Millican (Oxford: Oxford University Press, 2007), p. ix. Hume makes this rejection clear in A Treatise of Human Nature, when he writes, “It is usual with mathematicians, to pretend, that those ideas, which are their objects, are of so refined and spiritual a nature, that they fall not under the conception of the fancy, but must be comprehended by a pure and intellectual view, of which the superior faculties of the soul are alone capable. The same notion runs through most parts of philosophy, and is principally made use of to explain our abstract ideas, and to shew

Goethe and Intuitive Induction

387

rejection of universal concepts5; and, second, the acceptance of a new metaphysics,6 broadly speaking, the metaphysics of early modern natural science, which combined a commitment to the complete mathematisation of all natural phenomena (and the relegation to purely subjective status of any phenomena not amenable to mathematisation) with the view that the true being of observable nature lies, not in its surface appearances, but in its deeper, atomic constituents and the mathematical laws governing them. It is this combination of assumptions that leads to Hume’s ultimately contradictory position that mixes skeptical arguments, which, if taken seriously, utterly undermine the possibility of scientific knowledge, with a partly covert acceptance of the scientific naturalism of his time. It should be noted that some scholars of Hume have questioned the interpretation of Hume as a radical skeptic, whose arguments lead to the denial of any order in nature, and have focused instead on what they take to be Hume’s naturalism. On this view, Hume’s arguments are meant not to undermine belief in causation, but rather to undermine all non-natural, metaphysical accounts of human knowledge. My own interpretation combines both elements, since in my view Hume’s skepticism is a consequence of his partly covert, dogmatic acceptance of scientific naturalism, and of the specific assumptions mentioned above. There is a connection between, on the one hand, Hume’s rejection of the distinction between sense-perception and intellect (and his identification of thinking with imagination), and, on the other hand, his partly-covert acceptance of a new metaphysics. According to Millican, the “metaphysical” thinkers against whom Hume argued, shared, despite their differences, some important assumptions, notably a view of the world as created by divine reason, and—relatedly—as potentially ‘intelligible’ to human reason. Hume’s how we can form an idea of a triangle, for instance, which shall neither be an isosceles nor scalenum, nor be confined to any particular length and proportion of sides. It is easy to see, why philosophers are so fond of this notion of some spiritual and refined perceptions; since by that means they cover many of their absurdities, and may refuse to submit to the decisions of clear ideas, by appealing to such as are obscure and uncertain.” David Hume, A Treatise of Human Nature: In Two Volumes, vol. 1. (London: J. M. Dent, 1961), p. 76. 5 Milton, pp. 69-71. 6 Louis Groarke, An Aristotelian Account of Induction: Creating Something From Nothing (Montreal: McGill-Queen’s University Press, 2009), p. 79: “the early moderns [and Hume among them] did not shake off metaphysics; they subscribed to a new metaphysics.”

388

Jakob Ziguras

special significance is as the first great philosopher to question both of these pervasive assumptions, and to build an epistemology and philosophy of science in no way dependent on either of them.7

All of this has the consequence that Hume approaches induction and causality in a way radically different from Goethe. Hume is interested, for the most part, in asking whether we can predict that a contingent empirical event will occur at a given place and time (for instance, whether the sun will rise tomorrow), or whether a given cause will have the expected effect—in his terms, whether one sensible phenomenon will be followed by another (for instance, the eating of bread being followed by nourishment). As he says, “All reasonings concerning matter of fact seem to be founded on the relation of Cause and Effect”8 since it is only by means of the idea that there is a necessary connection between one phenomenon (the cause) and another (the effect) that we can go beyond the evidence provided by memory and immediate sense perception. Hume’s denial of intellectual insight9 also means that he tends to conflate the traditional notions of causality and necessary connection with that of “power,”10 or “force.” In other words, he tends to objectify ideal relations into quasi-physical relations, inaccessible to the human senses. This is particularly evident in the following passage: The scenes of the universe are continually shifting, and one object follows another in an uninterrupted succession; but the power or force, which actuates the whole machine, is entirely concealed from us, and never discovers itself in any of the sensible qualities of body.11

For my purposes, it is important to note the way in which Hume’s position misrepresents the available epistemological options. First, Hume implies that we are faced with an either/or: either we believe that all causal claims about 7

Millican, in Hume, Enquiry, p. ix. Hume, Enquiry, p. 109. 9 Millican, in Hume, Enquiry, p. xxix. As Millican argues, Hume developed Locke’s empiricism “far more consistently [than Locke himself], ruthlessly dismissing all hints of pure rational insight … and deploying powerful skeptical arguments to undermine even the ideal of causal intelligibility. … our capacity for factual reasoning, instead of being a manifestation of angelic rational perception, turns out to be different only in degree from that of the animals.” 10 Ibid, p. xlii, “Hume consistently treats ‘power’ and ‘necessary connexion’ as equivalent.” 11 Hume, Enquiry, p. 136. 8

Goethe and Intuitive Induction

389

“matters of fact” are based solely on sense experience, or we must believe that contingent empirical phenomena can be derived (in other words predicted), purely a priori. Hume often identifies the latter option with the traditional accounts he criticises. For Hume, the latter is not an option because, according to him, we can always conceive (in other words, imagine) any empirical event we like, without contradiction, while the former cannot ground causal claims without vicious circularity. Hume suggests that if the latter option were possible, then a man with no previous experience of e.g. fire, should be able to predict that his hand will be burnt if he places it in the fire. Since Hume’s empiricist principles lead him to deny any form of intellectual insight (all thinking is a species of imagination), and since sense perception gives us no insight into the hidden “ultimate springs and principles” of nature, he is led to propose his alternative definition of causality, according to which the necessity pertaining to causal connections is, in fact, nothing but the psychological compulsion, born of habit, to expect a to follow b if we have often observed this in the past. In contrast, Goethe, like Aristotle,12 respects the difference between sense perception and intellection, recognises the role of an intuitive intellect in knowledge, and rejects the dualistic idea that knowledge aims at accurately representing an “external” world hidden behind a screen of representations. Instead, for Goethe, knowledge involves the discernment of the ideal or intelligible principles of sensible phenomena by a combination of painstaking observation, experimental variation, and finally, a form of insight that fuses sense perception and intuitive thinking, and whose “object” is the so-called Urphänomen, the ultimate goal of Goethe’s inorganic science. Goethe is interested in discerning essential features of phenomena, not in predicting contingent empirical events, either on the basis of pure sense experience or on the basis of purely a priori reasoning. Finally, he rejects the idea that the only necessity is so-called analytic a priori necessity, and aims, instead for an a posteriori necessity. It is important to note, in view of Hume’s opposition to metaphysics, that Goethe does not attempt to ground his phenomenological science of nature on metaphysics, at least not if metaphysics is interpreted as Hume 12

What Groarke, p. 38, says about Aristotle could equally be said of Goethe: “…Aristotelian induction is about causality. The main focus is not, as in modern philosophy, on predicting when (or how often) something will occur. The focus is squarely on understanding what is happening. This is where induction derives its logical force. Once we understand what exactly is happening, we can, for example, know how and when something will occur.”

390

Jakob Ziguras

seems, in part, to have interpreted it, namely, as a speculative discipline attempting to explain experience by appeal to super-sensible entities inaccessible to experience. Goethe’s appeal to an intuitive intellect—and to an intelligibility and necessity immanent in nature and accessible to the intellect—is not a speculative move, postulating something inaccessible to experience (“intellect,” “intelligible structure” etc.) in order to explain a given, the meaningful structure of phenomena. Rather, Goethe’s appeal is an experiential one. He clearly takes the intellectual perception of intelligibility in sensible phenomena to be an undeniable experiential (though not purely sensible) given. To the criticism that, in so doing, he unjustifiably transgresses the bounds of possible experience, Goethe would presumably reply that the denial of the intellect’s capacity to intuit the intelligible structure of nature is a piece of dogmatism that is untrue to experience and derives from the acceptance of a faulty metaphysics of the sort described above. In order to clarify the nature of Goethe’s phenomenological science of nature, it will be useful briefly to categorise his overall philosophical orientation, insofar as it is possible to determine this, since Goethe never wrote a systematic philosophical account of his views. Probably the least inaccurate description of Goethe’s overall philosophical orientation is “objective idealist.” He is an “idealist” insofar as he believes that the ground of reality is ideal, rather than merely physical, and insofar as he thinks that the goal of knowledge is the intuitive perception of an ideal structure immanent in the phenomena of immediate experience and not, as in the dualism he opposes, the explanation of the phenomena of immediate experience by appeal to postulated physical entities or processes “behind the scenes.” He is an “objective” idealist, because he does not psychologise either sensible qualities or intelligible ideas by reducing them to the contents of the individual, empirical mind. Goethe is certainly not a subjective idealist. His denial of the representationalist dualism characteristic of much modern philosophy is based not on denying the existence of the world, but on affirming that the ideal structure which knowledge reveals is part of the world and that it is itself the causal structure of the world and not merely the representation of some underlying realm of physical causes. This leads one to ask whether Goethe believes in the independent existence of a material substrate. Although I am not aware of any place where Goethe directly addresses this issue, the overwhelming tendency of his epistemology would certainly incline one to a roughly Aristotelian answer. Although Goethe always stresses the importance of perception and would probably say that, for human beings at

Goethe and Intuitive Induction

391

least, there is always some sensible remainder which escapes the transparency of understanding, he would certainly deny the existence of matter conceived of as a determinate entity utterly independent of mind and the idea. Matter in this genuinely “materialist” sense must be, from a Goethean perspective, a fiction, created for certain methodological purposes by abstracting from the always informed matter of actual experience. With regard to the apparent opposition between realism and idealism, the Goethean response would be roughly as follows: A realism based on the notion of a reality-substrate utterly independent of mind (not only the human mind, but mind in general) must in principle, degenerate into skepticism or dogmatism (the two are connected since skepticism arises by accepting the impossible epistemological requirements of such realism, while denying that they can be fulfilled). Goethe simply refuses to accept the Cartesian dualism of mind and matter. To put it only apparently paradoxically, Goethe is a realist in the genuinely idealist sense, because he does not subjectify sensory qualities (colours etc., are really part of nature) or ideas (the intelligible structure that science reveals may manifest in the human mind, but it is nevertheless the real structure of nature). Goethe can do this because he recognises, as both Aristotle and Goethe’s own Romantic and idealist contemporaries did, that one can see knowledge as part of nature, without opting for a reductive materialism. Human knowledge and creativity are, for Goethe, the highest realisation of nature itself. Thus reality is, for Goethe, a relational notion: reality emerges at the intersection between mind and nature and is not reducible either to subject or object. As Goethe memorably puts it: “Where object and subject touch, there is life.”13 The remainder of this paper will be divided into two sections. In the first section, I will give a general account of Goethe’s epistemology, and argue that it involves a conception of intuitive induction much like Aristotle’s, namely, a method which, starting from sensible examples, leads to the intuitive grasp of necessary structures discernible within, and explanatory of, the phenomena of nature. In the second section, I will consider the question of the specific type of necessity characterising the Goethean archetypal phenomenon. I will argue that the archetypal phenomenon represents an example of a posteriori necessity and thus contradicts the still widely accepted view that a posteriori truths are contingent. The necessity of the Goethean archetypal phenomena is a posteriori because it is discov13 Goethe, in Goethe on Science: an Anthology of Goethe’s Scientific Writings, ed. Jeremy Naydler (Edinburgh: Floris Books, 1996), p. 123 (FA X (37): 521).

392

Jakob Ziguras

erable only through experience. As such, the Goethean archetypal phenomenon is characterised by a form of necessity not recognised by Hume. 1 Goethe and the Archetypal Phenomenon In this section, I will discuss some of the main elements of Goethe’s theory of scientific knowledge, particularly as this relates to induction. My discussion will show how Goethe implicitly rejects the above-mentioned Humean assumptions: First, in contrast to Hume’s representationalism, which is parasitic on the idea of a quasi-sensible, but nevertheless unobservable, nature behind the scenes, Goethe’s science is thoroughly phenomenological, beginning and ending with phenomena given to experience. Second, Goethe, unlike Hume, respects the ancient distinction between sense perception and intellection and recognises the contribution that an intuitive form of thinking plays in the acquisition of scientific knowledge. It is this recognition that allows Goethe to develop a thoroughly phenomenological scientific method without degenerating into the chaotic phenomenalism that is the consequence, at least on one tradition of interpretation, of Hume’s inductive skepticism. Although Goethe repeatedly stressed the crucial role of the (unaided) human senses in the scientific study of nature, he was never an empiricist in the narrow Humean sense and never made the mistake of restricting human knowledge to the contents of sense perception. Goethe’s epistemology was always, as Schiller dubbed it, a “rational empiricism.” The term “rational empiricism” arose in the context of the correspondence between Goethe and Schiller in 1798. This discussion seems to have been precipitated by a letter from Goethe, dated January 10, 1798, in which he sent to Schiller a copy of his essay “The Experiment as Mediator between Object and Subject.”14 I will return to the content of this essay shortly. On January 15, 1798, Goethe sent Schiller a copy of another, shorter essay—“Empirical Observation and Science.”15 This gives a condensed account of his scientific method leading up to the perception of the Urphänomen, or archetypal phenomenon. Goethe begins this latter essay as follows:

14

Goethe, “The Experiment as Mediator between Object and Subject,” in Scientific Studies, trans. Douglas Miller (New York: Suhrkamp, 1988), pp. 11-17 (HA XIII: 1020). 15 Goethe, “Empirical Observation and Science,” in Scientific Studies, pp. 24-25 (HA XIII: 23-25).

Goethe and Intuitive Induction

393

Phenomena, which others of us may call facts, are certain and definite by nature, but often fluctuating in appearance. The scientific researcher strives to grasp and keep the definite aspect of what he beholds; in each individual case he is careful to note not only how the phenomena appear, but also how they should appear.16

If we approach Goethe with representationalist preconceptions (of the sort that underly Hume’s reasoning), we are apt to be puzzled. Goethe is simultaneously saying that phenomena are often “fluctuating in appearance” and that they are “certain and definite by nature.” What is puzzling, from a representationalist perspective, is that he is speaking about phenomena, in other words entities that are, by definition, cognitively accessible. If “phenomenon” is understood as a synonym for “mere appearance” then what Goethe says doesn’t make sense. It would make sense if he said something like, “The reality behind appearances is certain and definite by nature, while the appearances are often fluctuating in character.” He does not say this, however. Knowledge, for him, is not the attempt to grasp, by means of representations, a radically transcendent reality behind appearances. Rather, knowledge is the always finite participation of the knower in reality by means of phenomena made intelligible in act of knowledge. That Goethe is not talking about a reductive empiricism is made clear by what follows. In the next sentence, Goethe writes, There are many empirical fractions which must be discarded if we are to arrive at a pure, constant phenomenon … However, the instant I allow myself this, I already establish a type of ideal. But there is a great difference between someone like the theorist who turns whole numbers into fractions for the sake of a theory, and someone who sacrifices an empirical fraction for the idea of the pure phenomenon.17

Goethe is here attempting to explain how he understands the relationship between observation and theory. Goethe distinguishes his own epistemology from empiricism by noting that the scientist cannot stop at an indiscriminate description of particular sense-perceptions. In order to keep his view concerning what is essential to a particular phenomenon, the scientist will often need to ignore or “discard” certain inessential features of the phenomenon, which, to sense-perception, are given as part of the phenomenon. In other words, as Goethe also says, the scientific researcher must note not 16 17

Ibid., p. 24 (HA XIII: 23-24). Ibid., p. 24 (HA XIII: 24).

394

Jakob Ziguras

only how the phenomena appear, but how they should appear. As the scientist’s insight into the nature of the phenomenon increases, new aspects of the phenomenon given by sense-perception are judged with reference to an ideal. This appeal to a normative ideal might seem to go beyond experience and involve the scientist in an un-empirical speculation. Goethe would disagree. In this passage, the theorist who “turns whole numbers into fractions for the sake of a theory,” seems to stand for someone who attempts to explain the phenomena by means of their non-phenomenal atomic constituents. In contrast, although the second theorist may discard particular sensible elements in order to stay true to the pure phenomenon (which unites the sensible and the ideal), he nevertheless does so with reference to an intelligibility given in experience and made more explicit during the investigation. Just as it will always be necessary to bridge the gaps between the sensibly given “parts” making up the whole by means of an insight into the whole going beyond sense perception, so sometimes a view of the whole will allow one to integrate, or set aside, an incongruous part without sacrificing the essence. A good example, which Goethe would have endorsed, is given by Louis Groarke18: the odd, three-legged dog in no way threatens the truth of the statement that all dogs have four legs, since this is a statement of essence and not a statement about the contingent attributes of this or that dog. For Goethe, the pure phenomenon is not something perceived with the eyes alone.19 One “sees” the pure phenomenon only by means of a perception illuminated by thinking. Goethe continues as follows: For the observer never sees the pure phenomenon with his own eyes, rather, much depends on his mood, the state of his senses, the light, air, weather, the physical object, how it is handled, and a thousand other circumstances. Hence it is like trying to drink the sea dry if we try to stay with the individual aspect of the phenomenon, observe it, measure it, weigh it, and describe it.20

One cannot rely solely on the observation of particular instances, in the contingency of their appearance. To attempt to capture the pure phenomenon 18

Groarke, p. 141. Goethe, in Goethe on Science, p. 115 (FA XXIV: 432): “… there is a difference between seeing and seeing; … the eyes of the spirit have to work in perpetual living connection with those of the body, for one otherwise risks seeing and yet seeing past a thing.” 20 Goethe, “Empirical Observation”, p. 24 (HA XIII: 24). 19

Goethe and Intuitive Induction

395

by a mere description and enumeration of the individual phenomena is an impossible task. The infinite variety of the fluctuating appearances needs to be sorted by thinking. However, this is not a matter of constructing theories about unobservable entities behind the scenes. Here, Goethe’s affirmation of the human power of intuitive judgment (anschauende Urteilskraft) is crucial. Goethe aims to reach a state where the human mind “can come closest to things in their general state, draw them near, and, so to speak, form an amalgam with them just as it usually does in common empiricism, but now in a rational way.”21 This process of achieving cognitive identity with the pure phenomenon is composed of the following stages: 1. The empirical phenomenon, which everyone finds in nature, and which is then raised through experiments to the level of 2. The scientific phenomenon by producing it under circumstances and conditions different from those in which it was first observed, and in a sequence which is more or less successful. 3. The pure phenomenon now stands before us as the result of all our observations and experiments. It can never be isolated, but it appears in a continuous sequence of events. To depict it, the human mind gives definition to the empirically variable, excludes the accidental, sets aside the impure, untangles the complicated, and even discovers the unknown.22

We begin with the phenomena of everyday experience. While these phenomena are fluctuating for us, by nature they are definite. We proceed to refine these initial phenomena by means of experiment. Goethe is not stating that, in order to fulfil the second stage of the cognitive process, one must conduct experiments in the stricter sense. As we will see, repeated, painstaking observation and imaginative variation, in which sense perceptions are gradually integrated into a more and more clearly perceived intelligible context, are, for Goethe, the essential elements of “experimentation.” Also, the insight, which is the goal of experimentation, is not caused by the repetition, variation etc. The latter are merely means to an insight which may, in rare or in simple cases, be achieved without them. Although it is not possible here to attempt any detailed discussion of Goethe’s actual experimental method, some general points can be made. In “The Experiment as Mediator between Object and Subject,” Goethe begins by speaking of the need for the scientist to transcend the “natural

21 22

Ibid., p. 25 (HA XIII: 24). Ibid., p. 25 (HA XIII: 24).

396

Jakob Ziguras

way of seeing and judging things”23 that characterises our everyday experience. Normally we judge things as pleasing or displeasing in relation to ourselves. The scientist needs to transcend this natural subjectivity and begin to see “nature’s objects in their own right and in relation to one another … as a neutral, seemingly godlike being he must seek out and examine what is, not what pleases.”24 At first glance this may seem to be nothing more than an expression of the truism that science seeks objectivity. However, the kind of objectivity Goethe aims for is quite different from the objectivity sought by those who hold to the idol of the transcendent thing-in-itself. This Goethean “objectivity” is sought not by moving away from the phenomena, or attempting to find some impossible view from nowhere, but by going deeper into them; it is gained by allowing the object itself to speak. The student of nature needs to develop “the calm exercise” of his “powers of attention,” to observe each phenomenon with “the same quiet gaze” in order to “find the measure for what he learns, the data of judgment, not in himself but in the sphere of what he observes.”25 By patiently and meticulously observing a given phenomenon over a long period of time we gain a clear initial “concept of the object, its parts, and its relationships.”26 This initial grasp is refined by means of experiment. Goethe defines his notion of experiment as follows: “When we intentionally reproduce empirical evidence found by earlier researchers, contemporaries, or ourselves, when we re-create natural or artificial phenomena, we speak of this as an experiment.”27 For Goethe, it is not the purpose of experiment to prove a theory or hypothesis.28 As R. H. Stephenson puts it, “The whole point of Goethe’s 23

Goethe, “Experiment,” p. 11 (HA XIII: 10). Ibid., p. 11 (HA XIII: 10). 25 Ibid., p. 11 (HA XIII: 10). 26 Ibid., p. 11 (HA XIII: 10). 27 Ibid., p. 13 (HA XIII: 14). 28 Ibid., p. 14 (HA XIII: 5): “… I would venture to say that we cannot prove anything by one experiment or even several experiments together, that nothing is more dangerous than the desire to prove some thesis directly through experiments, that the greatest errors have arisen just where the dangers and shortcomings in this method have been overlooked.” Cf. H. B. Nisbet, Goethe and the Scientific Tradition (London: Institute of Gemanic Studies, 1972), p. 23: “… in the opinion of Newton—despite his famous hypothesis non fingo—the experiment is conducted in order to test a hypothesis, whereas Goethe … believes that experiments should not be designed to prove some preexistent hypothesis or theory, but rather to enlarge our knowledge of nature.” Cf. 24

Goethe and Intuitive Induction

397

experimentation is Darstellung (‘representation of an object, brought into relation with others in such a way that its significance is revealed’)...”29 Experiment assists the sorting of sense experience, of the initially unclear multiplicity of the phenomena being studied, into its essential elements. Any one experiment taken in isolation gives us only a limited view of the whole, i.e., of the type of phenomenon being studied.30 The individual experiments and the individual insights they afford us concerning a small sphere of phenomena, or concerning a single phenomenon, need to be linked into a whole series of “contiguous experiments.”31 We should not let the terminology of “experiment” mislead us into imagining that Goethe is speaking solely of a situation where a phenomenon is artificially created in controlled conditions. The essential thing is the repetition of experiences pertaining to the phenomena in a given field in as comprehensive a manner as possible and according to an order appropriate to the phenomena. The comprehensive series of experiments, with each growing by minute gradations from the preceding, is understood by Goethe as a single experience: Studied thoroughly and understood as a whole, these experiments could even be thought of as representing a single experiment, a single piece of empirical evidence explored in its most manifold variations. Such a piece of empirical evidence, composed of many others, is clearly of a higher sort. It shows the general formula, so to speak, that overarches an array of individual arithmetic sums. In my view, it is the task of the scientific researcher to work toward empirical evidence of this higher sort.32 Herbert Hensel, “Goethe, Science and Sensory Experience,” in Goethe’s Way of Science: a Phenomenology of Nature, ed. David Seamon and Arthur Zajonc (New York: State University of New York Press, 1998), p. 75: “Instead of verifying or falsifying a hypothesis conceived ideally, outside of experience, the important thing is to order the experiments in such a way that, in progressing through the series of experiments, the underlying idea becomes immediately intuitive.” 29 R. H. Stephenson, Goethe’s Conception of Knowledge and Science (Edinburgh: Edinburgh University Press, 1995), p. 11. 30 Goethe, “Experiment,” pp. 14-15 (HA XIII: 16-17): “Every piece of empirical evidence, every experiment, must be viewed as isolated. … Nothing happens in living nature which does not bear some relation to the whole. The empirical evidence may seem quite isolated, we may view our experiments as mere isolated facts, but this is not to say that they are, in fact, isolated. The question is: how can we find the connection between these phenomena, these events?” 31 Ibid., p. 16 (HA XIII: 17). 32 Ibid., p. 16 (HA XIII: 17).

398

Jakob Ziguras

Dennis L. Sepper33 distinguishes two important features of Goethe’s method. Firstly, there is this “systematic experimental variation, by which one gains a progressively more comprehensive acquaintance with the full range of phenomena possible in limited circumstances.”34 This experimental manifolding involves the gathering together of as full a range as possible of phenomena of a certain type. This gathering together is not a form of enumerative induction. The purpose of this method is to bring the phenomena under consideration as much as possible into a form that allows the ideal principles governing them to become visible. One is not aiming for the impossible goal of actual sensible comprehensiveness but rather moving towards the idea whose unity cannot, as such, be present in the spatio-temporally distinct sensible phenomena, but which the latter can nevertheless approximate more and more adequately until the moment when one grasps the underlying principles involved. The continuity between individual sensible phenomena will never be fully seamless. The move from the complex experiment or experience to the seamless unity of the idea always involves a leap of insight.35 Nevertheless, this method has its purpose. Goethe himself makes this very clear when he writes, Two needs arise in us when we observe nature: to gain complete knowledge of the phenomena themselves, and then to make them our own by reflection upon them. Completeness is a product of order, order demands method, and method makes it easier to perceive the concept [italics added]. When we are able to survey an object in every detail, grasp it correctly, and reproduce it in our mind’s eye, we can say that we have an intuitive perception of it in the truest and highest sense. … And thus the particular always leads us to the general, the general to the particular.36 33

Dennis L. Sepper, “Goethe and the Poetics of Science,” Janus Head 8, no. 1 (2005), pp. 207-227. 34 Ibid., p. 217. 35 Goethe, in Nisbet, p. 42 (JA I 6:75): “Experiments are mediators between nature and concept, between nature and the idea, and between the concept and the idea.” The distinction between “concept” and “idea” here is, broadly, the distinction between generalisations, products of the discursive, analytical understanding (Verstand), and what one might call concrete universals, discerned by the intuitive reason (Vernunft). 36 Goethe, “Polarity,” in Scientific Studies, p.155 (WA II: 11). Cf. Sepper (2005), pp. 217-218: “By means of the manifold variations of experiments one seeks an overall experience that will be unitary in two ways: in that the experiments performed are progressively evolved from one another by a series of small modifications, and in that

Goethe and Intuitive Induction

399

The point is not to amass evidence but to foster the discernment of the underlying principle, the idea of the phenomena. While the variation of experiments and their arrangement in a continuous series serve to provide a kind of empirical approximation to the unity of the idea and to foster its discernment, the attempt to reduce the phenomena to its most simple elements has another purpose. Sepper writes: Goethe’s way of science thus aims at an original experience, original in the sense not so much of being unprecedented as of taking or referring things back to their origins and placing them in fundamental relations to other things in the relevant field of interest. Several years later Goethe began using the term Urphänomen for the unity of what is experienced as single despite the manifold perspectives under which it appears (Ur- as a prefix in German refers to something original or foundational).37

If one can speak of Goethe’s method involving a kind of “induction,” it is in a very different sense from the mechanical, enumerative induction familiar today. As Hjalmar Hegge says: Goethe is altogether closer … to the Aristotelian tradition in science than to the Galilean-Newtonian. His view of induction recalls Aristotle’s ‘intuitive induction,’ though Goethe has also applied his view extensively in practical research, and at the same time formulated it more precisely than did Aristotle on just this point.38

Thus, in a sense, whether we speak of Goethe’s method as inductive depends on whether we use the word in its modern sense or in its Aristotelian sense, where the latter presupposes intuitive thinking as the source of the insight necessary to grasp the principle operative in the phenomena.

one has seen how the small modifications affect and vary the outcome while still remaining basically the same type of experimental phenomenon (for example, refraction of light through an aperture.)” 37 Ibid., pp. 215-217. 38 Hjalmar Hegge, “Theory of Science in the Light of Goethe’s Science of Nature,” in Goethe and the Sciences: A Reappraisal, ed. Frederick Amrine, Francis J. Zucker and Harvey Wheeler (Dordrecht: D. Reidel, 1987), p. 213. Cf. Goethe, “Letter to Zelter 5/10/1828”, in Goethe’s Letters to Zelter, trans. A. D. Coleridge (London: George Bell and Sons, 1892), p. 334 (HA XII: 440): “When one considers the problems of Aristotle, one is astonished at his gift of observation, and at all that the Greeks had an eye for; only they err in being over-hasty, for they go directly from the phenomenon to the explanation …”

400

Jakob Ziguras

One of the clearest presentations of this aspect of Goethe’s thought is that of Rudolf Steiner.39 On the Goethean view, according to Steiner, science is …a matter … of connecting sense perceptible facts. These connections, however, are precisely what manifest themselves so unclearly, so untransparently, in experience. One fact a confronts us, but at the same time numerous other ones do also. As we let our gaze sweep over the manifoldness presented here, we are totally in the dark as to which of the other facts have a closer relationship to this fact a and which have a more remote relationship. Some facts may be present without which the event cannot occur at all, and others are present that only modify it; without these the event could indeed occur, but would then, under different circumstance, assume a different form.40

We can see here many of the elements from Goethe’s “Empirical Observation and Science.” In order to grasp the pure phenomenon, the phenomenon “certain and definite by nature,” we must strip away the nonessential phenomena surrounding it. This may be done either physically, by simplifying the conditions under which the phenomenon occurs, or in imagination. A very good example of the latter is the example of the lunar eclipse, which Aristotle discusses in the Posterior Analytics. In trying to understand a lunar eclipse from our usual perspective, on the earth, we are faced with many other phenomena which are not directly relevant and which obscure the nature of the phenomenon in question. However, if, as Aristotle suggests, we imagine ourselves standing on the moon, we will be able to see directly (at least in imagination) the earth blocking the light of the sun from reaching the moon and from this can arise the universal. Usually we need to alter the order of the phenomena or the perspective from which we view them. This is the task of experiment as Goethe describes it. Ultimately, says Steiner, “We have to create conditions such that a process will 39

Cf. Roger Smook, “Rudolf Steiner on the Presuppositions of Goethean Science,” Idealistic Studies 22, no. 1 (1992), pp. 68-81. Although Steiner is sometimes overlooked in the literature, I agree with Smook, who writes: “I believe there is no philosopher who has entered more thoroughly into the spirit of the Goethean scientific enterprise, or tried harder to spell out its presuppositions, than Rudolf Steiner.” Steiner’s basic works on Goethe are: Rudolf Steiner, The Science of Knowing: Outline of an Epistemology Implicit in the Goethean World View, trans. William Lindeman (New York: Mercury Press, 1988); Rudolf Steiner, Goethean Science, trans. William Lindeman (New York: Mercury Press, 1988); Rudolf Steiner, Goethe’s World View, trans. William Lindeman (New York: Mercury Press, 1985). 40 Steiner, Goethean Science, pp. 75-76.

Goethe and Intuitive Induction

401

appear to us with transparent clarity as the necessary result of these conditions.”41 Steiner continues as follows: Such a phenomenon, now, in which the character of the process follows directly and in a transparently clear way out of the nature of the pertinent factors, is called an archetypal phenomenon (Urphänomen) or a basic fact (Grundtatsache). This archetypal phenomenon is identical with objective natural law. For in it is expressed not only that a process has occurred under certain conditions but also that it had to occur. Given the nature of what was under consideration there, one realises that the process had to occur.42

Interestingly, one of the examples Steiner gives to illustrate the idea of the archetypal phenomenon is Aristotle’s example of the lunar eclipse: “When one object is standing between a source of light and another object, it will cast a shadow upon this other object.”43 We can see from Steiner’s formulation how radically the Goethean perspective brings into question the assumptions of a Humean empiricism. We have here a science of nature that stays strictly with the phenomena and involves no hypothetical explanatory entities, but which nevertheless aims at necessary truths, which, however, are not merely analytic a priori truths. Steiner continues: We see that we can remain completely within the phenomena and still arrive at what is necessary. The inductive method adhered to so much today can never do this. Basically, it proceeds in the following way. It sees a phenomenon that occurs in a particular way under the given conditions. A second time it sees the same phenomenon come about under similar conditions. From this it infers that a general law exists according to which this event must come about, and it expresses this law as such. Such a method remains totally outside the phenomena. … Its laws are the generalisations of individual facts. It must always wait for confirmation of the rule by the individual facts. Our method knows that its laws are simply facts that have been wrested from the confusion of chance happening and made into necessary facts [italics added].We know that if the factors a and b are there, a particular effect necessarily takes place. We do not go outside the phenomenal world. The content of science, as we think of it, is nothing more than objective happening. Only the form according to which the facts are placed together is changed.44 41

Ibid., p. 76. Steiner, Science of Knowing, p. 80. 43 Ibid., p.81. 44 Ibid., p. 80. Cf. also p. 83: “rational empiricism … takes nothing other than objective processes as content for science; these objective processes, however, are held together 42

402

Jakob Ziguras

Steiner makes a number of important points here. It may seem that Goethe’s method is akin to the inductive method as Steiner describes it. Have I not said that Goethe’s method involves observing a number of instances of a given phenomenon, in order to determine the conditions under which the phenomenon necessarily occurs? Is this not a case of seeing that the same phenomenon has occurred on a number of occasions and from this inferring “that a general law exists according to which this event must come about”? Not at all: the crucial difference lies in the role that intuitive understanding plays in the Goethean method. The modern inductive method proceeds solely by observing that a certain phenomenon repeatedly occurs in a certain way. From a sufficiently large number of such observations it derives a general law, a law which is a generalisation made on the basis of these particular observations, e.g., all swans are white. In this classic example, the generalisation is based solely on the fact that a certain number of swans have been seen to be white. There is no suggestion of understanding why the swans are white. 45 The force of the inductive generalisation derives solely from the large number of observations and a presumption about the regularity of nature. Of course the crux of the problem is determining what amounts to a sufficiently large number of such observations. Strictly speaking no finite number of observations will be sufficient. No amount of appearances will ever justify an inference to a reality hidden behind appearances, which, from a Humean perspective, includes the reality transcending present sense perception and memory. Similarly, the assumption about the regularity of nature is, as Hume himself recognised, itself open to the objection that since its ultimate warrant can, on an empiricist view, only be empirical, i.e., inductive, it is itself based on the uncertain foundations of the observed regularity of nature. In preparing for the perception of the Urphänomen the researcher may, initially, have nothing to go on but recurring patterns.46 But this is less by a web of concepts (laws) that our spirit discovers in them. Sense-perceptible processes in a connection with each other that can be grasped only by thinking—this is rational empiricism.” 45 It should be emphasised that, for Goethe, such a ‘why’ question would not be answered by means of some single hidden cause external to the organism (even a purely physical cause would be “external” to the organism in the sense that it would not explain the feature as part of a living thing). The answer, instead, would most likely relate the whiteness both to its relation to the wholeness of the organism and the organism’s relation to its lifeworld. 46 Goethe, “Excerpt from ‘Toward a Theory of Weather’ 1825,” in Scientific Studies, p. 148 (HA XIII: 311): In dealing with a phenomenon and attempting to grasp its inner

Goethe and Intuitive Induction

403

a matter of inferring inductively and more a matter of seeing patterns. The Urphänomen is neither derived nor inferred from empirical observations; nor is it a generalisation from them. It is seen in and through them. The point here is not to deny that discursive reasoning may contribute to the investigation but only to emphasise the irreducible element of understanding, which can never be replaced by any mechanical deduction or inference on the basis of some psychological compulsion, causal mechanism, or logical formalism. It is because Goethe’s method is based on the intuitive seeing of the idea in the phenomena, that he avoids the insoluble problems that plague the modern notion of induction. It is because of this seeing that we do not …fail to recognise in a single doubtful case a truth which has stood the test in many other instances, but may instead pay due respect to the law even when it seeks to elude us in the phenomenal world.47

In other words, unlike an inductive generalisation in the modern sense that is refuted by even a single counter instance, the Goethean method can integrate the doubtful case because it is seen in the context of an understanding of the nature of the phenomenon in question. The relationship between particular observations and the idea seen in the phenomena is expressed by Goethe when he writes: “To grasp that the sky is blue everywhere, one does not have to travel around the world.”48 Hjalmar Hegge has said that, in his Theory of Colour, Goethe was aiming at “an axiomatizing of the domain of colour qualities … a deductive system for the phenomena of light and colour, but without quantification of the phenomena.”49 Unlike the mainstream physical theories of colour which deal with a mathematised or quantified representation of the phenomena, Goethe never quantifies the phenomena. Secondly, he avoids incorporating the colour qualities “within a causal schema in which the causes lie outside the domain of the colour qualities themselves.”50 This is because, for Goethe, an explanation of colours in terms of underlying causes of a different kind gives no truly scientific understanding of them. The goal of a science of nature is the understanding of given phenomena in the necessity law, “… we think it right to start with its clearest aspect, i.e., the aspect most frequently repeated under similar conditions, the one which points to a constant regularity.” 47 Goethe, in Nisbet, p.15 (LA I: 10). 48 Goethe, in Stephenson, p. 188 (FA XIII: 47). 49 Hegge, p. 202. 50 Ibid., p. 196.

404

Jakob Ziguras

of their appearance and inter-connections within their own determinate sphere. For Goethe, the ultimate goal of science is not the grasp of separate, underlying, causes. (Heitler notes that the German word for “cause” (Ursache) is a compound of “Sache” meaning “matter, affair” and the prefix “Ur-” which has the sense of “primal,” or “archetypal.” Thus the etymology of the word “cause” in German contains the idea of a “primal fact.”51) As Goethe says, “here it is not a question of causes, but of the conditions under which the phenomena appear; their consistent sequence, their eternal return under thousands of circumstances…”52 Thirdly, Goethe rejects the subjectivisation of sensory qualities based on the ontological interpretation of the distinction between primary and secondary qualities. What does Hegge mean by an “axiomatisation of the domain of color qualities”? Hegge notes that Goethe sought to emulate the method of the mathematician in a certain regard. This may seem strange in view of Goethe’s total avoidance of mathematics in his colour science. However, what attracted Goethe to mathematics was not the quantitative content but the logical form, the rigour, precision, and certainty attaching to the steps involved in a mathematical proof. Hegge writes that Goethe’s aim is to …arrive at a comparatively small number of simple, well-defined elements, corresponding to the axioms of geometry, that is, expressions which are not further reducible to others, but express basic concepts in the system from which the other elements are derived. Goethe calls these ‘Urphänomene,’ or primal phenomena and he describes them and their use as follows: “These [primal phenomena] can be formulated in short, pregnant sentences, compared and—as they are developed—arranged and brought into such a relationship with one another that they, just like mathematical statements, regarded individually or in their interrelationships, remain firm.53

Goethe’s Theory of Colour is …based upon statements (referring to ‘primal phenomena’) which are alleged to be both true and primary, and also upon the assumption that the connections between the various elements are necessary.54

51

Walter Heitler, “Translator’s Note,” in Goethe’s Way of Science: A Phenomenology of Nature, p. 68. 52 Goethe, “Empirical Observation,” p. 25 (HA XIII: 25). 53 Ibid., p. 202. 54 Ibid., p. 205.

Goethe and Intuitive Induction

405

Goethe aims to integrate the phenomena into an order based on a few selfexplanatory, basic, and necessarily true phenomena, or necessary facts, and through this to enable the demonstration (in the sense of the making visible) of the necessary connections between the phenomena of that particular science. However, in contrast to the Humean idea that any claims about nature not derived from sense experience must involve deduction a priori, for Goethe, the deductive stage deals with facts whose necessity is a posteriori. Goethe expresses the movement from the particular to the universal and from the universal to the particular as follows: In general, events we become aware of, through experience, are simply those we can categorise empirically after some observation. These empirical categories may be further subsumed under scientific categories leading to even higher levels. In the process we become familiar with certain requisite conditions for what is manifesting itself. From this point everything gradually falls into place under higher principles and laws revealed not to our reason through words and hypotheses, but to our intuitive perception through phenomena. We call these phenomena archetypal phenomena because nothing higher manifests itself in the world; such phenomena, on the other hand, make it possible for us to descend, just as we ascend, by going step by step from the archetypal phenomena to the most mundane occurrence in our daily experience.55

In view of the fact that the final objects of Aristotelian intuitive induction are often thought of in linguistic terms—as, for instance, definitions, or universal statements of the form “All men are mortal”—it is important to clarify that, for Goethe, the ultimate elements of science are always phenomena themselves, and not their representations in language. The primary archetypal phenomenon in the Theory of Colour is “light or darkness seen through a turbid medium.” Goethe gives two clear examples of this: First, light seen through a moderately turbid medium appears as yellow and progressively darkens to red as the turbidity of the medium increases, a phenomenon observed in the setting of the sun; second, darkness seen through an illuminated medium appears blue, a phenomenon observable, for example, in the fact that the darkness of space, seen through the illuminated atmosphere, appears as blue. Although Goethe does state what could be taken as a very loose and poetic “definition” of colour— “Colours are the deeds and sufferings of light, what it does and what it endures”—the goal of his scientific method is not simply the formulation of 55

Goethe, “Theory of Colour,” in Scientific Studies, pp. 194-195 (FA XXIII/1: 80-81).

406

Jakob Ziguras

the universal principle that all colours arise from the interaction of light and darkness as mediated by a turbid medium. As Goethe puts it, in the introduction to the Theory of Colour: In reality, any attempt to express the inner nature of a thing is fruitless. What we perceive are effects, and a complete record of these effects ought to encompass this inner nature. We labour in vain to describe a person’s character, but when we draw together their actions, their deeds, a picture of their character will emerge.56

This is not the expression of any sort of skepticism about our ability to understand the inner nature of things. Rather, it is an expression of Goethe’s insistence that the inner nature of a phenomenon is not different from the phenomenon and hence that we should never think that we can explain a phenomenon by replacing it with some linguistic or mathematical representation. In the case of the Theory of Colour, the “deductive” stage involves showing that all of the particular phenomena of colour can be derived from the archetypal phenomenon by complicating the initial conditions in various ways. This derivation then amounts to something like a portrait of the domain of colours, which does not merely reduce the nature of colour to an abstract definition but rather presents the full range of the phenomena of the domain of colour as contained within the archetypal phenomenon. Goethe’s approach to the study of colour is clearly very different from the now dominant mainstream of physical science. Whatever one might think about his particular claims—and many advocates suggest that his distinctive methodology and philosophy of science are more important than his particular results—it is crucial to keep in mind that Goethe’s goals are fundamentally different from those of mainstream modern science. Ultimately, Goethe is not interested in the kind of grasp of “efficient” causes that allows one to predict either the necessary or the probable occurrence of some contingent natural event, a grasp that gives us an increasing technological control over nature. The ultimate goal of his science is neither prediction nor control but rather a contemplative insight into the simple, intelligible essence of a certain domain of phenomena and the tracing of its particular realisations in this or that specific context. The archetypal phenomenon, described in the Theory of Colour, is not a separate, objectified “cause” that in some physical sense brings it 56

Ibid., p.158 (FA XXIII/1: 12).

Goethe and Intuitive Induction

407

about that particular colours arise when they arise. As Goethe writes in a letter, “The Urphänomen is not to be regarded as a basic theorem leading to a variety of consequences, but rather as a basic manifestation enveloping the specifications of form for the beholder.”57 In a sense, the archetypal phenomenon and its particular realisations in the full range of possible colours are one and the same. There are no particular colours that are not somehow realisations of this relation of polarity between light and darkness. Similarly, there is no archetypal phenomenon that is radically distinct from its realisations. As Henri Bortoft has emphasised, it is perhaps better to think of the archetypal phenomenon as a way of seeing rather than a thing seen, a way of seeing which gathers together the scattered phenomena of colour into a wholeness. If one were to criticise Goethe for failing to really explain colour, he would presumably answer that genuine phenomena are in the end fundamental and therefore irreducible to anything other than themselves. There may well be a relationship between the colour red, considered as a distinct qualitative reality which arises in specific relations between the world and the perceiver, and other, non-qualitative aspects of reality. However, Goethe would argue that it is absurd to claim that the one is reducible to the other. The Theory of Colour strives to portray what one might call the “concrete universal” of colour, which includes both all of the particular realisations of the archetypal phenomenon and the wholeness which envelops them. There is, in his view, no more basic “explanation” of colour, if one wants to remain with colour itself rather than discussing other non-qualitative aspects of reality; there are no more basic “explanatory entities.” This radically different conception of “explanation” will inevitably seem strange to those committed to the idea that explanation must be in terms of external causes. Goethe’s judgement on the latter approach is telling: some people “are not satisfied to behold an Archetypal Phenomenon. They think there must be something beyond. They are like children who, having looked into a mirror, turn it around to see what is on the other side.”58

57

Goethe, “Letter to von Buttel 3 May 1827,” in Goethe on Science, p. 106. Goethe, “Conversations with Eckermann 18/2/1829,” in Goethe on Science, p. 108 (FA XII (39): 311). 58

408

Jakob Ziguras

2 Necessary Facts? As Hegge notes, Goethe’s approach goes against the grain of certain widespread philosophical assumptions which derive, in part from the empiricist tradition, and in part from the Kantian. It is generally assumed that …the a posteriori element in cognition is contingent and that only the a priori is apodeictic, necessary. Or in other words, inasmuch as there are apodeictic elements in cognition, these it [the prevailing view] takes to be a priori, whether understood as forms of our understanding, as “conditions of the very possibility of experience” in Kant’s sense, or in a more empiricist vein as ‘conventions.’59

In this concluding section, I will briefly consider the nature of the a posteriori necessity sought by Goethe and suggest how it relates to the Humean critique of induction. Although he makes no mention of Goethe, an article by Charles F. Kielkopf60 provides a very clear and interesting way of approaching Goethe’s conception of an a posteriori necessity. Kielkopf begins by stating: The notion that in a valid argument the connection between grounds and consequent must be analytic renders insoluble some of the major problems of philosophy and prevents the development of a nondeductive logic.61

One obvious consequence of this is the problem of induction.62 He suggests that the problem of induction requires, for its solution, the discovery of a form of nonanalytic, or synthetic, necessity. We can go a long way towards resolving the problem of induction if we can discover some “synthetic necessary truths;” or, in other words, necessary truths, derived from experience, which do not involve merely the explication of truths already contained in the definition of a given thing. It should be noted that I differ from Kielkopf on one point: he refers to the truths he discusses as “synthetic a priori.” I think this is an unfortunate formulation, since it suggests that these truths are discovered by merely thinking about concepts in separation 59

Hegge, p. 210. Charles F. Kielkopf, “Deduction and Intuitive Induction,” Philosophy and Phenomenological Research, 26, no. 3 (1966): 379-390. 61 Ibid., p. 379. 62 Ibid., p. 379: “Since it is never inconsistent to assert that A’s are correlated with B’s while denying that A’s cause B’s, and since it is never inconsistent to assert that some S are P while denying that all S are P, we have the problems of induction.” 60

Goethe and Intuitive Induction

409

from experience, which is clearly not the case in the examples he gives. Kielkopf then presents an example to illustrate his point: Consider the configuration of letters … RVER ... Call this configuration A ... It is empirically true that there is an E in A. But we can read off more than empirical truths from this configuration; we can read off that there must be an E in A. We do not read off that the figure had to be written on the line above, nor do we read off that the figure had to be named A. But given the configuration was written down and called A, we can see that it does contain an E and we read off that it must contain an E. If there were no E in A, A would not be the configuration that it is. We have recognised A as an RVER; it is inconceivable that a configuration is RVER without an E. ... Consequently, we determine that “containing an E” denotes an essential feature of A.63

From this particular insight into one of the essential properties of RVER, we can derive the general necessary truth that all RVER’s necessarily contain an E. Now, someone may respond that we are dealing here only with the necessity of analyticity. The statement “RVER contains an E” is only a logical consequence of the definition of “RVER.” This, Kielkopf argues, is wrong. There is no way of forming a definition of “RVER” without first recognising the non-analytic necessity that pertains to the form of “RVER” itself. For in attempting to give a definition we could never justifiably restrict all of the elements that would have to be added to cover all of the essential features of “RVER”: that it contains two R’s, that it contains two letters between the two R’s, and so on. Any such definition is simply the making explicit of a prior recognition of the essence of “RVER” itself. Still, “RVER” is an arbitrary combination of letters, whereas, presumably, natural phenomena are not arbitrary in this way. So, how far can this example take us in understanding Goethe’s views of induction? One useful feature of this example is that it allows us to distinguish Goethe’s position from any kind of reductive determinism. The emphasis on discerning the essential, and thus necessary, features of a phenomenon might seem to suggest that, for Goethe, every natural phenomenon is, at a deeper level, necessary, in the sense of being absolutely determined. However, this is not the case. Although it is very difficult to determine precisely what Goethe’s views are on the origin of the world and on the nature of human freedom, there is, I think, no conflict between the necessity of certain natural phenomena (as he conceives this), and the reality of human, or even divine, freedom. 63

Ibid., pp. 380-381.

410

Jakob Ziguras

Consider the following example: I draw a triangle on a piece of paper. I can now discern certain essential features of the shape before me. However, the concept of the triangle is not like a hidden efficient cause forcing me to draw the triangle. We are dealing here with different levels of explanation. The absolute necessity that characterises the relationship between the triangle and its essential features—such as having three sides—does not equally apply to the event of my drawing the triangle. The concept constrains what I draw, in so far as I must draw a shape fulfilling certain criteria if I want to draw a triangle; however, it does not determine that I draw it now. This latter fact will, ultimately, only be explicable in terms of my rational intention to, for example, illustrate a point, teach someone geometry, etc. If we now turn to consider the relationship between necessity and contingency in nature as a whole, we might say the following: In a sense, it doesn’t matter, for the purposes of Goethean science, whether nature is the contingent result of free, divine creativity, or has always existed, or arose by chance from a purely physical “cause.” Goethe is, at least in his inorganic science, for the most part simply uninterested in causation of this more “efficient” sort. (I do not mean to imply here that, if the world is created, this act of creation should be conceived of in crudely “efficient” terms. I have expressed myself in intentionally simplified terms to make a point.) To use Kielkopf’s formulation, Hume’s arguments are typically aimed at inferences concerning whether or not an “RVER” will be written at a certain place and time, in other words, whether or not a contingent event will or will not occur. He thinks that we can clearly conceive of any empirical event as either happening or not happening. Approaches like Kielkopf’s and Goethe’s have quite a different goal. From the Goethean perspective it makes no difference whether we are dealing with the properties of geometrical figures, arbitrary patterns of letters, or phenomena of colour. In all cases, the goal is not to predict whether particular phenomena will occur at a certain time and place, but rather to discern the essential properties of the phenomena and in this way to lead them back to their most basic principles, which Goethe calls the Urphänomene, in each phenomenal domain. Such an approach can, of course, lead to prediction. One can state, with full certainty, that if “RVER” is written on a piece of paper tomorrow, it will, necessarily, contain an R. However, prediction is secondary to understanding. Prediction here pertains, so to speak, to the essence, rather than the existence, of the phenomenon in question. There is no attempt to

Goethe and Intuitive Induction

411

predict that some essence will, necessarily, be instantiated at some point in space and time, but only that if it is instantiated, the particular RVER, or triangle, etc., will, necessarily, have certain features. Thus, although Goethe never uses this terminology, his method involves a form of intuitive induction that may, finally, be characterised as follows: Intuitive induction is not, primarily, a form of argument. Rather, it involves sorting and synthesising experience, then discerning, in this plurality, more basic, exemplary phenomena (by reorganising the originally given phenomena or stripping away extraneous elements) which are characterised by a radiant self-evidence. Such phenomena achieve a union between the sensible and the intelligible and reveal in their particular, exemplary being the essence of all the phenomena of that type. Hume opposes such a notion of intellectual insight by arguing that, if the discernment of necessary connections were a work of reason, any such discernment should be as perfect upon perception of only one instance as it would be after the perception of many. But of course this is precisely what thinkers like Goethe and, incidentally, Aristotle say does happen. The difference is that Goethe, like Aristotle, recognises that since the intuitive intellect is a faculty that can be trained, there are differences in the degree of “wit” possessed by different people.64 While someone whose wit is either naturally quick or has been made so by training can discern the principle in one example, the slower student may need many. Contrary to Hume’s arguments, this happens even in the case of mathematical examples. As any teacher of mathematics will confirm, it takes some students a long time and many examples to “get” what other students understand from the first. In support of his sharp distinction between relations of ideas and matters of fact, Hume states the following: Propositions of this kind [pertaining to relations between ideas] are discoverable by the mere operation of thought, without dependence on what is any where existent in the universe. Though there never were a circle or triangle in nature, the truths, demonstrated by Euclid, would for ever retain their certainty and evidence.65

This is, on the face of it, a strange admission for an empiricist to make. In what sense could there be truths about, e.g., triangles, if triangles did not, in

64 65

Aristotle, Posterior Analytics, 1.34.89b10-21. Hume, Enquiry, p. 108.

412

Jakob Ziguras

some form, exist, at the very least in the imagination?66 Surely, if we are talking about triangles, we are speaking about a definite phenomenon, either a physically present image of a triangle, an image present in the imagination, or else the universal concept (although in view of his rejection of universal ideas, Hume cannot consistently appeal to this). In fact, the only way we can make sense of this statement is to subscribe to the dualistic metaphysics mentioned earlier. In other words, we need to make a sharp distinction between a putative physical world, existing forever hidden behind a screen of representations, and a subjective, inner realm of consciousness that is somehow not part of “the universe.” Although Hume could hardly have denied that triangles are sensibly present in the world (whether as drawn on blackboards, or on paper, or imagined), the way he expresses himself suggests a dualistic separation of the sensible and the ideal. As an empiricist, he must see the origins of all ideas, including those of geometric figures, in sense impressions. However, here, he also wants to argue that geometrical truths are purely a priori. This incongruity is explainable, ultimately, with reference to Hume’s denial of the role of intellectual insight in empirical knowledge. If Hume had realised that knowledge involves the working together of sense perception, discursive thinking, and intellectual intuition (but an intuition directed at the immanent intelligibility of the sensible world), then he would have realised that any phenomenon, including a triangle, is simultaneously sensible (or imaginable) and ideal. He did not realise this, or at least did not believe it, and so was forced to defend a dualism which opposes a chaotic sensible world, concerning which no necessary knowledge is possible, and a purely a priori realm, which buys its necessity at the cost of being completely separated from the world of experience. Goethe does not go down this path and hence turns out to be far more empirical than Hume. He is uninterested in speculating about hidden causes 66

Cf. Eckart Förster, The 25 Years of Philosophy: A Systematic Reconstruction, trans. Brady Bowman (Cambridge: Harvard University Press, 2012), p. 263: “As the example of mathematics shows, it cannot hold in principle that merely because something is found in the subject it cannot also be true in nature—even if we as yet have no insight into the ground of the agreement. The crucial point in our context, however, is that every mathematical construction, though carried out within the subject, is wholly free of any kind of subjectivity. It makes no reference whatsoever to the subject that carries it out. It stands beyond subject and object, we might say: beyond the subject because the construction is in no way affected by it; and beyond the object because the construction is valid not only for the individual object thus constituted, but for all objects of the same kind.”

Goethe and Intuitive Induction

413

different from the ideas which give intelligible structure to the phenomena of sensible nature. In view of the various seemingly insoluble problems deriving from the Humean approach, it would seem that an alternative approach like Goethe’s merits a closer consideration by philosophers than it has received up till now.

Lonergan’s Solution to the “Problem of Induction” Hugo Meynell University of Calgary

Abstract: In his essay, Meynell argues that the well-known difficulties connected with the problem of induction are due to the defective principles of classical empiricism (and its heir, logical positivism). These difficulties are to be resolved, Meynell claims, by a setting-out of the right epistemology, namely that which ensues from ‘the generalized empirical method’ propounded by Bernard Lonergan. Meynell argues for Lonergan’s position mainly by means of arguing against classical empiricism, because the former is claimed to be the contradictory of the latter, which itself proposes a self-defeating judgment about knowledge. Lonergan’s generalized empirical method is described in terms of a three-fold process inherent in being rational: 1) attentiveness to experience, 2) constructive intelligence, and 3) reasonable judgment. The correct epistemology and metaphysics, which takes account of the role of all three terms of the process, may be referred to as ‘critical realism.’ Meynell sums up his views by stating that the basic thesis of a critical realist metaphysics is that the real world is nothing other than what is to be known through attentiveness to experience, fertility in intelligently conceiving hypotheses or possibilities, and reasonableness in judging which hypotheses are the case or not.

Introduction In this chapter, I will argue that apparent puzzles about induction can be adequately resolved by an appeal to Bernard Lonergan’s perspicacious epistemology. I believe that ‘the problem of induction’ is largely an artifact of the classical empiricism represented best by the work of David Hume and Bertrand Russell. Once one grasps the correct epistemology, which is adumbrated by Aristotle and fully worked out in the ‘generalized empirical

416

Hugo Meynell

method’ of Lonergan,1 it ceases to be a problem. What I want to do in what follows is briefly to set out and justify Lonergan’s ‘generalized empirical method’ and then show how it solves the problem of induction. 1 Lonergan’s Threefold Process It is well known to philosophers, of course, that there are some judgments that are self-defeating or self-destructive without actually being selfcontradictory, the most famous being ‘the liar paradox’. What are not so often noted, as Andrew Beards has pointed out, are the important epistemological consequences of this fact.2 Suppose I say, ‘With the words I am uttering here and now, I am stating what is false.’ It follows that, if what I say is true, it is false, and if it is false, it is true. It is to be noted, that in distinction from simple contradictions, who makes such utterances is crucial. If I say, ‘With the words you are uttering here and now, you are telling a lie’, no paradox is involved. If I say, ‘With the words I am uttering here and now, I am telling a lie,” logical havoc ensues. Similar considerations apply to the statements ‘I never make a true judgment,’ and ‘I never make a judgment for good reason.’ Each must be taken as a falsifying exception to itself, if it is to be taken seriously. It is not very usual for persons to actually make such a judgment. But it is quite common for them to say what apparently implies it. For example, it might be implied that no one ever makes a true judgment or that no-one ever makes a judgment really for good reason. This seems to be the case when we consider the implications of behaviourism or of reductionist materialism in psychology. According to behaviourism, as expounded by the late B. F. Skinner, it is mere pre-scientific ‘mentalism’ to say, ‘I make that judgment because I have good reason to do so’; every judgment, including the judgments constitutive of psychological behaviorism itself, is made due to a history of positive reinforcement of innate biological impulses. Similarly, in accordance with reductive materialism, it is never really true that a person thought or wrote anything because it was rational for them to do so. Such a way of talking would be permitted, if at all, only as a shorthand for an explanation in terms of physics and chemistry; that is, the reason why someone writes something is because the laws of physics and chemistry operate in certain ways beyond our control. Lonergan, in acknowledgement of such paradoxical issues, labels as a ‘counter-position’ 1

See B. J. F. Lonergan, Insight: A Study of Human Understanding (Toronto: University of Toronto Press, 1992), pp. 95-96, 268. 2 See Andrew Beards, Insight and Analysis (New York: Continuum, 2010), chapter 1.

Lonergan’s Solution to the “Problem of Induction”

417

any judgment that is incompatible, in the last analysis, with its being stated for good reason.3 What is it to make judgments for good reason and for them to be well-founded? It is, as Lonergan expresses the matter, for them to be due so far as possible to attentiveness, intelligence, and reasonableness. We may be attentive to our sensations, feelings, and resultant imaginings, as emphasized by classical empiricists; but we may also be attentive, as John Locke and Edmund Husserl noted, but David Hume, Bertrand Russell and classical empiricism at large forgot, to the operations of our minds upon these inner realities—by questioning, hypothesizing, marshalling evidence, judging, deciding and so on. Intelligence is a matter of envisaging possibilities, forming hypotheses—what intelligent people do easily and often, and what what stupid people are relatively restricted in their capacity to do. (It is rather odd that Sir Isaac Newton, perhaps the most outstanding hypothesis-former who ever lived, said ‘I don’t form hypotheses.’) Reasonableness is the capacity to judge that some hypotheses are actually or probably accurate, in the light of the evidence to which one has attended. (What Newton in fact seems to have meant, to put it in our terms, is, ‘I am not merely envisaging hypotheses; I can point to a great deal of evidence which makes it certain, or at least overwhelmingly probable, that my hypotheses are true.’) It is rare, unless her organs are deficient, for someone to admit that she has never had the experience of seeing or hearing, or attending to, what she has seen or heard. Similarly, a lecturer will not usually begin a classroom session by informing his class that he has never come to an understanding—or even a misunderstanding—of anything. Again, a scholar will not often start a contribution to the periodical literature by admitting that she never weighed the evidence for or against a judgment, least of all in composing the present article. One cannot admit to never being attentive, intelligent, or reasonable, without disqualifying oneself from all serious investigation or discussion.4 It should be observed that, while there is an important connection between well-foundedness and truth, they are not identical. A judgment might be highly rational (attentive, intelligent, and reasonable), and yet fail to be true. There may be relevant evidence to which one has not attended, 3

Lonergan, Insight, pp. 413-15, 513, 519-20, etc.; Method in Theology, pp. 249-54, 270-71, 321, etc. 4 See Lonergan, Method in Theology (London: Darton, Longman and Todd, 1971), pp.16-17.

418

Hugo Meynell

possibilities which one has not envisaged. And yet judgments tend to be true so far as they are rational. The haruspex examining the entrails of cats may hit on the truth about who shot the president of the republic; the conscientious court of law, employing a large team of skilful and assiduous investigators, may yet fail to do so. But, to find out whether the haruspex was right, you would still have to be as rational as possible. Of the gap between well-foundedness and truth, there are many instructive examples from the history of science. In Aristotle’s time, for example, it was quite a well-founded judgment that the earth was not spinning on its axis or careering through the heavens and that the ‘fixed stars’ were set in a solid crystal sphere. After all, the oceans are not incontinently pouring over the surface of the globe, and there is not a constant gale blowing in the same direction, while the ‘fixed stars’, in contrast to the wandering ‘planets’, retain their positions relative to one another. We now know, of course, that the spinning of the earth does not have these consequences, so there is no need to postulate the crystal sphere. Aristotle’s epistemology, metaphysics, and ethics are in some ways astonishingly up-to-date. His treatise On the Heavens is outdated, but what he claimed there was not foolish, given the narrow range of empirical knowledge available in his time. We know that it is false simply due to a more extensive and thorough application of rationality—of attentiveness, intelligence, and reasonableness—than was possible in Aristotle’s time and situation. The role of questions and of the answers to questions is also to be noted. Two kinds of questions are to be distinguished in this connection: questions the answers to which are acts of intelligence, and questions the answers to which are acts of reasonableness or reflection. The second kind of question presupposes an answer to the first kind of question. The first calls for a hypothesis, the envisagement of a possibility; the second asks whether the hypothesis is true or not, whether the possibility is the case or not. I may be puzzled by the grimaces of a car-salesman directed at another salesperson; the possibility that they are trying to cheat me may then occur to me, and this possibility may be confirmed or disconfirmed by my subsequent experience. A single observation of a bird may induce a birdwatcher to suppose that she may have come across a rarity, but the apparent peculiarities of the plumage may turn out, on the basis of later observations, to be due merely to a trick of the light. I have seen a reproduction of the photograph of a bubble-chamber which first induced Murray Gell-Mann to envisage the possibility that there were quarks, but it is one thing to

Lonergan’s Solution to the “Problem of Induction”

419

consider the possibility that there are quarks, another to confirm that it is probably or certainly so. It is characteristic of questions for reflection that they may be answered ‘Yes’, ‘No’, or ‘Perhaps,’ in a way in which questions for intelligence may not. I cannot, except perhaps facetiously, answer ‘yes’ or ‘no’ to the questions, ‘What is the explanation of this unexpected streak on our photographic plate?’, or, ‘Why is there a stench in this apartment?’ But I may do so to the question, ‘Is it because of the passage of a previously unknown type of fundamental particle?’, or ‘Is it due to the fish which I bought some days ago, and which I may have forgotten to put in the fridge?’ The motions of the planets, as recorded by Tycho Brahe, gave rise to questions in Johannes Kepler’s mind, since they seemed compatible neither with the old geocentric assumption, nor with the then newfangled Copernican account, according to which the planets are moving round the sun in perfect circles. Suddenly, Kepler hit on the possibility that they were each following an elliptical orbit round the sun and that the straight line from the sun to each planet covered an equal area in an equal time (so that the planet was moving fastest at its perihelion, slowest at its aphelion); this accounted both for Brahe’s observations and for all those which have subsequently been made. A British ornithologist may be surprised by the especially conspicuous eye stripe of what she had taken to be a sedge-warbler, and it may suddenly strike her that she could have a specimen of the rare aquatic warbler before her. This supposition may be confirmed or falsified by subsequent observations on the part of herself or others. Let us call the business of being attentive to experience, being intelligent in hypothesizing and envisaging possibilities, and being reasonable in making judgments, which are all involved in coming to know, ‘the threefold process’. Let us say, furthermore, that a person is ‘rational’ so far as she effectively commits herself to that process. Other examples of types of fact to be known by the threefold process are those of the past and those concerning other minds. In these kinds of cases—as opposed to knowledge of what is in your neighbour’s living-room, or whether your Department Chair is in her office—what is known, or to be known, is at first sight very different from what is sensed or perceived, or to be sensed or perceived, though sensation or perception certainly provide grounds for the knowledge in question. In the cases of your Department Chair and of your neighbour’s living room, you can apparently enjoy direct perception of what you are trying to know, but, in the case of other minds, the past, and the theoretical

420

Hugo Meynell

things and properties postulated by physicists and chemists (mass, electron, valency, and so on), you cannot. Behaviourism in psychology follows from the assumption that what is knowable, at least in a fully ‘objective’ or properly ‘scientific’ sense, is after all only what we can perceive; what is supposed to go beyond this is merely ‘subjective’, at best a convenient manner of speech. The same assumptions applied to theoretical physics issue in ‘operationism’: what can be perceived, and in particular the perceivable results of experiments, is real, while unobservable theoretical entities, like positrons and gluons, are merely practical devices for recording what is perceived or anticipating what is to be perceived. The absurd consequences of the assumption probably come out most vividly when one applies it to historical inquiries. When we are asking questions about Horatio Nelson or King Henry VIII, all that we can perceive that is relevant to the matter is marks made in documents and noises made by academic authorities deemed to be specialists on the relevant places and periods. It seems to follow that Nelson and King Henry are in the last analysis nothing but convenient practical devices for anticipating one set of possible marks or noises and for not anticipating others. I submit that this is a little hard to swallow. If one holds, to the contrary, that what is to be known is to be known in judgments intelligently and reasonably made on the basis of what is perceptible without necessarily being a matter of what is perceptible itself, then no such paradox remains. 2 Arguments Against Classical Empiricism and Logical Positivism It has actually been maintained in some quarters (I take it on the basis of considerations such as the ones that I have just mentioned) that historical knowledge is impossible.5 One wonders what kind of knowledge is possible, and how and why, if historical knowledge is not. Perhaps the authors have at the back of their minds some such contrast as that made by Bertrand Russell, between ‘knowledge by acquaintance’ on the one hand and ‘knowledge by description’ on the other. Whatever may be stated or implied by the classical empiricism of Hume and Russell, we are directly conscious, not only of our sensations and feelings, but of the operations of our minds—in questioning, envisaging hypotheses, marshalling evidence, judging, deciding on the basis of our judgments, and so on—with respect to our sensations and feelings. To anticipate what I will argue at greater length later on, I believe that the 5 See The Philosophy of History. Talks Given at the Institute of Historical Research, London 2000 – 2006, ed. A. L. Macfie (Palgrave Macmillan, 2006).

Lonergan’s Solution to the “Problem of Induction”

421

well-known difficulties connected with the ‘problem of induction’, of which Hume is the best-known exponent, are due to the defective principles of classical empiricism. They are to be resolved not, as some would propose in effect, by an abandonment of epistemology in favour of common-sense realism, scientific materialism or whatever, but by a setting-out of the right epistemology that ensues from ‘the generalized empirical method’ propounded by Lonergan. As was noted by John Locke, we have ‘ideas of reflection’ as well as ‘ideas of sensation’ or feeling.6 We are aware of the operations of our minds upon our senses and feelings, as described briefly above, as well as of merely undergoing them, and accordingly can use the corresponding ‘ideas’ as themselves data for inquiry. There is no need for us to have direct experience of causal relations, for example, in order to believe reasonably in their reality; we can intelligently conceive their possibility and reasonably affirm their reality as the result of inquiry into our own experience. Other well-known epistemological puzzles, like that of our knowledge of other minds and of the remote past, may be similarly resolved. It is self-defeating to deny that we can make true judgments or judgments for good reason; reality, or the actual world, is nothing other than what true judgments are about and what judgments for good reason tend to be about. On the basis of my experience and the reported experiences of others, I may conceive the possibility that all ravens are black, and, in the light of more experience, reasonably affirm that they are so. Similarly, Einstein conceived the possibility that the general theory of relativity was true; it was reasonable to affirm that it was so on the basis of observations made of stars in the neighbourhood of the sun during a solar eclipse, which tended to confirm it and to falsify the previously-accepted Newtonian theory. Einstein’s theory also accounted more satisfactorily for the precession of the perihelion of Mercury, which for some time had been a headache for astronomers. A story could be told of the astronomer William Herschel who, in a state of great excitement just after he had first glimpsed the planet Uranus, asked a lay acquaintance to check the observation which he had made through his telescope, as he himself did again some time later.7 In subsequent years, the acquaintance would say, ‘Well, Sir William, I did observe a palpable disc against a background of points of light and later I noticed 6

John Locke, Essay Concerning Human Understanding (London: J. M. Dent, 1947), Book II, chapter i, section 4; chapters vi and vii. 7 It is certainly apocryphal, since I have just made it up to illustrate my point.

422

Hugo Meynell

that the disc had moved in relation to that background, but I could never understand what all the fuss was about.’ The scientific expert, as one might express the matter, has no privilege over the clear-sighted layperson with respect to observations as such, though she will know what to look for and the significance of the observations once made. I, who have no expertise whatever in subatomic physics, can see the pattern of streaks on the photographic plate alluded to earlier, but it took the erudition and vast intellectual talent of Murray Gell-Man to suspect the existence of quarks on that basis. Does what I have argued so far amount to ‘knocking logic’? Not a bit of it. Deductive logic is a matter of inferring strictly from judgments and is necessary if those judgments are to be tested adequately. But, even after this has been done, the deductions still have to be matched with observations. Reasonableness includes deductive logic, but it consists in more than that. Someone may protest, ‘But all that we need for the acquisition of knowledge of the world, apart from experience and deductive logic, is inductive logic.’ This is unhelpful, if all one means by ‘inductive logic’ is whatever one needs, apart from experience and deductive logic, for acquiring knowledge of the world. It has been objected that the famous ‘verification principle’ of the logical positivists self-destructs, since it is neither true by definition nor to be confirmed by experience that every true proposition is either true by definition or to be confirmed by experience. Rudolf Carnap is credited with the heroic suggestion that the verification principle was a bit of nonsense which had the great virtue of stopping you from uttering other sorts of nonsense, but few were satisfied with this answer to the problem. As to Lonergan’s ‘generalized empirical method’, knowledge has both an empirical and a nonempirical component: we are attentive to experience, but we also identify hypotheses and make reasonable judgments. (The knowledge we uncover qualifies, in Kantian terms, as the non-analytic a priori.) It is the contradictories of the principles of Lonergan’s account which self-destruct—that knowledge is only a matter of definition or that knowledge is only a matter of empirical observation. Lonergan’s insistence on the logical component of the empirical method was anticipated by Aristotle’s suggestion that someone who did not accept the principle of non-contradiction was no better than a vegetable.8 (If, in the case of any judgment you make, you could, with equal conviction, state its contradictory, then you can really make no judgments at all.) 8

Metaphysics IV, 4, 1006a15.

Lonergan’s Solution to the “Problem of Induction”

423

It was more closely anticipated by Aquinas’ argument against the Averroists. One consequence of Averroism was that the active aspect of thought did not belong to the human individual, but only to the Agent Intellect, which did not pertain to the human individual, but was a single transcendent being. It followed from this that human individuals, including Averroists, did not think, and, if so, concluded Aquinas, they were not worth arguing with. It might be claimed that contemporary subatomic physics forces us in any case to abandon the principle of non-contradiction. I believe this to be a mistake. ‘Wavicles’ (wave-particles)—quarks, leptons and so on—are certainly very odd objects from our point of view, which is that of middlesized beings who perceive and talk about, in the first instance, middle-sized objects. If we must imagine ‘wavicles,’ we have to do so sometimes in terms of waves, sometimes of particles. But we know them strictly in mathematical terms, admittedly verified by appeal to observation. The scandal involved in acknowledging the existence of such intrinsically unimaginable objects becomes less when we remember that force, mass, and acceleration, entities which we have been used to for centuries, are also strictly speaking definable only in mathematical terms and consequently such that we cannot really make imaginative pictures of them. It is an a priori truth that reality, or the actual world, cannot be other than what is to be rationally known; that is, what is to be known by intelligent and reasonable inquiry into experience. Aristotle’s koan in the De Anima, to the effect that the soul is in a manner all things,9 is in an obvious sense clearly and outrageously false. Yet, perhaps it hints at what I believe to be the truth, that the ‘external’ and ‘objective’ world is ‘outside’ the mind or soul only in a manner that the pre-critical or uncritical person would never suspect: not so much ‘out there’ as opposed to ‘in here’, but what qualifies as the terminus of the process of human coming to know— the ‘what is to be known’ that we access through an exercise of the ‘mind’ or ‘soul’. (The ‘inhere’ conception of mind is, among other things, a staple of materialism; as a well-known anthropologist, Lionel Tiger, confidently informed me, ‘the mind is the brain.’) It has been said to be the problem of the foundations of knowledge that to seek them inevitably leads either to arbitrary dogmatism or to infinite regress. (As Ann Levey put it to me, it’s a case of ‘choose your poison’.) Some have inferred that the problem is insoluble and that this does not matter: knowledge has no foundations, and we can easily put up 9

De Anima III, 8, 431b22.

424

Hugo Meynell

with that. I find this surprising. If this is taken literally, it implies that the judgment that the moon consists mainly of silicon has no better foundation than the judgment that it consists entirely of green cheese. (The siliconbelief, ultimately, does not have a better basis than the green-cheese belief.) Many recently have proposed ‘wide reflective equilibrium’ among one’s judgments as either constituting adequate foundations for knowledge or providing a substitute for them. The trouble with wide reflective equilibrium is that it is a wax nose, to be turned in any direction that suits a person. If you are Alvin Plantinga, the wide reflective equilibrium constituted by your beliefs will include belief that there is a God and that this God is uniquely revealed in Jesus Christ. If you are Kai Nielsen, on the contrary, it will include the firm belief that there is no God. About thirty years ago, a book was published with the title Groundless Belief, by M. E. Williams. It was well and intelligently written, and showed an impressive command of the relevant literature. But the whole enterprise represented by the book struck me as highly paradoxical. Is the belief that belief is groundless supposed to be groundless? But, if it were, how could one possibly argue for it? I am arguing here that the belief that belief may be grounded is grounded, and other beliefs may be grounded as well. The self-destructiveness of logical positivism may be taken to be an instance of a general dilemma pointed out by Wittgenstein in the Tractatus Logico-Philosophicus. A framework is set up, enabling you to determine once for all, apparently, whether a proposition in the last analysis makes sense and so what it would be for it to be true or false. But the framework itself is inevitably nonsense, according to the application of itself. This does not apply to Lonergan’s generalized empirical method, from which it is to be concluded both that foundations for human knowledge are needed and that they can be provided. The foundations of the edifice which is human knowledge are the contradictories of self-destructive judgments. What works positively—i.e., Lonergan’s observing, hypothesizing, judging method—is the foundation for human knowledge. What it is for judgments to be self-destructive, I tried to show in the earlier part of this paper. It is tempting to get rid of intelligence and reason in favour of deductive logic and then to claim that knowledge properly speaking is simply a matter of experience and deductive logic. The radical empiricism which culminated in logical positivism in fact did this. According to the framework which the logical positivists adapted from Wittgenstein’s Tractatus (though Wittgenstein himself was never a logical positivist), all meaningful propositions which were not true merely by virtue of the

Lonergan’s Solution to the “Problem of Induction”

425

significance of their terms could be subjected to a truth-conditional analysis, in the following sense. The truth of each ‘atomic’ or ‘elementary’ proposition consists in its ‘picturing’ an elementary fact. The truth of any ‘molecular’ proposition is nothing other than the truth of all the constituent atomic or elementary propositions; they are ‘truth-conditions’ of it, and it is a ‘truth-function’ of them. A ‘proposition’ that is neither an elementary proposition nor a truth-function of elementary propositions (always assuming it is not true by definition) is nonsense. It seems natural to take this ‘picturing’ in the sense of experiencing of particular sense-data or sense-contents—such as a pale blue image taking up the centre of my visual field, or the sound as of an oboe playing a mezzo forte in your immediate vicinity, or a faint smell as of rotting vegetables; this crucial step was taken by the logical positivists. This had the acceptable consequence that all the ‘propositions’ of traditional metaphysics or religion lacked significance; they were mere pseudo-propositions. What was not so acceptable was that the same appeared to apply to the propositions of ethics and morality. It was inferred that such locutions as ‘cruelty is bad’ and ‘cheating on one’s taxes is wrong’ were not actually meaningful as propositions but, all the same, had an important function, that of expressing emotion or influencing behaviour. To say ‘cruelty is bad’ is to get something off one’s chest; to say ‘cheating on one’s taxes is wrong’ may influence oneself or others in such a way as to make them less likely to behave in such a way in future. Later, it was regretfully noted that the same really applied to statements of theoretical science. Some answered (in a manner interestingly anticipated by Berkeley) that statements of theoretical science were indeed nonsense, since they were not truth-functions of elementary propositions which pictured experience, but all the same were very useful devices for getting from one meaningful proposition to another, for instance, from where Venus was to be observed today to where it would be observable in thirty days. Others were persuaded, for reasons like these, to abandon logical positivism. It does seem natural to say that the verisimilitude of the judgments both of common-sense and of science is a matter of their confirmation by experience, their falsity, of their disconfirmation by experience. And yet, perhaps the logic of truth-functions does not quite hit off the nature of this relationship, and this is connected to the fact that the operations of intelligence and reasonableness cannot be reduced to logic, unless ‘logic’ is taken in such a misleadingly wide sense as to include them. One may compare the case of the relation of the meaning of a written communication to the letters

426

Hugo Meynell

of which it is made up. ‘To b or not to b ; that is th qu stion.’ Even though I have left out each instance of the occurrence of the commonest letter of the alphabet, I am sure that most readers will immediately recognize the quotation. And the same would be the case a fortiori if I had left out any other letter. I suggest that much the same appears to any course of experience, as well as the facts which are to be intelligently conceived and reasonably affirmed on the basis of that course of experience. 3 The Objectivity of a World ‘Out there’ But how, after all, do we get from our “subjective” judgments, however rational, to “objective” knowledge of a world supposed to exist independently prior to any of our judgments, of which indeed we and our judgments form a tiny and insignificant aspect?’ ‘Reality’, or ‘the actual world’, can in the last analysis be nothing other than what true judgments are about and what judgments for good reason tend to be about. One is ‘objective’, in the only worthwhile sense, to the degree that one is rational. What one might call ‘the idealist point’ is that the real world is only to be known through constructive acts of intelligence. But it is a limitation of traditional idealism, so far as it does not admit that some of these intellectual constructions are to be confirmed as probably or certainly true through reasonable judgment on the basis of experience. ‘But how can one ever get to know of an objective world, a world out-there, by exercising such essentially subjective dispositions as attentiveness, intelligence and reasonableness?’ Epistemological reflection, backed up by consideration of the history of philosophy from Locke to Hegel, suggests that the real world may be ‘out there’ in a way one might not otherwise have thought. It looks, in fact, as though ‘genuine objectivity’ were nothing other than ‘the fruit of authentic subjectivity’10 as unrestrictedly attentive, intelligent, and reasonable. Such ‘authentic subjectivity’ is transcultural; cultures may be transculturally evaluated as more or less frustrating or encouraging it. Very briefly and summarily, Locke thought that the ordinary world apparent to the senses was dependent on the senses and that what really existed ‘out there’ was the world as described by Newtonian science. Berkeley protested that the intelligible world of Newton should more properly be ascribed to the operations of human intelligence, that the criterion of real existence was perceiving or being perceived. Kant inferred that, since the sensible world was dependent on the senses and the intelligi10

Lonergan, Method, pp. 265, 292.

Lonergan’s Solution to the “Problem of Induction”

427

ble world on the operations of human intelligence, things in themselves— what there really was ‘out there’—were unknowable to us. Fichte and Hegel concluded that the postulation of such ‘things in themselves’ (the ghostly things naïve realism assumed to be ‘out there’), made no sense in the last analysis; there was only mind or spirit coming into possession of itself through the progress of science and philosophy. The conclusion to this dialectic, as affirmed by the ‘critical realism’ which issues out of Lonergan’s ‘generalized empirical method’, is that real things are nothing other than what are to be known by intelligent inquiry followed by reasonable reflection into experience. Idealism correctly repudiates naïve realism and emphasizes the creative role of the mind in forming hypotheses and envisaging possibilities. But it neglects the role of reasonable judgment in establishing that some of the hypotheses or possibilities are certainly or probably true or false of the world. ‘Facts are what true statements state,’ declared J. L. Austin,11 rightly, in my opinion. I would add, they are what well-founded statements tend to state, and statements are well-founded so far as they are backed by the threefold process. They usually obtain prior to and independently of being stated, but all the same, as I have already argued at length, their nature is intimately related to their being state-able in principle. The world of common sense and common experience, where one moves as matter of course from experience of facts to judgment, is the one in which every human being lives on pain of failure to survive, except in special environments (e.g. nurseries, asylums) deliberately designed to ensure such survival in incompetents. Alasdair MacIntyre will have it that facts came into existence at about the same time and place as wigs for gentlemen, when it became fashionable to talk in terms of them.12 I retort that it seems natural to say that ‘Sirius is between five and ten light-years away from the Earth’ is a fact and that this fact might have been the case even if human beings had never evolved at all, let alone become astronomers. MacIntyre’s view seems to lead straight to individual or social subjective idealism, where Sirius and its distance from the Earth depend on human opinions. In support of his view, MacIntyre cites P. F. Strawson,13 who maintains that the universe, if we stripped the facts from it, would be none the worse. I think it more natural to say 11

I am indebted to Mr. C. J. Dixon for this useful quotation. See J. L. Austin, ‘Truth’ (Philosophical Papers [Oxford: Clarendon Press, 1961]). 12 A. C. MacIntyre, Whose Justice? Which Rationality? (Notre Dame, IN: University of Notre Dame Press, 1988), p. 357. 13 P. F. Strawson, ‘Truth’, in Logico-Linguistic Papers (London: Methuen, 1971).

428

Hugo Meynell

that, short of facts, which are the case prior to and independently of any rational creature stating them—e.g., ‘Thorium is a radioactive element’; ‘There are two giant planets in the solar system outside the orbit of Saturn’—there would not be a universe at all. (Is not the existence of the universe itself a fact?) As I argued briefly earlier, there are three salient kinds of fact, namely, of the past, of the contents of other minds, and of scientific theory, where what is to be judged is other than anything that can be perceived. The facts to be known by the natural sciences differ from those to be known by the social or human sciences, in that in the case of the latter, though not the former, the objects as well as the subjects of possible knowledge are to some extent at least attentive, intelligent, and reasonable. Thus, short of the self-destructive judgment that rational judgment is unreal, the social or human sciences are not reducible to the natural sciences. Many commonsense judgments about perceivable things and persons in one’s immediate environment are not revisable in the same way as scientific or historical judgments. I am not likely to revise the judgment that I am or was sitting at my computer at about three o’clock on the first Tuesday afternoon in December 2011 or that the table at which I am or was working is or was pale brown and made of wood. All sane and sufficiently mature human beings have had this kind of knowledge of the medium-sized things and properties of things that make up their environment. As a result of the centuries-long investigation that has culminated in contemporary physics, we do not hold that the ancient Greeks or Israelites were wrong in believing such-and-such trees, rocks, and patches of salt water to have been in their immediate environment. When Xenophon tells us that the ten thousand Greeks saw the sea, we assume, unless we have reason to believe that Xenophon was trying to deceive his readers on the matter (which we have not), that the sea was really where they seemed to see it and consequently believed it to be. Where the facts about what the people around them felt and thought were concerned, Greeks and Israelites were probably about as much subject to error or deception as we are ourselves; on the facts of science and history they were certainly a great deal more ignorant. On those matters, the knowledge (well-founded and true belief) that they had was the result of carrying, or having carried, the threefold process so far, but no farther. It will be seen that the real world, of what is to be known by the threefold process, includes, at least in a sense, the ‘worlds of’ or ‘worlds for’ different human individuals and communities: what they believe or assume about the world. As sociologists and anthropologists assume, I can

Lonergan’s Solution to the “Problem of Induction”

429

find out their beliefs and opinions by being rational with respect to the relevant evidence, just as I can in the case of Betelgeuse, thallium, or the campaigns of Lucullus. Herein lie the principles for the armistice of the socalled ‘science wars’ of the early twenty-first century, which are fought between natural scientists on the one side and sociologists of science and anthropologists on the other. Natural science is a matter of progressively finding out how the world really is, independently of human opinions about it. The real world is not just an aspect of the ‘world for’ a particular cultural community. Indeed, the ‘worlds for’ particular communities, so I have just argued, are themselves parts or aspects of the real world progressively discovered by social science; we employ the threefold process to find out what people in other societies believe or have believed about how things are, as we do to find out about how things are in general. It is to be noted that, unless individuals or communities were at least to some extent rational with respect to middle-sized objects in their environment, they would not survive. One has to have true beliefs about sabretooth tigers and poisonous berries in order to react appropriately to them. In some ways, ‘primitive’ humans may be more rational than ‘civilized’ ones. It is said that Australian aborigines are able to detect subterranean water on the basis of surface signs in a manner that could never be rivaled by most people of European descent. And isn’t it at least conceivable that we might learn something—e.g., about our relations with the spirits of the recently dead—by examining the relevant evidence, and so come to believe that members of comparatively ‘primitive’ societies have beliefs about certain matters that are closer to the truth than our own? It may be asked whether there are other kinds of fact, such as transcendental, moral, or transcendent (as distinct from transcendental) facts. Transcendental facts are those about knowledge and the knowable, and the relation of the one to the other, of the kind that I have been arguing to be real from the beginning of the paper. It is often disputed whether there are ‘moral facts.’ It appears to me that, on the basis of what I have already argued, to all intents and purposes there are, and moral knowledge is therefore possible. We may conclude, on the basis of the relevant evidence, that lying is in general a bad thing, or that it is on the whole, except perhaps in special circumstances, better to be kind than cruel. There are moral facts of a more particular kind, too: ‘To treat her with such contempt was very wrong of me’; ‘To slap that child for no better reason than that you were in a fit of temper was a bad action on your part.’ If we are to do what is good as well as to know what is good, we have to add another ‘transcendental

430

Hugo Meynell

precept’ to our threefold methodology of attentiveness, intelligence, and reasonable judgment: ‘Be responsible’.14 To be responsible is to act in accordance with one’s rational judgment of what is good or right. How do we determine what is right or morally good? Roughly, by appeal to what promotes happiness (of course, in others as well as in ourselves) and fairness. No tight logical connection is involved; but that applies to science in relation to experience as well. It is, of course, highly responsible to determine to be as rational as possible. That (i) a thing is x is largely a matter of its being a or b, does not entail that (ii) there is a tight logical connection between a thing being x and its being a or a thing being x and its being b. This is left out of account by those who infer ethical subjectivism, relativism, emotivism or prescriptivism from G. E. Moore’s so-called ‘naturalistic fallacy’ argument. It is the former kind of relation that obtains between moral goodness on the one hand and the promotion of happiness and fairness on the other.15 A good and healthy attitude to other people, and indeed to oneself, seems to be quite largely a matter of being open to surprising evidence as to what they may think and feel, rather than fixing them to the Procrustean bed of one’s ingrained assumptions.16 (To behave in that last manner causes a great deal of human suffering, particularly within human families.) The reader may notice a parallel at this rate between good human relations and good science, at least as this was conceived by Sir Karl Popper. One may actively search for evidence against the more self-serving aspects of one’s self-image, just as one can search for evidence against one’s pet theory in one of the natural sciences.17 Are there any transcendent (as opposed to transcendental) facts? That will depend on whether it is rational to suppose that there is a God, or, if there is, that God has revealed, say in a book or an institution or both, 14

See Lonergan, Insight, chapter xviii; Method, pp. 20, 53, 55, 231-2, 302. Cf. G. E. Moore, Principia Ethica (Cambridge: Cambridge University Press, 1953; originally published 1903). See Hugo Meynell, Freud, Marx and Morals (Basingstoke, England: Macmillans, 1981), chapter 6. Also, ‘Christian Apologetics in an Era of Philosophical Chaos’, in Border Crossings. Explorations of an Interdisciplinary Historian. Festschrift for Irving Hexham, ed. Ulrich van der Heyden and Andreas Feldkeller (Stuttgart 2008). 16 See R. D. Laing, The Divided Self (Harmondsworth, UK: Penguin Books, 1967); R. D. Laing and A. Esterson, The Families of Schizophrenics (London: Tavistock Publications, 1966). 17 See K. R. Popper, Objective Knowledge. An Evolutionary Approach (Oxford: Oxford University Press, 1972). 15

Lonergan’s Solution to the “Problem of Induction”

431

something of the divine nature and purposes for humankind. Someone might argue that the fact that reality is, on the account I have given, through-and-through intelligible, is best explained if there is something like intelligence at the bottom of it.18 The general lines of what such a being might be expected to reveal, given the human plight, could also be argued.19 4 Epistemology and Metaphysics: Critical Realism Epistemology, which includes tackling the problem of induction, may be regarded as the study of what it is to come to know. Metaphysics attends to the overall nature and structure of the world that is thus to be known. There is an idealist point to be taken into account by the metaphysician, but there is also a characteristic idealist oversight that should not be neglected. The point is that an adequate general account of the overall nature and structure of the world, as assayed by metaphysics, is centrally affected by the fact that conscious subjects such as ourselves come to know it as they do. The idealist oversight ignores the fact that, all the same, the world very largely exists and is as it is prior to and independently of (at least finite) conscious subjects. If the empiricist exaggerates the role of experience in coming to know, idealism rightly emphasizes the role of constructive intelligence, but neglects that of reasonable judgment. The correct epistemology and metaphysics, which takes account of the role of all three (experience, constructive intelligence, and reasonable judgment), may be referred to as ‘critical realism.’ The fact is that one’s theory of knowledge, of what it is to know or to come to know, cannot but have repercussions on one’s theory of ‘being’, of what there is to be known. It is easy to dismiss positivism, or radical empiricism, as incoherent, as indeed it is, but it is perhaps more fruitful in the long run to envisage it as the thesis in a quasi-Hegelian triad, with idealism as antithesis and critical realism as synthesis. The basic thesis of a critical realist metaphysics is that the real world is nothing other than what is to be known through attentiveness to experience, fertility in intelligently conceiving hypotheses or possibilities, and reasonableness in judging what hypotheses are the case or not the case. Empiricism overemphasizes the first but neglects the second and third; idealism takes adequate account of the second but is apt to neglect the first and the third; critical realism takes adequate account of each element of the threefold process. 18 19

Lonergan, Insight, chapter xix. Lonergan, Insight, chapter xx.

432

Hugo Meynell

Evidently there are very many things about the world that we do not know. The fact remains, however, that we can, here and now, form, as one might put it, a second-order conception of ‘reality’, ‘the actual world’, or whatever, as what we would progressively come to know if we were rational (attentive, intelligent, and reasonable) to an indefinite extent. In connection with the well-used phrase, ‘the external world’, it is to be noted that at this rate ‘the world’, or ‘reality’, turns out to be ‘external’ in a way somewhat different from what one might spontaneously have supposed. ‘I’, as a subject of knowledge or well-founded true judgment, am not exactly inside my skin or inside my scalp as my brain is, nor is ‘the external world’ exactly ‘outside’ it. My brain, as well as the rest of my body, turns out to be a very minor and insignificant part of the world in the sense of what I can make well-founded and true judgments about. ‘The mind is the brain’ is something of a mantra for contemporary materialists; in that case, the mind is certainly within the skull, and the vast majority of what is to be known is definitely outside it. But, popular as materialism is, not least among some philosophers, the only thing it has going for it, so far as I am concerned, is the falsity of subjective idealism (including the sociological version of this, which seems currently popular). The materialist is certainly correct in insisting that, before any (human) person existed, there were rocks, planets, oceans and chemical elements; for all that, if we are to find out the truth about these things, we only have our ‘subjective’ mental processes to go on. Yet it is difficult to see what else it has going for it, except perhaps a proper if confused respect for natural science. At a conference in the east of Canada in the mid nineteeneighties, someone earned himself a round of applause, which I fear may have been not untinged with irony, by the declaration: ‘Oh no, materialism isn’t a metaphysics; it just happens to be true.’ Immanuel Kant sees why one might as well say that the world of Newtonian science is an intellectual construction (following Berkeley), as that the world of sense-experience is dependent on our senses (as Locke did). That notoriously leaves him with things in themselves as unknowable. However, as Fichte and Hegel in effect point out, the cat without sensible or intelligible properties is not so much a mysterious cat-in-itself as no cat at all. I think that, to express it very briefly and summarily, the answer to this nest of problems is that idealism is half right: we need intellectual constructions to get at reality, and of this, as Hume makes clear (hence his waking of Kant from his dogmatic slumbers), our aporiae with causality are a crucial sign, but that doesn’t stop reality, as open to our probing

Lonergan’s Solution to the “Problem of Induction”

433

through rational inquiry, from existing prior to and independently of our intellectual constructions. Yet this epistemology, as well as the metaphysics to which it leads, comes with an apparent price-tag. God may well be deemed to come back into the picture as the intelligent will accounting for the intelligible facticity of the world. Plato, Aristotle, and Lonergan all think that the intelligibility of the world requires something like an intelligence to account for it; Kant’s ‘Copernican revolution’ is to the effect that we put it there ourselves. To sort out the implications of the fact that, in a sense, we intellectually construct the world—not only the world of theoretical science but of historical facts and other minds—and that we, at the same time, find it intelligible prior to and independently of ourselves— seems to me about the most crucial task of philosophy. It would appear to be an aspect of Kant’s greatness that he rubs our noses in this problem. 5 The Problem of Induction What application do the results of our discussion so far have to induction as such? The general consensus among philosophers is that while we cannot do without induction, we cannot justify it. To cite Russell, ‘What these (Hume’s) arguments prove—and I do not think the proof can be controverted—is, that induction is an independent logical principle, incapable of being inferred either from experience or from other logical principles, and that without this principle science is impossible.’20 As Louis Groarke sees it, it is misguided to think that we can prove the first principles of science or morality. ‘We cannot prove the first principles of human knowledge (including induction), for there is nothing we can use to prove them. There is nothing prior to first principles. We have to create them out of nothing.’21 ‘Prove’ is a strong word. But perhaps we can give good reasons which amount to more than mere assertion. One may usefully distinguish what may be called the ‘primary’ from the ‘secondary’ problem of induction. The former involves the kind of inference we make from the observation of ninety-nine black ravens, and of none that are not black, to the generalization ‘all ravens are black’. The latter involves the kind of judgment that we make from any set of evidence to a statement of what is supposed to explain such evidence when no deductively valid inference can be made from the evidence to the explana20

A History of Western Philosophy (London: Allen and Unwin, 1946), p. 700. Louis Groarke, An Aristotelian Account of Induction. Creating Something From Nothing (Montreal: McGill/ Queen’s University Press, 2009), p. 429. 21

434

Hugo Meynell

tion. According to the arguments made famous by Hume,22 we cannot justify induction. For all that we cannot do without it, if we are to get by in the world at all, let alone investigate the universe scientifically, we cannot support it logically. How do we know that the hundredth raven will be black, just because the previous ninety-nine were so and none failed to be so? We assume, and we cannot but assume. To take Hume’s famous example that the sun will rise tomorrow, we have successfully assumed it in the past, but why should the future be like the past? We may appeal to something like ‘the uniformity of nature’, but on what is the conviction of ‘the uniformity of nature’ based, other than, as Hume suggests, our mental habits? We expect the future, in general terms, to be like the past, and, fortunately, it turns out that we are right. As his view has been expressed, the glue constitutive of the causal nexus is in the last analysis merely psychological. On the basis of the ‘generalized empirical method’23 that I have sketched, of course, as opposed to classical empiricism, there is no good reason to believe this. I can reasonably judge that there is a causal connection between the impact of a brick and the breaking of a window on the basis of my repeated experience. It has been suggested that, if we are to find a solution to the problem of induction, we should resort to the work of Aristotle.24 But Aristotle takes little trouble to justifyepagǀgƝ or induction, and what he does come up with does not appear to show the great philosopher at his most impressive. Suppose we argue inductively from the propositions ‘Angela Merkel has two legs; Margaret Thatcher has two legs; Monica Lewinsky has two legs’, to the general proposition ‘All women have two legs.’ Such justification as Aristotle appears to offer makes gestures towards either (i) Angela Merkel, Margaret Thatcher and Monica Lewinsky are all the women there are; or (ii) There is no woman other than Angela Merkel, Margaret Thatcher and Monica Lewinsky who does not have two legs (give or take a few with genetic defects or who have undergone severe accident or surgery). It is obvious that (i) is outrageously false, and we are in no position to know (ii). As Robin Smith sees the matter, Aristotle simply does not provide a 22

David Hume, A Treatise of Human Nature, ed. D. G. C. Macnabb (London and Glasgow: Collins, 1962), Book I, Part iii, Sections 2-4, 14; Enquiry Concerning Human Understanding (Enquiries Concerning Human Understanding and the Principles of Morals, ed. L. A. Selby-Bigge [Oxford: Clarendon Press, 1975]), Section V, Part 1. 23 Lonergan, Insight, pp. 95-6, 268. 24 See Groarke, Induction, passim.

Lonergan’s Solution to the “Problem of Induction”

435

complete account of induction, and any attempt to infer one from what he has left us can only be a matter of speculation.25 Smith carries conviction by his learning, the context of his publication, and the fact that he apparently has, in contrast with Groarke and me, no axe to grind. Nonetheless, the germ of the solution is to be found earlier in the second book of the Posterior Analytics.26 Aristotle has there distinguished between four kinds of question that may be asked about phenomena in the pursuit of knowledge, which he then reduces to two. These turn out to be identical with the ‘questions for intelligence’ and ‘questions for reflection’ (to use Lonergan’s terminology) which I distinguished at the beginning of this paper. Answering the first kind of question requires the elaboration of a hypothesis; answering the second kind of question means determining whether the hypothesis is true or not. In marked contrast to the discussion ofepagǀgƝ as such, this passage is the expression of one of ‘The Philosopher’s’ greatest strokes of genius. Unfortunately, he does not explore this topic for long, but goes on to the discussion of other matters. Conclusion I would like at this point to try to summarize what I have attempted to argue. Though the argument is essentially Lonergan’s, I shall deliberately, so far as possible, avoid Lonerganian terms of art in formulating it. 1. The denial of the judgment that one ever makes true judgments, or of the judgment that one ever makes well-founded judgments, is self-destructive. 2. Judgments may sometimes fail to be true, though they are well-founded, given the limitations of their place and time (the history of science provides many examples), but well-founded judgments do head towards truth. 3. The world, or reality, is nothing other than what true judgments are about and what well-founded judgments tend to be about. 4. One’s judgments are well-founded so far as they are a result of: (a) paying attention to the relevant experience (in a broad sense), (b) using intelligence in envisaging a sufficiently wide range of possibilities or hypotheses that might account for that experience, and (c) being reasonable in affirming to be so in each case the judgment which does best account for it. 5. ‘Induction’ is a rather misleading term for the somewhat complex process that I have just summarized: of inference from experience to sound 25

Robin Smith, ‘Logic’, in The Cambridge Guide to Aristotle, ed. Jonathan Barnes (Cambridge: Cambridge University Press, 1992), pp. 30, 32. 26 Posterior Analytics II, 2, 89b36-90a 34; cf. Metaphysics IX, 9, 1051a 22-33.

436

Hugo Meynell

judgment based on that experience. It is only a problem if one approaches it from the point of view of classical empiricism, rather than by way of the ‘generalized empirical method’, which is attentive not only to experience in a narrow sense, but to our awareness of the operations of our minds upon such experience.27 Finally, a visiting motorist in Ireland was once asking his way; he was told, ‘If oi were goin’ to Ballyskulty, oi wouldn’t be startin’ from here.’ You can’t get to a solution to the problem of induction from the position of classical empiricism, as Hume showed once and for all. There are indeed hints of how to get there in Aristotle, but not where they are generally sought. You can, however, arrive at a solution by way of Lonergan’s ‘generalized empirical method’. Appendix I have tried to make my case about induction on the basis of its own intrinsic merits as I see them, and not by appeal to the authority of Lonergan or anyone else. Yet I must confess to a conviction that his dealing with the topic of induction and related basic issues in philosophy is a principal source of Lonergan’s claim to be a major philosophical luminary, as opposed to an eccentric minor talent, let alone, as one of his detractors has expressed the matter, a purveyor of ‘sheer pedantry’. After expounding the theory of knowledge, using mainly mathematical examples that I have attempted to summarize and justify here, Insight pursues the consequences through natural science, philosophy of nature, depth psychology, politics, metaphysics, hermeneutics, ethics, natural theology and Christian apologetics. Verbum28 traces the historical roots of this theory of knowledge in the work of Aristotle and Aquinas and shows how Aquinas applies it to construct a systematics of the Trinity, which is endorsed by Lonergan himself. A brief and relatively lucid account by Lonergan of his theory of knowledge is to be had in ‘Isomorphism of Thomist and Scientific Thought’.29 27

Frederick E. Crowe, ‘Introduction’ to Lonergan, Collection (London: Darton, Longman and Todd, 1967), p. xx: “(T)he ‘problem’ of induction as such gets short shrift in Insight. True enough, the first half of the book is largely concerned with the same activities as are studied in the alleged problem; but for Lonergan the real problem is simply that of accurate understanding, and when this is solved the problem of induction disappears.” 28 Verbum: Word and Idea in Aquinas (London: Darton, Longman and Todd, 1968). 29 In Lonergan, Collection.

Induction as a Pragmatic Resource Nicholas Rescher University of Pittsburgh

Abstract: Rescher argues for a pragmatic understanding of induction, which shows the nature of induction to be an erotetic procedure, i.e., a process for securing answers to questions on the basis of insufficient information. It is an instrument for question-resolution in the face of imperfect information intended to secure the best available answer, given the existing conditions in which we must conduct our epistemic labors. Induction is a matter not really of inference but of plausible conjecture and of truth estimation, resulting in an estimate that is tenable and capable of providing reasonable warrant for rational assurance. Since this process usually involves a search for the enthymematic premise that is plausibilistically optimal (namely that premise which, relative to the information in hand, represents the smoothest enthymematic supplementation of the background information), the inductively appropriate answer is the correct one, not categorically, but as best we can determine it and is true according to the best available judgment of the matter. Plausibility is shown to be a matter of cognitive systematicity. By its very nature, induction involves the risk of error, yet seeks to be a risk-of-error minimizing erotetic process. Induction is best seen as an estimation technique, a methodology for obtaining answers to our factual questions through optimal exploitation of the information at our disposal. Accordingly, induction is on a pragmatic approach, rather a matter of “inference to the best systematization” than one of “inference to the best explanation.”

1 The Nature of Induction Older textbooks on reasoning processes characterize induction as a mode of inference from the particular to the general, but this characterization is clearly overly restrictive. When I surmise that Henry is presently home because his car is in the driveway, I am reasoning inductively, and yet my inference is particular and not general. Hume-influenced theorists often characterize induction as a matter of inference from the past to the future.

438

Nicholas Rescher

But the preceding car-in-driveway illustration shows that this need not be the case at all. Again, induction is sometimes described as inference from a part to the whole—from a sample to an entire population; for example from a few testdriven autos of a certain model to the whole population of this type of auto. But when I surmise that on the next occasion you will select an action film because that’s what you did the last few times we went to the movies together, I need not endorse the idea that you will always prefer action films. The fact of it is that “induction” covers a rather wide and diversified range, including such inferential transitions as: particular o general past o present-or-future sample o population examined cases o as-yet unexamined cases Yet all of these represent particular modes of inductive reasoning: individually they are neither typical nor universal with regard to induction in its entirety. A comprehensive characterization of induction must be sought elsewhere. On the whole and in general, induction is a mode of reasoning that moves from premises that present presumably acceptable data to conclusions that make claims whose information extends above and beyond what those premises provide for. What induction thus does is, in effect, to outrun the information-at-hand in an endeavour to enlarge the range of knowledge, by answering on a merely suggestive basis questions that information at hand does not resolve in a decisive way. Induction, so conceived, is a very diversified and much-inclusive mode of reasoning that admits of a wide variety of realizations as regards the cognitive transition at issue: particular to general, past to future, sample to population, instance to type, etc. The generic function common to all of these instances is the transition from given premises taken as established to conclusions that transcend the limitations of their informative range. What is, from the standpoint of deductive logic, a blatant fallacy of reasoning defines the very nature and constitutes the very reason for being on inductive inference.

Induction as a Pragmatic Resource

439

2 Induction a Matter of Doing the Best We Can at Questionresolution Induction is a tool for use by finite intelligences, intended to secure not the best possible answer (in some rarified sense of this term), but the best available answer, the best we can manage to secure in the existing conditions in which we do and must conduct our epistemic labors then and there. Of necessity, its reach is restricted to what lies within our cognitive range: it obviously cannot deal with issues that might lie outside our conceptual horizons (as quantum electrodynamics lay beyond those of the physicists of Newton’s day). The “available” answers at issue have to be found within some limited family of alternative possibilities within our intellectual reach. Induction is not an occult matter of an intellectual alchemy that transmutes ignorance into knowledge; it is a mundane and realistic human resource for doing the best we can in the circumstances in which we find ourselves. Consider a question of the form: “Are the Fs also Gs?” The situation here is akin to that of a multiple-choice examination, where one can respond: (1) Yes, all of them are. (2) Never—none of them are. (3) No, some are and some aren’t. (4) Don’t know; can’t say. This pretty well exhausts the range of alternatives. Now when in fact all of the observed Fs (over a fairly wide range) are indeed Gs, our path seems relatively clear. Alternative 4 is not an answer—it is a mere evasion of the question, a response of last resort, to be given only when all else has failed us. Alternative 2 is ex hypothesi ruled out by the information at hand in the circumstances. The choice between 1 and 3. And we naturally opt for the former. The governing consideration here is the matter of plausibility— specifically that secured by uniformity. For 1 alone extends the data in the most natural way, seeing that this response alone aligns the tenor of our general answer with the specific information we actually have in hand. It is, accordingly, this resolution that affords the “inductively appropriate” answer in the postulated circumstances.

440

Nicholas Rescher

To be sure, to say that induction represents the search for plausibilistically optimal answers, is not to deny that it (like all question-answering devices) enjoys the privilege of maintaining silence and responding “can’t say” as the proper reply in certain circumstances. Quite the reverse. If we ask, “Which side of this (fair) die will come up?” this is exactly what induction would reply: we just cannot effect a rationally defensible resolution here. No inductively appropriate answer is available. (And this situation would still obtain even if the die were loaded in favor of one side.) Yet this sort of negativity is something the inductive enterprise seeks to minimize. But why not always opt for safety in answering our questions, systematically selecting the noncommittal pseudo-alternative “none of the above”? Why not decline all risk of error and simply follow the path of skepticism: in accepting nothing whatever you will accept nothing false? The answer is simple: nothing ventured, nothing gained. The object of the cognitive enterprise is clearly to secure truth (and not simply to avert error!). This, after all, is a definitive task of inquiry, the venture of cognitive gapfilling—of securing information as best we can. Stephen Barker has formulated the point at issue clearly and cogently: Of course it is true that further observations would be bound to eliminate many of these competing hypotheses; but to say that we ought to suspend judgment and wait for more data is to miss the point, for our problem here is to use the data that we have got and in the light of them make a reasonable judgment about which hypothesis we should accept. It is inappropriate to appeal to data that are not yet obtained, for our decision always has to be based upon the evidence that we have got, not upon evidence that we have not got. We never obtain more than a finite quantity of data, and no matter how excellent these data may be there will remain always innumerable different hypotheses consistent with them. We cannot forever defer our choice among the competing hypotheses, forever waiting for more data to be collected; we must be able to come to some reasonable decision in the light of a finite collection of evidence.1

In valid deduction, we are in the fortunate position of having premises that provide conclusive grounds for our conclusions: We have situations of fully supportive pro-information. Induction effectively inverts this proceeding, resolving the questions we face correlatively with the

1 “Formal Simplicity as Weight in the Acceptability of Scientific Theories,” Philosophy of Science, 28 (1961): 162-171, p. 164.

Induction as a Pragmatic Resource

441

minimum of contra-indications. We seek to minimize the as-yet visible risks in the inevitably risky venture of cognitive gap-filling. Nevertheless, the “best available answer” at issue here is intended in a rather strong sense. Its acceptability-claims must not merely be stronger than those of the alternatives; they must be substantially stronger, a difference more substantial than is reflected in any mere difference in probability, since the most probable cannot eo ipso be reasonably claimed as true. The quest for information hinges on the distinction between good and bad answers, between answers that have little or nothing to be said for them and answers for whose acceptance there is adequate systematic warrant, everything taken into account. An inductively appropriate answer must qualify as our best estimate of the true answer in a noncomparative sense that encompasses being a good answer pure and simple. We want not just an “answer” of some sort, but a viable answer—an answer to whose tenability we are willing to commit ourselves. Induction is not to be a matter of “mere guesswork” but of “responsible estimation” in a serious sense of the term: it is not just an estimate of the true answer that we want, but an estimate that is sensible and defensible: tenable, in short. The provision of reasonable warrant for rational assurance is the object of the enterprise. The informative insufficiency of the premises in relation to an inductive conclusion means that induction always to some extent involves a leap in the dark. And we make such a leap not fecklessly “for the fun of it,” but because there is no way to avoid doing so if answers to our questions are to be obtained. The salient point here is that in its reliance on information above and beyond anything that the premises provide for means that inductive reasoning is a matter not really of inference but of plausible conjecture. Nevertheless, inductive reasoning can be, and normally is, a matter of tighter connection than the merely statistical correlations at issue with Bayesian probabilities. It generally envisions a higher linkage of evidential support than statistical frequency correlations can provide. Inductive reasonings close the gap between available information and the answers we propose to our questions by looking to greater security of connection because presumably plausible and well-evidentiated enthymematic premises are at work. But still a gap is always there. A being in total possession of the facts— never beset with information gaps that needed to be followed through running cognitive risks—would never need to venture into inductive

442

Nicholas Rescher

inference. God has no need to reason inductively: not for him are the challenges to cognitive estimation. 3 Induction as Truth Estimation For the sake of concreteness, let us consider a typical (albeit super-simple) inductive issue. Let it be that we have before us the inductive arguments set out in Display 1.

______________________________________________________ Display 1 SAMPLE INDUCTIVE ARGUMENT • There is smoke there (and suitable background considerations)

• There is smoke there (and suitable background considerations)

• There is smoke there (and suitable background considerations)

•

•

•

______________________________________________________ ?There is fire there.

?There is a smoke-flare There.

?There is a smokedischarging storage container there

______________________________________________________ The inductive task is to determine which one of these alternative answers to the question “What does yonder smoke portend?” is to qualify as the “most promising” in the sense of identifying the particular addendum Ei that is, relative to the given data of K, the plausibilistically optimal alternative at our disposal—where the “plausibility” at issue turns on the matter of “best fit” with respect to the information at hand. The inductively appropriate answer to the question at issue corresponds to the outcome of this search for the enthymematic premise that is plausibilistically optimal—namely that premise which (relative to the information in hand) represents the smoothest enthymematic supplementation of the background information. On this enthymematic analysis, inductive argumentation involves a characteristic two-step process: (1) possibility-elaboration, that is, the conjectural proliferation of the spectrum of alternative possible answers accompanied by a process

Induction as a Pragmatic Resource

443

of finding the appropriate enthymemes for each such answer by determining the best ways of closing the “epistemic gap” that separates those answers from the given “data of the problem.” (This survey need not include all theoretically available alternatives, but can merely span them by some suitable covering process.) (2) possibility-reduction, that is, the reduction of these alternatives through elimination of some of them. This is to be done by assessing the relative plausibility of the materials needed to close the enthymematic gap encountered en route to the solution in question. That is, we use an analysis of comparative plausibilities as a reductive device for seeking out the plausibilistically optimal alternative(s) within this manifold of possibilities. Notice how this perspective indicates that it is desirable to distinguish between an inductive argument (which is simply an enthymematic argument whose factual conclusion outruns the information provided by its premises), and inductive argumentation considered as the general procedure of inductive reasoning, a complex process in the course of which very different sorts of reasonings—including not only deductive inference but also conjectural and plausibilistic argumentation—will enter in. From this perspective, induction leaps to its conclusion instead of literally deriving it from the given premises by drawing the conclusion from them through some extractive process. Whewell put the point nicely. “Deduction,” he wrote, “descends steadily and methodically, step by step: Induction mounts by a leap which is out of the reach of method [or, at any rate, mechanical routine]. She bounds to the top of the stairs at once …”2 We cannot pass by any sort of inference or cognitive calculation from the “premises” of an inductive “argument” to its “conclusion” because (ex hypothesi) this would be a deductive non sequitur—the conclusion (in the very nature of the case) asserts something regarding which its premises are altogether silent.3 Clearly the paradigm mode of inference—of actually deriving a conclusion 2 William Whewell, Novum Organon Renovatum (London: J. W. Parker and Son, 1858), p. 114. 3 The force of Dickinson Miller’s principle must be acknowledged: “There are no intermediate degrees between following from premisses and not following from them. There is no such thing as half-following or quarter-following.” Dickinson S. Miller, “Professor Donald Williams vs. Hume,” The Journal of Philosophy, 44 (1947): 673684, p. 684J.

444

Nicholas Rescher

from the premises—is actual deduction,4 and this paradigm does not fit induction smoothly. As one recent writer has felicitously put it, our inductive “conclusions” are “not derived from the observed facts, but invented in order to account for them.”5 Thus regarded induction is thus not so much a process of inference as one of estimation—its conclusion is not so much extracted from data as suggested by them. With inductive reasoning there is always an epistemic (or conjectural) gap between the premises and the conclusion, a gap that is large or small depending on the information required as supplement to the premises to guarantee the conclusion: is it minimum in scope—small, trivial, plausible, will established—or is it the opposite, ambitious and extensive? Clearly, we want to accomplish this gapfilling step in the least risky, the minimally problematic way. Induction, on the present approach, is seen as a method (or family of methods) for arriving at our best estimate of the correct answer to questions whose resolution transcends the reach of the facts in hand. In view of the unescapable equation of “correct” with “true” we may characterize induction as a process of truth-estimation. Given the information transcendence at issue in such truth-estimation, we know that induction does not guarantee the truth of its product. Indeed, if the history of science has taught us any one thing, it is that the best estimate of the truth that we can make at any stage of the cognitive game is generally to be seen, with the wisdom of hindsight, as being far off the mark. Nevertheless, the fact remains that the inductively indicated answer does in fact afford our best available estimate of the true answer—in the sense of that one for whose acceptance as true the optimal overall case be constructed with the instruments at hand. The need for such an estimative approach is easy to see. Pilate’s question is still relevant. How are we humans—imperfect mortals dwelling in this imperfect sublunary sphere—to determine where “the real truth” lies in matters of scientific fact? The consideration that, at the level of matters of generality, we have no direct access to the truth regarding the world, that, indeed, it is doubtful if one can make any sense at all of the notion of 4

This perspective supports F. H. Bradley in his critique of J. S. Mill’s view of induction on the basis of the consideration that inference as such is impotent to accomplish the move from particulars to universals: that it is only legitimate to argue from some to all if it is premised that the particulars at issue share some universal character. 5 Carl G. Hempel, Philosophy of Natural Science (Englewood Cliffs: Prentice Hall, 1966), p. 15.

Induction as a Pragmatic Resource

445

“direct access” here—is perhaps the most fundamental fact of epistemology. The demand for necessitarian certainty is pointless here—hyperbolic assurance, precision, accuracy, etc., are simply unavailable in matters of scientific inquiry. We have no lines of communication with the Recording Angel. We live in a world not of our making where we have to do the best we can with the means at our disposal. We must recognize that there is no prospect of assessing the truth—or presumptive truth—of claims in this domain independently of the use of our imperfect mechanisms of inquiry and systematization. And here it is estimation that affords the best means for doing the job. We are not—and presumably will never be—in a position to stake a totally secure and unblinkingly final claim to the truth in matters of scientific interest. But we certainly can indeed make our best estimate of the truth of the matter. We can and do aim at the truth even in circumstances where we cannot make any categorically secure pretentions to its attainment, and where we have no alternative but to settle for the best available estimate of the truth of the matter—that estimate for which the best case can be made out accordingly to the appropriate standards of rational cogency. And systematization in the context of the available background information is nothing other than the process for making out this rationally best case. In the enthymematic circumstances of the case we have and can have no logically airtight guarantee that the “inductively appropriate” answer is true. The inductively appropriate answer is the correct one, not categorically, but “as best we can determine it”—true according to the best available judgment of the matter. Of all writers on induction, Hans Reichenbach has come closest to taking this line: “The inductive inference is a procedure which is to furnish us the best assumption concerning the future. We do not know the truth about the future, there may be nonetheless a best assumption about it, i.e., a best assumption relative to what we know.”6 Induction is and remains an estimation procedure. The fact that we have an inductively warranted answer in hand must never be taken as a basis for shutting the door to further inquiry. It is in just precisely this sense of affording the best attainable assurance of rational cogency that we propose to “justify” induction in this discussion. It is certainly not a failproof, sure-fire instrument for generating certified correct answers, something which would in the very nature of the case be infeasible in these information-transcending cases. Rather, it is a method for doing the 6 Hans Reichenbach, Experience and Prediction (Chicago: University of Chicago Press, 1937), pp. 348- 349.

446

Nicholas Rescher

job at issue—that of truth estimation—as well as it is possible to do in the epistemic circumstances of the case. Since a process of truth-estimation is at issue, inductive cogency as such is not purported to provide a theoretically failproof basis for answering our questions about how things stand in the world. Indeed, the history of our cognitive endeavours shows the fallibility of induction only too clearly. There is no justification—and no need—for maintaining that induction is an inherently idyllic mode of truth-estimation—all that need be argued is that it’s the best one we’ve got. The accuracy or “validity” (as it is generally called) of an estimation process—its capacity in general to yield estimates that are close to the true value—cannot in the present case be assessed directly but will reflect itself in our confidence in the estimates it yields, a confidence which, in the context of a “best fit” process, will turn on the issue of the tightness of fit. Such a view of induction as a procedure for truth-estimation contrasts importantly with certain alternative approaches. For one thing, it rejects the notion that induction is a theory about the constitution of nature. (How, save inductively, could such a theory ever be substantiated?) And, as we have said, it denies that induction is a rule of inference that moves ampliatively from lesser premises to larger conclusions. For, the legitimation of such a rule would call for a rule-warranting thesis whose status would be vitiatingly problematic. As will be seen, its avoidance of such difficulties yields important advantages for the estimative approach to induction from the standpoint of justificatory argumentation. 4 The Risk of Error With inductive reasoning our cognitive proceeding conforms to the following pattern: • There is some reason to think that p • There is within the range of present cognition no visible reason of countervailing weight to think that ~p ?It is reasonable to maintain that p The guiding idea is that since there is some cogent ground for supposing p to obtain and no impeding obstacle thereto—and since p meets our cognitive needs of the moment—we are entitled to give it the “benefit of doubt” at least pro tem, until cogent counterindications come to view.

Induction as a Pragmatic Resource

447

Induction is not an unfailing procedure for obtaining certifiably correct knowledge. A certain amount of cognitive risk is always run. It is a matter of this-or-nothing with respect to answering a question we are determined to resolve. To be sure, given that estimation involves us in making a conjectural erotetic leap, we cannot avoid occasional mistakes. However, it is a key task to minimize this negativity. This means that induction is less a process of inference than a process of rational conjecture—a methodology of answering our questions in a way that runs the least contextually achievable cognitive risk. Any step beyond the information securely at hand involves the risk of error. But the mission of inductive reasoning is to provide us with a means for constituting a body of information that combines the maximum amount of issue-required correct information with the minimum amount of incorrect misinformation. In its move beyond the deductive reach of secured information induction runs the risk of error. But the aim of the enterprise is to minimize this risk while yet providing answers to our questions. By its very nature induction seeks to be a risk-of-error minimizing erotetic (i.e., questionresisting) process. Induction represents a cognitively serious effort at closing an information-gap in such a way that—everything considered—we can regard it as epistemically well-advised to accept the indicated results. This quest for a cognitively optimal answer makes induction a matter of systematization geared to considerations of best fit within the framework of our cognitive commitments. The widespread, indeed virtually universal tendency is to think of induction as a process of inference—a matter of characteristic modes of ampliative inference for drawing larger conclusions from informatively lesser premises. To reemphasize: the present approach is very different in its orientation. It sees induction not as a characteristic mode of drawing conclusions, but as an estimation technique, a methodology for obtaining answers to our factual questions through optimal exploitation of the information at our disposal. Thus regarded, induction is at bottom an erotetic (question-answering) rather than an inferential (conclusionderiving) procedure. Instead of inferring “All Xs are Ys” from premises of the form “This (and also that) X, is Y”, we take the line of conjecturing that the former is the best available answer to the question “What is the Y-status of the X’s?” given the epistemic situation created by the premises. Induction thus conceived is the methodology of ampliative reasoning for secur-

448

Nicholas Rescher

ing the “best available answer” to our questions—for rational optimization in our quest for information that transcends the “materials in hand.” It accordingly represents a method of conjecturing—specifically a method for estimating the correct answer to a question as well as this can be done through cognitive harmonization with the (inherently insufficient) information in hand. The point may be further elucidated by noticing that the crucial difference between inference and conjecture has a financial analogue. The evidence-in-hand is akin to what is offered as collateral for a loan and inference to an appraisal of its value. But conjecture goes beyond this and comes to be a matter of how much credit one can and should extend. The difference between the two is that inference is a matter of deriving a conclusion substantially warranted by prior evidence, while conjecture leaps beyond the assurance of available substantiation to provide a tentative answer to our questions in the most plausible way. Seen in this perspective, induction is more dialectical than inferential because it looks not just at what is best evidentiated (by having the strongest pro-argument on its side) but rather by looking to what is least counter-evidentiated in being safe against the strongest con-arguments. Inference looks to what is the best (and ideally the optimally) evidentiated by way of pro-indications; conjecture rests content with what is least counter-indicated by way of con-indications. 5 Induction and Systematization This “best available answer” approach to induction bears some points of kinship to the “inference-to-the-best-explanation” approach (seeing that in many cases the route to the best answer is bound to proceed via the best explanation).7 However, the two approaches are by no means identical, and the advantages lie with the former. Thus suppose, for example, that we want to know “Is p the case or not?” in a circumstance where Smith, a generally reliable source, reports that p (and where no other significant information regarding the truth status of p is otherwise available). Our 7

As far as I know, this approach was first formulated by Max Black as a (mis-?-) interpretation of Popperianism: “Those who agree [with Popper] would rewrite putatively inductive inferences to make them appear explicitly as [optimal] hypothetical explanations of given facts.” Max Black, “Induction” in The Encyclopedia of Philosophy, vol. 8, ed. by P. Edwards (New York: Macmillian and The Free Press, 1967), p. 173. Its rationale is given fuller articulation by Gilbert Harman in “The Inference to the Best Explanation,” Philosophical Review, 63 (1966): 241-247; and also in his “Knowledge, Inference, and Explanation,” American Philosophical Quarterly, 5 (1968): 164-173.

Induction as a Pragmatic Resource

449

present, enthymematic-plausibilistic approach would lead us to maintain that p is true—which is clearly the inductively appropriate answer to the question at hand. Its reasoning would run roughly along the lines of the enthymeme: • Smith generally speaks the truth [ex hypothesi] • ?Smith speaks the truth in this case • (In this case) Smith says that p [ex hypothesi] ?p is the case The enthymematic premise at issue (“This case conforms to the general run”) is clearly more plausible than its alternatives in the circumstances assumed to be operative—including the absence of counter-indications of any sort. And so, given the conditions of the problem, the argument runs a smooth course to the desired conclusion. By contrast, however, an “inference to the best explanation approach” would not enable us to get past “Smith believes that p”—which is, after all, a vastly better explanation of Smith’s saying that p than p’s being the case would be. (To be sure, p’s being the case may well in its turn form part (but only part) of the best explanation of Smith’s believing that p. But that’s another matter. Granted, if Smith is a paragon in epistemic virtue (seriously committed, conscientious, etc.) and if the circumstances are such that Smith is afforded good evidence for his beliefs, then the move from Smith’s beliefs to what is the case becomes plausible. But what we are now engaged in is providing a systematic account of the entire context.) Again, suppose it to be known that someone won a prize for good work in language-study at an American school early in the previous century. The question is: What sort of prize was he awarded? Given the circumstances, the inductively indicated answer is clearly a book, considering their predominant popularity for this sort of purpose. But there is no “inference to the best explanation” operative here. For what is being explained? That he was given a book? But this is the very item in question and not a given fact in need of explanation. That he won a prize? Surely the best explanation of this is that he did superior work. While the model of inference to the best explanation works splendidly in some inductive contexts (the move from the smoke to the fire, for example), it simply does not work in general. Accordingly, induction is on our approach rather a

450

Nicholas Rescher

matter of “inference to the best systematization” than one of “inference to the best explanation.”8 What saliently differentiates systematization from other, more limited cognitive processes such as explanation, or axiomatization, or estimation, etc. is its very comprehensiveness. With explanation we generally answer why-is-it-so questions, with systematization the entire repertoire of relevant questions—including how, when, where, in what way, and even why-doyou-say-it’s-so—comes into play. For systematization encompasses all of them, the object being to exhibit, insofar as possible, the whole network of cognitive connections—be they logical, semantical, implicative or probabilifying—that prevail among the putative facts at issue. Throughout inductive contexts, plausibility is a matter of cognitive systematicity: the standards of inductive plausibility inhere in the parameters of cognitive systematization. We must accordingly undertake a brief examination of the ideas at issue in the traditional concept of a system as an “organic unity” of mutually collaborative units. The principal factors at issue here—the parameters of systematicity, as we may dub them—include preeminently the following items: (1) completeness: comprehensiveness, avoidance of gaps or missing components, inclusiveness, unity and integrity as a genuine whole that embraces and integrates all its needed parts (2) cohesiveness: connectedness, interrelationship, interlinkage, coherence (in one of its senses), a conjoining of the component parts, rules, laws, linking principles; if some components are changed or modified, then others will react to this alteration (3) consonance: consistency and compatibility, coherence (in another of its senses), absence of internal discord or dissonance; harmonious mutual collaboration or coordination of components, “having all the pieces fall into proper place” 8

For a more detailed account of what is at issue throughout the plausibilistic deliberations of this chapter, see the author’s Plausible Reasoning (Assen: Van Gorcum, 1976). A whole treatise can and should be devoted to the issue of systematization. (See, for example, the author’s Cognitive Systematization [Oxford: Basil Blackwell, 1979].) One important consideration is that explanation tends to move from the general to the particular while systematization will move in both directions. A metaphysical principle such as that of pan-explicability does not explain our scientific successes but certainly stands in systematic coherence with them.

Induction as a Pragmatic Resource

451

(4) functional regularity: lawfulness, orderliness of operation, uniformity, pattern conformity, normality (conformity to the “usual course of things”) (5) functional simplicity and economy: elegance, structural economy, tidiness in the collaboration or coordination of components, harmony and balance, symmetry.9 (6) functional efficacy: efficiency, effectiveness, adequacy to the common task, versatility and range and power of operating principles. These are some of the characterizing parameters of systematization. After all, systematization is not just a matter of constructing a system, however jerry-built it may prove to be, but of constructing it under the aegis of certain standard criteria. A system, properly speaking, must exhibit all of these various parameters. (Think, for example, of the control system for a manufacturing process or the life-support system of a space capsule.) But a system need not exhibit all these facets of systematicity to an equal degree—let alone perfectly. They reflect matters of degree, and systems can certainly vary in the extent to which they embody these characteristics, and in the manner of their embodiment as well, since the rather schematic nature of these “parameters” leaves a good deal of context-specific detail to be filled in. But no system can be found or constructed that lacks a substantial combination of these desiderata, simply because they constitute the guiding standards which govern the process of systematization and determine the claims of its products to be characterized as a “system.” If a system (an economic or social system, for example) were to lose one of these characteristics in substantial measure—if its coherence, or harmony of functioning, or end-realizing effectiveness were substantially diminished—then its very existence as a system would be compromised.10 To be sure, our present concern is not with systematicity per se, but specifically with cognitive systematicity as based on the conception that our information about the world is to constitute part of a system of knowledge. 9

On the range of considerations at issue here cf. Elliot Sober, Simplicity (Oxford: Clarendon Press, 1975). 10 For a further development of these issues, and a fuller exposition of the parameters of systematicity, see the author’s Cognitive Systematization (Oxford: Basil Blackwell, 1979).

452

Nicholas Rescher

Accordingly, the parameters of systematicity must, in this present context, be construed in a specifically cognitive sense. And the key fact for our purposes is that, thus construed, they afford our criteria of inductive plausibility—of the acceptability-qualifications of our answers to information-transcending questions. Instead of merely representing a facet of the organization of our (otherwise pre-existent) knowledge, systematicity is to provide an operative force in the very constituting of what we count as knowledge. While inquiry is a process of enlarging the information at our disposal, of yielding new items to be added to the stock of our acceptances, such question-answering is not just a matter of getting an answer, but a tenable answer—one the merits acceptance within that body of “already established” information that provides the materials for our further systematizations. And systematic harmonization itself furnishes us with the operative norms here, so that inductive acceptability becomes a matter of systematic fit—and indeed a matter of the tightness of that fit. In sum, we use system not just as organizer of what we accept, but as a Bradleian arbiter of acceptability—a standard of what we are to accept, or at any rate endorse pro tem until such time as discordant counter-indications come to view. One very important point must be stressed. To someone accustomed to thinking in terms of a sharp contrast between organizing the information already in hand and an active inquiry aimed at extending it, the idea of a systematization of conjecture with experience may sound like a very conservative process. However, this impression would be quite incorrect. The systemic approach to induction must not be construed to slight the dynamical aspect. The present analysis sees systematization itself as an instrument of inquiry—a tool for aligning question-resolving conjecture with the (of itself inadequate) data at hand. The factors of completeness, comprehensiveness, inclusiveness unity, etc. are all crucial aspects of system, and the ampler the information-base, the ampler is the prospect for our systematization to attain them. The drive to system embodies an imperative to broaden the range of our experience, to extend and expand the data-base from which our theoretical triangulations proceed. In the course of this process, it may well eventuate that our existing systematizations—however adequate they may seem at the time—are untenable and must be overthrown in the interest of constructing ampler and tighter systems. Cognitive systematization is emphatically not an indelibly conservative process which only looks to what fits smoothly into heretofore established patterns, but one where the established patterns are themselves

Induction as a Pragmatic Resource

453

ever vulnerable and liable to be upset in the interests of devising a more comprehensive systematic framework. 6 The Pragmatic Dimension In sum, then, induction is not really a mode of inference, strictly speaking, but rather one of estimation. It is a tool of inquiry designed for settling our questions within some particular context of inquiry. We are driven to truthestimation because we cannot get by some direct pathway at “the truth, the whole truth, and nothing but the truth.” But with any such estimation we cannot avoid the question: “How good is good enough?” And this issue of “good enough” is inseparably linked to the issue of the purpose at hand and the requisites at work if the needs of the situation are to be met. And this marks induction as a resort being deployed within a setting of particular goals and objective purposes. Moreover, the presence of cognitive risk is inevitable in induction if the erotetic aims of the enterprise are to be realized by resolving our questions. And the now-inevitable issue of risk acceptability contextualizes the issue to the range of purpose operative in the situation at hand. Induction, thus regarded, is an instrument for question-resolution in the face of imperfect information. It is a purposive device for the realization of particular cognitive ends. And the rationale of the venture roots in the fact that we have questions and seek for answers to them. Induction is, accordingly, an erotetic procedure—a process for securing answers to questions on the basis of issue-resolvingly insufficient information—i.e., answers that reach beyond the deductive consequence of information that is already securely in hand. All of these considerations combine to show that induction is, in the final analysis, a venture in practical/purposive rather than in strictly theoretical/illuminative reasoning.

Jumping the Gaps: Induction as First Exercise of Intelligence Louis F. Groarke Saint Francis Xavier University

Abstract: Among contemporary philosophers, the Humean view of induction as an unreliable, enumerative, and invalid argument form has achieved such dominance, any competing account seems almost unthinkable by comparison. Groarke claims that the received view is based on a series of misunderstandings that do not survive close scrutiny. This chapter has two goals. First, Groarke sets out to demonstrate where the received Humean account of induction goes wrong. Second, he aims to present a positive account of induction, defined, in allegedly Aristotelian terms, as a mental leap between incommensurable epistemological categories that cannot be properly or completely explained in terms of one another. Induction is, we might say, a way of moving between apples and oranges, between irreducibly different possibilities or ways of understanding the world. Because he believes that induction is pervasive in human thought, manifesting itself in a wide variety of contexts and forms, Groarke does not attempt to provide any complete taxonomy of inductive reasoning. He is content instead to indicate, in a general way, the direction in which, he believes, future research into induction needs to go. Although other philosophers who disagree with the Humean account may or may not agree with the vision Groarke sketches out here, the essay provides, at least, one way forward.

Introduction So where are we? This volume contains a series of essays that discuss and analyze the philosophical and logical problems associated with induction.1 In this concluding essay, I aim to push some of these arguments further so as to arrive at an alternative definition and explanation of induction. As the previous chapters do an admirable job of covering the subject matter from 1

The author would like to thank Paolo Biondi and others for comments on earlier drafts of this paper.

456

Louis F. Groarke

diverse historical angles—something I myself have tried to do elsewhere— I will not focus on any scholarly exegesis of traditional doctrines but endeavor to piece together a positive account in opposition to the received Humean view. In the main, I agree with the criticisms of standard Humean treatments raised by almost all these authors. The account of induction I propose derives from the Aristotelian outlook on epagǀgƝ (induction) discussed by contributors such as Paolo Biondi, Christopher Byrne, Joseph Novak, and Paul Schollmeier among others. It could be seen, I hope, as an extension of the alternate tradition McCaskey identifies with William Whewell, Francis Bacon, Socrates, and Aristotle, too. My description of what induction entails is also in agreement with the perennial understanding Ernest McCullough discusses in his philosophical dialogue. It could be further understood as an extrapolation from the scholastic account proposed by Matthew Kostelecky; it dovetails with Henry Veatch’s “neoscholasticism” as discussed and amended in the chapter by Douglas Rasmussen, and it squares with Goethe’s approach to science elucidated by Jakob Ziguras. It also, I believe, better captures the role of induction in science, mathematics and geometry as recounted by authors such as Jude Dougherty, James Kelly, Dwayne Raymond, and John McCaskey. It presents a more “metaphysical” perspective than Nicholas Rescher’s pragmatism but tries to delve into the nature of the mental insight that Rescher describes as “inference to the best systematization.” It acknowledges the importance of Bernard Lonergan’s innovative emphasis on “insight” in the “generalized empirical method” described in Hugo Meynell’s chapter. Finally, it picks up on (while respectfully disagreeing with) some of the themes raised in Peter Lopston’s carefully qualified treatment of Hume’s standard account. This is not to suggest, of course, that my colleagues here will agree with my treatment of induction, in whole or even in part. The aim of this collection is not unanimity—something philosophers are not very good at—but a fairer, more nuanced account of induction that acknowledges and extends the traditional realist understanding ignored or misunderstood by so many mainstream authors. I hope to begin here the work of elaborating a critical modern account of induction that accurately captures what this species of cognition entails, as well as its place in the epistemological, metaphysical, scientific, practical, and moral economy.

Jumping the Gaps

457

1 The Hertz Experiment Begin with an analogy. In 1887, Heinrich Hertz (1857-1894) demonstrated that by making a spark jump between a pair of metallic spheres, one could trigger a similar event between the pointed ends of a distant coil of copper wire. This pioneering work prepared the way for the first radio-wave transmitters and was widely taken as a proof of the transmission of electromagnetic energy through space as described by James Clerk Maxwell’s equations. In the original setup, the spark-gap generator performed like a rudimentary radio-transmitter; the coil of wire, like a radio-receiver: whatever production of sparks happened at the transmitter end could be picked up and replicated at the receiver end. Somehow, the electromagnetic disturbance that produced the first spark was able to reach across the room and induce a similar spark-jump across the gap between the two metal ends of the cooper wire. This physical process, I want to suggest, provides an apt physical metaphor, on several levels, for what happens in induction. W. D. Ross, the revered Aristotelian commentator, maintains that induction is “the flash of insight by which we pass from knowledge of a particular fact to … the corresponding general principle.”2 This is a familiar view. Despite its limitations, it captures an element of truth. Inductive argument, familiarly conceived, moves from particular instances to a universal conclusion. Because the scope of a universal far exceeds the scope of any collection of particulars, the only way to arrive at the conclusion is by jumping from incomplete evidence to an inevitably tentative conclusion. Just as the initial spark in Hertz’s experiment is induced to jump beyond its place of origin to a different location, the mind, in induction, is able induce a similar jump over the divide that separates the inaccessible universal from particular instances. This is not, as anyone who has studied the history of metaphysics knows, an inconsequential gap. But that is not all. There is a second parallel to be noticed here. This leap over the gap from particular to general knowledge can be communicated to other minds. Just as the forces that gave rise to the initial spark in the Hertz experiment are able to somehow reach through space and induce a second similar spark to jump across a similar metal-to-metal gap, the original mind in induction is able to induce other minds to leap with it over to this new possibility. Other reasoners can immediately see what the conclusion is and understand 2

Ross infelicitously adapts this view to Aristotle. W. D. Ross, Aristotle’s Prior and Posterior Analytics (Oxford: Clarendon Press, 1965), 50.

458

Louis F. Groarke

how the original knower got there. They can imitate the original mental leap to the conclusion. And there is yet a third parallel to be considered. Hertz and his followers found (to simplify somewhat) that illuminating the experimental setup produced more and larger sparks (because of what is now known as the photoelectric effect). It was as if the presence of light facilitated sparkgeneration both at the transmitting and the receiving end of the apparatus. But the traditional understanding traces the source of induction to its origins in intelligence understood as a kind of intense immaterial “light” that the knower shines on things to understand them more clearly. Just as one needs light to facilitate the production of sparks in the Hertz experiment, one needs a general power of mental illumination in order to induce the mental leap to the universal. Without the “light” of human intelligence, one cannot trigger the leap over the epistemological gap. This is why, according to traditional thinkers, animals cannot induce universal conclusions—because they lack the light of human intelligence. But, although there is more to say on this topic, let us move on. I am not presenting here an argument from analogy—one of the uses of induction—but merely trying to capture in vivid, accessible terms, what induction, at its very origins, entails. Like any analogy, this comparison involves an incomplete likeness. Nonetheless, it captures three important properties of induction: (1) the way induction jumps the gaps between incommensurable epistemological categories, arriving at a conclusion that somehow exceeds the premises; (2) the way induction jumps the gaps, so to speak, between minds so as to induce a similar sort of gap-jumping spark in listeners; and (3) the dependence of induction on the “light” of intelligence. There is more to say about each property, but at least this is a start. I aim now to show that the popular Humean account fundamentally misunderstands what induction is about and, in a more positive vein, to define induction, more accurately and much more broadly, as a leap between irreducibly different cognitive categories. 2 A Brief Account of the Received View There are many problems with contemporary Humean accounts of induction so that one wonders how best to start a discussion without misleading the unsuspecting reader. The easiest way to enter into the fray is perhaps by

Jumping the Gaps

459

reviewing the received understanding. Begin then with a brief survey and thorough criticism of the usual way of dealing with induction.3 Academic philosophers trace back the present ideas about induction to David Humes’s An Enquiry Concerning Human Understanding, first published in 1748. On this Humean account, which has been critiqued in previous chapters, induction is mostly about prediction. Hume believes that we cannot see into the deep causes behind things and must base our expectations about future events on what we have grown accustomed to in the past. This has grave consequences. To use an example that is reiterated endlessly in the literature: Someone who keeps encountering black crows naturally jumps from this past experience of crows to the conclusion that all crows are black. If, for instance, you tell them you have a pet crow, they will, doubtless, assume that it is black. But suppose you selected an albino crow for a pet because it seemed so special. The implied inference, “your pet bird is a crow, all crows are black, therefore your pet crow is black,” fails. It comes to the wrong conclusion because the implicit induction “all crows are black” fails. As it turns out then, our past experience may be unreliable; there is no guarantee that what we are used to (what hume calls custom or habit) will provide us with the correct answer about future events. It could be said, in logical terms, that induction is an invalid argument form. As the logic textbooks invariably insist, inductive arguments do not guarantee the truth of their conclusions. The premises in such arguments can be true and the conclusion false. This failure of inductive reasoning to satisfy rigorous deductive standards only adds to broader suspicions about the possibility of knowledge. At first glance, what is usually termed “the problem of induction” may seem like a small matter. If induction cannot logically guarantee its conclusions, could it not offer an approximate take on the world? Isn’t it enough if induction is usually right? If we can confidently say that the next crow is almost always black, should that not suffice as a rule of thumb? If, as Hume insists, we cannot be one-hundred-percent sure that the next slice of bread will be as nourishing, that snow will always be cold, that the sun will rise again tomorrow morning, or that the next fried egg will taste just about the same as the last one, this almost invariably turns out to be the case. So what is the problem? 3

I have discussed the status of induction and many of the issues raised here, in unpardonable detail, in a book-length treatment that focuses on Aristotle. Louis Groarke, An Aristotelian Account of Induction: Creating Something from Nothing (Montreal & Kingston: McGill-Queen’s University Press, 2009).

460

Louis F. Groarke

The problem is that philosophy is a meticulous business. To argue that our predictions about the future are a matter of mere habit or custom turns science into psychology. It undermines any pretense to scientific knowledge. How can my previous habits provide a secure basis for future prediction? On the Humean account, we must reason: I saw the sun rise yesterday, and the day before that, and the day before that ... I am used to seeing the sun rise; so I can know that it will rise tomorrow morning. But this is not scientific reasoning. To make my predictions about the morning sunrise dependent on nothing more than what we are accustomed to is a very tenuous affair. Dressing up the argument in some version of probability calculus only disguises the problem. Suppose I make a parallel argument: I saw my mother in the kitchen yesterday morning, and the day before that, and the day before that … I am used to seeing my mother in the kitchen every morning; so I know that I will see my mother tomorrow morning. Surely, something is seriously wrong here. The necessity of seeing my mother in the kitchen every morning—even if I were to see her there every morning for my entire life— can never equal the necessity of the sun rising each morning. Why? Not merely because many more people have seen the sun rise every morning than have seen my mother in our kitchen every morning, but because there is something about the nature of the sun (really, about the nature of the earth’s rotation) that is vastly different than the nature of my mortal mother. The number of observations of each event seem disastrously after the fact. Basing all our knowledge about future prediction on what we have been used to up to now rather than on the nature of things themselves seems highly inadequate. Dissatisfaction with this conventional Humean account has motivated most of the essays in the present volume. We cannot consider Hume’s comments about the unreliability of induction apart from his treatment of cause and effect. Hume, an archempiricist who is hostile to traditional metaphysics, rejects the idea that the mind can discern any necessary link between cause and effect. The human mind, on his account, is able to access the “sensible qualities” that characterize things but not the “secret powers” that give rise to those sensible qualities. We light a candle and immediately feel heat. Event A, lighting the candle, is followed by event B: production of heat. All we experience is B following A. We can never peer into what causes the heat. When we repeat this process over and over we come to expect B to follow after A. This is all there is to causality. We have never observed a cold candle—a candle that emits coldness—but this possibility cannot be ruled out. Our own experience

Jumping the Gaps

461

is, by necessity, limited; we can never observe all candles past and future, and so perhaps, somewhere, there was, is or will be a cold candle that befuddles our entirely fallible expectations. It must be said. Hume’s attitude to science (and the attitudes of his more recent disciples) seems almost schizophrenic. He dogmatically champions the reliability of science, ridiculing the idea that there could be exceptions to the laws of nature (miracles). But really, he provides sparse logical justification for such attitudes. It is one thing to merely assert that science constitutes the paradigm case of knowledge. That counts for little. How can one reconcile Humean inductive skepticism and science? One cannot undermine the authority and reliability of induction without undermining the authority and reliability of science. If Hume’s views on induction are true, we can never arrive at universal scientific laws. The best we might do is trade in generalizations that reflect the limits of our own personal experience. Providing some account of the nature of the world that must be true will be forever outside our grasp. Hume, who is a shrewd operator, is not unaware of the calamitous conclusion towards which his own philosophy of induction tends. He tells us: The understanding, when it acts alone, and according to its most general principles, entirely subverts itself, and leaves not the lowest degree of evidence in any proposition, either in philosophy or common life. [… Oftentimes …] I am ready to reject all belief and reasoning, and can look upon no opinion even as more probable or likely than another. Where am I, or what? From what causes do I derive my existence, and to what condition shall I return? ... [When] I am confounded with all these questions, ... I dine, I play a game of backgammon, I converse, and am merry with my friends; and when after three or four hours’ amusement, I would return to these speculations, they appear so cold, and strain’d, and ridiculous, that I cannot find in my heart to enter into them any farther.” 4

Hume proposes here the Omar Khayyam solution to inductive skepticism: drink, converse and be merry! In this essay, I will try to replace that mere practical strategy with a more hopeful philosophical account.

4

David Hume, A Treatise of Human Nature, ed. L. A. Selby-Bigge (Oxford: Clarendon Press, 1888) § 4, 7, 5-9 (pp. 266-269).

462

Louis F. Groarke

3 Preliminary Problems with the Received View 3.1 Conflating Accidental and Non-Accidental Properties My primary goal here is to present a positive account of induction, but criticism of the standard view can lead to corrections which point in a more promising direction. Begin then with several brief criticisms of the usual account. The first problem is that proponents of the standard view who aim to demolish the reliability of induction as a source of knowledge rely on special pleading. Examples of black crows and such like miss the point almost entirely. These are “silly examples” because they deal with the accidental or contingent properties of things. Traditional philosophers focus on inductions about necessary or essential properties. They would agree that inductions about accidental or contingent properties are inconclusive. Of course they are. But that is because they are about accidental or contingent properties. It does not follow that necessary or essential inductions are equally inconclusive. Ancient Epicureans and Stoics debated the issue of induction. Zeno, the ancient Epicurean (not the Eleatic follower of Parmenides), presents the following argument in support of induction: Within limits, then, we may allow for variation [among humans] due to the influence of climate, food, and other physical conditions; but … in spite of variations, there are properties which in our experience are universal. Men are found to be liable to disease and old age and death; they die when their heads are cut off, or their hearts extracted; they cannot pass through solid bodies. By induction we infer that these characteristics belong to men wherever they may be found, and it is absurd to speak of men under similar conditions as not susceptible to disease or death, or as having the ability to pass through iron as we pass through the air.5

Surely, there is some sense to this. An albino crow is within the realm of possibility, but do we really accept, to borrow Zeno’s examples: that the next (living) human being we meet may be headless? Or that cutting out someone’s heart (without replacing it) might be a minor inconvenience? (Of course, someone in the modern age could get a heart transplant, but that is a different matter.) Or that people in Egypt or Africa or the Orient can walk right through 5

Cited in Allan Marquand, “The Logic of the Epicureans”, in Allan Marquand, Christine Ladd Franklin, Oscar Howard Mitchell, Benjamin Ives Gilman, Studies in Logic (By Members of the John Hopkins University) (Boston: Little, Brown, and Company, 1883), p. 7; see pp. 1-11; ebook also available online. The original citation is from Philodemus.

Jumping the Gaps

463

concrete walls? Or that there are human beings—of the same natural species as us—who never grow old and die? (Or, to borrow an example from Nelson Goodman, that all green emeralds will simultaneously turn blue or red or yellow next Sunday at time T = six o’clock?) Hume, who has a penchant for sensational puzzles, lumps all sorts of properties together when delving into the nature of induction. In the Enquiry, he writes: From causes which appear similar we expect similar effects. This is the sum of all our experimental conclusions. … But the case is far otherwise. Nothing so like as eggs; yet no one, on account of this appearing similarity, expects the same taste and relish in all of them.6

Surely, the taste of an egg is a contingent attribute that depends on all sorts of factors (like the freshness of the egg, the way it was cooked, what the chicken was eating, and so on). It is not on a par with questions about whether the sun will rise tomorrow morning. The latter is a necessary consequence of the universal law of gravitation; the former is a matter of happenstance. It is a vicious simplification to treat all kinds of inductions as epistemologically equivalent. The Humean focus on prediction seems, in any case, misplaced. Aristotelian induction revolves around our knowledge of the natures of things. Induction is, first and foremost, a way to understand what something is. What something is influences, of course, how it will behave in the future. Still, philosophers in the Aristotelian and scholastic traditions differentiate between accidental, necessary, and essential attributes. If we hope to discover conspicuous examples of absolutely reliable inductions, the best place to look would be in cases involving necessary and essential attributes. This is why we can be absolutely certain that there are no headless men, that people do not walk straight through concrete walls, or that everyone eventually gets old and dies—because having a head or a solid body or aging with time: these are necessary traits of being human. More on this below, but it should be clear that pointing out that inductions about accidental or contingent properties are not one-hundredper-cent reliable does not prove very much. Serious investigation demonstrates, anyways, that armchair inductions about black crows bear little resemblance to what actually happens in science. Scientists (in this case, ornithologists) learn about the difference between necessary and contingent 6

Hume, An Enquiry Concerning Human Understanding, § 4, 2, 31 (p. 36).

464

Louis F. Groarke

features through their work. Ornithologists know, for example, about albinism, which has been observed in all families of North American birds.7 Surely, a wise ornithologist would make the following induction: there are albino pigeons, albino swallows, albino song-birds, albino penguins, albino hawks, albino ravens, and so on. So there must be albino crows. So the conclusion that your pet crow is black may be mistaken, but this is a minor hiccup that does not undermine the epistemological authority of the science of ornithology as a whole. Induction itself provides a correction factor that warns us away from oversimplified conclusions. Note, in passing, that human intelligence is capable of distinguishing between the necessary and contingent properties of things. Broadly put, this happens through an intelligent appraisal of the various features of our experience. We will not explore exactly how such distinctions arise here, but we must insist that this is a mundane aspect of ordinary knowledge. Even an elementary school student quickly realizes that the sum total of the interior angles of any triangle has a fixed value, whereas the sum total of the length of the three sides of a triangle can vary endlessly. The former is a necessary property of triangles; the latter is an accidental property. Suppose we had an induction that ran: “the perimeter of this first triangle is ten centimeters; the perimeter of this second triangle is ten centimeters, the perimeter of this third triangle is ten centimeters; therefore all triangles have perimeters equal to ten centimeters.” As even the schoolchild immediately recognizes, this would be a preposterous conclusion. Nonetheless, one could make an entirely reliable induction, using the same logical form, about the interior angles of all triangles adding up to one-hundred-andeighty-degrees. 3.2 “Relations of Ideas” Unable to Explain All Necessity Humeans do have a strategy for dealing with necessary truths. On the one hand, Hume argues that “matters of fact” are always contingent—they can always be otherwise. On the other hand, he argues that the way we define our terms, “relations of ideas,” can produce necessary truths. To borrow another overused example: the statement “all bachelors are unmarried men” is necessarily true because the phrase “unmarried man” is a definition of the term “bachelor.” These terms are related in such a way as to guarantee the truth of the statement. This necessary truth is, however, a linguistic truth. It is a matter of pure convention. The logical necessity only pertains 7 John Terres, The Audubon Society Encyclopedia of North American Birds (New York: Alfred A. Knopf, 1980), s.v. “Albinism.”

Jumping the Gaps

465

to the way we use language; it has nothing to do with the true nature of things in the world. This is why the Humean account cannot explain how we induce necessary (or essential) truths about the world. It restricts any discovery of necessity to what is, from a scientific or metaphysical point of view, a linguistic side-show. This is not principally a paper on Hume, but it is important to point out that his theory of “relations of ideas” seems untrustworthy. The problem is that he proceeds as if our definitions of words do not ultimately derive from the nature of the world. Of course, words are, to some degree, an artificial invention. We do not define terms solely by convention. Some definitions are imposed on us by the nature of things in the world. Consider the statement: “Define the value of ʌ (pi) as equal to 3.14159265359...” This is, surely, a necessary truth. But we do not decide, as a matter of mere convention, that “ʌ is equal to 3.14159265359...” The meaning of this statement is forced upon us by the nature of circles in the world. We observe what a circle is and calculate this precise and necessary value. If someone wanted to insist that “ʌ is equal to 3.270,” they would just be wrong. They are wrong not merely because they have used words incorrectly but because this answer does not correspond to the nature of reality.8 3.3 Invalidity: A Logical Red Herring The standard Humean view has tentacles that reach out everywhere. The following reference to that ubiquitous source of conventional wisdom the undergraduate e-reference Wikipedia serves to demonstrate just how widespread the Humean account has become. The Wikipedia entry on “inductive reasoning” informs the reader that the difference between inductive and deductive reasoning is that the former is unreliable in a way that the latter is not. Citing the 2007 edition of Copi’s well-read logic textbook as an authority, the anonymous authors tell us: Inductive reasoning (as opposed to deductive reasoning) is reasoning in which the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion. While the conclusion of a deductive argument is supposed to 8 Some readers may want to substitute Kant for Hume here. We cannot delve into Kant’s more sophisticated metaphysics in any detail. Simply note that his notion of “synthetic a priori judgments” falls prey to similar objections. On this Kantian view, logical necessity that pertains, for example, to mathematics is solely an aspect of the invariable human mind, not of the real nature of the world (which is on Kant’s view, inaccessible). One could argue that Kantian anti-realism, rigorously pursued, logically leads to skepticism, but I do not have time to investigate that line of reasoning here.

466

Louis F. Groarke

be certain, the truth of an inductive argument is supposed to be probable, based upon the evidence given. It is a common fallacy to state that inductive arguments reason from the specific to the general, while deductive arguments reason from the general to the specific.9

I want to suggest, in sharp contrast, this now standard way of defining induction misrepresents the difference between deductive and inductive reasoning. (The “common fallacy” of identifying induction with the movement from particular to general is, at least, closer to the truth.) The accepted dogma is then that inductive arguments are invalid and that deductive arguments are valid. Invalidity is, allegedly, the essential trait of inductive reasoning. But this by-now orthodox account confuses validity and certainty. Even if inductive arguments have uncertain conclusions, they are not invalid. As scholars in present-day argumentation theory have shown, inductive arguments depend on an unspoken or implicit premise. (They are, in this sense, enthymemes.)10 Consider the induction: “This crow is black; this crow is black; this crow is black; therefore, the next crow I see will be black.” The implicit premise here is: “all crows have the same color.” (Note that the claim that all crows have the same colour is significantly different from the claim that this or that individual crow is black.) But once we make this hidden premise explicit, the conclusion follows necessarily: “This crow is black; this crow is black; this crow is black; all crows have the same color; therefore, the next crow I see will be black.” If the premises of this argument are true, the conclusion must be true. This is a valid argument. This kind of closer analysis, which supplies a valid line of reasoning, is always possible with any inductive argument. Aristotle, of course, has his own way of dealing with the validity issue. As several of our authors discuss, he uses the concept of “convertibility” to secure the validity of the inductive syllogism.11 We can quickly paraphrase this way of understanding things in propositional rather than syllogistic form (for familiarity’s sake). Suppose someone was to argue: “This crow is black; this crow is black; this crow is black; the color of these crows is convertible with (i.e., it is identical to) the color of all crows; 9

“Inductive Reasoning,” Wikipedia, http://en.wikipedia.org (accessed Sept. 6, 2013). The reference is to I. M. Copi, C. Cohen, & D. E. Flage, Essentials of Logic (2nd ed.) (Upper Saddle River, NJ: Pearson Education, Inc., 2007). 10 Groarke, Leo, "Informal Logic", The Stanford Encyclopedia of Philosophy (Spring 2013 Edition), Edward N. Zalta (ed.), URL = (accessed Sept. 6, 2013). 11 Convertibility is discussed in Prior Analytics II.22-23.

Jumping the Gaps

467

therefore, the next crow I see will be black.” Or, to express Aristotle’s thought in a slightly different way: “This crow is black; this crow is black; this crow is black; feather color is a necessary property of all crows; therefore, the next crow I see will be black.” But these are both valid arguments; their conclusions follow necessarily. I have discussed all this in more depth elsewhere. As these brief analyses demonstrate, the problem with inductive arguments is not validity but uncertainty about what is precisely true; put another way, the problem is veracity rather than validity. The hidden premises in the three re-constructed arguments are: “all crows have the same color,” “the color of these crows is convertible with (i.e., identical to) the color of all crows,” and “feather color is a necessary property of all crows.” As it turns out, these premises are not, rigorously speaking, correct. This is why the conclusion “the next crow I see will be black” may be false. If, however, these premises happened to be true, each conclusion would follow with complete logical rigor. The unreliability of inductive argumentation derives then from worries about the truthfulness of the premises; it is not because of any invalid pattern of reasoning. Logically, this is at least an important precision. But, although more could be said, let us move on. 3.4 Metaphysically Misleading Exceptions Another confusion that has undermined confidence in induction as traditionally conceived is the selection of apparent counter-examples to induction that do not really count as genuine or at least insurmountable counterexamples on the traditional metaphysical view. Suppose we have two individuals: a Humean accountant and a naive biologist. The skeptical accountant takes a modern numerical view of induction; the biologist takes, somewhat tentatively, an essentialist Aristotelian view. Imagine the following conversation: Accountant: Tell me something about dogs? Biologist: Well, dogs have four legs. Accountant: You sound like an old-fashioned essentialist! Is having four legs an essential feature of being a dog? Biologist (worried): Well, no, it can’t be the defining feature. Cats, cows, horses, and weasels also have four legs. Accountant: OK. So it’s a necessary feature. It is a necessary property of a dog. Biologist (suspiciously): I guess so.

468

Louis F. Groarke

Accountant: You mean all dogs have four legs. Biologist: Sure. Accountant: How do you know that? Biologist: Have you ever seen a dog? Just observe dogs and you will see that they have four legs. Accountant: Hmmm, I see, you are making an induction. But induction is unreliable. Because all the dogs you have seen have four legs, you are assuming that future dogs and all the dogs in the world and every species of dog will all have to have four legs. Biologist: I guess so. You have to base your science on empirical results. Accountant: My silly man! I once saw a dog that had only three legs. One leg was amputated after a car accident. And it was still a dog! Biologist: Well… Accountant: And there was a story in the newspaper of a deformed puppy that was born without back legs. It was an awkward-looking monster, poor thing! But even though it only had two legs, it was still a dog. Biologist: Hmmm… Accountant: And did you hear about the sicko burglar who cut all legs off a guard dog and left it for dead. Sickos! Even though the dying thing had no legs, it was still a dog when it was lying there, without legs, bleeding to death. Biologist (befuddled): I am not sure what to think. Accountant: So much even for necessary properties! So much for Aristotelian necessarianism! Aristotle’s approach to induction was too simplistic! What is going on here? The accountant believes that he has found counterexamples to the inductive conclusion that all dogs have four legs. Counting at least three cases of dogs with less than four legs, he believes that he has conclusively shown that four legs are not a necessary feature of being a dog and that this shows, once again, that induction is unreliable. (Indeed, there is a surreptitious induction going on here: because this, this, and this instance of induction is unreliable, induction is inherently—i.e., necessarily—unreliable. But leave this viciously circular line of reasoning aside.) In fact, however, these are not true counter-examples from an Aristotelian viewpoint.

Jumping the Gaps

469

The universal (inductive) conclusion “all dogs have four legs” means, on an Aristotelian account, something like “it is of the nature of dogs to have four legs,” or, somewhat awkwardly, “four-leggedness belongs to the nature of doghood.” Aristotle, who was initially a student of Plato, thinks that there is an ideal form that dogs strive to possess. When this form of “dog-ness” is adequately, properly, fully expressed—there will be four legs. And indeed, this is what happens. The counter-examples the Humean accountant points to are all exceptional instances of injured, diseased, or mutilated dogs. Because of contingent factors, the doghood of these dogs—their nature—has been obscured, prevented from any full expression. These are not dogs that embody or express what a dog at its best is or even what a dog is when it is undamaged. When an Aristotelian claims that “dogs have four legs,” he is commenting on the natures of things, not merely on the numerical frequency of properties. The accountant overlooks natures and focuses on the mere presence of properties which is, in a deeper sense, uninformative. A traditional metaphysical philosopher would find this focus on purely quantitative considerations highly superficial. Imagine a watercooler conversation with the same two characters; this time, about popular culture: Biologist: That actress you were talking about has a beautiful face. She is the epitome of feminine beauty! Accountant: But she played a very ugly witch with a long nose in a recent movie; and they made her look like a haggard old woman with scabs all over her face in another one; and she once played a misshapen science fiction monster. Boy she did look ugly then! Biologist: But she was wearing make-up. Those were not her real looks. They only made her look as if she was ugly. You are mistaking appearances for reality. This is actually a similar problem. The accountant believes that he is coming up with three counter-examples because he has counted three occasions in which the actress did not have a pretty face. From an Aristotelian perspective, this misses the point entirely. Ugly appearances do not constitute true evidence against the attractiveness of the actress—even if it is a matter of counting three of them. It is what the actress “really looks like” that the biologist is talking about; the accountant’s counter-examples that the actress looked ugly on this and this and this occasion are beside the point.

470

Louis F. Groarke

Granted the argument about dogs is about a species; the argument about the actress is about an individual. And there may be individual, undisguised dogs that only possess one or two or three legs. Traditional metaphysicans surely understood this. Still they would have viewed such exceptional instances as something that disguises the true nature of what a dog is. Suppose, to push the point, a certain cruel king decided to cut the legs of every dog in his kingdom at birth so that there were only threelegged dogs left in that part of the world. This would not change the nature of doghood. It would be—metaphysically speaking—a ruse, a way of merely disguising what the true nature of a dog is. These three-legged dogs would look like something they are not. Viewed from a traditional metaphysical perspective, counting anomalies, wayward observations, is not enough to show that some property is not a necessary or even an essential trait of something. One could engage this kind of misunderstanding on many levels: Accountant: What is the essence of a teacup? Biologist: I am not sure; it is a thing that holds tea. Accountant: But my grandmother had a very old set of teacups that had cracks in them. If you poured tea in them, it would immediately drain out. They couldn’t hold a thimbleful of tea. But they were still teacups… Obviously, the accountant has not learned his lesson. Cracked teacups are damaged teacups. It is not the cracks that make them teacups; it is the fact that they were made to hold tea that makes them teacups. Because of contingent circumstances, they have become imperfect expressions of what a teacup is. Looked at without understanding, they obscure the “essence” of teacupness. To be a teacup is, first and foremost, to be a thing that holds tea. The moral of these little dialogues is that we should not be too hasty to accept, at face value, the numerical counter-examples present-day philosophers present to prove that induction is unreliable. We need to consider such issues thoughtfully. The fact that something happens very ocassionally in a certain way is not always a transparent window into the deep nature of things. If things in the world possess natures (essences), and if such natures are sometimes obscured or stymied by disease, deformity, happenstance, or accident, this does not prove that generalizations about the underlying natures are, in a genuine metaphysical sense, unreliable. The accounting method—merely counting how many times one observes

Jumping the Gaps

471

something—is no adequate replacement for deep understanding. (Someone might deal with the case of the rare albino crow in the same way; they might consider albinism as a disease, a deformity that obscures the genuine nature of what it is to be this sort of a bird.) It seems important to add that one regularly meets with this appeal to anomalous instances in ethics. Take the moral law: “Thou shalt not steal.” This might be construed as an inductive generalization. It is tantamount to saying that “all instances of stealing are morally wrong.” Anti-moralists, in confronting such ideas, borrow the Humean line and immediately go to work looking for counter-examples. What if you steal bread to save your starving children? How could that be wrong? But as medieval scholastics, Thomas Aquinas and even John Locke point out, this is not, rigorously speaking, stealing. It is generally accepted that a family that is genuinely starving has a right to food. A shop-keeper is morally obliged to give them bread for free. Otherwise, they can take it without his permission. So this is not a genuine counter-example.12 It does not undermine the general principle that stealing is wrong, because it is not even, properly construed, an instance of stealing. We cannot explore moral issues here. Suffice it to say that ethics requires casuistry in odd situations. 3.5 The Uniformity of Nature John Stuart Mill believed he could rebut Humean inductive skepticism by adding a premise to all inductive arguments to the effect that “nature is uniform.”13 The Baconian-derived idea was that slowly but irrefutably the evidence builds up to show us that we must accept that nature basically remains the same through time. Once we accept that premise, however, the logic of induction unproblematically follows. This way of looking at things is sometimes called “uniformitarianism,” a term coined by William Whewell. Admittedly, there is something to Mill’s suggestion. We normally assume that the fundamental nature of the world does not radically change, and this assumption grounds our inductive reasoning. Adding a perhaps hidden premise to this effect is yet another way of turning inductive arguments into valid arguments. Critics complain, however, that this approach begs the 12

Cf. Louis Groarke, Moral Reasoning: Rediscovering the Ethical Tradition (Don Mills ON: Oxford University Press, 2011), pp. 402-403. 13 John Stuart Mill, A System of Logic, Ratiocinative and Inductive, Bk. III, Ch. III, § I. For a more contemporary defense of this idea, see John Graves, “Uniformity and Induction,” in The British Journal for the Philosophy of Science, Vol. 25, No. 4 (Dec., 1974): 301-318.

472

Louis F. Groarke

question. How do we know that nature is uniform? Presumably, through induction. Because nature has been uniform in the past, we infer that it will be uniform in the future. But how can we use a premise that relies on the soundness of induction to prove the soundness of induction. That would be circular reasoning. It would be tantamount to maintaining that induction must be reliable because induction is reliable. Unless we have already assumed that the movement from particular experience to future prediction is trustworthy, this approach logically collapses. John Graves tries to salvage Mill’s methodology with a reinterpretation. He writes: What actually happens seems to be this: when mankind made its first inductions, there was neither the possibility of nor the recognized need for any justification. People simply made them, whether from natural instinct or Humean habit. Gradually, we became aware of the fact that inductive predictions were remarkably successful in a wide variety of cases, and that our inductions could be organized in a hierarchy of increasing generality. Uniformity of nature was finally seen as the apex of his hierarchy. … For Mill, scientific induction must be founded on spontaneous induction, and an appeal to uniformity just reflects our self-conscious awareness of the full implications of our methodology.14

Graves turns the principle of the “uniformity of nature” into an afterthought; it is something that comes about after we have completed innumerable inductions about more specific issues. But how does this help? What is this generality of generalities based on but prior question-begging examples of inductive reasoning? Graves concedes that scientific reasoning is dependent on spontaneous—uncritical—induction. It operates through Humean habit. But this turns the “uniformity of nature” principle, once again, into an unreliable prejudice based on what we have been accustomed to in the past. I do not want to suggest here that believing in the uniformity of nature is somehow unsound, incorrect, or illegitimate. Mill correctly points out that we all believe, at some fundamental level, that nature is uniform. This is assumed in our induction. But Mill, who is a radical empiricist like Hume, is unable to securely buttress induction from attacks by modern-day skeptics. There is, in any case, a better way of fixing these problems, one that can be recovered from an assiduous reading of the Aristotelian tradition.

14

Graves, “Uniformity and Induction,” p. 303.

Jumping the Gaps

473

3.6 Hobbes’ Principle: Probability Approaches Hume’s skepticism about induction is foreshadowed by many developments in the history of philosophy we cannot explore here.15 Suffice it to note that the view commonly associated with Hume can be found, in its essentials, in John Locke, and even earlier. A hundred years before Hume’s Enquiry, Thomas Hobbes, in his Leviathan (1651), a text better known for its political and moral content, explains the predicament of someone who wishes to predict the future: Sometimes a man desires to know the event of a [future] action; and then he thinketh of some like action past, and the events thereof one after another, supposing like events will follow like actions. … Such conjecture, through the difficulty of observing all circumstances, be very fallacious. But this is certain: by how much one man has more experience of things past than another; by so much also … his expectations the seldomer fail him. … Applying the sequels of actions past to the actions that are present [is done] with most certainty … by him that has most experience, but not with certainty enough. And though it be called prudence when the event answereth our expectation; yet in its own nature it is but presumption. For the foresight of things to come … belongs only to him [i.e., God] by whose will they are to come. From him only, and supernaturally, proceeds prophecy. [But] the best prophet naturally is the best guesser; and the best guesser, he that is most versed and studied in the matters he guesses at, for he hath most signs to guess by.16

Hobbes presents future prediction based on past experience as inconclusive “presumption,” as “very fallacious” “conjecture,” and as guessing which can never be done “with certainty enough.” These are, of course, tropes that Hume and others pick up. Hobbes is, however, slightly more optimistic than Hume. In spite of all these problems, he still believes that the man with more experience of things has a better chance of getting future predictions right. To write this out as a general rule of thumb: “the more examples of something we observe, the more certain our inductive conclusions.” Call this line of thought Hobbes’ Principle. The mathematics of probability is a refinement, in one way or another, of Hobbes’ Principle.

15

See J. R. Milton, “Induction Before Hume,” in Dov M. Gabbay, Stephan Hartmann and John Woods, eds., Inductive Logic, Volume 10 (Handbook of the History of Logic) (Amsterdam, The Netherlands: Elsevier B.V., 2011), pp. 1-42. 16 Thomas Hobbes, Leviathan, J. Gaskin, ed. (Oxford: Oxford University Press, 1996), Part 1: Ch. 3, pp. 17-18.

474

Louis F. Groarke

Some contemporary authors then try to rescue induction from the jaws of Humean (or Hobbesian) uncertainty through probability theory.17 Timothy McGrew, who espouses a “direct inference” Bernoullian approach to the Bayesian probability calculus, strikes a hopeful note. He writes: It would be difficult to overestimate the influence Hume's problem of induction exercises on contemporary epistemology. … There is depressingly little sign of consensus on the underlying problem. … And no small part of it lies in the conviction of a considerable number of philosophers that Hume's problem … is quite simply and clearly insoluble. … I will argue that the form of [Bayesian probability] I am defending provides the key to the refutation of Humean skepticism—theoretical and practical, historical and modern—regarding induction.18

I cannot enter into the details of McGrew’s highly plausible response to Humean skepticism here. Simply note, to start, that probability methods and traditional Aristotelian accounts of induction are focused on different things. The probability calculus is mostly about prediction; the traditional Aristotelian approach is a search for explanation. (The Dougherty essay nicely points out this difference.) Aristotle never was a sophisticated statistician. He does not provide any precise mathematical way to move from counting observations to predictions. His approach is to look for necessary or essential connections, for mutually exclusive properties, or, in the case of contingent events, to rely on rough-and-ready generalizations. (Raymond’s account of the co-demolition test provides a very plausible historical account of what Aristotle and other ancients were thinking about when they approached induction.) It must be acknowledged that modern probability theory admirably fills a gap left by Aristotle, whose scientific focus was not on the accidental and contingent. An example may help capture the difference between these two approaches. The famous French mathematician Pierre-Simon Laplace (17491827) was so bold as to calculate “the odds on the sun rising the next day… to be 1,826,214 to one.”19 To be fair, he himself adds a note that nothing 17

I would like to thank Professor Vlastimil Vohánka at Palacký University, Olomouc for useful comments which made me return to these issues, hopefully in a more illuminating manner. 18 Timothy McGrew, "Direct Inference and the Problem of Induction," The Monist Vol. 84, No. 2 (April 2001): 153-78. 19 He used the so-called Rule of Succession, based on the idea that the sun had already risen1,826,213 days (by his calculation). Colin Howson and Peter Urbach, Scientific Reasoning: The Bayesian Approach (Chicago and LaSalle, Illinois: Open Court, 2006), p. 269.

Jumping the Gaps

475

can stop the sun rising.20 Still, for the simple sake of illustration, compare probabilistic and Aristotelian approaches as they would apply to the question of whether the sun will rise tomorrow. One the one hand, we can calculate the probability of the sun rising based on how many times it has risen in the past. On the other hand, we can inquire into the universal law of gravitation and, through a deep understanding of the physics of cause-andeffect, determine that the sun must rise tomorrow morning given the mass of the earth, the speed of its rotation, its angular momentum, and so on. Whatever their understanding of physics, traditional Aristotelians are after this second kind of explanation. It is by understanding the nature of the sun, the earth, and of mass and movement (etc.) generally that we discover what must happen (because things are the way they are). Calculating probability is one thing; ascertaining the epistemological ramifications of probability interpretations is quite another. We cannot deal with all the mathematically-important nuances here. Suffice it to say that the probability calculus depends on some version of Hobbes’ Principle, which stipulates that the accuracy of our predictions improves with a larger sample size (more experience). What statisticians call the “law of large numbers” states, in effect, that as the number of trials increases (ever approaching infinity), the results of our calculations will inevitably converge to the expected value of the predicted variable. (Leave aside possible problems with related notions of infinity.) Suppose, to use a concrete example, we begin recording the number of heads that turn up in consecutive tosses of a fair coin. According to the law of large numbers, the probability of heads will converge inevitably to 50% as we perform more and more tests. The “true probability” of heads will equal the frequency with which that particular outcome occurs in the (very) long run, when our trials involving coin-tosses are repeated an ever largee number of times. If, however, this is all well and good, the law of large numbers seems to be just a slightly different restatement of Mill’s uniformity of nature principle, which leaves probability treatments open to similar criticism. As long as we assume that the (deep) nature of things in the world does not change, such calculations seem reliable. But how can we use these same calculations to prove that the world does not change. This is an assumption we need to get the theory off the ground; it is not something that is proved by the theory. (The uniformity of nature assumption serves here, in Aristotelian terms, as a first principle. It is a worthy candidate for 20 Cf. E. T. Jaynes and G. L. Bretthorst, Probability Theory: The Logic of Science (Cambridge: Cambridge University Press. 2003), pp. 387–391.

476

Louis F. Groarke

such service. But we induce first principles; we do not arrive at first principles through calculation or deduction.) Authors like McGrew make an assumption that they use to buttress their Bayesian approach. McGrew himself, who proposes an attractive model of Bayesian “direct inference” explains: Just as the classical syllogism warrants our concluding, from (1.) “All G are X” [and] (2.) “a is a G,” with full assurance, that (3.) “a is an X,” so the proportional syllogism … licenses our inference from (1’.) “m/n G are X” [and] (2’.) “a is a G,” with assurance m/n, that (3’.) “a is an X.” … We use the classical syllogism but rarely: our major premises are not of the form “All falling barometers portend storms” or “All red-meated watermelons are sweet” but rather the more modest form that falling barometers generally portend storms and most redmeated watermelons are sweet. … The native wit of mankind … [accepts] that if “All M is P” makes it certain that any one M will be P, then “Nearly all M is P” makes it nearly certain, and has quite satisfactorily predicted its storms and purchased its melons accordingly. Indeed, the classical syllogisms Barbara and Celarent… can readily be seen as limiting cases of the proportional syllogism when m=n and m=0, respectively. From this point of view, statistical syllogisms constitute a spectrum of inferences. … The conclusion, as in the traditional syllogism, is always categorical, but the strength of the argument varies with the proportion cited in the major premise.21

I want to emphasize that I have nothing to object to this quasi-Aristotelian approach to probability. But it cannot serve as an adequate epistemological response to Humean skepticism, at least not by itself. Notice two important aspects of McGrew’s treatment. On his account, what is uncertain, in a measure of m/n, is whether “a is a G.” But the judgment that the claim is m/n uncertain is not uncertain. Humean skepticism—indeed, any consistent skepticism—goes much deeper. It insists that our judgments about the uncertainty of our claims are just as uncertain, which renders the initial calculation of uncertainty unreliable (indeed, entirely unreliable). McGrew’s treatment accepts, we might say, first level uncertainty but not second-level uncertainty. It grounds probability calculations on our intuitive, logical sense of the world. But this intuitive sense is just what Hume is attacking. We need, at least, to answer his arguments. The second issue to notice is that probability treatments all have to start somewhere. We have to begin with prior assignments for probability that derive presumably from our observation of the world. In the classical 21

McGrew, “Direct Inference.” He is citing from Donald Williams, The Ground of Induction (New York: Russell & Russell, 1963), p. 39.

Jumping the Gaps

477

examples—a shuffled deck of cards, a fair coin toss, or a urn filled with a random mix of colored marbles—we have some prior information about the number of alternatives and the circumstances upon which we can base our probability calculations. We know, for example, that there are fifty-two cards in a card-deck, that there are four suits, that there are three face cards, one Ace of Spades, and so on. On this basis, we can confidently calculate probability and make predictions. But this is not what our experience of the world is like on the Humean model. On Hume’s radical empiricist account, all we know about the world derives from our observations of mere appearances. We are unable to see into the true causes or natures of things. To use the card example as an illustration, it is as if we do not know beforehand that there are fifty-two cards, four suits, three face cards, and one Ace of Spades. We cannot assume that the future will resemble the past. Suppose then that the identity of individual cards may change unpredictably as we are manipulating them: the Queen of Hearts may unexpectedly become the Ace of Spades, which suddenly becomes the Two of Diamonds, which transforms itself into the Six of Clubs. Or, suppose someone could suddenly turn over a thirteen of hearts or a three-and-a-half of clubs. Or that Nature is dealing us cards in a sneaky, underhanded way. And, as Humeans would have it, suppose—this is the key—that we cannot hope to understand the true causes behind such changes. How then could we reliably calculate the probability of this or that sequence of cards turning up? We could not, and yet Nature is infinitely more complex than a deck of cards. In a textbook discussion of scientific reasoning, Colin Howson and Peter Urbach present Bayesian probability as an objective method of inference much like deductive logic. In their words: “The most natural way of interpreting the Bayesian formalism [is to view it as] a set of valid rules for deriving probabilistic consequences from probabilistic premises.”22 The Bayesian formalism does not supply us with premises; it only tells us how to move from them—once we have them—to a mathematically-valid conclusion. Howson and Urbach insist that “prior probability assignments” are “exogenous considerations,” and, as such are “outside the scope of the theory.”23 Think of it this way. We need numbers to do arithmetic. Once we have them, we can add and subtract. But if there could be someone who had no inkling of numbers, this person would be at a complete loss. Once we abstract out numbers from our experience of the world, we can add and 22 23

Howson and Urbach, Scientific Reasoning, p. 297. Howson and Urbach, Scientific Reasoning, p. 301.

478

Louis F. Groarke

subtract, but adding and subtracting presuppose that we already have a concept of numbers. In the same way, we can use probability theory to calculate the chances of something happening, but we need to begin with an understanding of the world that provides us with prior probability assignments. This understanding always presupposes some type of the uniformity of nature principle. 3.7 Antirealism and Atheism: Inevitable Skepticism The alternative approaches to induction offered in this text are, for the most part, Socratic, Aristotelian, Thomistic, Baconian, Whewellian (or even Randian) in character, as McCaskey points out. Rescher’s pragmatist approach offers an interesting alternative. But, sometimes, even pragmatism seems to concede too much to the contemporary anti-realism that derives from Hume. Broadly speaking, we can identify two metaphysical traditions in philosophy. Call the first tradition, realism. The realist tendency in metaphysics includes seminal authors such as Aristotle and Aquinas as well as a long celebrated sequence of both followers and even competitors. It might even include the “anti-metaphysical” Positivists, who seem to believe very strongly in a restricted number of natural kinds, except that the Positivists offer such a meager metaphysics that their realism is sometimes more uncritical assumption than metaphysical theory. Metaphysical realism emphasizes the knowability and the uniformity of the individual natural kinds that make up the world. It traces causality back to the epistemologically accessible natures that constitute things on a fundamental level. It operates, to borrow an expression from Henry Veatch, according to a “what logic.” On these accounts, the best or most accurate way of understanding the world is through accurate descriptions of the true natures of things. We can call the second, competing tradition in metaphysics antirealism or nominalism. The antirealist school includes diverse historical authors such as the Ancient Skeptics, Ockham, Al-Ghazali, Malebranche, Locke, Hume, Mill, as well as many contemporary philosophers approaching problems from a Continental perspective. (It could even be said to include Descartes in his more skeptical moments.) The antirealist emphasizes the unknowability or even the non-existence of natural kinds understood as the ultimate engines of causality in the world. They push natural kinds, we might say, out of reach, into some mysterious, inconclusive, indeterminate, arbitrary, or surface category. Antirealists tend to be suspicious of traditional metaphysics and induction, whereas realists, who

Jumping the Gaps

479

have taken quite a beating in modern philosophy, embrace traditional metaphysics as a path to understanding and express confidence in induction. Antirealism limits science to a search for prediction. Although realism accepts an important role for prediction, it identifies knowledge, in a superior sense, with cause-and-effect explanation. (These historical generalizations cannot, of course, capture the complexity of individual positions, but they do serve as a rough-and-ready way of mapping out competing philosophical viewpoints.) Hume inserts himself into the antirealist tradition (largely, it would seem, as a result of his youthful reading of Malebranche) but without embracing the theism that many earlier authors used to make metaphysical sense of the world. At the same time, he expresses an unshakeable confidence in the worldview advanced by modern science. As I have already suggested, however, this seems incoherent. Confidence in the practice of science seems to presuppose some form of realism. Hume believes that induction is unreliable, that things in the world cannot be properly organized into natural kinds, that we cannot see into the deep properties and natures that cause events in the world to happen as they do. This is why we cannot predict the future. (There are, of course, other ways of saying the same thing. One might assert, for example, that Locke’s approach to substance—knowledge of which arises through induction—unglues things from their properties and makes prediction impossible.) But how would science, on this antirealist model, even be possible? Science endeavours to discover and precisely describe the order manifested in the world by natural kinds with predictable properties. Get rid of natural kinds, metaphysically or epistemologically, and what is left to explain the order in the world—if there really is order that we can access? The critic could complain that Hume should logically embrace complete skepticism, including skepticism of science. Seen from a realist perspective, order in the universe is ultimately caused by the natural kinds that make it up. The periodic table, for example, is one successful way of scientifically dividing material things into natural kinds. This chemical classification presupposes that there are basic things in the world that possess necessary and even essential properties. These basic things, the elements, must have certain properties in order to be what they are. And this is all the realist needs to ground a reliable theory of “chemical induction” that can account for the science of chemistry. If something is oxygen, it must have eight electrons, an atomic weight of 16, two empty p orbitals, and so on; all of which account for observable

480

Louis F. Groarke

properties we can accurately predict. Humean skepticism about induction seems to belittle this achievement. After all, we induce the periodic table; we derive general categories from specific observations. If the periodic table is rigorously true, at least one form of induction is rigorously true. To be scrupulously fair about such things, if one wants to be an antirealist and save science, there is an escape hatch that is off-limits to Hume. Traditional nominalists like Occam, Al-Ghazali, Malebranche, and even Descartes, acknowledge some kind of trustworthy Deity as the source of all the natures in the world. (Descartes’ response to absolute skepticism hangs by this one thin thread: that the nature of God is necessarily so good that He cannot deceive us.) Theism, of this metaphysical sort, can be used to stop the collapse of antirealism into utter skepticism. Even if natural kinds were unstable or non-existent, God could still look down from Heaven and force His always-consistent Will on the world. Through some Divine Ordinance He might impose regularity on the world in a way that makes induction and science possible. Even if causality in the universe does not arise from natural kinds but arises directly from Divine intervention (as in Berkeley’s idealism), this recourse is enough to save metaphysics and science. But Hume, who is in principle hostile to all things religious, cannot avail himself of this metaphysical solution. He is caught, it seems, in a double bind. In the absence of natural kinds, in the absence of a Providential God, whence arises this necessary order in the world that science claims to explain and chronicle? The best we can do in an antirealist universe without a Divine source is to rely on predictions based on past experience that can be overturned at any future moment in time. Articulating a scientific “explanation” of the world may serve as a useful myth that motivates and orientates discussion and endeavor in popular practical, pedagogical, and political realms but, considered as a rigorous epistemological alternative, it must fail conspicuously. The consistent believer in science seems faced with an either-or choice: take up realism and embrace belief in (accessible) natural kinds or take up a certain kind of voluntarism that, the critic might complain, uses God as a Deus ex machina. Hume and his followers paradoxically profess dogmatic belief in science while rejecting realism and theism. Any such account seems logically untenable. Approaching science with a post-modern relativism (which is objectionable on other grounds) would make more sense. 3.8 A Realist Starting Point: The Correspondence Thesis Alan Robert Rhoda, in a recent doctoral dissertation from Fordham, tries to solve the Humean problem of induction from a modern analytic perspec-

Jumping the Gaps

481

tive. Offering an account that balances carefully between internalism and externalism in modern philosophy of mind, he explains his overall view: In order for explanatory [i.e., inductive] inference to get off the ground we have to accept what I call the correspondence thesis, that there exists a significant and fundamental correspondence between knower and known, between our cognitional makeup and the intelligible structure of reality. I argue that acceptance of this thesis is epistemically responsible because it is methodologically necessary— any attempt to responsibly pursue adequate grounding for our beliefs has to assume that reality is knowable, and knowable by us. 24

But this seems like saying that the correspondence thesis is what we need to have knowledge, so the correspondence thesis must be true. Obviously, the Humean skeptic could complain that any such inference would beg the question. Rhoda’s heart is, no doubt, in the right place. The problem here is that the “correspondence thesis,” a legacy of Descartes, who unwittingly pushes metaphysics out of reach. It is a pragmatic necessity, as Rhoda correctly insists, in that we need it to climb out of the quicksand of bottomless skepticism. Of course, traditional realists believe that our perceptions correspond, grosso modo, to the true nature of the world. However, as Kostelecky correctly points out in his treatment of Aquinas, they do not accept that worries about about epistemological correspondence neede any full-length, meticulous treatment. They come closer to suggesting that such worries present, at best, a pseudo-problem. Contemporary philosophers such as Rhoda may misunderstand the realist tradition. Traditional realists do not typically try to argue their way to a robust belief in a knowable external world. They might have objected that it was wrong even to offer such an attempt. As Aristotle says, we do not reason our way to first principles. We induce first principles through the direct, critical exercise of intelligence. On the traditional view, there is, strictly speaking, no philosophical “problem of correspondence.” This is not, they seem to think, where to start a philosophical theory, by trying to come up with arguments that satisfy a crazy person’s logic so as to prove to them that the external world perceived by our senses actually does exist in a way that corresponds to our perceptions. To be convinced that one has to provide a logical argument for things like this is already to fall into the antirealist trap. It is, like Descartes’s absolute skeptic, to argue our way out 24 Alan Robert Rhoda, “The Problem Of Induction: An Epistemological And Methodological Response.” (PhD dissertation, Fordham University, December 2003), pp. 4-5.

482

Louis F. Groarke

of our commitment to reality and then try to argue it back in again. But this is to dig a hole in our common sense belief so deep, we may never climb out again, no matter how hard we try. The way modern philosophers approach the correspondence thesis seems to misstate the problem. On the realist account, we begin our theories with language that is inextricably attached to things in the world and therby tied to realist assumptions. Reality permeates everything we talk about. We can, of course, ask any manner of questions or conceive of make-believe worlds of all sorts, but this does not detract from our initial realism. The attitude to reality Kostelecky attributes to Aquinas is representative of the mainstream generally. These historical authors do not attempt to prove that we can have knowledge. They assume that we can have knowledge and then set out to describe, explain, and evaluate how we go about acquiring it. We generally take the correspondence thesis for granted. If we want to provide an account of its origins, we must do so by means of induction, not through deductive argument. Why do we believe that our sense perceptions tell us the truth about reality? Yes, we all know about optical illusions, hallucinations, mirages, and so foth, but why should this invalidate this general truth. The exception proves the rule, as the saying goes. Perceptual errors are noticed and evaluated with reference to generally correct perceptions. They do not prove that all perception is mistaken; only that individual perceptions are mistaken. How do we achieve confidence in perception? The general truthfulness of perception is a “presumption” that is forced on us by the inexorable nature of the external world. We confront something larger than us, of longer duration, that does not respond to our will, that forces its nature upon us whether we like it or not. In a way that other authors in this collection explain, this realization is an induction. It is a leap to something that is more than sense perception, to an axiomatic principle that cannot be accounted for purely in terms of observations. But this induction—that there is a determinate world out there with which we are in direct contact— is a sign of intelligence. It is a way of making good sense of what happens to us in a universal way. The difference between the abject skeptic (or the solipsist) and the sane person is precisely this induced belief. The sane person quickly comes to the realization (in childhood) that what we can know about and respond appropriately to the world outside us—or we very quickly die. This understanding about our unchosen environment includes belief in something over and beyond the mere images inside our heads.

Jumping the Gaps

483

Analytic philosophy has made much hay about the correspondence thesis. But the debates that swirl around such issues, although couched in the exacting logic of systematic philosophers bent on turning philosophy into a science might be viewed, at least by many traditional realists, as beside the point. The Great Hope that Descartes embraced was that if only we can find a system, a recipe, an algorithm, a deductive syntax for logical argument, then we could fill all the gaps and come to metaphysical conclusions that are fully accounted for in terms of prior evidence. The idea was, in part, that we could logically—i.e., deductively—prove the correspondence thesis. But this is never going to happen. The external world we believe in far exceeds the narrow limits of our own experience. There is an expansion of belief here that goes far beyond the content of our individual perceptions. It is a necessary expansion of belief that posits a new incommensurable category—objective existence independent of our own perception—that we have to believe in to make sense of the world. We discuss what is happening here in sections 5.4-5.6. For the moment, simply note that the so-called “correspondence thesis” does not arise through deductive argument (as many modern philosophers have wished) but through an inductive leap to a new possibility that precedes deductive logic properly construed. 3.9 Looking Through the Glass: A Comparison Finish this preliminary discussion and critique of Humean inductive skepticism with a comparison. Imagine we have two individuals; we will call them Blind Harry and Able-Sighted Harry. Now suppose Blind and Able-Sighted Harry are both familiar with a noise-machine, like a complicated mechanical wind-up toy, that emits a wide variety of noises: squeaks, knocks, whirrs, chimes, rings, and so on, in some complicated but regular sequence. Now suppose Blind and Able-Sighted Harry are asked to predict what noise will happen next. Blind Harry makes his prediction on what he has heard in the past. Suppose that every time he has heard “ding-dongbuzz-tick,” it has been followed by “wham!” If he now hears the same sequence “ding-dong-buzz-tick,” he may reasonably predict that the next noise will be “wham!” This is all that he knows. This is what he is used to. This is all the evidence he has. So it makes good sense for him to assume that the next noise he hears will be what he has heard in the past. But what about Able-Sighted Harry? Well, suppose the entire contraption is housed in a transparent glass case that puts its complicated mechanism on display. Able-Sighted Harry is

484

Louis F. Groarke

able to look into the glass case and see the cogs and teeth and pulleys and springs that make this noise-contraption operate. If he is a really intelligent fellow, he might be able to figure out the precise mechanism that is producing these sequences of sounds. Suppose then that he is able to accurately predict what the next sound will be because he understands how the machine operates. Even if makes the same prediction that the next noise will be a “wham!” he does this on a completely different basis. Blind Harry will never be able to use this visually-based method of prediction. This is, however, in metaphorical terms, the stark difference between Humean and Aristotelian induction. Hume and his followers maintain that we are all like Blind Harry. We cannot see into the true causes of things. Our predictions about the future may turn out to be right, but there is no logical necessity that pertains to the prediction-making process. The secret mechanism of noise-making may, after all, be designed to produce surprising sequences of noises at random intervals. Aristotle and his followers maintain, in sharp contrast, that at our best we are all like Able-Sighted Harry. We can peer into the mechanism of nature, into the deep causes of things. Once we understand how the parts are organized inside the machine, we can predict the necessary effect. Induction here is not enumerative, numerical, or statistical. It is based on an insight into the natures behind the surface phenomenon. This presupposes a very different kind of mental process than Humean induction. Contemporary philosophers have come to believe that the AbleSighted Harry model of induction is a naïve account of what Blind Harry is doing. They overlook the possibility that we may be able to see into the nature of things. They insist on this in various ways. They point perhaps— to cite only one example—to scientific evidence like the Copenhagen interpretation of quantum mechanics, which claims that probability is the best we can get when it comes to the most fundamental phenomena. (Keep in mind the Copenhagen interpretation is not a scientific result but a metaphysical thesis, which, for a wide variety of specialist reasons, one need not accept as the final word.) But even if explanation is not fully available in specialized scientific contexts, it seems readily available in most science. The review of actual episodes of explanation from the history of science by Dougherty and McCaskey support this claim. Surely, whenever possible, cause-and-effect explanations are to be preferred to mere statistical predictions. Finish this section with one important qualification. In our thoughtexperiment, what makes Able-Sighted explanation possible is not restricted

Jumping the Gaps

485

to more of the physical world. Able-Sighted Harry is a smart individual. He seizes on the “immaterial principles” of physical mechanics that are necessary to any explanation of the noise-machine. On traditional accounts, induction does not only entail a movement from the particular to the universal, but even more importantly, a movement from sense-perception to the conceptual. Science relies on principles that, although they originate in observation, move beyond it to some sort of concept, principle, axiom, or assertion. No one perceives the value of “ʌ” (pi) directly. They infer it from a geometrical analysis of the circle. No one perceives, on a metaphysical level, the link between cause-and-effect; they infer it from their experience of events in the world. No one perceives, again, on a logical level, the principle of non-contradiction; they infer it from how things happen or exist in the world. The same sort of reasoning applies to modern-day science. No one even perceives the force of gravity directly; they see objects fall (or the movement of planetary bodies) and they infer the existence of invisible gravity from these physical events. On the traditional view, this sort of inference is principally what induction is about, as we now need to explain. 4 A Contemporary Aristotelian Alternative I began this essay by comparing the mental process of induction to the Hertz experiment in which an electromagnetic field is used to induce a spark to leap between two metal balls, an event, which in turn, precipitates a similar jump between two metal ends by a distant spark. Obviously, this analogy was not available to Aristotle! It captures, however, salient features of the Aristotelian understanding. Consider then, at some length, what this physical analogy picks out as three essential aspects of logical induction: (1) induction is a flicker or blaze of direct intelligence; (2) induction is a jump between epistemological incommensurables, and (3) induction is a movement that can be directly communicated to another reasoner, who leaps in unison across the same epistemological gap. 4.1 Induction is Not Primarily an Argument First, let us move beyond the very narrow interpretation of induction usually presupposed in modern logic. The present-day account views induction chiefly as a propositional argument about future prediction. To begin with, it should be readily apparent (as Rescher points out, for example) that future prediction is not the essential point of induction. If I induce, from present-day evidence, that the dogs in ancient Athens had four legs, or that the crows in prehistoric North America were black, or that the

486

Louis F. Groarke

philosophers in the Middle Ages consumed mead and wine greedily, these inductions involve a movement backwards, not forwards, in time—this is “retrodiction,” not prediction. But they still qualify, even on the Humean model, as inductions: I have not observed all the dogs in ancient Athens, all the crows in prehistoric North America, or all the drinking bouts of Medieval philosophers. Indeed, I have not even observed a single instance of these things. So the logical movement is, technically speaking, ampliative, from incomplete evidence to an all-embracing generalization. So such inferences still count as inductive. But even if we accept that this correction is not momentous, there is a more serious issue lurking below the surface. What Hume did not seem to notice was that the movement from a particular to a universal already occurs at the initial stage of concept formation. However this process precisely operates, the point is that when we move from our individual experience of particular things to concepts that describe those things, we have already arrived at a universal. I have only experienced individual dogs, but the word ‘dog,’ which I must use when discussing relevant issues, applies to all dogs in the universe, past, present and future! We do this so naturally, we overlook just how remarkable this movement from sense perception to the conceptual is. Again, when I use the word ‘red,’ I am referring to anything and everything that is or was or will be red in the history of the world. I must move from my experience of individual red objects to a universal concept that applies to all red objects in the world. This is why traditional authors identified induction with the jump from sense perception to the conceptual. The Humean tradition focuses squarely on propositional arguments that are, in an important sense and as many of our authors indicate, after the fact. (McCaskey presents an excellent, handson report on this issue from a scientific perspective.) When we formulate the concepts we represent by words, a process traditionally known as “abstraction,” we are already engaged in the ampliative movement that is a central feature of induction. This initial flicker or blaze of intelligence is the starting point for all induction. In the Posterior Analytics, Aristotle discusses how we arrive at first principles. He explains: “the memories, though numerically many, constitute a single experience. And that experience, that is the universal when established as a whole in the soul—the One that corresponds to the Many, the unity that is identically present in them all—provides the starting point

Jumping the Gaps

487

for art and science.”25 The universal in the soul, “the One that corresponds to the Many” is, in the first instance, a concept; and only, in the second instance, a universal proposition. In both cases, one thing stands in for many things, and puts on display the unity in them all. The word ‘cow,’ for example, stands for all cows; the universal proposition ‘all cows are mammals’ attributes the same property to all cows. In both cases, there is an implicit induction. To say that there are ‘cows,’ is to say that these animals all share the same (essential) nature. To say ‘all cows are mammals’ is to do the same thing but by specifying something about what that nature is. In both cases, one must leap from the physical perception of individual instances to a universal understanding that includes more than what can be perceived. In the Western tradition, mainstream philosophers have tended to emphasize the divide between sense perception and reason. Boethius, to cite only one example, presents the senses [sensus] and imagination [imaginatio] in a debate with reason [ratio]. He writes: Suppose that the senses and imagination thus oppose reasoning, saying, “The universal natural kinds, which reason believes that it can perceive, are nothing; for what is comprehensible to the senses and the imagination cannot be universal…” To this reason might answer, that “it sees from a general point of view what is comprehensible to the senses and the imagination, but they cannot aspire to a knowledge of universals, since their manner of knowledge cannot go further than material or bodily appearances.”26

The sense and imagination (which sees in phantasms or “images”) grasp physical things individually; reason “sees” conceptual things universally. We have here two incommensurable categories or “kinds” of knowing. One cannot be accessed, comprehended, appreciated in terms of the other. The function of induction is then to jump the gap that separates one incommensurable category from the other; as human beings we start in individual sense perception but are somehow able to leap over to concepts, to a universal way of apprehending and understanding things. Boethius argues that the mind possesses a “greater power, of more effective force by far than that which only receives the impressions of material 25

Aristotle, Posterior Analytics II.19, 100a5-8 in Aristotle, Posterior Analytics; Topica, transl. by H. Tredennick (Cambridge: Harvard University Press, 1960), slightly emended. 26 Boethius, The Consolation of Philosophy, transl. by W. V. Cooper (London: J.M. Dent and Company, 1902), p. 158.

488

Louis F. Groarke

bodies.”27 It is not then, as the radical empiricists later claimed, that the mind is a tabula rasa, an empty mirror that somehow passively reflects whatever impressions the senses bring its way. No, not all! The mind has an active power that orders and organizes and understands (with effort) what all these things are. The rational mind moves beyond sense perception to create a new level of apprehension that cannot be contained within or reduced to what went before. Whatever term we use for what is happening—intuition, intellection, insight, non-discursive reason, noesis, epagǀgƝ, intellectus, intelligentia, the natural light of reason, agitation of wit, colligation, abduction, systematization—there is a mental dynamism that, in induction, draws a mental spark from particular sense experience. The mind energetically leaps across a cognitive divide to some new, incommensurable way of understanding the world in terms of universals. Our very use of language presupposes induction; without induction, true language (which is derivative from concepts) would be impossible. But it all begins, somehow, in the light of pure intelligence. Somehow, when we turn the spotlight of intelligence on the world, this produces mental sparks that bring an uncanny understanding. The contemporary view that induction as an (invalid) argument form that goes from particular premises to a universal conclusion omits any serious consideration of where even dedcution starts. To go from, ‘this, this, this crow is black; therefore all crows are black,’ is, of course, an inductive movement in logic; but already, when someone uses the words ‘crow’ and ‘black,’ there is a necessary widening of human experience beyond the boundaries of our original perceptions. We only see individual birds and individual instances of black, but we are somehow able to turn these perceptions into universal ideas that represent a genus of bird and a genus of color. Already, even before we get to the stage of saying ‘this crow is black,’ we have performed two inductions, one involving the concept of ‘crow,’ the other involving the concept of ‘black.’ When we join these two concepts together in a single proposition, we perform another, higher-level induction. 4.2 The Mental Spark Knowledge does not begin in argument but in a mental spark, an inductive movement of pure intelligence. We can differentiate accordingly between discursive and non-discursive reason. In discursive reasoning, we combine words to produce sentences that we then combine into arguments. In nondiscursive reasoning, we intelligently “see” that something is the case. We 27

Boethius, The Consolation, p. 156.

Jumping the Gaps

489

can even do this wordlessly and without arguments. Historical thinkers view induction, first and foremost, as a non-discursive movement of direct apprehension and, only secondarily, as an argument form. When Aristotle shows how one can convert an induction into a syllogism in the Prior Analytics, he is not suggesting that this is what induction fundamentally is, but only that there is a clever way to transform what happens in induction into a deductively-valid demonstration.28 The resultant inductive syllogism hinges on an insight into shared natures (convertibility) that comes about through an intelligent understanding of observation (not through argument). Completing the syllogism requires the addition of an extra, non-deductive (non-syllogistic) step to the process that is needed to definitively tie the premises to the conclusion. Older authors often referred to non-discursive modes of reasoning as intuition. When they spoke of intuitively understanding, they did not mean, as in the modern dispensation, that we understand the deep nature of things by feeling. They meant that we can arrive at an understanding without formulating premises in support of a conclusion. When Pascal famously writes, “Le cœur a ses raisons que la raison ne connaît point” [The heart has its reasons that reason does not know at all], he does not mean, as popular culture would have it, that feelings supply us with deeper knowledge.29 He meant that the first principles of mathematics, logic, philosophy, and religion can only be accessed through direct acquaintance not through proof or argument. The “heart” here is the ability to sense the truth directly, without recourse to discursive logic. In heartfelt knowledge, an inner conviction arises, not from argument, but from our direct familiarity with things. Doubtless, there are religious overtones here, but there is also an epistemological point. Mathematics must begin with axioms that we discern, without proof, as true. Knowledge, more generally, must begin in first principles that we grasp by an active, holistic operation of intelligence that shrewdly sees what is the case. Although Pascal, who was something of an amateur philosopher, probably did not realize this, his account of the origins of knowledge nicely squares with the traditional realist account. We might also point out that the traditional realist view of induction is closer to the artistic and literary concept of “inspiration.” Thomas 28

Cf. Aristotle, Prior Anlaytics II.22-23 for some largely misunderstood passages. The argument is about a necessary link between bileless animals and longevity. Biondi deals with this syllogism very well. 29 Cf. Louis Groarke, “Philosophy as Inspiration: Blaise Pascal and the Epistemology of Aphorisms,” Poetics Today 28:3 (Fall 2007): 393-441.

490

Louis F. Groarke

Aquinas, for example, associates the engine of induction with angelic cognition (intelligentia or intellectus), which does not arise through the labor of deductive argument—gradually piecing things together—but through a decisive intellectual gaze that sizes up things immediately. Induction is then a higher sort of reasoning. It is not about calculation, about counting, about arriving at a sum total where all is accounted for. It is, like inspiration, about grasping an idea through an accelerated and often sudden insight, through some sort of mental penetration. It involves some sort of gestalt switch, the recognition of a pattern, a felicitous discovery, a glimpse inside a nature, and so on. It cannot be reduced to some sort of microscopic mechanism. (Modern thinkers sometimes try to reduce it to an occult mechanism, but that is because they are only able to conceive of intelligence as deduction.) We must emphasize that even in this root sense of intuition, induction is traditionally regarded as a species of cognition. It does not succeed by luck, by guessing, by blind trial and error, or through some bout of divinelyinspired insanity. The original flash of understanding is a genuine instance of true intelligence. It is not merely that someone is suddenly filled with a deep conviction that they know or discern or understand something. The insight has to turn out to be, on hindsight, a real instance of knowledge. Think of the most famous moment in the history of scientific discovery: the legendary eureka! moment of Archimedes. Whatever is literally true about how the solution to his puzzle arose, we can be certain that it did not arise from a logical argument but through intense concentration on a puzzle that erupted in an insight. This is the kind of thing that typically lies behind induction. Although I have elsewhere expressed some disagreement with Lonergan’s approach to induction ably presented here by Meynell, his notion of “insight” nicely captures the active power of mental acumen that is behind the inductive leap. Think of a crossword puzzle. The clues in a crossword are designed to provide incomplete information. They are intentionally obscure and fragmentary. The crossword puzzle solver is momentarily stumped, thinks hard, and suddenly hits upon the answer. This does not happen by increments. It is not a matter of merely adding up information. It is a matter of jumping from incomplete evidence to an answer that exactly solves the problem. There is one correct answer. It is not as if anything goes. There is a criterion of success. Somehow a creative release of mental energy, induction provides a correct insight into the needed information.

Jumping the Gaps

491

Arthur Koestler popularized his own account of this aha! experience in his idiosyncratic treatment.30 One can list endless examples of this sort of thing in pure and applied science: Kekulé’s discovery of the ring structure of benzene, Guttenberg’s invention of the printing press, Percy Spencer’s invention of the microwave oven, Descartes’ discovery of coordinate geometry, Philo Farnsworth’s invention of television, Crick and Watson’s discovery of the double-helix structure of DNA, and so on. These episodes in scientific history all hinge, I would argue, on some sort of induction, a brusque movement from inevitably incomplete observation to an understanding that can be applied universally. This sort of thing is usually portrayed as an instantaneous process, but this may be, of course, a dramatic simplification. Literary and artistic “inspiration” seems largely inductive in character, although the parallel is not exact. Whatever art is (a large topic we cannot explore here), it is not, primarily, about making logical arguments. In art, the point is generally to produce a powerful emotional effect through some kind of revealed understanding. At the same time, artists and writers speak of a felicitous leap to the unexpected, which is supremely efficacious in terms of fulfilling specific artistic goals. There is no mechanism, no algorithm that suffices to explain what is going on; but there is a type of intelligence at work. In the case of truly great art, it may be a matter of “contriving” a new artistic species that perfectly fits the context. This is not entirely unlike what happens when a gifted scientist leaps to some original physical discovery. Other scientists, confronted with the same data, do not see where it leads. It takes an intellectual ability, a canniness that is able to leap—inspiration-like—to the right original conclusion. Insomuch as art has conceptual content it requires induction, for as we explain below, we can only arrive at concepts through induction. But whatever we think art is precisely, it can perhaps be meaningfully construed as a crossing over from one incommensurable category to another. One might maintain, for example, that the Romantics “invented” a new way of seeing the world that had to be discovered through some momentous application of intuition or insight, that the Romantic vision cannot be adequately explained or accounted for in terms of earlier art, that individual Romantics were responding to a historical imperative that was imposed on them from the outside, and so on. This parallel could be developed further, but let us leave aesthetics aside and return to epistemological considerations. 30

Arthur Koestler, The Act of Creation (London: Hutchinson & Co., 1964).

492

Louis F. Groarke

In a discussion of induction, Biondi writes, “the act of noƝsis [mental illumination] can only take place in an instant, in the flash of the moment. This knowing in an instant, which may continue over a period of unitary time, must not be confused with thinking in time proper to rational [i.e., argumentative] discourse.”31 Biondi points out, at the same time, that the entire process of knowledge acquisition may involve a more gradual realization, involving thinking and rethinking, “interspersed with and helped along by occasional moments of insight.”32 I want to argue that the most important issue, as far as the inductive side of knowledge acquisition is concerned, is the leap from one incommensurable category to another. I accept that this may happen in a variety of ways. Still, the image of a spark leaping over the abyss is appropriate. At the very heart of the inductive process is a buildup of mental energy that, at some point, somehow, mysteriously and quickly moves from incomplete evidence to a felicitously apt answer. Philosophers of science (most famously, Hans Reichenbach) distinguish between “the context of discovery” and “the context of justification,” but this distinction risks obscuring the knowledge-making feature of the original insight. Induction is not a matter of mere psychology. It is not as if the thinker simply feels (or “intuits” in the modern sense) their way to something true and correct. There may be, for example, a feeling of elation (as inspiration) but that is not sufficient to count as an epistemological realization. To talk as if “justification” differs sharply from discovery seems to turn scientific discovery into a lucky guess that only passes epistemological muster when we start to think about it after the fact. This hardly does justice to the genuine intellectual accomplishment involved at the beginning of the process. The scientific genius “sees” a truthful idea but they also see, simultaneously, how or why the idea is true. The original insight involves both knowledge of the idea and the reason behind the idea that makes it true. Later testing provides incontestable physical evidence that the idea is, indeed, true, and that the thinker experienced a genuine insight into the nature of things. It is not, however, that the truthfulness of the idea is only revealed in later testing (as it seems to me, an author like Lonergan wants to suggest). Aristotle proposes a distinction between induction and scientific demonstration that is perhaps a better way to distinguish between these two stages of science: the first, leading to the 31

Paolo C. Biondi, Aristotle: Posterior Analytics II.19 (Quebec, Canada: Les Presses de l’Université Laval, 2004), p. 238. 32 Biondi, Aristotle, p. 248.

Jumping the Gaps

493

intellectual discovery; the second, putting knowledge of the discovery on display. But the first stage is already a matter of rationality in action. If induction requires a powerful capacity for deep insight (in traditional terms, a kind of intellectual illumination), we could delve into the origins of this ability. But where precisely this mental light comes from or how it arises is not the issue here. Whatever we believe about the story of human intelligence, we are capable of something that is neither lucky guess nor deductive inference, which leaps, so to speak, to the truth across some incommensurable gap. The point is induction happens: people do have revealing insights into the essential or necessary or accidental nature of things. Induction comes, we might say, in all shapes and sizes. We marvel at great leaps of genius in the history of science, but there are innumerable smaller leaps we all engage in so often we take them for granted. Every time we jump up from one epistemological category to another epistemological category that moves decisively beyond the original information, there is some kind of induction going on. As we cannot catalogue all the different kinds of inductive insight here, suffice it to say that this critical capacity is an essential part of human thought and reasoning generally. 4.3 Deduction Stands or Falls Together with Induction The old Cartesian idea that deduction is the only way to prove that our knowledge is above suspicion haunts philosophy even today. Contemporary philosophers want to differentiate between untrustworthy induction and trustworthy deduction. Strangely though, they seem to have forgotten that even Descartes’ deduction is rooted in a prior act involving the intuition of simple ideas that are seen by the natural light of reason to be true. Whatever we think of Descartes, I want to argue here that deduction must stand or fall together with induction. Epistemic suspicion directed only towards induction is incoherent. We need the mental spark of induction as a prior stage that makes deduction possible. Put another way, correct induction is a necessary condition of correct deduction. The epistemological priority of non-discursive reason over discursive reason is, in fact, a defining feature of traditional theories of induction. Once we understand where induction begins, at the level of concept formulation, it becomes obvious that any repudiation of our mental abilities to move from specific to general would undermine human discourse generally. If our abilities to go beyond the particular to the universal are unreliable, every idea is unreliable. Hume wants to operate solely on the level of sense perception. This is why he denies the link between cause and

494

Louis F. Groarke

effect. But this is (to borrow Boethius’ point) like the senses (and imagination) informing reason that cause-and-effect does not exist because it is outside their scope of expertise. Of course, they do not perceive it, reason would, no doubt, reply. It is a higher reality that must be penetrated by intelligence, not by sense perception. One cannot access the idea of causeand-effect unless one jump across a gap to a higher level of apprehension, something Hume, with his misplaced emphasis on perception simpliciter, is unwilling to do. Modern logicans are particularly worried about induction. If, however, induction is vulnerable, so is deduction; for deduction always presupposes a prior induction. Consider, briefly, three examples from formal (or tehnical) logic. Consider categorical statements of the sort ‘All S is P,’ which are commonly used in basic syllogistic. This A statement is a universal claim about all ‘S.’ Notice, however, the formula ‘All S is P’ is also a universal representation of all such universal statements. But no logician has ever encountered (or read, or heard) all the universal statements in the world. That would be an impossible feat. What happens is rather that every individual logician meets with particular universal statements and induces a universal formula (or kind) that represents them all. The ‘All S is P’ designation represents, in effect, the formal concept that includes all universal affirmative statements. Through induction then, we are able to arrive at a concept that we can then use to set a standard for logical correctness. If induction was impossible (or untrustworthy), we could not do this. The most basic syllogistic would not be possible. Or consider Bertrand Russell’s famous logical exegesis of the pseudo-statement: ‘The King of France is bald’. This false statement commits a double-question fallacy (among other things) for it includes at least two separate claims: (1) that there is a king of France, and (2) that he is bald. But the first claim is false—there are no kings in France since the French Revolution—which makes the second claim nonsensical—a non-existent person cannot be bald. Russell separated out these claims using the following predicate notation: ‫׌‬x[(Kx & ‫׊‬y(Ky ĺ y=x)) & Bx]33

33

Cf. Irvine, A. D., "Bertrand Russell", The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL = (accessed August 29, 2013).

Jumping the Gaps

495

Translated into English, this reads: ‘there exists an x [‫׌‬x] such that x is the king of France [K] and [&] this x is the only king of France [for any y that is king of France must be identical with x: y=x] and [&] also, this x bald [Bx]’. We will not dally with all the logical issues here. Simply note that Russell’s use of the existential quantifier [‫ ]׌‬separates out the property of existence and applies it to the imaginary individual who is supposed to be the king of France. But, as the metaphysical tradition recognizes, the property or quality of “existence” is a very puzzling thing. Since when has anyone perceived the object ‘existence’ out in the world? Existence is, of course, not an object. It does not sit on the shelf among the flowerpots, or the cutlery, or the philosophy books. We do not perceive the property of existence; we infer it. We arrive at the idea ‘existence,’ when we “abstract” it from our experience of the world. We see existent objects and somehow distill or deteach or isolate the universal property of ‘existence’ in our minds. We can then invent a symbolism to inject this idea into our predicate calculus. But this would not be possible without induction—i.e., without the mental leap from observed objects to a universal property “existence.” We need something here that operates at a higher level than sense perception. We could say the same thing about concepts like “being a king,” or “baldness,” but we will not pursue this analysis any further. (Even the concept of “France” is an abstraction, something true “made up” by human minds.) Or, finally, consider another puzzling case that we often take for granted: the null set in set theory. The null set functions like the number zero in arithmetic. It is a set without any members. (Really, it is the set that is the absence of a set, but leave that paradoxical wrinkle aside.) How do we come up with the idea of the null set in the first place? Nothingness, which the null-set “represents,” is not even (as Parmenides correctly argues) localizable in the world. Obviously, there is no empirical object called the “null set” we can observe. So we cannot go directly from a perception of something in the world to the idea of a null set the way we go from our observations of black crows to the idea that crows are black. Somehow we have to induce the idea of nothingness from more complicated circumstances of our experience. We observe, perhaps, that the glass is empty, that there is no one in the room, that a desert is the absence of trees. However we do this, we have to leave behind the realm of sense perception and leap across an epistemological gap up to a different level of conceptual discourse. We do this through induction. Without induction, this woulkd be

496

Louis F. Groarke

impossible. (And, needless to say, set theory would, slowly but surely, unravel.) But even this is not strong enough. The dependence of formal deductive logic on induction is even deeper than this. Even the syntax of formal logic is a product of induction. We can distill, so to speak, the formal structures that characterize good arguments and express them in universal symbols and signs to produce an abstract system that operates on a universal scale that leaves sense perception far behind. Compare logic, on this score, to mathematics. Consider the most basic arithmetic. Where does arithmetic come from? It seems to come from the nature of things in the world. Presumably, we derive numbers from our observations of groups of entities in the world. No one has observed the number ‘3,’ but we do observe three oranges and three apples and three squares of chocolate and three books, and are somehow able to abstract/invent/isolate/create the concept ‘3’ to represent the quantity of every such grouping in the world. Next, we put the three oranges and another four oranges into the same bag, and the bag now holds seven oranges. We are able to represent what is going on here in universal symbols: ‘3+4=7.’ This is rigorously true. It tells us something reliable about the world. When we do arithmetic, we use the numbers on their own, dropping off any explicit reference to things in the world. But the formalism retains its implicit link to the quantitative properties of the world. This is why arithmetic is so useful, and why it is relevant to the practice of science. Through these universal abstract techniques—which are only accessible through induction—we are able to adroitly capture something true and exact about things in the world (an informative role that is not adequately captured in any Humean account of mathematics based on the “relations of ideas”). Presumably, formal logic does the same thing. It is a human creation that captures in universal terms what happens when we consistently think through the logical properties of things and claims; hence its power and importance. This “realism” (or “representationalism”) views formal logic as principled method of abstract reasoning that takes us to the right conclusions. If formal logic bore no relation to good reasoning in the world, if its syntax was merely a matter of arbitrary stipulation, why would we view it as anything other than a clever distraction? Formal logic is either a product of induction—it somehow takes away something that characterizes individual instances of good thinking on some universal, immaterial level; or it is a clever game that people play with no deeper significance. (One wonders, in

Jumping the Gaps

497

some esoteric contexts, if the connection is still there, which can only help to eliminate the relevance and the authority of such specialization.) This essay is mostly about induction as it occurs within a scientific context. It is worth noting, however, that induction is essential to other fields as well. Again, brief consider morality. Moral discourse, like scientific discourse, depends on universals. We might even think of moral rules as a syntax for combining practical concepts. Think of the beloved parable of the Good Samaritan.34 The lawyer asks Jesus “Who is my neighbor?” And Jesus responds by telling a story that deftly turns the parochial term “neighbor” into a universal category. But this is a kind of induction. (As Schollmeier points out Aristotle also thinks of parables and fables as rhetorical inductions.) The point of the imagined Good Samaritan episode is that everybody who needs our help is our neighbor. We are supposed to move beyond family members, beyond next-door neighbours, beyond fellow citizens, and beyond those who share the same religion, to embrace as a “neighbor” anyone in need. Jesus is, in effect, identifying a new “natural kind”—a moral natural kind—that is to authoritatively guide our behavior. He supplies a definition that identifies the essence of something—neighborliness—which is a traditional role for induction. He does so by drawing away a universal moral insight from one particular (imagined) incident. This, then, is an exemplary case of moral induction, which involves an expansion of key terminology so that it covers as many cases as possible. 4.4 Incommensurables: The Side and the Diagonal The spark in the Hertz experiment jumps across a gap to a different surface. I have argued that induction requires an analogous jump across a gap to something that cannot be adequately or completely accounted for in terms of what went before. Induction, traditionally construed, could be defined as a form of cognition (the genus) that is acquired through a mental leap from one kind of cognition to another, notably, from sense cognition to conceptual understanding (the differentia). It is this leap across the cognitive breach that distinguishes induction from other kinds of cognition. Somehow or other, the mind summons up some sort of intellectual impetus that carries it across an epistemological gap in one fell swoop. The knower begins with one kind of awareness and ends up, so to speak, on a different plane, looking back at the world from a higher, more universal, vantage point. 34

Luke 10:25-37.

498

Louis F. Groarke

There is a common misconception about induction that permeates much of the literature. As other authors in this anthology point out (Ziguras, for example), Humeans generally assume—as Hobbes’ Principle would suggest—that the crucial issue about induction has to do with the number of samples or instances we examine. On this account, induction accumulates authority in gradual increments. The strength of our argument improves as we investigate more and more examples of the thing in question until we finally arrive at a “perfect induction” that includes a physical examination of every example. But this is to misunderstand what induction is about. One can never eliminate the leap that is required to get to the conclusion of an inductive argument or, more generally, to the universal insight that is the defining characteristic of an inductive process. Even in the most mundane cases, the movement from mere observation to a conceptual understanding requires a jump to some new epistemological category. It is an empiricist confusion to suggest that understanding is merely a matter of accumulating more and more sense impressions. Observing all the crows in the world is not the same thing as formulating the concept ‘crow’. Again, observing many black crows is not the same as piecing together and understanding the sentence: ‘many crows are black’. In each case, the former may impel us towards the latter realization, but once we arrive at the level of conceptual or universal discourse, we have moved on to a level of thought that transcends the merely perceptual. One way or another, depending on the precise issue under consideration, the successful termination of an inductive process requires a leap to something incommensurably different. Induction requires, to awkwardly mix metaphors, a jump from apples to oranges. It doesn’t matter how many apples we observe—they will never add up to a single orange. But we arrive at the concept of an orange even though (to continue with the metaphor) we only perceive apples. Attempts to solve the so-called “problem of induction” by removing the need for a leap over some sort of irreducible difference seem wholly misdirected. This is as if one hoped to solve the problem of induction by turning it into deduction. But the difference between induction and deductin is that induction requires, in terms of our initial analogy, a jump across a gap. The most obvious jump is from sense perception to the conceptual. This may involve a leap to a new concept, to a universal claim, to a definition, to a first principle, or to an explanation. But however this happens, one can never eliminate the leap. We can jump over it, repeatedly, so that we no longer notice the gap, but the basic gap remains all the same:

Jumping the Gaps

499

this is an immovable feature of how the human mind knows the world. As we shall see, there are inevitable cracks, fissures, breaches in our ways of knowing the world that can never be filled or papered over. Consider then, without any attempt at providing a complete taxonomy, some pertinent examples of incommensurable epistemological difference. The Greeks originally used the term “incommensurable” (asummetros) to describe lengths that cannot be measured by any common unit of length. There is, to use the most obvious example, no common unit can measure in any whole number multiple both the side of a square and its diagonal (or, to say the same thing, the hypotenuse and the adjacent sides of a right angle triangle).35 No unit, however small, goes evenly (without a remainder) into both. Any unit that fits into a side of a square a whole number of times will not fit into the diagonal a whole number of times. And vice versa, any unit that fits into the diagonal a whole number of times will not fit into the side a whole number of times. We can say — algebraically expressed — there is no common unit c such that the side = mc and the diagonal = nc where m and n are whole numbers. This was an alarming state of affairs for the Pythagoreans (and others) who believed in an orderly, mathematically-rigorous world. It was as if there was an applesand-oranges aspect of fundamental reality that was utterly resistant to elimination. It was as if there was some obstinate irrationality here that mathematical computation could not (and still cannot) remove. We tend to take this for granted, but all this is very strange. Suppose we have two groups of mathematicians. We draw the tiniest right-angle triangle (however arbitrarily small). The first group takes the length of the side as the basic measuring unit; the second group takes the length of the diagonal as the basic measuring unit. The first group measures things in the world in terms of so many sides; the second group measures things in the world in terms of so many diagonals. Each group can do arithmetic and geometry and measure things in the usual way using their respective units. When it comes to comparing their measurements, however, they will not be able to calibrate their competing systems precisely. A side will never be ½ diagonal, or ¼ a diagonal, or 1/5 a diagonal or 1/64 or whatever; and vice versa. No integer ratio of these basic magnitudes is possible. The two measuring systems just do not compute. They are, in an entirely resistant way, incommensurable. 35

Hipassus of Metapontum (5th century B.C.E.) is tentatively credited with this discovery. Theodorus of Cyrene (5th century B.C.E.) is sometimes credited with geometrically proving incommensurability.

500

Louis F. Groarke

For the Greeks, who thought of mathematics in ratios (or proportions), the side-diagonal problem presented an insuperable difficulty. There is no way around this problem. If the first group of mathematicians draws a square using the unit sides, the diagonal of the square will be in the diagonal-units, which they cannot measure precisely. If the second group of mathematicians draws a square using the unit diagonals, the diagonal will be in the side-units, which they cannot measure precisely.36 In both cases, the side and the diagonal of this one figure as measured by each group of mathematicians will remain incommensurable! What is important here is that there are two different kinds of length, which cannot be adequately expressed or precisely measured in terms of one another. There is a gap that cannot be bridged. We can jump from one length to the other; we can measure in terms of side-units or diagonal-units, but we cannot remove this deep divide—it is a permanent feature of reality. In contemporary discourse, we tend to disguise these embarrassing breaches in epistemological protocol. In our search for smooth explanation, we invent vocabularies and artful ways of avoiding, understating, and circumventing the gaps. Even in mathematics we do this. In contemporary number theory, for example, the issue of the side and the diagonal is dealt with in terms of an irrational number: the square root of two: ¥2.37 (A square with sides of one unit of length will have a diagonal equal to the square root of 2.38) To invent a symbol ‘¥2’, to call it an “irrational number,” or “root two,” or “radical two,” or to provide (approximate) computational strategies only disguises what is going on. We mostly overlook just how radical the notion of the square root of two is. It is not simply that ¥2 cannot be expressed as a whole-number fraction or as a multiple of such a fraction. Or again, that ¥2 cannot be expressed as a terminating or repeating decimal or as any combination of such decimals. Rigorously speaking, there is no number that is equal to the square root of two. We will never arrive at a number that times itself will (rigorously) equal 2, no matter how long we extend the decimal expansion equivalent to ¥2. We cannot find such a number. No such number has ever been discovered; no such number ever will be discovered. It is as if there is a hole, a 36

Socrates inadvertently does this in the Meno. There are other familiar irrational numbers: pi (ʌ), Euler's Number (e), the Golden Ratio (ij), ¥3 and other surds, etc. 38 The double square Socrates has the slave boy trace out in the Meno hides a complication, for the sides of the square (given the Pythagorean Theorem) must be, of course, a function of ¥2. 37

Jumping the Gaps

501

gap, in the number line. We like to paper over this gap, using nomenclature and a formalism that makes it sound like there is a genuine number there. But, rigorously speaking, metaphysically and logically speaking, this is smoke and mirrors. Doubtless, the invented concept of the ¥2 is mathematically useful. But what we call the ¥2 is only an approximation that is supposed to represent no one (or no computer) has ever found, not a precise value. This is why the Pythagoreans, who wanted to insist that everything is a number, were so upset with the discovery that the diagonal was, in effect, a function of ¥2. Here was a magnitude that, rigorously speaking, could not be assigned a proper number! We cannot pursue these issues at length. The rationalist might decide to redefine what a “number” is so as to be able to include quantities that can never, in principle, be calculated. This is, in effect, what we tend to do. But redefining our words only hides the problem. Perhaps we could talk of accessible and inaccessible numbers, or of “exactitudes” and “approximatives.” But this sort of thing begs the question. The value of ¥2 is not approximate in the way my estimation that there were about fifty people at Sunday mass this morning is approximate. The ¥2 is not approximate to the degree that there is something insufficient or inexact or wrong with our analysis. It is, to truly speak, rigorously or strictly approximate. The “exact nature” of whatever this apparently non-existent number is is to be approximate. Perhaps we can distinguish then between abstract mathematical objects that can be known exactly and those that can only be known approximately. But the important point here is that the latter category cannot be reduced to the former category. They are incommensurable. Irrational numbers such as ¥2 are not, in any case, the only irreducibly different number group. There are other incommensurable categories in number theory: evens versus odds, negative inbtegers versus positive integers, prime numbers versus non-prime numbers, imaginary versus nonimaginary numbers, and so on. In each case, we have something new that cannot be adequately explained in terms of what went before. An even number is not a different sort of odd number; a negative integer is not a different kind of positive integer; a prime number is not a different expression of a non-prime number, and so on. In each case there is a divide, a gap that separates abstract categories that, in some specific sense, cannot be adequately characterized in terms of one another. This relates to what induction, at its origins, is about: acknowledging and adequately expressing incommensurable difference.

502

Louis F. Groarke

The Pythagorean episode of the diagonal and the side is about being forced to acknowledge incommensurability. The Pythagoreans were unhappy with a world where this was necessary. We moderns, like the Pythagoreans, tend to reductionism. We want to intellectually domesticate reality, to transform it into a place where everything is a straightforward expansion or extension or multiplication or division of everything else. We want every justifiable conclusion to be deductively accounted for, in complete detail, by what came before. Such aspirations are naïve or uninformed or exaggerated or simplistic or dishonest. The issue here is not lack of rigor. Induction is a rigorous acknowledgement of what must be the case: that there are categories that cannot be reduced to one another and that we must deal with these categories truthfully. We can be skeptical about induction but only because, if we are willful about it, we can force ourselves to be skeptical about any claims whatsoever. Because mathematics operates on an abstract level, it is always dependent on prior inductions. But that is not all. Key mathematical notions of a limit, derivatives, asymptotes, and infinite sets, for example, all hide incommensurable gaps. Or consider formal geometry (very ably discussed by Dwayne Raymond). The three most basic concepts in Euclidean geometry are the point, the line, and the plane. Note that these are discrete—i.e., incommensurable—concepts. We rigorously cannot express what a line is without adding a new dimension to the idea of a point; and we cannot express what a plane is without adding a new dimension to the idea of a line. This is just basic geometry. And this is not all. Basic geometry begins with the point. A point in geometry is a single location; it possesses no size, for anything that possesses size would have to contain more than one point. But no one has perceived a point without size out in the world. So how do we arrive at this concept so that we can begin rigorous geometry? There are, no doubt, various possibilities. Perhaps someone could perform the following induction: Premise 1: This point, which is smaller than that other point, gives us a more precise measure of location. Premise 2: This other point, which is smaller still, gives us a yet more precise measure of location. Premise 3: And yet again, this other, even smaller point gives us an even more precise measure of location. First Conclusion: The smaller a point is, the more precise the location it represents. (This is a general (induced) principle.) Second Conclusion: Therefore, the smallest possible point—a point without size—will give us the most precise location possible. (Another leap to an utterly precise, though paradoxical, possibil-

Jumping the Gaps

503

ity.) This logical sequence contains two inductions: the first, by which we mentally arrive at an unempirical principle that covers every case of something; the second, by which we mentally arrive at a concept that has, rigorously speaking, no instantiation in the world. Consider only the second induction. Even though no one has ever seen a true geometrical point (without size), we are able to intuit such things as a necessary prelude to geometry. We leap here to a suitable concept, but the evidence is incomplete, not merely in an enumerative sense but in a much more radical way. Even if we were to observe everything in the world that could be construed as a point, we would still have to mentally leap from this evidence to something more: the idea of a perfectly exact (but dimensionless) location. Induction here is from evidence that is in principle incomplete to a new, incommensurable possibility. We must somehow move from observation to something beyond our experience of mere objects in the world. We cannot investigate all this complexity here. Suffice it to say that even in mathematics—geometry, arithmetic, calculus, statistics, probability theory—even here, in the most rigorous paradigms of deductive validity, we discover and—(without realizing it) regularly leap over—incommensurable difference. Induction, I argue, is that rational (intelligent) process which acknowledges and surmounts (without removing) inevitable gaps in knowledge. Geometry begins with points, lines, and planes that cannot be observed in the world. Only after we have leapt to these three (incommensurable) possibilities can we begin the work of rigorous geometrical demonstration. We do not prove what a point, a line, or a plane is. We do not even, rigorously speaking, define them (for there are no more basic concepts in geometry we could use to define them). It would be disingenuous to suggest that they come from nowhere, as if they were arbitrary creations. They come, presumably, from intelligent sense perception. We see what looks, imperfectly, like points, lines, and planes in the world and we induce the idea of the ideal point, the ideal line, and the ideal plane. We can then go on to rigorously prove universal truths about—to use Platonic terminology—the square-in-itself, the circle-in-itself, the triangle-in-itself, and so on. But none of this would be possible without a prior intuitive leap to something we never perceive in the world. 4.5 Inducing Incommensurables: More Examples The Humean this-crow-is-black account turns induction into an incomplete accounting game. Hobbes’ principle, “the more examples we observe, the

504

Louis F. Groarke

more certain our inductive conclusions,” makes it sound like the problem with induction is simply that we have not collected enough evidence. This is, as we have shown, misguided. The jumping across a gap that induction entails is not a matter of insufficient evidence. It doesn’t matter how much evidence one collects; in genuine cases of induction, the gap inevitably remains. We have already pointed to the mental jump from sense perception to concepts and from particulars to universals as standard examples of inductive reasoning. To push the point home, briefly analyze, in addition, four specific cases of induction here. Induction has a very wide scope (as Kelly points out) that includes metaphysical, philosophical, pratical, and moral as well as scientific and mathematical concepts. Consider first the basic idea of infinity. As Descartes correctly points out in Meditation Three, all human experience is finite. Even if one could, for example, count individual objects forever, one could never arrive at an infinite pile of individual objects. Or, again, even if one could travel in a spaceship across the universe forever, one could never traverse an infinite distance. So how then do we come up with the idea of infinity? We have to leap here to a new, incommensurable possibility that cannot be explained or expressed in what went before. Without induction, this would not be possible. (Whether we agree or not with Descartes’ argument that this proves the necessary existence of God is a different matter.) Once we have the idea of infinity, we can start to formulate rigorous mathematical proofs about infinity like Georg Cantor, but these proofs will always have an inductive element given the empirical inaccessibility of infinity. Or consider the general notion of personal identity: myself remaining myself continuously through time. This notion can never be constructed by complete inspection (through memory) of every moment of my life. In the first place, I am sometimes asleep and unconscious. But even if I could remain wide awake my entire life—even I could keep checking to make sure that it is me that is having all these experience—this would not be enough for a coherent notion of personal identity. A self is not just a flow of experiences—it is the thing that has the experiences. It is, in metaphysical terminology, a substance, a whole that is greater than the sum of its parts. As Hume correctly indicates, individual experiences have to be tied down, attached, tethered so to speak, to something which persists through them all. Surely, the content of each waking moment differs drastically. If we are not to become different people in succession, there has to be something that remains the same through all these differing mental states, something that remains what it is despite the sometimes turbulent changes

Jumping the Gaps

505

it regularly undergoes. The only way to get to this level of deep sameness is by a leap to an all-encompassing new possibility: the idea of a human self (or a soul). This idea presupposes more than experiences added together continuously; it presupposes something that is (so to speak) lying underneath and acting as the ground for those experiences. One cannot get to this idea by anything other than induction. Or again, consider the existence of free will (at least a moral necessity). Free will can never be explained in terms of (deterministic) scientific laws. (So much the worst for compatibilism.) I do not mean to suggest that free will is incompatible with scientific laws. Not at all. The laws of science can be satisfied in more than one way. Once we posit free will, we have an individual that can comply with the laws of physics by standing up or sitting down; either action is entirely explicable in terms of the very same laws of physics. The difficult question is: how do we arrive at this idea of free will. How do we begin? We cannot perceive free will out in the world. We may feel unconstrained but this feeling does not, by itself, constitute an idea of free will. We must somehow induce the idea that human beings possess free will. We must leap from the obvious fact that everything seems caused by something else to the idea that there are things that are not caused by anything else. This is a prodigious leap, which is why the determinist begs to differ. The idea that we should settle all such issues by deductive argument seems little short of hopeless. There is no way to get rid of these gaps. Any attempt to deductively derive the existence of free will from our observations of the world (or ourselves) will come up short. This all-important realization about human agency requires a leap to a new incommensurable possibility. This involves something more than adding up all the evidence. We could say that the existence of free will is, in Aristotelian terms, a first principle. It is not something we deductively prove; it is something we start with. Once we have arrived at the idea, we can make moral sense of human striving. Without it, we cannot make moral sense of human striving. It is not an irrational idea; indeed, it explains a great deal in hindsight. But we need induction to get the idea off the ground. (Obviously, there is more to say here, but we must move on.) In a world punctuated by gaps between different possibilities, we need induction. The periodic table is a fourth example of specifically scientific induction. We jump from element to element (and from group to group, from period to period, and from block to block). It is not as if one element slowly fades into the next so that we are left with one slow

506

Louis F. Groarke

continuum of deepening shades of grey. There is discreteness to what is going on. The physical properties of different groups of elements are remarkably and decisively different. And this is what the world is like. In all sorts of other ways. Perhaps the modern metaphysician wants to trace all this back to some sort of “emergentism” that sees new possibilities that suddenly materialize and reveal themselves. But how or why this metaphysically happens is not the issue here. We do encounter irreducible difference. It is enough to notice that this is a feature of the world with which reasoners have to contend. We cannot undertake any kind of systematic account of all the possibilities here. It is enough to say that we need induction to know and to cross over the gaps between different kinds of things present in the world. 4.6 Mathematical Induction Contemporary thinkers claim that mathematics is deductive. It proves things in a way that induction cannot. But this confuses the issue. It is not the capacity to prove or justify something (a complicated issue) that characterizes or defines induction. What makes something a matter of induction is a leap over an epistemological gap, whether proof is available or not. Consider the case of so-called “mathematical induction” (which Christopher Byrne astutely identifies with Aristotle’s fleeing army analogy in the final chapter of Posterior Analytics II). Marc Lange assures us that “Examples of inductive logic … must be sharply distinguished from ‘mathematical induction,’ which is a form of deductive reasoning.”39 This is the received view. But Lange, like many authors, conflates two different issues: (1) whether something can be proved; and (2) whether something requires a leap from incomplete evidence. He assumes that (1) and (2) are equivalent, but further consideration shows that they are not. We can only touch on the issue here. Notice, however, to begin with, that in mathematical induction we usually prove that a (mathematical) statement is true based on the set of natural numbers. In effect, we show that because the proposed formula works for successive values of “n,” it must hold true for all values of n. Formally, mathematical induction usually proceeds in two steps: In Step 1 (the “base case”), we prove the formula holds for n=1. In Step 2 (the “inductive step”), we assume that it holds for 39

Marc Lange, “Hume and the Problem of Induction,” in Dov M. Gabbay, Stephan Hartmann and John Woods, eds., Inductive Logic, Volume 10 (Handbook of the History of Logic) (Amsterdam, The Netherlands: Elsevier B.V., 2011), p. 43.

Jumping the Gaps

507

n=k and then prove it is true for n=k+1. As we have already proved the case for n=1, it must then logically hold for every successive number. Examples of this sort of thing abound in the textbook literature. But consider, more closely, what all this entails. In mathematical induction we are arguing that because some formula is true of successive numbers in a list of possible values, it must be true for all values that could be included on that list. But is this so different from, say, an induction about necessary properties? Suppose, per impossibile, we were to make a numbered list of all the plants that ever existed: plant 1, plant 2, plant 3, and so on. We could, on this basis, perform a quasimathematical induction: Step 1 (base case): We demonstrate that because plant 1 needs metabolism and because metabolism requires water, plant 1 will require water. Step 2 (the inductive step): We assume that some plant on the list requires water and then demonstrate that because the next plant on the list has the same nature—it also needs metabolism—this plant must need water as well. So, we conclude that all plants require water. What have we done here? We have proven that “requiring water” is a necessary property of being a plant. Granted, this induction is not truly mathematical because it is not truly about quantity. Nonetheless, it relies on the same form of reasoning as mathematical induction. The two processes are not so different. In both cases we extend what we do to successive members on the entire list. We apply what happens in observed or inspected cases to unobserved or uninspected cases. Neither case operates by an exhaustive case-by-case inspection. The logical inference here operates by extrapolation. We reason (correctly) that what must be true for a very small number of successive cases must be true for all cases. Why? Because all individual cases share the same nature. That this is “proved” in mathematical induction through rigorous formulae does not detract from the inductive nature of the process. We cannot get to our conclusion without a mental leap to a universal truth that hinges on a select but incomplete sample of representative cases that stand in for all other cases. Issues about proof or logical rigor are mostly a distraction here. If we want to determine whether an inference is truly inductive, we need to determine whether some irreducible difference or separation has been breached. We have already pointed out that the difference between particular knowledge and universal knowledge requires such a leap. According to traditional metaphysicans, a universal species is not merely a collection of individual instances; it is a nature—an essence or a quiddity—that expresses itself in individual instances; it is something that lgically regulates or

508

Louis F. Groarke

determines the nature of those instances. (Just as in the mathematical case.) We do not have to accept the ontological reality of universal principles (like Plato) to agree to this type of analysis, but we do have to recognize that individual instances do not constitute just another, unconnected physical instance. Individual instances possess the same nature, which is how we are able to leap from particulars to universals that form the first principles of science, or logic, or math, or even morality, and so on. Rigorous theoretical inquiry would be otherwise impossible. Contemporary authors like Lange seem to assume that because the operations of mathematics are rigorously logical, they do not involve inductive reasoning. This is a misleading generalization that seems to be based on a misunderstanding of what induction is. We arrive at a genuine inductive insight through an exercise of rationality (understood as intelligent discernment), not through mere emotion or lucky guesses. These leaps that we are forced to make are, in the best sense, cognitive or epistemological. They may admit of “proof” or rigorous justification but that does not detract from their inductive nature. (Again there is more to say here, but let us move relentlessly on.) 4.7 Second-Hand Induction: Induction by Mimesis We have discussed induction as a flicker of intelligent light and as a leap between incommensurable categories. In the Hertz experiment I referred to at the beginning of this paper, I pointed out that the electro-magnetic field that produced the first spark was also able to induce a similar spark at a distance. I want to suggest likewise that the mental spark behind an initial induction can trigger similar sparks in other knowers. The jump across the gap is replicated in minds that, so to speak, witness what has happened. We should not trivialize this important aspect of inductive reasoning. This “action at a distance” is a key feature of human knowledge. The English term ‘induction’, is a translation of the Latin ‘inductio,’ which is, in turn, the Latin equivalent of Aristotle’s Greek term ‘epagǀgƝ.’ The Liddell and Scott tells us that the root verb, ‘epagǀ,’ has to do with bringing, setting, urging on “as hunters do dogs,” applying to horses as a charioteer whipping on his team, to the leading on an army, to winning others over to one’s views, or to bringing forward a legal or political proposal. And this is what happens in induction. Individuals who articulate original insights are able to pull along other people with them. It is not merely that the rest of us accept the same conclusion on authority. The first induction is a way of triggering the same discovery in other people.

Jumping the Gaps

509

In the Posterior Analytics, Aristotle writes, “It is like a rout in battle stopped by first one man making a stand and then another, until the original formation has been restored.”40 Although Aristotle is referring here to the way a single mind induces universals, we could also use this image as an apt metaphor for the way in which induction affects other people. It spreads, so to speak, from person to person, until we all can take a stand against the enemy—ignorance. This coheres with the root notion of the word. We might distinguish between first-hand and second-hand inductions. First-hand induction has to do with an original or untutored discovery one makes on one’s own. Second-hand induction has to do with the discovery that arises in the mind of someone when following the lead of someone else. Induction is so natural we take it for granted, but the process has to begin somewhere. Consider how children learn geometry in elementary school. At some point, children have to learn, for example, that the interior angles of all triangles add up to one-hundred-and-eighty degrees. Presumably a teacher draws a triangle on the blackboard, while students follow along, “jumping” to the same conclusion, under the guidance of the teacher. This is a second-hand induction. It is not, properly speaking, an argument from authority. The students are not supposed to believe this because the teacher tells them to believe this. The idea is to put them in a situation where they come to the realization—they discover what must be the case— according to their own lights. It is not enough to have students watch a mental spark flash by in the mind of the teacher. Students must experience a similar spark of discovery or insight inside themselves. (If particular students lack academic ability, we can try all we can to impart the mental leap but to no avail. They can perhaps memorize what the teacher says but this is not, in any genuine sense, to understand it.) This is, of course, the way Socrates teaches the slave boy in the Meno. He does not make him memorize anything. The slave boy follows, so to speak, in his mental footsteps. Socrates’ demonstration to the slave boy is genuinely “ampliative.” It requires a jump from knowledge about one square to (necessary) knowledge about all squares. Through the inspection of a single diagram, Socrates teaches the slave boy a universal truth about the “square-in-itself.” It is as if he cleverly pushes the slave boy to the verge of a realization and then allows him to jump over to the other side of the divide by himself. At a precise point, it suddenly dawns on the boy—given Socrates’ instructions and a diligent look at the diagram—that a square made of diagonals must be twice the size of the original square. We might call this 40

Aristotle, Posterior Analytics, II.19, 100a12-13 (transl. H. Tredennick).

510

Louis F. Groarke

Socratic approach induction by mimesis, or by imitation. Interestingly enough, once the induction has been completed, the conclusion we reached through imitation often seems blindingly, unforgivably obvious. 5 Can Induction be Justified? The “problem of induction” has monopolized philosophical discussion since Hume. It is seldom noticed that the criticisms brought against attempts to shore up induction can be turned against the Humean dogma itself. Logic textbooks dutifully report that induction is inherently unreliable, but this universal assertion is itself an induction. No one has investigated every individual inductive argument to verify that, indeed, they are all unreliable. Textbook authors may insist that we use the phrase ‘inductive argument’ as a label for any unreliable argument, as if the unreliability of induction was merely matter of definition. If, however, this was the case, then (to borrow a line from G. E. Moore) the statement ‘inductive arguments are unreliable’ would simply mean ‘unreliable arguments are unreliable’, which is a mere tautology. In fact, textbook authors unthinkingly fix the property ‘unreliability’ to all arguments that possess a certain structure; that is to say, they preform an induction about inductions. If, however, induction is unreliable, it will follow that this inductive generalization must also be unreliable! We can approach all these problems from still another angle. Return, for a moment, to the difference between Mill’s and Hume’s account of induction. We could formally present Mill’s approach to induction as follows: Premise 1: X has had property p in the past. Premise 2: Nature is uniform. Conclusion: So we know that X will have property p in the future. We could formally present the Humean view as follows: Premise 1: X has had property p in the past. Premise 2: The future is unpredictable. Conclusion: So we cannot know that X will have property p in the future. Clearly, these are opposing takes on the problem of induction, but which is the better argument? The received view insists that the second premise in the Humean account, ‘the future is unpredictable’, is more credible than the second premise in the Millean account, ‘nature is uniform’. But why? Hume supports this premise about future unpredictability by pointing out, for example, that the taste of future eggs may noticeably vary. This is not merely a case of highly selective evidence (or special pleading). Whatever example one uses, it is a huge leap to go from particular instances of future unpredictability to the (possible) idea that the fundamental nature of things in the world can, for no apparent reason, change. Is this a reliable induc-

Jumping the Gaps

511

tion? Is it any more reliable than the ‘nature is (in fundamental respects) uniform’ principle? It does not seem so. The critic may respond that the Humean premise is better because it is a weaker claim. It only affirms that the future may be different, not that it will be different. But does it really follow that the idea that the sun may not rise tomorrow morning is more readily believable than the idea that the sun will rise tomorrow morning? It seems that anyone who wants to suggest that the future is unpredictable (in this respect) has the burden of proof. It does not always follow, as Sextus would have us believe, that skepticism is the more modest epistemological claim. In the case of the sun not rising, future unpredictability seems far-fetched if not outright absurd. The principle of natural uniformity seems more credible than any principle of future unpredictability when it comes to fundamental issues, for all sorts of reasons. It seems an empiricist’s fancy to think that incomplete enumerative induction about future prediction of the kind Hume privileges is the only or even the most important kind of inductive reasoning. We have defined induction as cognition that requires a (justified) mental leap over a gap between incommensurable categories of cognition. Thus construed, inductive reasoning pervades all human thought. We formulate concepts, convert individual observations into universal claims, elaborate definitions, enumerate first principles, set out logical and mathematical axioms, demonstrate geometrical truths, discover scientific theories, abduce best explanations, produce compelling aphorisms, and so on: all these processes depend on some sort of induction. But we do not have time to survey, in any systematic way, all the diverse possibilities here. Contemporary, Humean-based accounts of induction are mostly template treatments based on an empiricist recipe that misconstrues or overlooks key bits of evidence. Hume, for example, bases his inductive skepticism on the notion that the future is unpredictable. For one thing, he does not investigate, in sufficient detail, the basis of our notion of time. How do we discover the nature of past, present, and future time? The past and the future are, strictly speaking, inaccessible. Every moment of our lives, we only live in the present. So how do we know anything about the past or the future? Because we are able to mentally leap from the present where we always live to a concept of past, present, and future as connected but incommensurable categories. We posit the fixed nature of the past; we posit the open nature of the future, and we posit our location between the two in the present. But this way of locating ourselves within time is all inductive. We cannot, rigorously speaking, undertake an empirical inspection of any

512

Louis F. Groarke

past moments and future moments. It does not follow that our way of ordering time is unreliable, or based on feeling, or even irrational. We take our concept of time for granted but we could not make sense of the world without it. Can induction then be justified? Unlike most contemporary logicians, we have separated the issue of whether an instance of reasoning is deductive or inductive from the issue of proof or justification. We need not rush to a post-modern extreme that might treat all inductive conclusions with the same respect. If someone hits on an idea they believe in, this is not enough to ensure the correctness of their line of reasoning. Induction needs to be held to epistemological standards if it is to count as genuine knowledge. In examining inductive claims, we need to take into account criteria of logical necessity, reasonableness, clearness, distinctness, sufficiency, relevance, plausibility, and so on. And we need to be on the lookout for contradictions, inconsistency, ambiguity, equivocation, special pleading, mere rationalization, and so on. As Kostelecky suggests, inductions are in some sense, proven through hindsights. Some apparent inductions that we hit upon in our intellectual explorations turn out not to be genuine inductions (in an epistemologically secure sense) at all. But this is too large a subject to enter into here. We can rigorously prove inductive conclusions. As Socrates shows in the Meno (and as Raymond shows in his chapter), this is what happens in geometry. A single diagram proves a universal conclusion. It is just that we have to accept, from the beginning, the validity of the leap from one diagram to all the others. We all do this; indeed, we consider irrational any one who would not follow suit. As “deductivists” in modern argumentation theory further demonstrate, induction is a valid argument form. Valid arguments may, no doubt, reach false conclusions, but the contemporary tendency to superimpose the deductive-inductive distinction on the validinvalid distinction does not stand up under close scrutiny. We need a more penetrating account of these issues. If the ancient account of induction argued for in this essay is correct, it definitively subverts the reductionist hope (around since at least Leibniz) that reasoning can be reduced to mechanism. Radical doubt may have inadvertently become, in the modern age, the philosopher’s favorite pastime. We know that the willful skeptic can find a reason to doubt anything at all. But the easiest thing to doubt, in an empiricist age that demanded complete proof, was induction. Except that inductive skepticism, consistently applied, slides into utter (not merely methodological) skepti-

Jumping the Gaps

513

cism. We cannot doubt the reliability of induction without denying the possibility of knowledge, from its origins upwards. In the Posterior Analytics, Aristotle writes: Of the intellectual faculties that we use in the pursuit of truth some (e.g., scientific knowledge and intuition [epistƝmƝ kai nous] are always true, whereas others (e.g., opinion and calculation [doxa kai logismos] admit falsity; but no other form of knowledge except intuition [nous] is more accurate than scientific knowledge [epistƝmƝs]. Also first principles [archai] are more knowable than demonstrations [apodeixis]. […] It follows that there can be no scientific knowledge of first principles: and since nothing can be more infallible than scientific knowledge except intuition, it must be intuition that apprehends the first principles.41

Aristotle believes that induction, which operates through the light of nous (intellect or intuition), comes before and provides the first principles for deductive demonstration (apodeixis).42 Seen from this perspective, the modern search for a deductive justification of induction seems weirdly backwards. Induction comes first in the process of knowledge formation; deduction comes second. The modern view confuses these issues. It puts the cart before the horse. Because we have been impressed with the rigor of deduction, we try to use it to prove inductive reasoning. But we have already used induction, in the first place, to set up the basic framework that makes deductive reasoning possible! To believe that we can use deduction to support induction is like believing that the second-floor in our two-story house supports the first floor (odd examples aside)! Aristotle would have believed that anyone who makes such unreasonable demands is demonstrating their own confusion. Induction builds the foundation that supports the rest of the house of knowledge. If induction is flawed, the rest of the edifice crumbles. Realism, the view that we can know the world, is not something we deductively prove. It is a necessary beginning point for intelligible discourse. On the Aristotelian view, the ultimate basis for induction is the human ability to peer into the nature of things. This flicker of mental light does not arise by any mere enumeration of examples or through some sort of rote mechanism, but through intelligent insight, by some sort of creative, spark-like leap that solves the riddle presented by the deep nature of things. If we can know what things are, induction is possible. Anything that possesses a specified nature will have to possess the properties that define 41 42

Aristotle, Posterior Analytics II.19, 100b5-12 (transl. H. Tredennick). Pace authors like Joseph Owens, G. L. Owen, and Terrence Irwin.

514

Louis F. Groarke

that nature. Whether this thing exists in the past, the present, or the future is of no consequence. One cannot possess the specified nature without possessing certain necessary and essential features. Anything else would be illogical. The present Humean understanding, which focuses on future prediction of accidental traits, does not seem to capture, in any adequate way, what induction is about. We are at an impasse. The only way out of the present state of aporia is by starting all over again. We need to look again to some form of that dreaded Aristotelian essentialism, a metaphysical view that has been caricatured and pilloried by philosophers for several centuries now. We will have to accept that the straw man of Aristotelianism that modern philosophers have knocked to the ground is only that, a straw dummy that bears little resemblance to what is best in the epistemology and metaphysics of historical theories.

Epilogue In the introduction of this anthology the editors expressed the hope that this collection of papers would provide a platform for dialogue among schools of philosophy, specializations within philosophy, and in other disciplines. We would be pleased if this volume were to generate further responses that push alternative philosophical reflection on the cognitive process called induction further. At this point, then, we may ask ourselves, where could we go from here? A first step in new research would obviously be to set aside the Humean paradigm on induction. Implicit in the word ‘paradigm’ is a reference to an entire conceptual framework from within which induction is to be understood. A paradigm shift requires setting aside this framework for a more workable system of background assumptions. As a number of essays in the anthology have noted, Hume’s conception of the inductive process presupposes numerous epistemological and metaphysical claims. There are more issues at stake, here, than induction alone. There are wide assumptions about what philosophy is, about what constitutes an acceptable philosophical method, about the deep nature of rational argument, and so on. All of these constraining assumptions—logical, epistemological, metaphysical, and philosophical—must be seriously re-evaluated and, if necessary, replaced with more plausible principles that would make induction less problematic. One of the first assumptions to jettison is the unreasonable skepticism regarding the human mind and its cognitive abilities. As Kostelecky points out in his chapter, contemporary epistemology is driven by a skeptical agenda. This is not an epistemological attitude shared, however, by all those holding alternative views on induction. They, and the historical figures whose views they endorse and perhaps rework, are much more confident in our abilities to acquire knowledge of the world. Without diminishing the difficulty of the task, they do think we are capable of scientific knowledge of reality. It is certainly a paradox worth pondering that philosophy should be haunted by such radical skepticism and metaphysical doubts, at the moment in Western history when the newly-established sciences soar and begin to provide humanity with incredible amounts of knowledge about the physical world. Although the developing scientific method does not take physical reality at face value, as it appears to our senses in common experience, it still successfully describes and explains many aspects of this world we do

516

Epilogue

observe and experience. The first scientists of the 16th and 17th centuries do not seem to be burdened with skeptical doubts about the world’s existence, and they do not harbour many doubts about our ability to acquire knowledge of the universe. They do not wonder whether reality is intelligible or doubt whether the human mind can access this intelligibility. How could Hume’s skepticism baffle philosophers so shortly after Newton has so firmly and stupendously established classical physics? In the face of such astounding evidence of the enormous gain in scientific knowledge over the past several centuries, it is perhaps surprising to see so many philosophers still battling the specter of epistemic skepticism. An assumption closely related to the unreasonable skepticism uncritically accepted by contemporary academic philosophers is the epistemological goal of a complete rational justification of knowledge. Unbounded justification by reason is the correlate of unbounded skepticism without reason. If skepticism is to be reconsidered, then the nature and extent of rational justification must be re-examined as well. Is induction, and is any knowledge that might be acquired through the inductive process, something that requires rational justification? To think induction requires rational justification seems misguided, for induction plays an ultimate role in all knowledge formulation. As such, it concerns the starting points in the construction of knowledge. As the ancient philosophers acknowledged, these starting points, or first principles, must simply be accepted and understood before any sort of argumentation, of which justification is one form, can take place. Otherwise we end in an infinite regress. Those philosophical approaches that exclusively identify reason with argumentation (or even with deduction) need to be revised or rejected. Philosophers, particularly in the Anglo-American tradition, act as if we must provide a reason, a rationally justifiable basis, for everything. But we cannot give a reason, at least not an argument, for everything. To keep demanding reasons—a reason for this reason for this reason for this reason ad infinitum— such attempts would produce an unachievable infinite regress in search of epistemological justification. One can disguise what is going on, by muddying the waters, by equivocation or by circular reasoning (using the same idea as premise and conclusion in the same argument), but this is only subterfuge. No wonder skepticism is so rampant! If the practice of rationality is to avoid ending in failure, certain things must be accepted on their own terms. Such an attitude is rational or reasonable, though not in the sense of always having an argument. Those things that we accept to start with, through the intelligent appraisal of experience, comes to us through induction.

Epilogue

517

Once we get out of the habit of unthinkingly equating reason with argument, we will not uncritically acquiesce to the surprisingly pervasive view of induction as, primarily or even exclusively an (invalid) argument form. But argument requires logical inference. If induction is said to be related to the starting point of knowledge and argument, we cannot picture it primarily as a logical inference. Any logical inference or reasoning process associated with induction depends upon (a) prior non-argumentative act(s) of the mind. This is what older authors referred to as “intuition.” Intuition was not a matter of mere feelings; it was a matter of discerning what the case is immediately, not through the laborious process of argument, but through direct discernment, through an act of penetrating intelligence that sees what is the case without having to add together premises to arrive at a conclusion. As explained in the introduction to this volume, the philosophical tradition before Hume considered induction, in very wide terms, as a mental capacity or cognitive movement capable of producing general concepts, propositions, and arguments. We use induction, on this older realist model, to discover the basic starting points within any given field of study. All knowledge in the field ultimately depends on these unproved but “intuited” first principles. We cannot give up on intuition without giving up on all knowledge claims. In light of this necessary dependence of all knowledge on induction, should not the goal of constructive philosophical reflection be, not justification, but explanation of the inductive process? (As Biondi intimates, on this narrow point at least, Hume is correct. It is not a matter of logically justifying what is going on in induction through some sort of transcendental argument but of observing and explaining what intelligently obtains in the thick-and-thin of everyday human experience.) There are various ways in which one might go about exploring, descriptively, what happens in induction. One could, for starters, go back to the basis and look at what the brain is doing in induction. In contemporary analytic philosophy, authors who focus on philosophy of mind turn towards sometimes reductionist accounts of cognitive science and neurobiology. Indeed, the preparation of this anthology happens to coincide with the announcement of two major initiatives on brain research, namely, the U.S. BRAIN (Brain Research through Advancing Innovative Neurotechnologies) Initiative and the European Union’s Human Brain Project. (In spring 2013 U.S. President Barack Obama announced funding for this research initiative would be included in the 2014 budget. The Human Brain Project Summit held in 2013 is the project’s inaugural event. In Canada, Chris Eliasmith, Director of the Centre for Theoretical Neuroscience at the University of

518

Epilogue

Waterloo, is currently heading a research project called Spaun (Semantic Pointer Architecture Unified Network).) Such research initiatives in neuroscience of the human brain and cognitive psychology are welcome, even if they are, at times, overly influenced by computational models of the mind and privilege a narrow focus on applied medical knowledge. Their findings might contribute, directly or indirectly, to our understanding of how the brain operates when it engages in induction and generates basic generalizations. (In this connection, exploring the apparent division of cognitive functions between the right and left brain could also bear fruit. The right brain, it seems, encloses a capacity for holistic perception and the left brain, a capacity for conceptualization. One side is able to grasp unity or coherence in multiple phenomena, whereas the other is able to insert facts and experience into a larger theory, definition, or explanatory framework. Could it be that rational insight, the Aha! experience, arises when the two sides operate simultaneously (or serially?) in reaction to the same incoming stimulus. Seeking to discover or clarify our explanations of how these cognitive activities operate in the process of inductive reasoning seems a more fruitful labor for philosophers reflecting on the latest scientific findings of brain research.) This sort of empirical research into the hardware of the brain is insufficient, however. Cognitive psychology as well as philosophy of mind must not lose sight of the assumptions they make whenever attempting to understand the mind and mental operations. Philosophers such as John Searle and Thomas Nagel, as voices of dissent, keep all philosophers of mind on their toes. The act of understanding (experience) is not reducible to mere computation, and semantics cannot be reduced to syntax. We must avoid oversimplifying the full richness of human thought in order to fit it into the straitjacket of our research purposes. An improved understanding of how we conceptualize thought must supplement the findings of cognitive psychology and neuroscience. Rescher’s notion of cognitive systematicity, Rasmussen’s reflections on logical intentions, McCaskey’s view of induction as fundamentally a logic of classification, Groarke’s account of induction as leaping over epistemological gaps and all similarly relevant notions show that part of what goes on in induction occurs at an intensional, conceptual level. Older philosophies considered this process in terms of abstraction. One way or another, logic and philosophy can contribute to a better understanding of concept formation and conceptual relations, especially when it comes to understanding sense experience or the observation proper to scientific experiment.

Epilogue

519

Another matter for philosophical reflection would be the archetypal phenomenon of Goethe (Ziguras) and the geometrical diagrams and text of Euclid (Raymond). In both cases we are dealing with a particular thing observable to the senses and yet simultaneously observable to the intellect as something universal in character. Somehow the human mind is capable of having an abstract and universal view of concrete, particular things. How does the mind accomplish this perception or insight? What kind of abstraction, if any, is involved? Philosophers could try to define this cognitive act with more precision and clarity. This volume establishes clearly—as Biondi establishes early on—that induction requires reason and intellect since these are responsible for devising the concepts and propositions that render sense experience intelligible. It is conceptualization and the idealization of sense experience that enables the mind to discern ‘things’ and the natures of things experienced through the senses. It is not, as Empiricists sometimes seem to suggest, that observation is one thing and rationality is another. Reason pervades, structures, and orients observation to produce understanding. Acceptance of this basic fact would force philosophers to dispose of Hume’s view of induction as being a cognitive process entirely under the aegis of sense perception without reason. It would also lead us to forego Hume’s fork, the mutually exclusive divide between sense experience and reason. Various papers in this collection argue against this influential Humean dichotomy. In its place, we could elaborate a description of the operations of the mind where the senses, memory, imagination, and reason or intellect all work together to provide a holistic and coherent picture of reality. How does the mind discern the relevant and significant facts within the blurring whirl of sensory experience? How is the factual and intellectual wheat separated from the chaff? How does a theoretical paradigm get established? McCaskey’s essay offers one path worth taking for further examination of these questions. The social character and sociology of knowledge offers yet another, rather different, path. Philosophy of science could offer another avenue of future research on the inductive process. How would the inductive method in science be understood if we were to follow any of the alternative views proposed in this anthology? McCaskey’s essay (like Dougherty’s and Kelly’s chapters) shows that we would have a more accurate depiction of what actually occurs in scientific practice if we construe induction in a SocraticAristotelian manner. As Popper’s falsificationist picture of science arose in

520

Epilogue

large measure as a way of skirting around the problems of induction, how would we view his proposal if those problems are dissolved? With a more successful account of induction, we could also arrive at a better account of scientific hypotheses and of their creative (not random) formation. With such an account in hand, we could perhaps better understand which hypotheses are open to falsification and should be tested and, why. We could clarify, furthermore, the similarities and differences between the induction of discovery and the induction of testing hypotheses or definitions, assuming there are two distinguishable processes of induction (as touched on by Novak and others in their essays). In the philosophy of biology, the epistemological status of essentialism could be reassessed. Even without accepting Aristotle’s view of the eternity of essences or natures, biology could still be essentialist. The Aristotelian view of induction crucially relies upon the existence of natural kinds in the world, which could be guaranteed simply by saying that individual organisms have a nature, namely that of their species. The specific nature exists in the world as long as individuals of that species still exist. Initial knowledge of these natures can and indeed must come through induction. Of course, our understanding of these natures would have to be informed by our knowledge of genetics (but genetics, in so much as it relies on generalizations, also relies on induction). Debates among biologists over the classification of difficult cases are, in fact, debates about biological definitions. Again, McCaskey’s contribution offers several thoughts on the relationship between induction and definitions, on the acquisition and clarification of concepts that express the essence or nature of things. As do Ziguras and Novak’s chapters. Philosophers interested in distinguishing definitions from a mere list of necessary properties could analyze such biological debates to study how induction operates in them. Yet another issue could be investigated. Rescher’s description of induction from a pragmatic viewpoint and Meynell’s description of Lonergan’s generalized empirical method are similar in this respect: both views describe a cognitive process that is open ended insomuch as it incorporates a continuous dialogue between human intelligence and the world as experienced. As the mind attempts to interpret the content of experience, the world or reality is identified with the most coherent and complete understanding of the world that human beings have at a given point in time. Human understanding always remains incomplete, but it has the ability to improve over time. Pierce famously compared scientific understanding to a

Epilogue

521

curve that approaches, ever and ever closer, to a prescribed limit. Such a picture of induction seems different from and is perhaps even incompatible with the Aristotelian picture of induction, which might be interpreted as claiming that human beings are, by nature, capable of achieving an unfettered understanding or a transparent rational insight into the very nature of things. It would be useful to investigate the differences (or resemblances) between the alternative views of induction presented in this anthology. In short, are any of these new (or old) perspectives incompatible in irreconcilable ways? If there are incompatible views, then we may have to choose among them. This choice would, it seems, require developing certain criteria to decide which understanding of induction is correct or better. If different views can be held to be compatible, however, this compatibility would have to be explained. It seems at least reasonable to maintain the compatibility of the Aristotelian account of induction and the pragmatist account or Lonergan’s account of the generalized empirical method. It could be argued that we are dealing with complementary processes of induction used at different stages of knowledge acquisition: initially, when our knowledge of some feature of reality is incomplete, the two non-Aristotelian accounts describe better the process of induction; when, however, we manage to gain rational insight into the given feature and are able to provide a definition of its nature, then the Aristotelian account of induction offers the better explanation. The task for philosophers would therefore be to delineate the conditions under which each process of induction would be employed, and when certainty in knowledge is possible and when it is not. This leads to a final problem. Are there, in any deep sense, different categories of induction? Groarke has proposed an allegedly Aristotelian taxonomy of induction elsewhere. Is the inductive leap to a generalization or a concept the same when dealing with different subject matters? Or are there identifiably different cognitive processes at work here? Because induction is such a necessary aspect of knowledge acquisition, it plays an often overlooked role almost everywhere in science and epistemology. Sorting through the details that distinguish this kind of induction from that kind of induction—assuming there are different types—would be worth serious philosophical scrutiny. In conclusion, these are a few of the paths that could be followed in future research on induction. This research would become a part of the new agenda for an epistemology that seeks to explain the nature of the knowledge we do indeed acquire as well as the conditions of (successful)

522

Epilogue

knowledge acquisition. It may be that we come to accept Kelly’s suggestion that induction is an analogous term designating analogous cognitive processes. But first, we must wake ourselves from our “dogmatic slumbers” regarding induction. Paolo C. Biondi Sudbury, ON, December, 2013 Louis F. Groarke Antigonish, NS, December, 2013

Contributors’ Biographies Paolo C. Biondi is an Associate Professor in the Department of Philosophy at the University of Sudbury (Laurentian University), Ontario, Canada. He has published a scholarly monograph, Aristotle’s Posterior Analytics II.19: Introduction, Greek Text, Translation, Commentary, and Critical Analysis (Collection Zêtêsis, Laval University Press, 2004) and several academic papers on Aristotle’s conception of experience and perception. Christopher Byrne is an Associate Professor and former Chair of the Philosophy Department at St. Francis Xavier University in Nova Scotia, Canada. He has published several articles on Aristotle’s physics and metaphysics in academic journals such as the Journal of the History of Philosophy, The Canadian Journal of Philosophy, and Apeiron: A Journal for Ancient Philosophy and Science. He is particularly interested in the issue of prime matter and its ramifications for metaphysics and natural philosophy. Jude P. Dougherty is Professor Emeritus and Dean Emeritus of the School of Philosophy of The Catholic University of America in Washington, D.C., USA, and Editor of the Review of Metaphysics. He has published several books such as Western Creed: Western Identity, The Logic of Religion; Jacques Maritain: An Intellectual Profile; and Wretched Aristotle: Using The Past To Rescue The Future. His most recent work is The Nature of Scientific Explanation (Catholic University Press, 2013). Louis Groarke is a Professor in the Department of Philosophy at St. Francis Xavier University, Nova Scotia, Canada. He is the author of An Aristotelian Account of Induction: Creating Something From Nothing (McGill-Queen’s University Press, 2009). Among other publications is a chronological treatment of the history of ethics, Moral Reasoning: Rediscovering the Ethical Tradition (Oxford University Press, 2011). He has published numerous papers on a variety of philosophical topics, including “A Deductive Account of Induction” in Science et Esprit (2000). James Kelly is currently a Visiting Scholar at Stanford University in Palo Alto, California, USA. His recent Ph.D. thesis was a comprehensive historical investigation of philosophical approaches to the inductive method. His research interests focus on inductive reasoning in science. He

524

Contributors’ Biographies

has published a response to Hume’s critique of induction in the Acta of a 2009 conference at the Pontifical University of the Holy Cross. Matthew Kostelecky is an Assistant Professor of Philosophy at St. Joseph’s College at the University of Alberta, Edmonton, Canada. His research focuses on 13th and 14th century metaphysics and theories of cognition. He has just published a monograph Thomas Aquinas's “Summa contra gentiles”: A Mirror of Human Nature (Leuven-Walpole/MA: Peeters 2013) in a series sponsored by the Thomas Instituut te Utrecht. He is interested in Platonic influences in Thomas and the role of intellectus in non-discursive reasoning. He has academic published papers on theological and philosophical method and on proper modes of speaking about God. Peter Loptson is a Professor in the Department of Philosophy at the University of Guelph in Ontario, Canada. He has published several books, among which Freedom, Nature, and World (University of Ottawa Press, 2007) and Theories of Human Nature (third edition, Broadview Press, 2006). He has also authored numerous articles in professional journals as well as book chapters and articles in reference volumes. He has written extensively on empiricism and rationalism and on historical figures such as Liebniz, Spinoza, Locke, and Hume. John P. McCaskey is a researcher and lecturer in the Program in History and Philosophy of Science at Stanford University, California, USA. His research interest is the history of science and scientific method. His Ph.D. dissertation focused on induction in Socrates. He has presented several papers on the history of induction at conferences and workshops in Europe and the USA and has published on Aristotelian induction in Apeiron. Ernest John McCullough is currently Emeritus Professor at Saint Mary's University College in Calgary, Alberta, Canada. His publications include Time as a Human Resource (edited with R. Calder, University of Calgary Press, 1991) and articles on natural law and in the history of science. One contribution to a recent anthology is entitled “Edith Stein and Intersubjectivity.” Hugo Anthony Meynell is currently retired. This distinguished scholar was a Professor in the Department of Religious Studies at the University of Calgary and is a Fellow of the Royal Society of Canada. He is a noted

Contributors’ Biographies

525

student of Bernard Lonergan. In addition to monographs on Lonergan, he is the author of Redirecting philosophy: Reflections of the Nature of Knowledge from Plato to Lonergan (University of Toronto Press, 1998). Professor Meynell is also the editor of several books and has published almost 200 articles on Lonergan, philosophy, religion, and other topics. Joseph A. Novak is an Associate Professor in the Department of Philosophy at the University of Waterloo in Ontario, Canada. He has presented numerous conference papers on various topics related to Ancient Greek, Hellenistic, and Medieval philosophy and published a variety of articles in academic journals. Work by him has appeared in Apeiron, Notre Dame Journal Of Formal Logic, Australian Logic Teachers Journal, Contemporary German Philosophy, New Scholasticism, Ancient Philosophy and History Of Philosophy Quarterly and Informal Logic. He has just completed a translation of Franz Brentano’s Aristotle’s Doctrine About the Origin of the Human Mind. Douglas B. Rasmussen is Professor in the Department of Philosophy at St. John’s University in Queens, New York, USA. He has co-authored a number of books and published over eighty articles in professional journals. He was the guest editor of “Teleology and the Foundation of Value,” the January 1992 issue of The Monist. He has been awarded grants and fellowships from the National Endowment for the Humanities, the Institute for Humane Studies, and the Earhart Foundation. Dwayne Raymond is an Assistant Professor in the Department of Philosophy at Texas A&M University in College Station. His recent Ph.D. dissertation at the University of Western Ontario featured a modern reconstruction of Aristotle’s modal logic. His research interests center around Aristotelian logic, ancient logic and the history of logic. He has published several articles in Apeiron and History and Philosophy of Logic, and has a book titled Inseparability and Polarity: At the Root of Ancient Reasoning presently under review with Parmenides Publishing. Nicholas Rescher is Distinguished University Professor of Philosophy at the University of Pittsburgh where he has served as Chairman of the Philosophy Department and a Director (and currently Chairman) of the Center for Philosophy of Science. In a productive research career extending over six decades he has more than one hundred books to his credit, includ-

526

Contributors’ Biographies

ing one scholarly volume on induction. He has been awarded the Alexander von Humboldt prize for Humanistic Scholarship in 1984, the Belgian Prix Mercier in 2005, and the Aquinas Medal of the American Catholic Philosophical Association in 2007. In 2011 he was awarded the premier cross of the Order of Merit (Bundesdienstkreuz Erster Klasse) of the Federal Republic of Germany in 2011. Paul Schollmeier is Professor in the Department of Philosophy at the University of Nevada, Las Vegas, USA. His research focuses on argumentation theory, rhetoric, ethics, and politics. His publications include a book, Human Goodness: Pragmatic Variations on Platonic Themes (Cambridge University Press, 2006), as well as a number of articles in academic journals such as Philosophy and Rhetoric, The Pluralist, Revue de Métaphysique et de Morale, Polis: The Journal of the Society for Greek Political Thought, Revue de Philosophie Ancienne, and Rhetorica: A Journal of the History of Rhetoric. Jakob Ziguras recently obtained a Ph.D. in Philosophy from the University of Sydney. His recent Ph.D. dissertation compared Aristotle's views on induction to Johann Wolfgang von Goethe's views on human knowing. He has published an article on Spinoza in Forum Philosophicum, and has had an article on Aristotle and Goethe accepted for publication by Epoche. He is currently in Germany on a DAAD research scholarship, working on converting his dissertation into a book.

Index a posteriori necessity 9, 389, 391 a priori knowledge 56, 72, 90, 96, 107 a priori necessity 389 abduction 154, 199, 369 abductive inference 50 Able-Sighted Harry 483-485 absolute skepticism 480 abstraction 108, 132, 137, 142, 147-48, 272-76, 287, 306-07, 325, 351-54, 358f., 486 accident 92, 177-78, 342f. accidental (attributes, features, properties, predicates) 98-100, 177-78, 207-09, 255, 283f., 286-87, 295-96, 462-64 Achilles 222 Ackrill, J. L. 254f. activity-idea (distinction) 381 actuality 82, 206, 266 actualization 267, 372-73 Adler, Moritmer J. 337f. Advancement of Learning (F. Bacon) 167f., 169 Aesop 194f., 216, 239 agent account of causality 257 agent intellect 123, 303, 316, 319, 423 agitation of wit 488 Agricola, Rudolph 162-63 aha! experience or moment 491, 518 Aisthesis 114 aitia 299 Al-Ghazali, (Abnj ণƗmid Muতammad ibn Muতammad) 480 Albert Magnus 368 albinism 464, 471 Alexander Aphrodisias 204f. algorithm 483, 491 ambiguity 175 ampliative 447, 486, 509 an est 368, 370-71, 373 anagkƝ also anagkaion 164, 259

analogy, analogies 158, 225 analysis 171, 268, 291 analytic necessity 409 Analytic philosophy 24, 79, 325, 483 analyticity 325, 409 Andronicus of Rhodes 52 animals 35-36, 83-85, 241 anschauende Urteilskraft 395 Anscombe, G. E. M. 149-58, 351f. anti-metaphysical 26, 478 anti-rationalist also anti-rationalism 28, 55, 57 anti-realism, antirealism 368, 478-480 apagoge 199 apodeixis 199, 221, 513 Apology (Plato) 214f., 216f. Apostle, Hippocrates 219 Apprehension 306, 370, 371, 489 Aquinas (Thomas) 199, 209f., 241f., 254, 320, 339, 351, 353, 379, 423, 490 archetypical phenomenon (Urphänomen) 385, 389, 391, 392, 401, 407, 519 Aristotelian essentialism 514 Arithmetic 309f., 496 art 491 asymptotes 502 attentiveness 417-18, 430-31 Augsburg Confession 40 Austin, J. L. 427 Averroists 423 Bacon, Francis 165-69 Bain, Alexander 162 bare particulars 357 Barker, Stephen 440 basic fact 401 Bayesian (probabilities, probability, probability calculus) 474, 47677

528

Beauty 165 Behaviourism 416, 420 Bell, John 157 Benardete, Jose A. 355 Berkeley, George (Bishop) 19, 62, 426 Bernoullian approach 474 Berquist, Richard 314f. best estimate 441, 444 best fit 442, 446, 447 Biondi, Paolo 294, 297, 492 Black, Max 448f. Blackburn, Simon 377-78 blank slate 101, 319 Blind Harry 483-484 Boethius 379, 487 Boltzmann, Ludwig 130 Bortoft, Henri 407 Bourdieu, Pierre 123-24 Bradley, F. H. 444f. BRAIN (Brain Research Through Advancing Innovative Neurotechnologies) 517 British empiricists 248 Butchvarov, Panayot 331f.-332f. calculative faculty 234 Carnap, Rudolf 422 Cartesianism, also Cartesian 383-84 Cartwright, Nancy 147-48, 150 cat gives birth (to pups example) 327-28, 342 categorical statement 494 causal necessity 119 causal powers 255-59 Causality 69, 73-74, 87-88, 117, 150f., 151, 153, 154-58, 256-57, 329, 388-89, 478, 480 cause and effect 65-66, 246, 350-51, 460 certitudo also certior 308-10, 318-20 chemical induction 479 cholera 184, 188-89 Chomsky, Noam 154 Christianity, also Christian 30

Index

Churchland, Paul 131-32 Circle 284-85, 289-92 circularity (logical) 336 Clarke, Richard 273 Classification 181-82, 190-91 Cleary, John 274 co-demolition test 274-76, 281-82, 286, 291, 293, 294-95, 298-99 co-exact properties 277-78, 283-87, 290 co-relatives 276, 276f. Cogitata et Visa de Interpretatione Naturae (Bacon) 169 cognitive systematicity 10, 450-51 Cohen, I. Bernard 139 Cohesiveness 450 Coleridge, Samuel Taylor 239f., 246f. Collection 77, 93 Colligation171-73 Colour 403-7 Commentary on the Nicomachean Ethics (Aquinas) also In Ethika 304 Commentary on the Posterior Analytics (Aquinas) also In Po An 306-12 common sensible objects also common objects 368, 98 complete induction 310-11 completeness 450 complex ideas 58-60 composite 7, 254, 258-59, 261-62, 264-67 conceivability 327f. concept formation 149, 369-70 conceptual analysis 111f, 324-25 conceptualization 339, 518-19 conclusion-deriving (inferential) 447-48 conjecture 441, 447-48 consecution 47-49 consilience (of inductions) 174 Consolation (of Philosophy) (Boethus) 487-88 Consonance 450

Index

constructive intelligence 431 context of discovery 492 context of justification 492 contiguity 75f. contingent (attributes) 462-64 contradiction 332-33, 335, 375 contraries 206-9, 242-43 conversion (logical) 112-13, 237-38, 297 convertibility (logical) also convertible 112-13, 235, 244, 466 Cooper, J. 267f. Correspondence 480-483 Cowan, Clyde 128 critical realism 431-33 crows (black) 459, 462-64, 466-67 Curie, Marie 126-27 Custom 73-75, 80-82 Darstellung 397 Darwin also Darwinian 35 De Anima (Aristotle) 295, 368 De Caelo (Aristotle) 202 De Hebdomadibus (Boethius) 379 De Partibus Animalium (Aristotle) 208 De Spiritu (Aristotle) 218 Deception 368, 372 deck of cards 477 deduction also deductive inference, deductive reasoning 11f., 112, 198f., 198-201, 224, 232, 273, 311, 362, 440, 443-44, 493-94, 513 deductive syllogism 235, 237 deductive-axiomatic reasoning 282 definition 108, 140, 168-69, 171-72, 175-79, 183-86, 188, 194-97, 204, 220, 225, 264-66, 287, 290, 291, 342-45, 347-49, 4089, 465, 520 demonstration 97-98, 107-9, 119-20, 149, 201-2, 204f., 204-6, 221-22, 283, 320-21 demonstrations of the fact 201

529

demonstrations of the reasoned fact 108 demonstrative knowledge 108 demonstrative syllogism 198, 314 dependency relation 274-76, 286f, 292, 292f. Descartes, René 321, 377-80, 382-84, 483, 504 determinism also determinist 505 Devitt, Michael 25 Dew 183-84 diagonal 497-502 diagram also diagrammatic 108-109, 277, 282-87, 289-92 diagrammatic inference 277 diairesis 214, 214f. dialectics also dialectic 214-15, 215f, 224, 227-29, 247, 296, 308-11, 311f., 317f., 317-18 Dialogues Concerning Natural Religion (Hume) 29-30, 35, 38f.-39f. differentia 164-65, 167 diorismos 284 Diotima 374 direct experience 367, 376-77 direct inference 474, 476 disciplina 308 discursive reasoning 403, 488 disengaged reason 377-78 Disputationes metaphysicae (Suarez) 381-82 Dissertation on the Passions (Hume) 16 Divine Essence 380-81 Divine Ideas 380-82 division 306, 311-15 DNA 152, 158 doctrina 308 dog (example) 77-78, 92, 394, 468-70 Dorling, Jon 143-44 dunamis 82, 101, 114 Durandus 380-82 Economos, Ariane 307f., 320f. efficient cause 255-56

530

eidos 164 Einstein-Podolsky-Rosen paradox 157 Einstein, Albert 143-45, 148, 421 elegchein 222 Elements (Euclid) 282, 293 elements (physical) 258-61, 263-64 Elenchus also elenchic 206f, 220, 221, 228, 375 Empedocles 276f. empeiria 85 “Empirical Observation and Science” (Goethe) 392-94, 400 empirical phenomenon 395 empirical possibility 328 Empiricism also Empiricist 58, 94, 117-122, 431 Energeia 99 Enquiries (Hume) 14 Enquiry also Enquiry Concerning Human Understanding (Hume) 30, 38, 54, 459 Enquiry also Enquiry Concerning the Principles of Morals (Hume) 28 ens rationis 320 enthymeme 215, 216f., 217-18, 232, 239, 310, 449 enumerative induction 399, 511 epagǀ 508 epagogai 201 epagǀgƝ also epagein 97, 97f, 163, 178, 196-97, 205-11 epagogic induction 370-71, 375, 384 epagogic reasonings 196 epaktikoi logus/logoi 196, 197 Epicureans 462 epideixis 222 episteme 214f. eristic 375 erotetic (leap, procedure) 9, 447, 453 error 372-73, 440, 446-47 esse 379 essence 99-100, 175-76, 179, 202-3, 205-6, 212-13, 264, 353f., 37071, 379-81, 394, 409-11, 470

Index

essential (attributes, features, properties, predicates) 89-90, 97, 107-8, 110-11, 114, 254, 319, 348, 370, 393, 397, 40910, 462-63 essentialism 8 estimate 441, 444-46 ethics 363, 365-67, 384, 471 Euclid 276-78, 282-91 Eudemian Ethics (Aristotle) 218-19 Euthyphro 164-65, 178 evolutionary biology 364 example (argument from) 232-33, 235, 236-38, 241-42, 247 exceptionless regularities 40 excluded middle (law of) 330, 340 exemplary phenomena 411 exemplification 221, 227 existence 65-66, 336, 354, 371, 379, 495 existential commitment 273 experiment also experimental reasoning 69-70, 83-84 “Experiment as Mediator between Object and Subject” (Goethe) 395 explanations 148, 256-57 Expositio super librum Boettii De Hebdomadibus (Aquinas) 379 extensional (logic) 297 externalism also externalist 302, 481 fables 239-40 family resemblance 211 Fermi, Enrico 127-28 Fichte, Johann Gottlieb 427, 432 final cause 167-68, 256 first principles 138, 252-54, 361-62, 475-76, 481, 486, 489, 513 first-hand induction 509 Fisk, Milton 330f. formal cause 167-68, 251-52, 254-59, 264-68 formal logic 496 formal signs 337, 339, 340

Index

531

Forms 375-77, 378 Förster, Eckart 412f. foundationalism also foundationalist 301f. four causes 263 Fraassen, Bas von 147-48 functional efficacy 451 functional regularity 451 functional simplicity 451

Hobbes, Thomas 473 Hobbes’ principle 473, 475, 503 Hooke’s law 190 Howson, Colin 477 Humanity 353f. Hume’s fork 8, 62, 109, 116, 519 Humean induction 33 hypothesis 173-74, 205-6, 206f., 208 hypothetical necessity 261, 264, 267f.

Gadamer, Hans-Georg 369-70 Galileo, Galilei 139-40, 148-50 Geach, Peter 226-27 generalization 7-8, 69, 172, 200, 247-48, 253 generalized empirical method 421-22, 424, 427, 520-21 genus also genera 176-78, 212, 233 geometry 282, 294, 296, 502-3 God 355-56, 381

ideal (normative) 140, 394 idealism also idealist 120-21, 390-91, 431-32 idealization 140, 145, 146 identity 336 imaginability 327f. imagination 59-62, 60f., 73-75, 75-79, 101-5, 487 imperfect induction 310 implication 331, 339 impressions 57-58, 59-62, 76 incommensurable(s) 497, 499, 503 inductive inference 70, 318 inductive syllogism 296-97 inductively appropriate 445 inference 447-48 inference to the best systematization 450 inference to the best explanation 449 infimae species 235-36 innate ideas 380 inner nature 406 insight 490 inspectio mentis 325, 341, 345 inspiration 489-91 instinct 83-84 intellect 99, 110-11, 131-33, 319 intellection 132 intelligence 417, 458 intelligibility 123 intuition also intuit 517 intuitive induction 411 intuitive understanding 402 invalid 465-67

Goethe, Johann Wolfgang von 9, 385-86, 388-400, 402-13 Goethean science 410 Good Samaritan 497 Gotthelf, Allan 267f. Graves, John 472 Greeks 275f., 279-81, 500 Green, T. H. 14 Groarke, Louis 10, 111f., 272-73, 394, 433 habit 73-75, 82-83, 101, 240, 245 habit of faith 320 Harper, Wiliam 126 Harré, Rom 155 Haruspex 418 Harvey, William 169, 179 Herschel, John F. W. 180-82, 183 Herschel, William 421 Hertz, Heinrich 457-58 hexis 82, 101 Hindus 280f. Hippias Major (Plato) 165, 204 Hippias Minor (Plato) 222-26

532

iron bar (floating example) 327-38, 342 irrational number 500-1 Joseph. H. W. B. 346-49 judgment 369, 416-418, 421-22, 426, 428, 435 Kant, Immanuel 432-33, 465f. katholou proton 167 Kelvin, Lord (William Thomson) 186 Kemp Smith, Norman 27 Kielkopf, Charles 408-10 Koch, Robert 184, 189 lambanein 211 Lang, Marc 506 law of identity 331 law of large numbers 475 Laws (Plato) 376 Leibniz, Gottfried Wilhelm 36-49 Letter from a Gentleman to his Friend in Edinburgh (Hume) 22 liar (paradox) 416 line (geometrical) 284-292 Lipton, Peter 154 Locke, John 19 logical necessity 327-28 logical positivism also logical positivist 424 logical possibility 326-28 Lonergan, Bernard 9, 416-17, 422, 424-25 Mach, Ernest 130-31 MacIntyre, Alasdair 427 major term 244, 297 Manders, Ken 277, 283, 285-86 material cause 254-55, 258, 261, 264-68 mathematical induction 262, 506-7 Mathematical Principles of Natural Philosophy (Newton) 125 Mathematics 147, 159

Index

Matter 391 matter of fact reasoning 245 matters of fact also matter of fact 62-65, 65-72, 88, 115, 242-46 maxim of metaphysics 324, 355 McGrew, Timothy 474, 476 Memory 59-62, 66, 86-87, 101-4 Meno (Plato) 509, 512 mental disposition (as knowledge) 383 Metaphysics (Aristotle) 204-5 Meteorologica (Aristotle) 207 Michelson-Morley experiment 144-45 Mill, John Stuart 14-16, 182, 471-72, 510 Miller, N. 285-86 Millican, Peter 387, 388f. mimesis 508-510 minor term 241, 244-45, 297 mode of discovery 362 mode of proof 362 monads, also monadic 42-44 moral facts 429 Mourelatos, A. P. D. 278-79 Mumma, J. 283-86 n-place predicates 286f. Nagel, Thomas 360-63 narration also narrative 363-67 natural necessity 329-31, 330f. Naturalism 18-20, 27-28, 72, 75, 387 necessary connection 350-51, 69 necessary facts 408 necessary truth 324-26, 331-37, 332f., 349f., 464-65 necessity 259, 261, 264, 330-31 Newton, Isaac 125-26, 139-45 noein, noesis 113-14, 272-74 nominal definitions 183-84 non-discursive reason 488 non-reciprocal dependency relations 275-76 nonprecisive abstraction 351-53 Norton, John 143 null set 495 number theory 500-501

Index

objective idealist 390 objectivity 396, 426 “Of the Reason of Animals” (Hume) 83 Ohm’s law 184-85 operationism 420 opposition 203, 211 organon 340f. ousia 99 Pap, Arthur 324 parables 239-41 paradeigma, paradeigmata 201 paradox of material implication 281 parameters of systematicity 450-52 particularity 370 Pascal, Blaise 489 Peirce, Charles Sanders 199-200 per impossibile 382 periodic table 479-80, 505 personal identity 504 Philebus (Plato) 367, 368-71, 375-76 philosophical induction 153 physical notation 338 Physics (Aristotle) 208-9, 371, 376 pi (ʌ) 465 picturing 425 piety 164-65, 178 Planck, Max 128-30 Plato 221, 227-29, 366-67, 369-74, 374-77 plausbilistically optimal 442-443 plausibility also plausbilistically 450, 442-443 pleasure 368-69 positivism 130-31 possibility-elaboration 442 possibility-reduction 443 possible intellect 319, 320f. Posterior Analytics (Aristotle) 97f., 252, 262, 312, 486 potentiality 82, 266 practical induction 236 pre-established harmony 36-37 pre-scientific induction 146

533

pre-scientific knowledge 136, 155 precisive abstraction 351-53 predicate logic 276f. prediction also predict 124, 410, 460, 473-77, 479-80, 483-84, 51011 pre-existent knowledge 308-311 prime number 501 primitive societies 429 Principia Mathematica (Newton) 139 principle of efficient causality 127-28 principle of excluded middle 330, 333f., 340-41 principle of non-contradiction also PNC 324, 326, 330-32, 340-41 principle of sufficient season 56, 118, 128 Prior Analytics (Aristotle) 6, 179, 221, 241, 279, 293 probability also probabilities, probable reasoning 2, 61-64, 70-72, 8789, 69, 245, 473-78 probability calculus 460, 474-75 probability theory 474, 478 problem of induction 3, 11, 38-39, 69, 137-38, 233, 242-44, 262, 303, 316, 408, 421, 433-36, 436f., 498, 510 proof 69-70, 89-90, 204, 284-91, 504, 507 proper sensible objects also proper objects 98-99, 368 protasis 284, 290 pure phenomenon 394-95, 400 Pythagoreans 499-502 quantum mechanics 128-31 question-answering (erotetic) 447, 452, 440 question-resolution 439, 452-53 quid est 368, 371, 373 quiddity 315-16 Quine, W. V. 333-35 quod 382 quod intelligitur 91f.

534

radical scepticism (see also scepticism) 19, 21-27, 43, 44, 387, 515 Rand, Ayn 187 ratiocination 308, 316 rational empiricism 392, 401f.-402f. rationalism also rationalist 49, 55-57, 62-65, 75, 90, 113f., 116-21 ravens (black) 433-34 realism, also realist 91, 95, 104, 121, 133, 147-48, 377, 391, 421, 427, 431 reality 87, 91-92, 102-4, 146-47, 270, 293, 334-37, 340-41, 355, 367, 376-78, 382-83, 390-93, 421, 426, 431-32, 482, 515-16, 520, 521 reason 2, 35-36, 45, 51, 55-57, 62-65, 70-72, 75, 84-85, 89-90, 96, 104-7, 110, 116-21, 363-65, 369, 377-78, 383, 487-88, 49394, 519 reasonable judgment 415-18, 430-31 reciprocal dependency relations 274-76, 290, 292, 295 recollection 60, 103-4, 229, 240-41 reductionist also reductionism 132, 360-62, 512 reductive materialism 391, 416 reflection 232, 234, 242 regula Socratis 169 Reichenbach, Hans 445 Reid, Thomas 16, 32, 346 relational (logical property) 203, 280, 337-38 relations of ideas 8, 62-64, 83-84, 105, 107-8, 111f., 116, 234, 242-43, 411, 464-65 relations of reason 338 relativism 335 representation also representational, representationalist 103-4, 132, 147, 156, 381, 389-90, 393, 496 representative (notions of truth) 382 rerum natura 8, 325, 330, 336, 339-44

Index

Rescher, Nicholas 520 retreat (of army example) 369, 373 Rhoda, Alan Robert 480-81 Ross, W. D. 433, 457 rule of inference 271, 292f., 446 Russell, Bertrand 494 Schiller, Friedrich 392 Scholastic 52-53, 377-79, 382-84 Science 97-98, 97f., 107-9, 123-25, 128, 135-38, 140, 148-49, 15658, 205, 236, 247-48, 253, 30810, 317-18, 399-406, 428-30, 461, 479-80 scientia 308, 310-11, 317f. scientific faculty 234 scientific induction 136, 138, 146, 153, 158, 317-18, 317f., 472, 505 scientific naturalism 387 scientific phenomenon 395 scientific realism 147-48 Searle, John 155 second-hand induction 508-9 secret powers 68-69, 460 self-contradictory 331-32 semantics 271 sense and intellect (distinction) 94-95, 99, 109, 111, 117, 135, 316, 356-57, 369, 374, 386-89, 48788 sense illusion 77, 368, 372, 482 sense perception 54-57, 63-64, 67-69, 73, 76, 78-79, 82, 84, 89-97, 99f., 101, 107-8, 114, 116-18, 120, 156, 202, 272, 293, 367, 388-89, 393, 394, 482, 493-495 senses 47, 58, 66-68, 70, 78, 84, 89, 94, 98-100, 110,114, 136, 158, 209f., 356-57, 368-69, 371-73, 375, 405, 426 sensible qualities 67-69, 86, 94, 98, 110, 389-90, 460 separation 295-96, 298-99 Sepper, Dennis 398

Index

set (theory) 495-96 Selby-Bigge, L. A. 14 side-diagonal problem 499 skepticism 19-21, 23, 26-27, 62, 69-70, 321, 372, 383, 391, 471, 476, 480, 511-12, 516 Smith, George 141 Smith, Kemp 27 Smith, Robin 210f., 434-35 Socrates 6, 151, 164-65, 175-78, 193-96, 214, 221-228, 370, 509 Socratic fallacy 226-27 Socratic induction 6, 163, 193, 196, 224, 509-10 Sophia (Lady Wisdom) 359-63 spark-gap-generator 457-458 special relativity 143-45 species 23, 88, 112f., 235-36 square 499-500, 509 square root of two 500 Stachel, John 145 Statesman (Plato) 376 Steiner, Rudolf 400-2, 400f. Suarez, Francisco 379-84 Suarezian 382-84 Substance 42, 77-78, 92-93, 92f., 98101, 251-52, 254-58, 370 syllogismos 210, 224 Suman, Seth 129 Swans 402 Syllogism 112, 183, 196-201, 219, 305-6, 305f. Syllogistic 200-201, 220, 296-98, 312-14, 494 Symposium (Plato) 366, 374 systematization 445, 448-56, 450f. teacup (example) 470 theism 479-80 Theodicy (Leibniz) 39 Theory of Colour (Goethe) 403-7 Thomas (Aquinas) 8, 209f., 254, 351, 379-80, 490 Thomson, Garret 57f., 91f. three-legged dog 394, 468-70

535

threefold process 416, 419, 428-430 tides 185-86 topic neutrality 271 Topics (Aristotle) 176-77, 179 Topology 277-78, 283-84, 286 topos 177, 212f. transcendental facts 429-30 Treatise (Hume) also Treatise of Human Nature 16-19, 22-23, 27-29, 29f., 53-54 Triangle 108, 284, 290-95, 410, 412, 464 truth-functionality also truth-function, 425 uniformity of nature 2, 37, 71-72, 329-30, 347-48, 350f., 434, 472, 475 universal also universality 94, 105, 107, 111-13, 112f., 115, 161, 174, 188, 191, 202, 213-14, 227, 236, 242, 247-49, 262-63, 270, 276, 282, 286, 293-94, 309-10, 370, 405, 457, 485, 508 Urbach, Peter 477 Ursache 404 use and mention (distinction) 345 validity also valid 56, 71, 174, 252, 314, 440, 446, 466-67, 512 Valla, Lorenzo 162-63 Venn diagrams 282 verae causae 181 verification principle 422 Vickers, John 137 Vienna Circle 124, 130 virtue ethics 219-220 virtus dormitiva 256 Von Wright, Georg 1, 65 way of ideas 346 Wells, William Charles 183 Westphal, Jonathan 38 Whately, Richard 162

536

Wheatstone, Charles 185 Whewell, William 161-62, 169-76, 171f., 182-83, 443, 471 Whiteness 368, 370-71, 379 wide reflective equilibrium 424 Williams, M. E. 424 Wilson, Thomas 162 wit 411 Wittgenstein, Ludwig 25, 26, 424 Xenophon 428 Zabarella, Iacopo 149 Zeno (the Epicurean) 462 Ziguras, Jacob 9

Index