Philosophical Episodes 9783110319934, 9783110319385

Citation preview

Nicholas Rescher Philosophical Episodes

For Mark Roberts in cordial friendship

Nicholas Rescher

Philosophical Episodes

Bibliographic information published by Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de

North and South America by Transaction Books Rutgers University Piscataway, NJ 08854-8042 [email protected] United Kingdom, Eire, Iceland, Turkey, Malta, Portugal by Gazelle Books Services Limited White Cross Mills Hightown LANCASTER, LA1 4XS [email protected]

Livraison pour la France et la Belgique: Librairie Philosophique J.Vrin 6, place de la Sorbonne; F-75005 PARIS Tel. +33 (0)1 43 54 03 47; Fax +33 (0)1 43 54 48 18 www.vrin.fr

2011 ontos verlag P.O. Box 15 41, D-63133 Heusenstamm www.ontosverlag.com ISBN 978-3-86838-123-8 2011 No part of this book may be reproduced, stored in retrieval systems or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use of the purchaser of the work Printed on acid-free paper FSC-certified (Forest Stewardship Council) This hardcover binding meets the International Library standard Printed in Germany by CPI buch bücher dd ag

CONTENTS Preface

Chapter 1: EROTETIC NEOPLATONISM

1

Chapter 2: NEO-PLATONIC RUMINATIONS ON OPTIMALISM AND THEISM

9

Chapter 3: ELEMENTS OF CLASSICAL ONTOLOGY

15

Chapter 4: AQUINAS AND WORLD IMPROVEMENT

23

Chapter 5: LEIBNIZ ON INFINITE ANALYTICITY

27

Chapter 6: LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

33

Chapter 7: LEIBNIZ CROSSES THE ATLANTIC

57

Chapter 8: KANT’S NEOPLATONISM (KANT AND PLATO ON MATHEMATICAL AND PHILOSOPHICAL METHOD)

77

Chapter 9: ON PEIRCE AND UNANSWERABLE QUESTIONS

89

Chapter 10: HEDWIG CONRAD-MARTIUS AND THE SELF-TRANSCENDENCE OF PHENOMENOLOGY

105

Chapter 11: THE WAR OF THE WORLDS

113

Chapter 12: WHAT EINSTEIN WANTED

129

Chapter 13: GÖDEL’S LEIBNIZ CONSPIRACY

155

Nicholas Rescher • Episodes

Chapter 14: THE BERLIN GROUP AND THE RAND CORPORATION (A NARRATIVE OF PERSONAL INTERACTIONS)

181

Chapter 15: ON INFERENCE FROM INCONSISTENT PREMISSES

189

Chapter 16: PHILOSOPHY IN THE WORLD OF LEARNING (ASPECTS OF A TWO-PERCENT SOLUTION)

193

References

195

PREFACE

P

hilosophical work comes in different sizes: there are systemic treatises, monographic surveys, philosopher-expanding texts. But there is also room for smaller studies that focus on highly particularized ideas and issues: studies that deal not with entire continents but with mere reefs and estuaries. The present essays are of this limited nature. Their aim is less to give a view of the overall lay of the land than to illustrate the diversity of the landscape. The present book continues my longstanding practice of publishing groups of philosophical essays that originated in occasional lecture and conference presentations. (Details are given in the footnotes.) Notwithstanding their topical diversity the essays exhibit a uniformity of method in a common attempt to view historically significant philosophical issues in the light of modern perspectives opened up through conceptual clarification. I am grateful, as ever, to Estelle Burris for helping me to put this material into a form suitable for publication. Nicholas Rescher Pittsburgh PA May 2011

Chapter One EROTETIC NEOPLATONISM

E

ver since Aristotle’s Categories, various theorists have put questions at the forefront of concern in matters of cognitive inquiry, assigning them logical priority over answers. After all, which theses one maintains will very much depend on what questions one is trying to answer. In the 20th century the English historian-philosopher R. G. Collingwood above all made this perspective the very centerpiece of his deliberations. In the spirit of such an erotetic approach to philosophical deliberation, is it instructive to begin with an inventory of the traditional “big questions” of metaphysics: • What exists? • What is it like? • Why is it there? • Why is it there as is? On such a methodological approach to metaphysics, one is to begin by looking not at theses or theories, but rather at the inventory of questions that delimits the field. However, even before attempting to answer such questions, it is proper and reasonable to set out the operative standards and criteria for adjudging an answer to be adequate—to look for the qualityassessment criteria for evaluating the merits of possible answers. The issue here is: what does an answer have to achieve to be accounted acceptable: what it is that is required of an adequate answer to qualify as such in metapysics?

Nicholas Rescher • Episodes

2

On such an approach, it proves to be instructive to follow as our model the path of Plotinus (205-270A.D.) in dealing with those “big issues” of ontological metaphysics. I. As regards: “What Exists” The answer here must clearly be comprehensive and allencompassing: it has to encorporate being-as-a-whole. It will not do to respond “sticks and stones and such.” For the problem here is not one of giving examples of what exists but rather is one of determining the overall scope at issue. And so an appropriate answer has to proceed in terms of what Plotinus called to en: reality: being-as-a-whole. Without existentially comprehensiveness, an answer cannot do the job. II. As regards: “What is it like?” An appropriate answer here must be descriptively amorphous. Any attempt to characterize reality as being of this or that sort marks itself as inappropriate through this very fact by leaving the other sorts aside. In answering this “What is it like?” question the best one can do is to respond: diversified. III. As regards: “Why is it there?” The answer here has to be that it is self-engendering of (causa sui), existence-experientially self-sufficient. To assign it to any external, self-distinct raison d’etre would be to make something different and distinct in a way that conflicts with its own all-comprehensiveness. IV. As regards: “Why is it as is?” The answer here has to be “Because the reasons for its being so are better (stronger) more compelling than any reasons for its being otherwise.” The ultimate rationale for the nature of existence has to render in considerations of rationality/optimality. Any really adequate explanation of the nature of existence has to some down in the end to its being so because this is for the best.

3

EROTETIC NEOPLATONISM

But what makes it so? Its very nature as the best affords most rational explanation. Since the interests/demands of rationality are the crux, we have it that that which “best satisfies the demands of reason” must be equated with that which “best serves the interest of rationality as a constituent factor of the cosmos. And here too we can look for guidance to neo-Platonism, which took existence to root in value. For it, ultimate explanation of why something exists and exists as it does—lies in that this is for the best. On this basis the crux of neo-Platonist ontology lies in the thesis that Those things are actual existents whose realization as such optimizes the rational comprehensibility of nature.

This is a thesis that focuses the three central features: existence, value, and intelligibility. And on this basis, the salient consideration is that only a reality shaped by the rational operations of mind to meet its own requisite can ultimately provide an answer to the question of being. For neo-Platonism, existence roots in the values encapsulated in realty as such. The crux of its position is that reality is basically rational. Lawful order is inherent on existence, and indeed explanatory of it. Where there is not just chaos but outright anarchy (lawlessness) nothing can evolve. Accordingly, rational order—intelligibility, in effect— determines and pervades existence ab initio. Of course it is—in theory—one thing to have conditions for appropriate answers, and quite another to have the appropriate answers themselves. But with these most fundamental and far-reaching issues the very magnitude of the question commits an acceptable answer to take a certain definite form. And those neo-Platonic hypostases are the crux here. Along just these lines, Plotinus, following in Plato’s footsteps, projected three fundamental metaphysical factors: I.

The One (to on): reality or being-at-large. The one or the whole is the primordial existential matrix. It is an undifferentiated chaos, devoid of order or structure of any kind. One can only say that it is, but not that it is this or that. For to say that being-

Nicholas Rescher • Episodes

4

as-a-whole is X-wise is to resort to a contrast between that which is X-wise and that which is not. But “being not X-wise” is still a form of being and we are thus caught up in a contradiction. Being itself (to on) cannot be grasped in its characteristic unity because cognition involves division (taxonomy, distinguishing dihairesis). It can only be apprehended by extraordinary intuitive insight distinct from ordinary conceptualized cognition. There is no knowledge of reality-as-such in the ordinary sense of the term, which involves conceptualization. At this level there is only an extra-ordinary (intuitive) apprehension of individual unity. It is an aperion in the sense of Anaximander, and no quantitative or qualitative limits can be imposed upon it. Even space and time have no relevancy to it. (In modern terms it is akin to the universe antecedent to the Big Bang.) II. Intelligible Structure (nous): rational order, systemic studies, cogent taxonomy. The world reshaping force of intelligence (mind, intelligence, spirit) impacts upon the primordial one (undifferentiated unity) to produce a series of successive developmental stages. (1) The first of these is a differentiation into distinguishable kinds, each subject to its own mode of lawful modus operandi, and thus providing a foothold for intelligence. Differentiation impacts upon irrational materiality in a way that forms this materiality a basis for intelligibility. (2) The material cosmos thus comes to be organized into macrostructures that exhibit lawfulness of different sorts (e.g., astronomical and biological). These structures provide further grist to the mill of intelligence. III. Soul (psychê): cognition, comprehension. The emergence of intelligent beings in the cosmos enable them to grasp (at least in part) the intelligible studies that nous has brought to being. Since this feeds upon the fruits of nous.

5

EROTETIC NEOPLATONISM

As Plotinus saw it, the cosmos in the course of its development gives rise to intelligent beings who are able to explore and internalize its intelligible structure. These intelligent beings represent the largest stage of cosmic development and constitute—as it were—the “crown of creation.” All this, however, describes the situation only at the level of aggregative generality. It considers how mind (viewed in its totality) deals with existence (viewed in its totality). It functions at the totalistic level of idealized generality. And this, of course, is not the end of the matter. For with Plotinus, as with Plato, there are multitudinous specificities in the created world which “participate” in those unifying ideas. However, matter, the material realm of concrete-existence, comes into the cognitive scheme of things only after the soul’s sensory experience has evolved intelligence to effect the classificatory differentiation between the spiritual and the material. From the angle of understanding, matter’s realm of concrete and diversified existence is not something basic. It is not on par with the three ruling hypostases but enters into the realm of understanding in a late and derivative manner. Crucial for Plotinus is the question of how the three developmental stages: • undifferentiated unity • differentiated existence with intelligible structures • structure-apprehensive intelligence are related. The preceding discussion has proposed two analogies in the interests of interpretative accessibility here, namely: temporal development in the order of being, and rational development in the order of explanatory understanding. But Plotinus himself does not adopt such a dualistic-perspective. Implementing the principle that reality’s understandability and the mind’s understanding must be coordinated, he fused these two factors into a single process of emanation (aporreusis). And this process, which at first look seems to be a rather

Nicholas Rescher • Episodes

6

mysterious procreative process, is actually nothing of the sort. For we know full well—and see nothing mysterious about—the process of taxonomic subdivision which divides most any kind of natural kind or group into subkinds or subspecies. And it is just this sort of thing— taxonomic subdivision (Platonic dihairesis)—that is at issue with Plotinus emanation. Nothing more mysterious is at issue here than what is familiar to every child who plays at the part of subdividing at issue with the game of “Animal, Vegetable, or Mineral?” As Plotinus sees it, generalities “emanate” with those abstract existents falling into particularized specificity: into innumerable natural kinds at different levels of generality. In elaborating the Platonic hypostases I amblichus later introduced a triadic perspective. He portrayed the emanative process of taxonomic division as having three stages which can be depicted essentially as follows: Even Integers I

II

III Odd

At the start at state I there is a macro-unit that remains constant [momê] (here Integers-as-a-whole). At stage II we introduce the principiam divisionis that divides this unit into parts and thereby leaves it behind (proodos). And at stage III the exhaustivity of that division returns it to the starting point [epistrophê] Here we are now enroute to the classificatory procedure later canonized in the long-influential “Tree of Porphyry” “Emanation” is at its core the move from kinds to subkinds. And the “One” is the ontological source, the fons et origo to all existence. Now one may well not want to follow Plotinus through the details of the complex picture of his metaphysical apparatus: the essentials of the matter for us are still found in those issues with which he too began his deliberations. • What exists? What does reality, viewed in its totality, comprise?

7

EROTETIC NEOPLATONISM

• What is it (the manifold of existence) like? • Why is it like that? Why should it be that way? These address, respectively, the content, the character, and the explanation of reality. And these are the focal issues of our present metaphysical agenda as well. So the fact remains that by means of his somewhat strange-sounding terminology, Plotinus grappled with the selfsame issues of ontological questions that are still very much on the agenda today.

Chapter Two NEO-PLATONIC RUMINATIONS ON OPTIMALISM AND THEISM

W

ith Plotinus prominent in the foreground, the neo-Platonists of classicalantiquity contemplated three fundamental principles of metaphysics: • Reality (“the One,” to on) • Rationality (“the intellect,” intelligible order, mind: nous) • Soul (“the comprehended,” understanding: psyche) In a rationally ordered universe whose nature as such is comprehensible to rational intelligences these three are fused into an indissoluble unity: a reality shaped by a rational order comprehensible to minds. Rational structure is the crux at once of the nature, the explanation, and the valuation of actual existence. The gap envisioned by later philosophers between actuality and normativity, between being and value, simply did not exist in NeoPlatonism. For here value—“the good” broadly construed—is the very crux and explanatory ground of being. Mainstream neo-Platonism espoused the cardinal thesis of Plato’s Timaeus that reality is inherently optimific—a manifold of being arranged for a realization of the best. Its commitment here is to what might be called the Principle of Optimality to the following effect: Within any finite range of alternatives A1, A2, . . . An that which is optimal—which is for the best, everything considered—is the one that actually obtains in reality’s make-up.

This is a patently metaphysical thesis in its insistence upon the creative efficacy of value, holding that evaluative optimality carries exis-

Nicholas Rescher • Episodes

10

tential actuality in its wake. The basic idea here is that an optimality that pivots on rational intelligibility is a truth-maker in that if affords—of and by itself—a sufficient reason for existential realization. It deserves note that such a position will, in the inherent logic of things, carry three important consequences in its wake, namely theism, optimism, and self-sustainingness. The Church Fathers were drawn to such a neo-Platonism as a doctrine readily geared to theological considerations. For as regards theism, note that the optimality principle provides for a direct pathway to establishing the existence of God via the idea that it would, everything considered, clearly be for the best if the world were the well-designed product of a benevolent creator—that is, if God existed and functioned in this role. As regards optimalism, let us consider the Principle of Optimality as per OPTIMALISM. If X is optimal, then X is actually so.

in relation to its converse: OPTIMISM. If X is actually so, then X is optimal

The former—optimalism—moves from value dominance to actuality; the latter—optimism—moves from actuality to value dominance. It is readily seen that these two theses are interrelated and interconnected. After all, it is a virtual tautology that: • It is optimal that the actual be optimal. This being so, (2) will immediately follow from (1). And as regards the converse—(1)’s following from (2)—suppose that not-(1) so that something (Z) were optimal but not actual. Then not-Z is actual. But now if (2) held, then not-Z would be optimal, contrary to Z’s postulated optimality. So not-(1) entails not-(2), and thus by contraposition (2) entails (1). Q.E.D. And it follows from these considerations that optimalism and optimism—construed in the presently operative sense—are effectively equivalent positions.

11

NEO-PLATONIC RUMINATIONS ON OPTIMALISM AND THEISM

Finally, s regards self-sustainingness, consider the questions of why it should be that optimalism obtains. Philosophers have usually sought to separate issues of fact from issues of value. They generally note and emphasize the difference between the questions “Is it true that p?” and “Is it (or would it be) a good thing that p?” But with Plato and throughout the Neo-Platonic tradition there is an ongoing effort to fuse these factors that are so decidedly disjoined in otherwise mainstream thinking. For optimalism sees the final causation of benefit and value as productively efficious. In the Platonic tradition it sees “the good” as productive and views reality as value-determined. On such an approach then it is a critical factor that the Principle of Optimalism is self-sustaining. On its basis the question “Why is it that optimalism obtains?” is answered in the selfsustaining basis of the consideration that this itself is something that is for the best. 2. THEOLOGICAL RAMIFICATIONS Note, however, that it would seem that neither optimalism nor optimalism is something necessary: if they hold true they will do so contingently. It is certainly possible—in theory and perhaps even seemingly in practice—that some actual arrangement in this world is not optimal. But if optimalism does obtain, then what is—or could be—its ground? Here we must begin with the question just what standard of merit is to be used in assessing the good at issue with optimality. Traditionally it is—and plausibly enough should—be the condition of well-being of the world’s intelligent beings—the extent of what their real and best interests are provided for. (In theory one need not be provincial about this and look just to the members of the species homo sapiens dwelling on this particular planet of ours: one can spread one’s view over the universe at large.) Why should it be that optimalism obtains? Clearly, one prospect here is the theistic grounding of optimalism: (TO) What is optimal is actual because a benevolent God has it be so. God grounds (produces, engenders, causes, effects) the

Nicholas Rescher • Episodes

12

operation of optimalism. Letting G be the theistic doctrine of God’s existence, and O the thesis of optimalism we here have a justifactory argument whose structure is: G → O. However, there also lies before us the prospect of a converse reasoning of optimalistic explanation of God’s existence: (OT) God exists because his doing so is optimal. The principle of optimalism grounds the existence of God. The reasons at issue here has the structure: O → G. There is, moreover, also a line of explanatory reasoning that contemplates the self-grounding of optimalism on its own basis: (SE) Optimalism actually obtains because its so doing is optimal. Structure O → O. However, grounding as such is not actually explanatory unless proceeds by way of recourse to something else of a somehow more fundamental character. So it is clear that reasoning of the format O → X or O → O does not really explain optimalism, seeing that O is here the input rather than the output of explanatory reasoning. Only X → O (with X ≠ O) will serve here. All the same, in the hermeneutic order of deliberation the selfsustaining coordination of G and O can instructively be contemplated via the entire tripartite complex of principles as per the coordinative cycle: G

O

This, however, is condition of things obtaining in the order of hermeneutic coordination rather than in that of productive explanation. As far as the later Neo-Platonists were concerned, Christianity was a godsent. In an era where self-explanation was no longer deemed as plausible, their commitment to optimalism’s efficient productivity of value

13

NEO-PLATONIC RUMINATIONS ON OPTIMALISM AND THEISM

as the ratio essendi of being required an explanatory underpinning which Christian theology was ready and able to supply. On this basis it is clear that what looks to be the most promising joins the Platonic (and neo-Platonic and Leibnizian) tradition and, in the spirit of the Church Fathers, proposes to see optimalism functioning on essentially theological grounds. * * * Neo-Platonism saw three inner factors as paramount in the ontologic domain: • Fact (to on: existence reality) • Value (nous: rational order) • Spirit (psyche: understanding) The critical insight of Church Fathers is the need for thematic heterogeneity in explanation. Absent circularity, we cannot explain fact in terms of fact without reaching the dead end of unexplained explainers. And the same holds for explanation in terms of values of in terms of supra-natural (i.e., theological) coordinators. But the systemic harmonization of all three domains is something else again. Fact

Value Spirit

An here the explanatory process is not a matter of ordinary posterior to power considerations but one of coordinating and meshing the considerations operative in all three thematic domains. As they saw it, coordinative rather than reductive explanation provided the crucial instrumentality of metaphysical explanation.

Chapter Three ELEMENTS OF CLASSICAL ONTOLOGY 1. TAXONOMY

O

ntology—the general theory of existence and nonexistence— greatly preoccupied the mediaeval schoolmen, and they left us a rich heritage of ideas on this subject with which subsequent theorists have struggled to come to terms. In particular there are some issues that continue to perplex and baffle theoreticians and down to the present day. The taxonomy of Display No. 1 is a logical place to begin a discussion of ontology. (Unlike the medievals, we here leave God aside, a being whose conception poses a very special and separate case.) All of the distinctions that motivate its divisions are crucial to understanding in this field. In particular this taxonomy incorporates the following distinctions: (1) • existing in reality (actually existing in the real world), versus • subsisting in the realm of mind as a thought-object of sorts. (2) • concreteness as a particular item of existence, versus • abstractness as a potentially generic feature or different terms (the so-called universals). (3) • thought-instruments for characterizing reality, versus • pure fictions of the unfettered imagination. In thinking about “modes of being” these distinctions are bound to play a critical role.

Nicholas Rescher • Episodes

16

_______________________________________________________ Display 1 ONTOLOGICAL TAXONOMY (MODES OF BEING/NONBEING) I. Reals or actuals (realia, actualia) A. CONCRETE (concreta) 1. SUBSTANTIAL (physical objects: individual trees, planets, dice, animals) 2. OPERATIONAL (natural laws and natural processes, personal dispositions, force fields, heat waves) B. ABSTRACT (abstracta) 1. NATURAL (non-created) a. qualitative descriptors (male/female, natural kinds, phenomenal colors) b. structural descriptors (numbers, shapes, structures) 2. ARTIFICIAL (man-made abstractions: letters on the alphabet, signals, poems) II. POSSIBILITIES (possibilia) 1. NATURE-BASED: Physically encorporated possibilities (developmentally possible features,, accidents, etc.) 2. MIND-BASED: Thought contrivances (entia rationis: fictionalia) a. Reality-applicable fictions (mind-projected thought tools: the north pole, the Eastern Standard time Zone) b. Pure fictions (mere creatures of imagination: the Easter Bunny, Sherlock Holmes) irrealia

________________________________________________________ One of the cardinal principles of ontology is the recursion thesis regarding the nature of existence: (RT) If X actually exists, then so do its substantial components and its natural features: its properties, relations, parts, com-

17

ELEMENTS OF CLASSICAL ONTOLOGY

ponents, structures, causal antecedents, and consequences, and analogous factors. So given any existent, this circumstance gives rise to a cascade of dependent existents. And it stands coordinate with the fact that there are two critically different kinds of features as regards concreteness heredity, namely the • concreteness preserving (parts, components, causes) • abstractive (kinds, processes [modes of comportment] Existence always carries over from a thing to its concreteness preserving features. Its abstractive features can only be said to subsist or have being: they lack real-world existence as such. Only real (realia) have unqualifiedly actual (authentic) existence. Possibilities can have a being of sorts insofar as they are realityinherent; otherwise they are mere fictions whose only “being” lies in being thinkable-about thought-objects. Abstracta can exist either by necessity (in the case of natural/structural abstracta) or contingently (in the case of artifactual abstracta). No abstracta have spatiotemporal existence as such, but artifactual abstracta do have an origination in time and natural abstracta can be instantiated or exemplified in actual (spatiotemporal) existents. It is important to note that the ontology of science is complex. For natural science is not concerned with existing concreta alone, but with their abstract natural features and their possibilities as well. Some types of things—phenomenal redness for example—can only be instantiated (exemplified) in a world in which various requisite things and processes (physical and psychological) are at work. With such processual reals, their realizability (and thereby reality) is a contingent fact. To illustrate the point at issue, let us ask:

Nicholas Rescher • Episodes

18

2. WHAT IS IT TO BE A BOOK? Note to begin with that there two sorts of “books” can be at issue— namely, the generic texts such as “Gone with the Wind” or “the Bible” and the various material objects that are their physical realization (viz. the items one finds on library shelves or “the Family Bible”. The latter are concreta; the former abstract. For the moment, it will be the latter that will concern us here. To be a book (in this concrete mode) is to be an artifact produced by someone with a view to being (at least possibly) read. And to qualify as such, an item must have pages that present an interpretable content (a text or “meaningful” illustrations of some sort). There are, accordingly, various appropriate ways of filing in the blank in: “It wouldn’t be a book of if didn’t - - -.” There are definite limits to the sort of objects that could appropriately be called a book. And one of the salient requisites is that various mind-involving capacities come into play here: “produced with a view to” and “being possibly read” and “carrying meaningful text” all being prominently included. It is thus clear that to qualify as a book is to be comprehended in a web of mental operations. In consequence the physical correlation of an object is not sufficient to qualify its characterization as a book. We have to inquire into the mode of its production and mode of operation. One thus needs to go beyond any of its observable features to determine whether something is a book—and to go here in the direction of its relatedness to minds with reference to what mind-equipped beings have done and can do with it. Being a book is a characterization, that cannot be based entirely upon for the observable features of an object. Its physical constitution as such does not make an object into a book. Being a book is a mind-correlative clarification. In a world totally bereft of minds there can be no such things as books. An item observably indistinguishable from a book evolved by natural processes in an entirely mindless universe could not be described as a book. Minds

19

ELEMENTS OF CLASSICAL ONTOLOGY

alone can endow an object with those features to as essential to their being characterized as books.1 3. A PROBLEM In the taxonomic scheme of Display 1 there is one category that is troublesome, namely B1. It would be philosophically convenient to abolish this category and consign the whole of abstraction to the artifice of mind, and thereby torelegate the whole of mathematics with tis concern for quantity and stance to the sphere of mind-contrived artifice. However, mathematicians have always resided this course, taking themselves to deal with a realm of abstract existence that have a structure and order all its own. Actually experienced phenomenal redness apart, there is also the redness-idea at issue in the hypothetical considerations that— If a world has a duly consonant sort of make-up, then its denizens of such-and-such a sort would see its tomatoes in the way we would characterize as being red.

Such conceptual redness is an artifactural thought-construction: its nature is hypothetically perfection. So here we have a duality of two related/cognate items; the one an abstraction from experienced reality, the other a thought created mind-dependency. Pure fictions are wholly mind-dependent. It there were no minds to assume, postulate, suppose them, pure fictions would vanish from the stage: the items they envision would disappear. And the same duality obtains with respect to abstracta. Without minds there would be no letter of the alphabet and no stop-signs. (That is, while those physical objects would still exist, they would no longer be characterized in the way at issue.) However, while minds are essential to artificial abstracta such as letters, they are not essential to natural abstracta like numbers. These are mind-independent in the manner of things inherent with minds is at most hypothetical. Is it false to say that

Nicholas Rescher • Episodes

20

• If there were no minds then there would be no integers (or no abstracta). To be sure, it is certainly true to say • . . . then there would be no ideas (or thoughts) of integers After all it takes minds to have ideas (or thoughts). But this is something else again, and But it would not be true to say that in the absence of minds there would be no integers or shapes or structures or other sorts. In this regard, numbers are not like books in whose nature as such mental operations are implicated. And so while it is certainly true to say There would be no letters of the alphabet if there were no minds to do symbol interpretation It would be decidedly false to say There would be no integers if there were minds to do counting. These two different types of abstracta are in a different ontological boat because we are dealing with actual mental products on the one side and with merely potential mental objects on the other. Numbers, unlike books, are not inherently mind-invoking artifacts. 4. ISSUES OF SPATIOTEMPORAL PLACEMENT As regards spatiotemporal emplacement there are three different types of things: 1. those that have actual spatiotemporal existence: concreta like trees. 2. those that have purely suppositional spatiotemporal placement: irrealia like Sherlock Holmes.

21

ELEMENTS OF CLASSICAL ONTOLOGY

3. those that have an origin in time but have no position in space: artifice-engendered abstracta like poems. 4. those that lack any spatiotemporal position at all: rational abstracta like shapes and numbers. Only the second and third of these are mind-involving in their conceptual makeup; the others can exist in their own right. Moreover, natural (i.e., non-artefactual) abstracta exist apart from the contingencies of the world’s actual furnishings—and thus irrespective of whether they are instantiated and also of whether they are conceived of or considered by the beings of this (or any other) world. These two different types of abstracta are in a different ontological boat because the mind-invoking status of the items at issue—as actual mental products on the one side and as potential mental objects on other other—are quite different. Abstracta are not ontologically of a piece. They certainly admit of possible realization or of possible consideration, but the actualization of these possibilities has no impact on the authenticity of their being as abstracta. 5. CONCLUSION Ontology matters because heeding these ontological characterizations enables us to avoid confusion and avert fallacious reasoning. In particular it enables us to avoid the “category mistakes” inherent in posing such categorically inappropriate questions as asking for • the age or origin of abstracta • the shape or color of the North Pole or of the Equator • the location or color of letters of the alphabet • the age or shape or placement of numbers Ontological taxonomy is an indispensible tool for keeping out intellectual bookkeeping and accounting honest.

Nicholas Rescher • Episodes

22

NOTES 1

Some phenomenological idealists maintain that “world” is in the same boat as “book” in this regard. They maintain that while there could, conceivably, be a universe without minds, that a world can only be constituted as such by the experience of intelligent beings.

Chapter Four AQUINAS AND WORLD IMPROVEMENT

W

hat recent discussions about Intelligent Design have largely overlooked is that the move from design to an omnipotent God calls for showing that the Designer’s plan is as good as it gets and cannot be improved upon. Otherwise intelligent design would take us no further than a Star-Warsian “Force” that may well have “designs” of its own, unworthy of an all-merciful deity and contrary to the nature of such a being. A few historical observations may be in order in this regard. The principle at issue with actual-world optimality—the Axiogenetic Principle as it may be called—originates in Plato’s Timaeus and runs deep throughout the neo-Platonic tradition. And among the scholastics St. Thomas Aquinas endorsed the Neo-Platonic principle that “Goodness is by its very nature diffusive of itself and (thereby) of being.”1 And he frequently invoked this principle in holding that the world is optimal because God acts for the best: Summo autem bono competit facere quod melius est. (“The highest good consists in producing that which is best.”)2 To be sure, the crux here is that God must be seen as neither in control of nor responsible for the free actions of creatures. What they do is something that God indeed makes possible, but remains something whose actualization is the product of their free choices. Only the former—i.e., what is possibilized is at issue with world purification as viewed from the angle of God’s agency. The merit of a world is thus a matter of its own inherent nature, independently of what its free agents may choose to do with it. On this basis, Aquinas stood committed to the idea that this world cannot be improved upon—at least in its essentials. Overall, the tenor of Aquinas’ deliberations stands as follows:

Nicholas Rescher • Episodes

24

1. A given particular thing can indeed be made better—albeit not in its essential, but only its non-necessitated, accidental respects: “God cannot make something better than it is essentially . . . It is analogous to knowing that God cannot make the number four to be greater than four, for then it would not be four but another number.”3 2. Although God could—in the just-indicated way—make certain particular things better than they actually are, he cannot make the entire universe better overall, since the world’s things are so interconnected that an improvement in one thing would thereby diminish the merit of the whole, owing to the interrelations required for a world’s overall harmonious coordination. “The universe cannot be better than it is, because its goal consists in the most fitting order of its components as arranged by God. If one part were improved, that would spoil the proportion of the whole design (as with one overstretched harp-string the melody is lost).”4

The point here is that those aspects of the world which (from our limited standpoint) look to be imperfections are part of the price that must be paid in view of the complex interconnection of things for the overall good of the whole. Those “natural evils” (as philosophers call them) cannot be recovered from a natural system able to support the life of intelligent beings without incurring greater negativities elsewhere. This treatment of the issue was to be developed in even greater detail and sophistication by Leibniz in his Theodicy of 1710. In this perspective, changing the condition of the things that exist in the actual world could not and would not improve upon this world’s overall goodness. All “improving” modifications that depart from the world’s actualities in some putatively positive respect would always be offset by collateral damage elsewhere.5 So in the end, Aquinas sees good reason for endorsing the Leibnizian contention that this world of ours is the best of possible worlds notwithstanding the fact that the contingent acts of some of its agents renders them less perfect than they could and ideally should be.

25

AQUINAS AND WORLD IMPROVEMENT

NOTES 1

Bonum est diffusum sui et esse. See for example, the Summa contra gentiles, I.38. Aquinas sometimes attributes the principle to (Pseudo-) Dionysius. See N. Kretzmann in MacDonald 1991, p. 217, who discusses the history of the principle.

2

Summa contra gentiles, II.45.

3

Aquinas, Summa theoligia, Pt. I. q. 25, art. 6.

4

Ibid.

5

If the approach here being attributed to Aquinas is to work out satisfactorily, one precondition must, however be carefully heeded. Let the idea of a scale of perfection or merit for types or genera of beings range upwards from the finite lower creations of this world to supra-mundane beings. It is essential that this scale stop well short of God himself, the all-perfect being. The distance in point of perfection between the deity and the highest created form must is just as “infinite” as the distance between God and the noblest of angels. As Aquinas himself put it: “between even the highest creature and God there is an infinite gap.” (Aquinas, Super libros sententiarum, I d 44, qu.1, art.2) If this were not so, then any finite realm of created beings would admit of impairment by alternatives that admit of improved alternatives.

Chapter Five LEIBNIZ ON INFINITE ANALYTICITY

“T

wo plus two is four.” “Caesar crossed the Rubicon.” Some propositions have to be inevitable and necessary. Others relate to matters of contingent and conceivably alterable fact. But what is the difference at issue here? How is the one kind differentiated from the other? Leibniz held that all (logical-metaphysically) necessary propositions can be demonstrated by a finite process of “analysis” that reduces them to overt tautologies via the substitution of definitions for all of the defined terms. For him, necessity thus became equated with finite analyticity via definitions. And he applied this perspective to matters of logic, mathematics, and metaphysics. Whether they agreed with this position or not, scholars and students of Leibniz’s thought have at least found this to be intelligible. However, Leibniz then went on to claim that even propositions about matters of contingent fact existence were also open to analysis and demonstration—albeit in this case only by an infinite process. And this looks to be decidedly problematic. For if a proposition is analytic at all, in any manner, be it finite or infinite—then how can it avoid being necessary? How can this infinite analyticity possibly betoken contingency? And what does infinite analyticity have to do with contingent factuality and existence? Even so devoted and deeply informed a student of Leibniz as Louis Couturat was haunted by these issues. After all, he complained, the mathematician can deal with information quite well—with infinite series, infinite sums, infinite divisions in dealing with such matters as integrals and combined fractions: So why could we not similarly accommodate the infinity of conditions in a truth of contingent fact and demonstrate it by a sort of calculus-like logical integration?” Here Leibniz does no more than reply, in a somewhat confused and embarrassed way, that the analogy is imperfect and

Nicholas Rescher • Episodes

28

incomplete, and that then a truth of fact would contain true factors that do not admit of any finite analysis, no matter how elaborate.”1

But Leibniz need not have been stymied here. For he had a ready response at hand. To see this clearly and to view what he had in mind in a more favorable light it is best to turn to a mathematical illustration—as was altogether usual with him. Thus consider the following line of thought: 3

1

3

1

Since 4 = 2 + 4 , we have it that 4 is the item which uniquely answers 1

1

to the description of “being the sum of 2 and 4 .” Accordingly, when (1)

1

1

x=2+4 3

then it is clear that 4 is uniquely qualified to count as “the item x at issue in (1).” And on this basis we have it that 3

(∃y) ([y = the x of (1)] & [y is unique in this role] & [y = 4 ]) In this way, the identity at issue with 3 4 = the item x that meets the condition of equation (1)

is subject to finite demonstration. But now what about 1

1

1

1

(2) x = 2 + 4 + 8 + 16 + . . .

In trying to proceed here on analogy with (1), we at once come up against the issue of existence—i.e., whether there indeed is a rational number that (uniquely) plays the role in question. Given (2), what we can indeed demonstrate finitistically are two conditional facts:

29

LEIBNIZ ON INFINITE ANALYTICITY

(i) If there indeed is a number answering to (2), then this number cannot be 1. And we can further demonstrate the conditional fact that (iii) If there indeed is a number answering to (2), then this number 1

1

is closer to 1 than is 1 - 2n and also than is 1 + 2n , for any particular integral value of n whatsoever. But that the number at issue with these hypothetical conditionalizations actually exists (and indeed is = 1) is something we cannot demonstrate on the basis of general principles of rational-number arithmetic. All that we can actually manage is to claim that 1 qualifies as the optimal (rather than uniquely correct) solution to the problem in question—viz. that IF there is such a rational number x, then it has got to be 1. Actual existence, that is to say, requires benign conditions. The salient consideration here is that the identity at issue in equation (2) above is not flatly demonstrable on logically mandated “general principles.” Its establishment requires an inherently infinitistic approach, and rests on an appeal to condition of optimal suitability. Only via considerations of optimality does the existence of such an x as a well-defined item—a particular real number—emerge here. And this perspective brings to view a general Leibnizian point, namely that it is only through an appeal to normative considerations of optimality (of fitness, economy, continuity, elegance of design, etc.), that the existence of certain entities comes to view. Mere finite analysis cannot do the trick. It leaves a gap that must be closed by appealing to optimality considerations. Accordingly, contingency enters the picture—the infinitistic complexity of the issue means that an appeal to factors over and above mere definitions are needed for the analysis to issue in the requisite uniqueness and definiteness required for a demonstration of existence.

Nicholas Rescher • Episodes

30

A comparison that encompasses an infinite scope becomes necessary. As Leibniz puts it in section 36 of the Monadology: A sufficient reason must also be present in contingent truths or truths of fact, that is to say, in the sequence of things dispersed through the universe of created beings. Here the resolution into particular reasons can go on into endless detail, because of the immense variety of things in nature and the ad infinitum division of bodies. There is an infinity of shapes and motions, present and past, that enter into the efficient cause of my present writing, and there is an infinity of minute inclinations and dispositions of my soul, present and past, that enter into its final cause. . . . . All this detail only contains other prior, or yet more detailed contingents each of which also requires a similar analysis to provide its reason [ad infinitum].

Analyticity as Leibniz sees it is a matter of establishing a demonstrable identity. But there are two pathways to this destination. One is the pathway of proof, of finite demonstration. Here we have it that A = B where B is (demonstrably) the only possible value of x for which A = x can be maintained.

This sort of (finitely) possible identity is at stake with the analysis of absolutely or “metaphysically” necessary truths. But above and beyond such finite analyticity, there is also the prospect that A = B where B is (demonstrably) the best-available value of x for which A = x can be maintained.

With Leibniz it is this sort of optimization-identity that is at issue with the (infinite) analyticity of contingent truth. For as he sees it, (A) A proposition P is true necessarily if it obtains in all (logically coherent) conditions and circumstances whatsoever which is to say that it obtains independently of any possible world arrangements. And this means that such a truth can be established on general principles which leave matters of world arrangements—actual or possible—entirely out of account.

31

LEIBNIZ ON INFINITE ANALYTICITY

(B) A proposition P is true contingently if it obtains under optimal conditions (in the best realizable world-arrangement). To demonstrate truth of the former (necessitarian) sort one can simply ignore any and all specific world arrangements—no comparison among them is required here. But to demonstrate truth of the latter (contingent) sort it is necessary to make a comparison among different possible world-arrangements. And this is where infinitude unavoidably comes into it. With Leibniz, then, the infinite analyticity of a proposition pivots on the circumstance of its forming part of a sine qua non requisite for optimization. And any process of showing this to be so requires an evaluative comparison among infinitely many alternatives. Necessity will emerge from general principles, but the optimalization at issue with contingency requires comparative evaluation of alternatives. And as Leibniz sees it, all judgments of existence require optimization— God alone here as elsewhere constituting the unique exception to the rule. So what Leibniz has in view with infinite analyticity qualifies a perfectly intelligible idea, readily understandable on the basis of mathematical analogies. There is, in the end, no reason to think, with Couturat, of his being “confused and embarrassed” about it. NOTES 1

Couturat, Logique, pp. 212-13.

Chapter Six LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE 1. MODES OF ETERNAL RECURRENCE

I

n the extensive philosophical literature the Church Fathers devoted to the issue of “eternal recurrence,” three significant distinguishable ideas came to be conflated, namely: I.

eternal recommencement: the unending succession of destructions and re-creations of the world over an ongoing series of cosmic phrases or cycles of world annihilation and rebirth (palinigenesis).1

II. eternal recurrence: the unending reappearance of certain event-occurrence patterns as per Wagnerian Leitmotivs or recurrently served menus. (Partial apokatastasis) III. eternal repetition: the cyclic repetition at the cosmic level of exactly the same overall sequence of events, with cosmic history akin to a movie that is screened over and over again. (Total apokatastasis)2 We here propose to use the term eternal recurrence as an umbrella expression to cover various of these forms of the teaching (recommencement, repetition, realignment, and replay).3 An early version of the eternal recurrence idea was pervasive in antiquity since Babylonian times which contemplated a vast cosmic conflagration (ekpyrosis) in which the world was destroyed (apokalypsis) only to be reborn anew, re-arising like the mythic Phoenix from its own ashes. And the corresponding idea of all-comprehending cosmic cycle over which the world becomes dissolved and then starts again, has figured on the agenda of philosophy since the dawn of the sub-

Nicholas Rescher • Episodes

34

ject.4 Such a conception of palingenisis played a key role in the physical theory of the Stoics who (somewhat dubiously) ascribed its origin to Heraclitus,5 who had indeed mooted a cyclic process of reciprocal transformation: X to Y and then Y back to X: And it is the same thing in us that is quick and dead, awake and asleep, young and old; the former are shifted and become the latter, and the latter in turn are shifted and become the former. . . .The way up and the way down is one and the same . . . in the circumference of a circle the beginning and end are common.6

But of course this sort of cyclicity does not entail all-inclusive repetition, and it would certainly be problematic to ascribe this idea to Heraclitus.7 The phoenix-reminiscent cosmic conflagration contemplated by the Stoics was thought by them to have a purifying and refining effect (katharsis), setting the stage for the sequential rebirth of a new, fresh and as yet uncorrupted world.8 And building on this doctrine they added the conception of an at least partial apokatastasis, now subject to the idea that some of the same events, episodes, and even items would be repeated in the various phases of cosmic history. In antiquity the theory of eternal return had two forms (III 1) an astronomical version of a reconstitution of the positions of the celestial bodies (stars and planets) in a complete recurrence of astronomical alignments. Thus the term apokatastasis (restoration, reestablishment) was used by Aristotle9 in a general sense, it came to be employed specifically to denote a return of the stars and planets to the same Zodiacal positions as in the former year.10 And with Chrysippus and the Stoics it came to be yet more demandingly in relation to the idea of a cosmic Great Year—a cycle when all heavenly bodies returned once more to their original position in the heavens—a signal for academia cosmic conflagration (ekpyrosis) and the resumption of a new cosmic cycle.11 As the latter Stoics saw it, there was to be a complete, detailed repetition of everything, with world history enduring on a re-play of world history exactly in complete and exact detail. Thus even individuals such as Socrates or Plato will come to be realized again in the future of the cosmos.12 Accordingly, this mode of apokatastasis became

35

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

a quasi-theological doctrine designed to ensure immorality, albeit in this mundane world. (It thereby anticipated—albeit quite differently— the Christian idea of rebirth (annagenesis) and resurrection of the body.13) And the Stoics were not alone in endorsing total apokatastasis. For, as Lucretius put it in his great Epicurean poem, De rerum natura: When you look back at the whole vast expanse of past time and at how varied the motions of matter are, then you may easily understand that these very same atoms—the ones of which we are now composed— have often before been places in the order in which they now are. Cum respicias immensi temporis omne praeteritum spatium, tum motus materiai multimodis quam sint, facile hoc accredere possis, semina saepe in eodem, ut nunc sunt, ordine posta haec eadem, quibus e nunc nos sumus, ante fuisse. (De rerum natura, III, 854-58.)

In classical antiquity—and well beyond—the conviction was prominent that if there is only a limited number of modes of occurrence, then over time the same entire history of the world is bound to repeat itself over and over again in cyclic recurrence. The basic idea was: Ÿ Finite modes of occurrence +

Limitless time for occurrence

Ÿ

Eternal repetition as per III

This conception has its difficulties, however. To be sure, if you are dealing with integer groups of length n, then only 10n different groupings of length n are available to you. So within a series of length 10n + 1 there will have to be at least one repetition of some n-length grouping. And within a sufficiently larger series, there will have to be at least two repetitions of some length n group. So within an infinitely long series there will indeed have to be an infinite number of repetitions of some n-length grouping, irrespective of the (finite) size of n so that some occurrence sequence will have to recur infinitely often. There is bound to be partial apokatastasis. But there certainly need not be any total apokatastasis: not every item-grouping must recur infinitely often—let alone cyclically. And so the most that we obtain in contemplating an unending historical process is

Nicholas Rescher • Episodes

Finite modes of occurrence

+

Limitless time for occurrence

Ÿ

36

Eternal repetition as per II

From a cosmological standpoint—and certainly from a philosophical standpoint—the eternal return of total apokatastasis along strictly cyclical (“everything all over again”) lines is decidedly implausible. Friedrich Nietzsche wrote: The number of states, alterations, combinations, and developments of this [self-maintaining] force [in nature] is, to be sure, tremendously large and practically “immeasurable”, but in any case also determinate and not infinite . . . Consequently, the development of this very moment must be a repetition, and likewise the one that gave birth to it and the one that arises out of it and thus forward and backward further! Everything has been there countless times inasmuch as the total state of all forces always recurs.14

But, as just noted this reasoning is quite fallacious. The fact that there is going to be some “eternal recurrence” in the overall series does not mean that any given segment is going to repeat.15 Repetition does not entail cyclic periodicity. After all, even with very simple repetitive systems—even ones that are very small and far beneath nature’s complexity—cyclic repetition need not be realized. Consider three planets moving with uniform velocity in circular orbit around a common center, as per the following diagram: A B C

Let it be that A completes one orbit in 2 days, B one in two days, and C one in one day. Then B and C will recur to their indicted initial positions every N days whenever N is even. But at no time when N is even

37

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

will A ever again be aligned with B and C in those positions. Notwithstanding the simple periodicities at issues, the indicted A-B-C configuration just cannot recur.16 Those three planets will never recover their initial alignment.17 2. ETERNAL RECURRENCE WITHOUT ETERNAL RETURN The ancients were not alone in committing the fallacy of believing that the finitude of occurrence modes entail total (rather than merely partial) apokatastasis. Thus Henrich Heine wrote: For time is infinite, but the things in time, the concrete bodies, are finite. They may indeed disperse into the smallest particles; but these particles, the atoms, have their determinate number, and the number of the configurations that, all of themselves, are formed out of them is also determinate. Now, however long a time may pass, according to the eternal lay of repetition, all configurations that have previously existed on this earth must yet meet, attract, repulse, kiss, and corrupt each other again. . . . And thus it will happen one day that a man will be born again, just like me, and a woman will be born, just like Mary—only that it is to be hoped that the head of this man may contain a little less foolishness.18

And Friedrich Nietzsche, who dubbed himself “the teacher of eternal recurrence,” had his Zarathustra contemplate coming to terms with “the doctrine of the eternal recurrence, that is, of the unconditional and infinitely repeated circular course of all things”.19 The Stoic apokatastasis was transmuted by Nietzsche into a hallmark of the supraman who is up to accepting the terrifying Sisyphean challenge of having to relive life as was.20 As he saw it, “My formula for human greatness is an amor fati that wants nothing different—not forward, not backward, not in all eternity.”21 But there is no reason to adopt a doctrine of apokatastasis that makes this demand upon us. Nor is there any need to require it if all that Nietzsche wants is people who combine the Spinozistic recognition of accepting what happens as inevitable with the fortitude of ascending it as such. The problem that has bedeviled the discussion of world destruction and rebirth (palinigenesis) from early on is the idea that an unending

Nicholas Rescher • Episodes

38

series of world stages implies an endless succession of identical world cycles, with the same occurrences repeating themselves over and over again as successive replays of the same story. The tendency has been to think that paliningensis somehow entails total apokatastasis. But various lines of deliberation conjoin to show that this is deeply problematic. After all, cosmological models of cosmic return have been on the agenda for some time.22 The equations of Einstein’s general relativity certainly admit models of cosmic palingenesis, and the big bang/big crunch theory cashes in on this possibility.23 But of course nothing here enjoins the cyclic repetition of the same events of a total apokatastasis. 3. ENTER LEIBNIZ The major philosopher who has given the closest attention to the issue of eternal recurrence is G. W Leibniz. In 1693 he started a series of studies of issues of eternal recurrence with a draft that was submitted to the Académie des Sciences in Paris and sent to its president, the abbé Bignon. Developed under the heading of palingenesis and apokatastasis these studies afford a highly instructive insight about Leibniz’s view of the human condition in its cognitive aspects, and specifically with regard to the limits of human knowledge.24 For Leibniz, it is a salient aspect of cognitively capable beings that they are symbol users and that their knowledge of matters of fact (in contrast to their perceptual phenomenology and their performatory, how-to knowledge) is unavoidably mediated by language. Whatever we factually know can be put into words, and what is put into words can—in principle—be put into print. This circumstance reflects—and imposes—certain crucial limitations. As Leibniz had it: So since all human knowledge can be expressed by letters of the alphabet, and one can say that one who understands use of the alphabet perfectly knows everything, it follows that it would be possible to compute the number of truths accessible to us, and thereby determine the size of a work that could contain all possible human knowledge.25

39

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

After all, only a limited amount of material—number of letters— can be presented per page. So even someone who reads a goodly number of pages per day (Leibniz supposes 100), and who does so daily for a very long time (Leibniz assumed a Methuselah with 1,000 years!), will take on board only a limited amount of material (365 x 105) pages. And with a limited number of statements per page (strangely, Leibniz fixes this at 1) our avid reader will take on no more than a fixed number of informative contentions in his very long lifetime.26 Since any alphabet devisable by man will have only a limited number of letters (Leibniz here supposes 24), it transpires that even if we allow a word to become very long indeed (Leibniz supposes 32 letters) there will be only a limited number of words that can possibly be formed (namely 24 exp. 32). And so if we suppose a maximum to the number of words that an intelligible statement can contain (say 100) then there will be a limit to the number of potential “statements” that can possibly be made, namely 100 exp (24 exp 32).27 Even with an array of basic symbols different from those of the Latin alphabet the situation is changed in detail but not in structure. And this remains the case of the symbols at work at those of mathematics, where Descartes’ translation of geometrically pictorial propositions into algebraically articulated from stood before Leibniz’s mind, to say nothing of his own project of a universal language.28 With an alphabet of 24 letters, there are 24 exp n words of exactly n letters. Accordingly, the total number of “words” with up to (and including) n letters will be 24 + 242 + 243 + … + 24n This formula was effectively proposed by Fr. Paul Guldin in his 1622 study de rerum combinationibus29 It yields a sum that comes to (24n – 1) x (24 ÷ 23), though all practical purposes we can take this to be 24n, seeing that that the sum’s big final term will eventually preponderate. And so a language whose average sentence is W words long and which has w words at its disposal will offer (at best) some w exp W sentence-candidates. Most of this vast number of symbolic agglomerations will of course be meaningless—and most of the remainder false.

Nicholas Rescher • Episodes

40

But this does not alter the salient and fundamental fact that— astronomical though it may be—the amount of correct information that can be put into language is finite.30 And so, on the combinatorial approach projected by Leibniz, the number of books will be finite—albeit very large. Thus let it be—for example—that a book has 1000 pages of 100 lines each of which has 100 letters. Then such a megabook will have room for 107 letters. With 24 possibilities for each of them, there will be at best 24 exp (10 exp 7) possible books.31 No doubt it would take a vast amount of room to accommodate a library of this size.32 But it would clearly not require a space of Euclidean infinitude.33 Accordingly, as Leibniz sees it, we arrive at the crucial conclusion that as long as people manage their thinking in language—broadly understood to encompass symbolic devices at large—the thoughts that they can have—and a fortiori the things that they possibly can know— will be limited in number.34 4. LEIBNIZ ON LIMITS OF LANGUAGE AND COGNITIVE FINITUDE In his official duties at the courts of Hanover and Wolffenbuettel, Leibniz was a librarian (as indeed Kant was to be for a time in Koenigsberg). Books were a matter of lifelong interest to him. And even in the seventeenth century when—as we ourselves see it—the impact of Gutenberg’s great innovation had scarcely begun to make itself felt, Leibniz spoke of “cette horrible masse des livres qui va tousjours en augmentant”,35 lamenting “une infinité de mauvais livres qui etoufferont enfin les bons et nous ramèneront à la barbarie”.36 The relation of the world of print to the real world was of great interest to Leibniz. Given that our thought proceeds by means of language, the limitedness of what can be said enjoins corresponding limits upon what can be thought. Thus let it be that the thought-life of people consists of the propositions that they consider. And let us suppose that people consider propositions at about the same speed at which they read, say 100 pages per hour, with each page consisting of 20 sentences. Now supposing a thought-span of 16 waking hours on average, it will then

41

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

transpire that in the course of a year a person entertains a number of thought equal to: 365 x 16 x 100 x 20 ≅ 12 x 106 Subject to the hypotheses at issue, this is how much material we would need to restate the thought life of a person for an entire year, and a lifetime might encompass some 80 times that. Now while this is indeed a lot, the fact remains that there is only so much thinking that a person can do. And these limits of language mean that there are only so many thoughts to go around. Once again we are in the grip of finitude. (Moreover, this encompasses fiction as well—our knowledge of possibility is also finite and fiction is for us just as much language limited as is the domain of fact.) So if, over time, there is a sufficient number of people, there will have to be some whose thought-life is identical. Given the finitude of the sayable—and thereby of the knowable— there immediately arises a troubling question that Leibniz does not hesitate to confront, namely that of an eventual recurrence in the cognitive domain. For let us suppose that the universe has a limitless future and that in this limitless future intelligent beings (not necessarily humans) will have a part. Now if the number of things that can be said and thought is finite, then a point of repetition must inevitably be reached. There will inevitably come a juncture when the saying that there is nothing new under the sun will be literally true within the realm of what can be thought and said. And so let us imagine a scriptorium of chroniclers who, ever assiduous in scribbling, put on record all of observed events and occurrences of the year. Here too repetitions must eventually set in. In due course the descriptive domain of world events must literally repeat itself, item by item. For there is, clearly, only a finite number of ways to fill in a text of a given length with letters. Thus (Leibniz observes) if a mega-book has 10,000 pages each of 100 lines each of which have 100 letters, then there will be room for 108 letters. And within a fixed number of letters at our disposal, say 25—a blank space included— there will be 25 exp (10 exp 8) possible mega-books. To symbolize

Nicholas Rescher • Episodes

42

this (finite) number—the number of possible mega-books of this scale—Leibniz adopts the letter N. He then turns to the idea of a universal public history—a history which, town by town, country by country, describes in detail the world’s public affairs during a given year. Such a history will of course be vast in scope. It will occupy many mega-books of the sort described in the preceding paragraph, say n of them. But clearly whatever be the size of the quantities at issue, N/n will be some definite finite number. And so, if the history of human kind is long enough, there will be no way to avert some recurrence or a repetition in its affairs beyond that number of years.37 Assuming that mankind survives sufficiently long in its present condition, and that a history of its public affairs can be produced, it will become necessary to re-tell parts of earlier history in exactly the same terms.38

Recall, to begin with, Leibniz’s calculation of the limited number of biographies or diaries that can be written in a language. And now assuming (with Leibniz) that the number of persons alive during a given year to be fixed at so-many individuals, each of whom comes equipped with his or her own determinate “Diary” for the year, there will be a grand overall total of personal diaries constituting (as it were) the Annals of mankind for that year. This (astronomical) quantity Leibniz designates as Q. Accordingly, if the history of mankind is long enough then its years will eventually outrun Q and: There will eventually have to be a time when parts of written human history must repeat themselves.39 Accordingly, we do well to realize that there is a crucial parting of the ways between a finite mind like man’s and an infinite mind like that which theologians ascribe to God. Our thought is language-bound and our knowledge symbolically mediated. But God’s is not, being free from the alphabetic/symbolic/linearly linguistic modus operandi of our thought. Accordingly reality—the product of God’s thought—is infinitely more complex than what one can manage to discern and describe about it in our human terms of reference. And in consequence, the reality that God’s creativity engenders—the realm of fact, if you

43

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

will—is vastly more complex than anything that the finite intelligence of human knowledge is able to encompass and outruns whatever limits and limitations our discourse involves. Accordingly, while Wittgenstein may be right and the limits of our language may delineate the limits of OUR world—our thought-world, that is to say—they are not the limits of THE world. For there is more in heaven and on earth than is encompassed in the manifold of our thought and discourse. 5. LANGUAGE AND LIFE It also becomes a real prospect that language cannot keep up with people and their doings. Suppose that the Detailed Biography of a person is a minute-by-minute account of their doings, allocating (say) 10 printed lines to each minute and so roughly 15,000 lines per day to make up a hefty volume of 300 fifty-line pages. So if a paradigmatic individual lives 100 years we will need 365 x 100 or roughly 36,500 such hefty tomes to provide a comprehensive blow-by-blow account of his life. But, as we have seen, the number of such tomes, though vast, is limited. In consequence, there are only so many Detailed Biographies to go around, so that it transpires that the number of Detailed Biographies that is available is also finite. This, of course, means that: If the duration of the species were long enough, then there would have to be some people with exactly the same Detailed Biography. Moreover, it also means that: If in the vastness of the universe there exists a sufficiently large number of intelligent beings then there would have to be some individuals with exactly the same Detailed Biography. On this basis, even a universe that is massively sizeable in its spatio-temporal extent can accommodate only so much descriptive variety. Eventual repetitions became inevitable. And, viewed in reverse, this poses an interesting question, namely: How much would the spatio-temporal extent of the world have to be limited in order to avert descriptive redundancy: to allow, for example, each intelligent creature to have its own unique Detailed Biography with its personalized life history. This of course would depend crucially on the amount of descriptive detail that is inserted into those Detailed Biographies. If the descrip-

Nicholas Rescher • Episodes

44

tive detail is infinitely refined then there need be no limitation at all. The needed differentiation would be provided for by the Leibnizian Identity of Indiscernables (the differentness of the diverse.) And moving on from Biographies (or Diaries) to public Annals we find much the same general situation. Thus suppose that (as Leibniz has it) the world’s population is one hundred million (that is 108) and that each generation lives (on average) for 50 years, then in the 6,000 years during which (we may suppose) civilized man has existed, there have existed some 1.2 x 1010 people—or some 1010 of them if we suppose smaller generations in earlier times.40 Recall now the above-mentioned idea of 36,500 hefty tomes needed to characterize in detail the life of an individual. It then follows that we would need some 36.5 x 1013 of them for a complete history of the species. To be sure, we thus obtain an astronomically vast number of possible overall annals for mankind as a whole. But though vast, this number will nevertheless be finite. Moreover, if the history of the race is sufficiently long, then some part of its extensive history will have to repeat itself in full with a parfaite repetition mot pour mot since there are only so many possible accounts of a given day (or week or year). For once again there are only a finite number of possibilities to go around and somewhere along the line it will transpire that men will act anew during their whole life acting in the same way in which others have already (ut homines novi eadem ad sensum penitus tota vita agerent, quae alii jam egerunt).41 To be sure, it would be rather unrealistic to suppose that humankind will last forever. But of course the universe is vast, and it would be far less unrealistic to suppose that intelligent life will always find a foothold somewhere in its limitless vastness: “Denique etiamsi non semper duraturum sit quale nunc est genus humanum; modo tamen semper ponamus existere mentes veritatem cognoscentes et indagantes.”42 But even if two symbol complexes—two books of annals, say, are identical, can they not always be differentiated by their wider context? Yes and no. It depends on how large those contexts are going to be. If we go just one year out, that triennium is just one more fixed timespan whose history can be told in a trilogy of annals that is exactly in the same position as the original: annal trilogies are just as limited in

45

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

number as are annals. It is only when we allow their context to become indefinite (i.e., potentially infinite) is size that we escape the bounds of contextual finitude. (And indeed at this point we take the step into transdenumerability.43) 6. OVERBECK’S QUESTIONS AND THE UNTENABILITY OF CYCICITY Reacting to Leibniz’s thesis that there is only a limited number of distinct accounts (be they personal biographies or public annals) Leibniz’s correspondent, the mathematician Adolph Theobaldus Overbeck (d. 1719) asked him four questions:44 (1) Must every history occur with the same period? The answer is clearly negative even if there were only two histories the pattern of the occurrence might be: (A always so far), A, B-once, A, B-twice, A, B-thrice, etc. Given only finitely many event-kinds, there must be repetitions: some segments must recur time and again. But there need be nothing periodic about this. (Otherwise—as Leibniz rightly remarked, there would be no irrational numbers.45) (2) Must any given segment of history recur? Again the answer was negative. For as the previous example shows, the sequence ABA will never recur. Accordingly, particular segment—a given fixed series of events—need never repeat. (3) Must SOME segment of a fixed size eventuality recur? The answer is affirmative because there is only a limited, finite number of different segments of this size, so that in continuing a series indefinitely there will have to be ongoing resort to one or another of them. (But not to any one in particular!) (4) Can there always be SOME segment [of a fixed size n] that has never occurred before? Here the answer was negative because

Nicholas Rescher • Episodes

46

(once again) there are only so many possibilities for a length-n segment. Since length-n segments are at issue—and there are only so many types of these—there must come a point when these finite possibilities are exhausted. And after this point a repetition cannot be avoided. The crucial point to emerge from Leibniz’s handling of Overbeck’s question is that while there must indeed be some repetitions (redundancies) in personal or public chronicles—and massive repetitions at that—there need be no larger periodicities. Recurrence will indeed transpire, but no particular pattern of recurrence is mandated. And— above all—the finitude of constituents does not entail any sort of cyclic periodicity: repetition there must be, yet not only can it be partial, but it need not be circular or cyclic.46 In an infinite series there must be (infinitely many) repetitions of some such segment. But not of any particular segment. And what is repeated can be a mere “space filler” in an evolving situation of ever-changing patterns. 7. LEIBNIZ ON THE GULF BETWEEN LANGUAGE AND REALITY And so, as his discussion makes clear, what Leibniz has in view with his apokatastasis is merely a restricted unending recurrence and not any full-fledged cyclicity. The crux, with Leibniz, is that some sector of history of any given length must ongoingly recur, and not that every sector of history of some given length must ongoingly recur. The latter, Nietzschean mode of eternal recurrence is not what Leibniz had in view. It is not the case that the events of the present era will repeat “if only one waits long enough.” For the repetition at issue no more than a merely phenomenal product of human finitude, of our inability to derive fine details beneath a certain level. Reality as such (ontologically speaking) is infinitely complex, infinitely differentiated when something seemingly recourse there is always a difference between the old and the new, albeit one that lies beneath the threshold of cosmic perception (and only open to those minute petites perceptions of which Leibniz is so fond). Only when we proceed at the cruder level of consciously noted and propositionally formulated will those on-

47

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

tological differences vanish amidst an epistemic blur. Recurrence there must be for Leibniz, but it is always only a seeming recurrence that figures at the level of the epistemology of finite intellects, and not at the level of ontology. (For Leibniz, actual full-scale literal recurrence is ruled out by his Principle of the Identity of Indiscernables. Those historical repetitions are accordingly only repetitions for us as finite knowers. They are artifacts of our cognitive limitations of our limited access to detail. The crux here is the imperfection of linguistic description—its inability to capture reality’s detail. For what repeats is described reality and not experienced reality. To illustrate: if all one tells about the weather is • above freezing vs. below freezing • rising barometer vs. falling barometer • sunny skies vs. cloudy skies then one only has eight alternatives for meteorological descriptions at one’s disposal. Over the course of nine days there is destined to be at least one repetition. But, of course, as one introduces more descriptive categories, the longer the prospect of repetition can be postponed. And as one moves on towards realty’s unending variability the prospect of repetition invariably vanishes. With Leibniz, order, simplicity, repetitiveness are substantially phenomena of oversimplification. Ontologically (for Reality) and theologically (for God) there is and can be no repetition. Everything that exists is unique. And so, as Leibniz saw it, the salient consideration lies in the essential finitude of human cognition and the continuity-infinitude of reality and God’s knowledge of it.47 The gap between the finite and the numberless infinite is as large as any gap can possibly be. And this gap is something we cannot possibly cross in operational fact but only in analogy. And the analogy at our disposal is that afforded by the differential and integral calculus. Overall, then, Leibniz held that homo sapiens thinks symbolically, and that the limited resources at our disposal make for an oversimplification in the representation of reality with the result that—if human

Nicholas Rescher • Episodes

48

thought continued indefinitely—repetition would become unavoidable. But such apokatastasis is an artifact lf human finitude—a product of man’s epistemic limitation and not a reflection of limited complexity in the ontological constitution of the real.48 * * * Much of the philosophical interest of eternal recurrence speculation lies in the idea that repetition carries an ethical challenge. Kant somewhere says that a rational individual would not want to live this life over and over again exactly as was. And his contemporary Benjamin Franklin acknowledges that given the chance he would correct various errata in his life. Idealists insist that we should so at that what we do now is what we would want anyone to do in the circumstances—our future selves included. One need not accept eternal recurrence as a world-descriptive fact to recognize that the very idea of this phenomenon can provide an interesting tool for thoughtful reflection. References Borges, Jorge Luis, El jardin de los senderos que se bifurcan (Buenos Aires: Sur, 1941). Burnet, John, Early Greek Philosophy (London: A. and C. Black, 1892). Ettlinger, Max W. (ed. and trans.), Apokatastaseôs pantôn an appendix to Leibniz als Geschichtsphilosoph (Munich: Koesel & Puslet, 1921). Fichant, Michael, G. W. Leibniz, De l’horizon de la doctrine humaine (Paris: Vrin, 1991). Halab, L. J., Nietzsche’s Life Sentence: Coming to Terms with Eternal Recurrence (London: Routledge, 2005).

49

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

Heidegger, Martin, Nietzsche: The Eternal Recurrence of the Same (tr. D. F. Krell (San Francisco: Harper & Row, 1984). Huebener, Wolfgang, “Die notwendige Grenze des Erkenntnisfortschritts als Konsequenz der Aussagenkombinatorik nach Leibniz’ unveroeffentlichem Traktat ‘De l’horizon de la doctrine humaine’,” Studia Leibnitiana Supplementa, vol. 15 (1975), pp. 55-71 (see pp. 62-63). Kaufmann, Walter, Nietzsche,Philosopher, Psycholigist, Antichrist (Princeton, NJ: Princeton University Press, 1974). Knobloch, Eberhard, Die mathematischen Studien von G. W. Leibnitz zur Kombinatorik (Wiesbaden, F. Steiner, 1973). Loewith, Karl, Nietzche’s Philosophy of the Eternal Recurrence of the Same (Berkeley and Los Angeles: University of California Press, 1997). Lukacher, Ned, Time-fetishes: The Secret History of Eternal Recurrence (Durham, NC: Duke University Press, 1998). Moles, Alistair, “Nietzsche's Eternal Recurrence as Riemannian Cosmology,” International Studies in Philosophy, vol. 2 (1989), pp. 21-35. Rey, Abel, Le retour éternel et la philosophie de la physique (Paris, Flammarion, 1921). Rutherford, Donald, Leibniz and the Rational Order of Nature (Cambridge: Cambridge University Press, 1995). Simmel, Georg, Schopenhauer und Nietzsche, Ein Vortragszyklus (Leipzig: Duncker & Humblot, 1967). Wilson, Catherine, Leibniz’s Metaphysics (Princeton, Princeton University Press, 1989).

Nicholas Rescher • Episodes

50

NOTES 1

A convenient entry into the extensive literature can be obtained from the Historisches Woerterbuch der Philosophie, svv. wiererkunft, ewige; palingenisis, apokatastasis; The terms go back to Plato’s idea of a great “cosmic year” for the positional recurrence of the heavenly bodies and figures in the pseudo-Platonic dialogue Axiochus (370B). The term is also biblical, occurring at Acts 3:21. In its later, theological sense, apokatastasis relates to Origen’s doctrine of the ultimate restoration of all men to friendship with God (a teaching sharply opposed by St. Augustine and ultimately declared anathema at the Council of Constantinople in 543). The theologian Johann Wilhelm Petersen (d. 1727) had published a treatise Mysterion apokatastaseôs pantôn which, as Leibniz wrote to Fabricius, he read soon after its publication with pleasure and profit (cum voluntate et fructu).[See Kortholt (Ravier Nr. 394), p. 116. (=Deutens, Vol. V, p. 278).] Leibniz contributed an extensive overview of the book to Eckhardt’s Monathlichen Auszug, in its issue of April 1701 (pp. 1-37). (An abstract of this review is given in Guhrauer, Leibniz’ Deutsche Schriften, vol. II, pp. 342-47.

2

On eternal recurrence in Stoic thought see Max Polenz, Die Stoa, 2 vol.’s (Göttingen: Vanderhoeck & Reprecht, 1964).

3

Many stories and films have been based on the idea of ongoing recurrence—the 1993 comedy “Groundhog Day” staring Bill Murray and the 2009 horror film “Triangle,” for example. (The Wikipedia article on “Eternal return” registers a plethora of other examples.

4

See John Burnet Early Greek Philosophy (London: A. and C. Black, 1892), pp. 156-163, and more generally Ned Lukacher, Time-fetishes: The Secret History of Eternal Recurrence (Durham, NC: Duke University Press, 1998).

5

On Heraclitus see Diogenes Laertuis IX, 9.

6

Fragment 78, 69, 70 (Bywater), tr. Burnet, Early Greek Philosophy (London: Macmillan, 1892), pp. 138-139.

7

Fragments 41-42 (Bywater); see Burnet, p. 136.

8

See Stoicorum Veterorum Fragmenta, Vol. II, pp. 598 and 606.

9

Aristotle, Magna Moralia, II, vii, 12.

10

Liddell Scott, Greek Lexicon.

11

The Stoic teaching of apokatastasis had been anticipated by the Pythagorean Eudenus of Rhodes. See Diels/Kranz, Die Fragmente der Vorsokratiker 58B34.

51

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

NOTES

Moreover, the Stoic idea of an inevitable reduplication in infinite time mirrors the earlier atomistic idea of an inevitable reduplication in infinite spatial reduplication of this world in an infinite manifold of other alternatives. See J. Warren, “Ancient Atomism and the Plurality of Worlds,” Classical Quarterly, vol. 54 (2004), pp. 354-70. 12

Stoicorum Veterorum Fragmenta, Vol. II, pp.184, 190, 625.

13

Acts 3:21 speaks of the “time of restitution of all things (apokatastasis tôn pantôn), which God has spoken by the mouth of all his holy prophets since the world began.” With the Church Fathers such a new world order was not to be a recovery of the status quo ante, but a second coming of Jesus issuing in a time “when all free creatures will share in the grace of salvation” (The Catholic Encyclopedia, s.v. apokatastasis). Matthew 19:28 describes Jesus as characterizing the Last Judgment as a palingenesia. And some church fathers took a position close to that of the Stoics. Thus origin envisioned a restitutio universalis. See Walter Stohmann, Überblick über die Geschichte des Gedankens der ewigen Wiederkunft (München, Kastner, 1917).

14

Nietzsche’s Werke, Grossoktav edition (Hamburg: Felix Meiner, 1986), Vol. XII, p. 51 (italics supplied). Nietzsche’s argumentation would plausibly engender its intended conclusion only for a universe of finite variety and pure chance. Martin Heidegger’s Nietzsche: The Eternal Recurrence of the Same, tr. D. F. Krell (San Francisco: Harper & Row, 1984) does not address the issue as such and is really an exposition of Heidegger than Nietzsche.

15

To be sure, in a series of finitely many states driven by pure chance any particular segment of n states is effectively certain to recur sooner or later. But this of course has no bearing on Leibniz’s very different position where pure chance is not an issue. For a study of the relevant scientific issues see Abel Rey, le retour éternel et la philosophie de la physique (Paris, Flammarion, 1921).

16

A more general argument to this conclusion was initially presented by Georg Simmel, Schopenhauer und Nietzsche, Ein Vortragszyklus (Leipzig: Duncker & Humblot, 1967), pp. 250-51.

17

The eminent French mathematician Henri Poincaré proved that a spatially bounded dynamical system must over a sufficiently long time return to within an arbitrarily small neighborhood of its initial state. Accordingly, within the range of physical situations envisioned by Poincaré, recurrence to within a close approximation is inevitable. But of course a near miss comes to “close but no cigar,” as the saying has it. In a world of operative chaos, even a diminishingly minute difference in situation can engender a massive difference in ultimate effect.

Nicholas Rescher • Episodes

52

NOTES 18

Quoted in Kaufmann, p. 318.

19

Quoted in Kaufmann, p. 317. See David F. Krell, Nietzsche’s The Eternal Recurrence of the Same (San Francisco: Harper & Row, 1979). In his Ecce Homo (1888), Nietzsche said that he regarded eternal return as “the fundamental conception” of Thus Spake Zarathustra. On these issues see Bernard Magnus, Nietzsche’s Existential Imperative (Bloomington: Indiana University Press, 1978).

20

Bertrand Russell says in his Autobiography that he would be glad to live life over again on the same terms. Immanuel Kant, by contrast, thought that a rational man would recoil with horror from the challenge of reliving his life as was.

21

Cited in Will Dudley, Hegel, Nietzsche, and Philosophy: Thinking Freedom (Cambridge: Cambridge University Press, 2002), p. 201. L. J. Halab, Nietzsche’s Life Sentence: Coming to Terms with Eternal Recurrence (London: Routledge, 2005) offers relevant deliberations.

22

See Abel Rey, Le Retour éternel et la philosophie de la physique (Paris: Flammarion 1927).

23

See also A. Moles “Nietzsche’s Eternal Occurrence as Riemannian’s Cosmology,” International Studies in Philosophy, vol. 2 (1989), pp. 21-35. And compare the reply by G. J. Stack, ibid., pp. 37-40.

24

Leibniz’s tract Apokatastaseôs pantôn was originally published (and translated) by Max W. Ettlinger, Leibniz als Geschichtsphilosoph (Munich: Koesel & Puslet, 1921). For an ampler treatment see G. W. Leibniz, De l’horizon de le doctrine humain, ed. by Michel Fichant (Paris: Vrin, 1991). This work assembles the relevant texts and provides valuable explanatory and bibliographic material. See also “Leibniz on the Limits of Human Knowledge,” ed. by Philip Beeley, The Leibniz Review, vol. 13 (2003), pp. 93-97.

25

Or puisque toutes les connaissances humaines se peuvent exprimer par les letters de l’Alphabet, et qu’on peut dire que celuy qui entend parfaitement l’usage de l’alphabet, sçait tout; il s’en suit, qu’on pourra calculer le nombre des verités dont les hommes sont capables et qu’on peut determiner la grandeur d’un ouvrage qui contiendroit toutes les connaissances humaines possibles. Louis Couturat, Opucules et fragments inédits de Leibniz (Paris: Alcan, 1903), p. 532.

26

Leibniz, De l’horizon, pp. 51-52.

27

Ibid., p. 44. By a somewhat different route Leibniz arrives at 10 exp (73 x 10 exp 10) as an upper limit. (See COF 96). This perspective requires the decomposition of larger textual complexes into their constituted units. Leibniz is of course perfect-

53

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

NOTES

ly aware that individual sentences can always be combined into longer units by conjunction, so that an entire book can be recast as a single megasentence and indeed totius seculi Historia pro magno aliquo dicto haberi potest. (See LH IV, Vol. V, Sect. 9, folios 4 recto and 7 recto). But even though Leibniz contemplates the prospect of superlong sentences (as per Huebener 1975, p. 59) the overall structure of the situation remains unchanged. 28

For details see Louis Couturat La Logique de Leibniz (Paris: Alcan, 1901).

29

In the generation before Leibniz, Fr. Paul Guldin had published (in 1622) a study de rerum combinationibus. Anticipating Leibniz, Guldin goes on to compute the number of different possible 1000 page books, the number of libraries needed to house them all, and the size of the terrain needed to hold all of these, which would exceed the whole of Europe. He states that the pages of these books would paper a path stretching not only around the earth but reaching far into the heavens: viam ostendimus qua itur ad Astras (Cited by M. Fichant in De l’horizon, pp. 136-38.)

30

Fichant, op. cit., p. 44.

31

Ibid., pp. 146-48. (Leibniz’s own sample calculation uses somewhat different numbers.) Leibniz further notes that with an alphabet of 100 letters the totality of such available statements would be 10 exp (73 x 10 exp 11), and comments that with 20,000 scribes it would require some 37 years to write out this number in full, if each scribe annually filled 1,000 pages with 10,000 digits each, and further that printing this number would take some two years with 1,000 printing presses each daily printing 1,000 pages. (Knobloch, Die mathematischen Studien von G. W. Leibnitz zur Kombinatorik, 1973, p. 88.)

32

Overbeck (op. cit., p. 93) notes that the number of grains of sand in the world— which Archimedes had put at 10 exp 50—is very small potatoes in comparison. The Sand-Reckoner of Archimedes, the grandfather of all studies of large numbers, introduces the idea of successively large ordains of magnitude via the relationship en = 10 exp (8n). Archimedes sees the diameter of the sphere of the fixed stars no greater than 10 exp 10 stadia and, on this basis states that the cosmos would be filled by 1000 e7 = 1050 grains of sand. See T. L. Heath, The Works of Archimedes (Cambridge: Cambridge University Press, 1897).

33

Leibniz, De l’horizon, p. 61.

34

On Leibniz’s studies of combinational mathematics see Eberhard Knobloch, “The Mathematical Studies of G. W. Leibniz on Combinatorics,” Historica Mathematica, vol. 1 (1974), pp. 409-30, as well as his Die methematischen Studien von G. W. Leibniz zur Kombinatorik, Studia Leibnitiana Supplementa, Vol. XI [Wiesbaden, Franz Steiner Verlag, 1973].

Nicholas Rescher • Episodes

54

NOTES 35

C. I. Gerhardt, Die philosophische Schriften von G. W. Leibniz, Vol. VII (Berlin: Wiedmann, 1875-1890.)

36

Klopp 10,17. Leibniz characterizes the world of print as “a vast ocean in which … the curiosity of mankind will finally be drowned. For if people continue to print books with such facility, someday neither the houses nor the streets will suffice for libraries, and indeed hardly whole cities.” (Annales imperii, Ann. 949 §16 [Ed H. Pertz,] Vol. II (1845), p. 575).

37

Leibniz, De l’horizon, pp. 67-68.

38

Ibid., p. 68. Compare “Si genus humanum in statu qualis nunc est per annos plus quam duret, necesse est redire prior annales Historias” (ibid., pp. 62-63). It might seem that Leibniz wishes his own discussion to illustrate the point.

39

Ibid., p. 71.

40

Leibniz, De l’horizon, p. 112.

41

Ibid., p. 54.

42

Ibid., p. 74.

43

The number of infinite sequences of finitely many symbols—say 0’s and 1’s—is of the cardinality of the reals. Such sequences cannot be completely enumerated because there will always be a missing entry that should be in the list but cannot be there because it differs from the i-th entry at the i-th place.

44

Leibniz, De l’horizon, pp. 89 ff.

45

Leibniz, De l’horizon, p. 89.

46

Nietzsche commentators seem to lose sight on this qualification. See, for example, Karl Loewith’s Nietzche’s Philosophy of the Eternal Recurrence of the Same (Berkeley and Los Angeles: University of California Press, 1997), pp. 89-91. See the Appendix.

47

“The proper comprehension of individual substances is impossible for the created mind because they involve the infinite. For this reason it is not possible to provide a perfect explanation (perfecta ratio) of the things in the universe. (Notes on Toland’s De Christianismo mysteriis, Dutens, Vol. V, p. 147.)

55

LEIBNIZ AND ISSUES OF ETERNAL RECURRENCE

NOTES 48

The deliberations regarding Leibniz borrow from my article “Coordinating Epistemology and Ontology in Leibniz,” in my Studies in Leibniz’s Cosmology (Frankfurt: ONTOS Verlag, 2006).

Chapter Seven LEIBNIZ CROSSES THE ATLANTIC

I

n 1967 Kurt Müller published a comprehensive survey of the Leibniz literature.1 It is striking that in this inventory of some 3400 items, no more than a handful issued from North America. It will seem unbelievable to contemporary North American Leibnizians that one can count on one’s digits the North American scholars who had published in Leibniz in the period up to 1956 when L. E. Loemker’s monumental English-language Leibniz anthology first appeared.2 The earliest American Leibniz publications are shrouded in mystery. The Gentleman’s Magazine published over four of its 1852 issues as long articles on Leibniz, and the Atlantic Monthly in its second volume (1858, pp. 14-32) included an informative and remarkably well-informed account of Leibniz’s philosophy in the light of recent publications. Both publications were anonymous. Much credit for getting Leibniz studies under way in America belongs to the Germanophile circle that formed in St. Louis in the postCivil War era, in particular to the group that centered around William Torrey Harris and the Journal of Speculative Philosophy founded by him in 1867. William Torrey Harris (1835-1909) was a professional educator, who served as Superintendent of Schools in St. Louis (1868-80) and subsequently as U.S. Commissioner of Education. He strongly fostered the interest in German culture on the part of many liberals who had emigrated to St. Louis after the 1848 repression at home, and was a leading light of the St. Louis Philosophical Society. In 1867 he established the Journal of Speculative Philosophy, the first American philosophical journal, which he edited until 1893. Several of the earliest American Leibniz scholars published in this journal. St. Louis’s “last hurrah” in this context occurred in the Congress of Arts and Sciences of the Universal Exposition of 1904, which brought to the city an array of the best philosophical minds of the era. Considering the prominence of Protestant clergy and seminaries in early higher education in the U.S.A. it is fitting that the North American Leibniz publication issued from such a source. Frederic Henry

Nicholas Rescher • Philosophical Episodes

58

Hedge, D. D. (1805-1890) was a Unitarian minister and transcendentalist theologian who wrote extensively on religious topics.3 A Harvard graduate of the class of 1861 he worked for many years as director of various important New England libraries. He translated much German literature and was also an assiduous hymalist, providing the now-standard translation of Luther’s “A Mighty Fortress is our God.” He also published a translation of Leibniz’s “Monadology” in the Journal of Speculative Philosophy (vol. 1, 1867, pp. 129-37), the first rendering of this work into English.4 A. E. Kroeger (1837-82) was a North American transplant. Born in Germany in 1837, he emigrated to the U.S. with his family in the revolutionary year of 1848. He served in the Civil War as an adjudant on the staff of General John C. Fremont. After the war he settled in St. Louis where he eventually became city treasurer. An indefatigable student of German philosophy, he translated both Fichte’s Science of Rights and Science of Knowledge,5 as well as various works of German literature. Kroeger also published translations of several of Leibniz’s essays: • “Considerations on the Doctrine of a Universal Spirit,” Journal of Speculative Philosophy, vol. 5 (1871), pp. 118-29. • “New System of Nature,” Journal of Speculative Philosophy, vol. 5 (1871), pp. 209-19. • “Leibniz’s Theodicy, [‘Abridgement of the Controversy Reduced to Formal Arguments’],” Journal of Speculative Philosophy, vol. 7 (1873), pp. 30-42. In 1869 Kroeger published in The North American Review (vol. 108, 1869, pp. 1-37) a substantial overview of recent publications by and about Leibniz, including both Guhrauer’s biography and Erdmann’s edition of Opera philosophica. This 30-plus page review, both informative and scholarly, qualifies as the first significant American contribution to Leibniz scholarship. [[Atlantic Monthly 1860.]] Thomas Davidson (1840-1900) was born and educated in Scotland. He moved to Canada in 1866, and subsequently resettled in St. Louis

59

LEIBNIZ CROSSES THE ATLANTIC

as a high-school classics teacher. He travelled extensively in Europe and devoted much effort to promoting the thought of Antonio Rosmini. Davidson developed a pantheistic theology that was greatly influenced by Leibniz’s Monadology, and during his American years published two Leibniz translations: • “Leibniz on the Nature of the Soul,” Journal of Speculative Philosophy, vol. 2 (1868), pp. 62-64. [Tr. of a letter to Wagner.] • “Leibniz on Platonic Enthusiasm,” Journal of Speculative Philosophy, vol. 3 (1869), pp. 88-93. [Tr. of a letter to Hansch.] George Martin Duncan (1857-1928) was trained at Yale and became Professor of Logic and Metaphysics there. In 1890 he published a useful collection of Leibniz papers ambitiously entitled G. W. Leibniz: Philosophical Works (New Haven: Yale University Press; 2nd ed. 1908). A work of over 350 pages, it included explanatory notes and useful bibliographic material. Overall, it first gave to English readers a fairly extensive conspectus of Leibnizian philosophy. Beyond other, non-Leibnizian publications, Duncan also wrote an extensive review of Bertrand Russell’s “Critical Exposition of the Philosophy of Leibniz” in the Philosophical Review, vol. 10 (1901), pp. 288-97; and of Louis Couturat’s La logique de Leibniz, ibid, vol. 12 (1903), pp. 64964. An important impetus to American Leibniz studies was provided by the Open Court circle that formed around Edward Hegeler, whose eponymous publishing firm launched The Monist in La Salle, Illinois in 1890. Hegeler (1835-1910) was an industrialist who, having made a fortune in the manufacture of zinc, devoted much money and effort to the study of thought regarding religion and philosophy—especially of Germanic provenience. Paul Carus (1852-1919), Hegeler’s Germanborn son-in-law, who came to the U.S. in 1884, became managing editor of the Open Court Publishing Company founded by Hegeler in 1887. From 1890 to 1919 Carus edited its philosophical journal, The Monist. With its interest in the liberal religion—Carus devised a “cosmic religion” theology—this journal has a broadly open-minded

Nicholas Rescher • Philosophical Episodes

60

approach to philosophy and took a special interest in German thought, Leibniz included. Alfred Gideon Langley’s translation of the New Essays published by The Open Court in 1896 was a substantial American contribution to Leibniz scholarship.6 Langley (1855-1927) took his BA and MA degrees at Brown University and remained there for many years as a Professor of Philosophy. Substantial parts of his New Essays translation were published in advance installments: • “Leibniz’s Critique of Locke,” Journal of Speculative Philosophy, vol. 19 (1885), pp. 275-99. [Nouveaux Essaies, Preface, and Bk. I, Ch. 1.] • “Leibniz’s Critique of Locke,” Journal of Speculative Philosophy, vol. 21 (1887), pp. 268-88. [Nouveaux Essaies, Bk. I, Chs. 2-3.] • “Leibniz’s Critique of Locke,” Journal of Speculative Philosophy, vol. 21 (1887), pp. 337-49. [Nouveaux Essaies, Bk. II, Chs. 1-2.] Though reviled by the subsequent translators of this work, Langley’s rendition of the Essays was adequate for many purposes, and came usefully equipped with appendices of relevant material as well as extensive indices. While Langley published little apart from his New Essays edition, he did write a substantial and yet unpublished biographical essay on E. G. Robinson, another Brown philosopher, who served as President there during 1872-89. Langley’s translation of the New Essays was followed by another Open Court publication in the translation by George R. Montgomery (1858- ca.1930 ) of the Discourse in Method together with the subsequent Arnauld correspondence, also published by the Carus Publishing Company (in 1902). Montgomery, a Yale Ph.D. and author of a well-received book on The Place of Values7 was for many years a member of the Yale Philosophy Department. He published nothing else on Leibniz, and his translation was in some ways imperfect. It was, however, reissued in 1924 with improvements by A. R. Chan-

61

LEIBNIZ CROSSES THE ATLANTIC

dler, who was philosophy professor and department chair at Ohio State University. Further interest in Leibniz at the Open Court publishing operation is represented by the special issue devoted by The Monist in 1916 to the celebration of the 200th anniversary of Leibniz’s death (vol. 26, no. 4).The aspects of this publication relevant to our present concerns will be noted below. Herbert Wildon Carr (1857-1931) was born in London. He had a virtually complete academic career in the UK, culminating as professor of philosophy at the University of London in 1918. However, after his retirement in 1925 he launched into a second career at the University of Southern California, even being president of the American Philosophical Association’s Pacific Division in 1928. He brought to the USA a longstanding interest in the philosophy of Leibniz, and published two books on the subject during his American phase: • Leibniz (London: Benn, 1929). • The Monadology of Leibniz: With an Introduction, Commentary, and Supplementary Essay (Los Angeles: USC Press, 1930). Carr also published several Leibnizian articles during this period, including: • The Reform of the Leibnizian Monadology,” The Journal of Philosophy, vol. 23 (1926), pp. 68-77. • “The Scientific Concept of Rationality: Leibniz and Newton,” The Personalist (Los Angeles), vol. 16 (1935), pp. 241-98. John Dewey (1859-1952) needs no introduction. One of his earliest—and least known—professional publications was: Leibniz’s New Essays Concerning the Human Understanding: A Critical Exposition (Chicago: S. C. Griggs & Co. 1888).8 In the Preface of this substantial work (of well over 160 printed pages), Dewey wrote: “I have also endeavored to keep in mind, throughout, Leibniz’s relations to Locke’s modes of thought and to show the Nouveaux Essais as typical of the

Nicholas Rescher • Philosophical Episodes

62

distinction between characteristic British and German thought.” The work was already announced in an 1881 prospectus for a new series of “German Philosophical Classics for English Readers and Students under the general editorial supervision of George S. Morris”9 in a prospectus printed in the Journal of Speculative Philosophy (Vol. XV, 1881, p. 323-24). Dewey’s Book is an impressive example of conscientious scholarship, especially considering that it was written before the publication of Langley’s annotated translation of the New Essays. Florian Cajori (1859-1930) was a prolific and able historian of mathematics. Born in Switzerland, he emigrated to the U.S. at the age of 16 and earned a Ph.D. at Tulane University. In 1918 he took up a specially created chair in the history of mathematics as the University of California, Berkeley where he remained for the rest of his life. Work on his informative multi-volume History of Mathematical Notations, led him into extensive dealings with Leibniz and he published numerous articles on his mathematical work. He also contributed an essay to The Monist’s Leibniz memorial volume: “Leibniz’s Image of Creation,” The Monist, vol. 26 (1916), pp. 557-76. Arthur O. Lovejoy (1873-1962), the Berlin-born son of an American clergyman, was trained at Harvard (M.A. 1897) and had a long academic career teaching philosophy at Johns Hopkins. A founder or the History of Ideas movement, he published in 1936 his widely appreciated The Great Chain of Being, based on his 1933 William James Lectures at Harvard. In this work, Leibniz—and in particular his ideas on plenitude and sufficient reason—played a prominent role. Wilmon H. Sheldon (1875-1981) taught philosophy for many years, first at Dartmouth and then at Yale. A prolific writer, he took a special interest in the ways of philosophical divisions and dualisms. He contributed an essay on “Leibniz’s Message to Us,” to the anniversary volume for Leibniz in the Journal of the History of Ideas (vol. 7 [1946], pp. 385-96). T. Stearns (or T. S. for short) Eliot (1888-1965) needs no introduction here. Born in Missouri he was educated at Harvard, the Sorbonne, and Oxford. While still working on a Ph.D. dissertation for Harvard, Eliot settled in Britain in 1914 and lived there for the rest of his life. Before cutting his academic ties to the U.S., Eliot contributed two essays to The Monist’s 1916 anniversary issue “The Development of

63

LEIBNIZ CROSSES THE ATLANTIC

Leibniz’s Monadism,” the Monist, vol. 26 (1916), pp. 534-57; and “Leibniz’s Monads and Bradley’s Finite Centers,” The Monist, vol. 26 (1916), pp. 566-576. Paul Schrecker (1889-1963) was born in Vienna and educated at the universities of Vienna and Berlin. In the 1930’s he worked on the Berlin Academy’s Leibniz edition. Refugeeing from Germany in the Nazi era—initially to France—he arrived in the U.S.A. in 1940. He taught philosophy at the News School (1941-46), Columbia University (1946-48), Bryn Mawr (1948-50), and the University of Pennsylvania (1950-1960). During his American years he published in France a collection of Leibnizian papers: Opuscules philosophiques choisis (Paris: Hatier-Boivin, 1954; 2nd ed. 1962). During his American period, Schrecker also published various studies on Leibnizian themes: • “Descartes and Leibniz in 1947” In their 350th and 300th Birthdays,” Philosophy, vol. 21 (1946). Pp. 205-33. • “Leibniz’s Principles of International Justice,” Journal of the History of Ideas, vol. 7 (1946), pp. 484-98. • “Leibniz and the Art of Inventing Algorithms,” Journal of the History of Ideas, vol. 8 (1947), pp. 107-16. • “Leibniz and the Timaeus,” Revue de métaphysique, vol. 4 (1951), pp. 495-505. • “Qui me non nisi editis novit, non novit,” The Library Chronicle (Philadelphia: University of Pennsylvania), vol. 20 (1954), pp. 24-31. • “Leibniz,” in Raymond Klibansky (ed.), Philosophy in MidCentury: A Survey, Vol. IV (Firenze: La Nuova Italia Editrice, 1959), pp. 142-46. Schrecker was instrumental in securing for the University of Pennsylvania Library a photocopy of the manuscript material of Leibniz’s Nachlass in Hanover’s Nethean Saxon State Library, which had fortu-

Nicholas Rescher • Philosophical Episodes

64

nately survived the war. (A copy of this material also went to U.C.L.A. via the good offices of R. M. Yost.) F. S. C. Northrop (1893-1992) took his Ph.D. in philosophy at Harvard in 1924 and then taught for many years at Yale University, chairing its philosophy department in 1938-40, and serving as Master of Silliman College during 1940-47. A highly prolific and many-sided philosopher, Northrop published a dozen books and countless articles. Among the latter was a piece on “Leibniz’s Theory of Space” in the Leibniz Tercentenary Issue of the Journal of the History of Ideas, vol. 7 (1946), pp. 422-446. Charles Hartshorne (1979-2001) was an amazingly versatile and productive American philosopher who taught for many years at several major universities (Harvard, Chicago, Emory, and Texas). A mainstay of American pragmatism and process philosophy, he also made major contributions to the 20th Century theological speculation. He contributed an essay on “Leibniz’s Greatest Discovery” to the 300 anniversary volume of the Journal of the History of Ideas (vol. 7 [1946] pp. 411-21). John Nason (1905-2001) graduated in philosophy from Carleton College and became a Rhodes Scholar, subsequently teaching at Swathmore College. A born administrator, he served as President of Swathmore from 1940-53, as president of the Foreign Policy Association from 1953 to 1962, and as president of Carleton College from 1962-1970. His philosophical studies led Nason to an interest in Leibniz and he published an article on the subject: “Leibniz and the Logical Argument for Individual Substances,” Mind, vol. 51 (1942), pp. 201-222 He also contributed an article on “Leibniz’s Attack on the Cartesian Doctrine of Extension,” in the Leibniz tercentenary issue of the Journal of the History of Ideas (vol. 7, 1946, pp. 447-83). Raymond Klibansky (1905-2005) another European refugee, and for many years professor of Philosophy at McGill University, published an essay on “Leibniz’s Unknown Correspondence with English Scholars and Men of Letters,” Medieval and Renaissance Studies, vol. 1 (1941), pp. 133-49. Philip Paul Wiener (1906-1992), was a native New Yorker who was a professor of philosophy at City College of New York from 1933 to 1968, and then taught at Temple University in Philadelphia from

65

LEIBNIZ CROSSES THE ATLANTIC

1968 until his retirement. A devoted adherent to the history-of-ideas movement, he published a “Note on Leibniz’s Conception of Logic and its Historical Context,” in the Philosophical Review, vol. 48 (1939), pp. 567-86, and “Leibniz’s Project of a Public Exhibition of Scientific Inventions,” Journal of the History of Ideas, vol. 1 (1940), pp. 232-240. He also edited Leibniz: Selections (New York: Scribner’s, 1951), an anthology for students. Robert Morris Yost (1917-1990) was a native Los Angelino who earned his Ph.D. at the University of California, Los Angeles where he taught until his retirement in 1982. In 1954 he published his (revised) doctoral dissertation on Leibniz under the title Leibniz and Philosophical Analysis (Berkeley and Los Angeles: University of California Press, 1954), arguing that what may look as metaphysical speculation in Leibniz might more correctly be classed as philosophical analysis. Yost never published further on Leibniz, but he was instrumental in also securing for his university’s library a photocopy of the Leibniz MSs in Hannover. Donald F. Lach (1917-2000) was born in Pittsburgh and, after earning his Ph.D. in history at the University of Chicago, became Professor of Modern History there, specializing in the relations between China and the West. His multi-volume series in Asia in the Making of Europe was a monumental scholarship. His other Leibnizian publications include “Leibniz and China,” Journal of the History of Ideas, vol. 6 (1945), pp. 436-55; and G. W. Leibniz: Novissima Sinica— Commentary, Translation, Text (Honolulu: University of Hawaii Press, 1957). Nicholas Rescher (1928- ) was another transatlantic transplant, arriving in the U.S. from Germany at the age of ten in 1938. He had become interested in Leibniz via Bertrand Russell’s book even before writing his Princeton doctoral dissertation on Leibniz’s cosmology during 1949-51.10 In the early 1950s he published several studies on Leibnizian themes, and in subsequent years did a good deal of further work on Leibniz.11 It is fitting to conclude this survey with a survey published at the close of the period that concerns us. It is due to Rulon S. Wells III (1919-2008). Born in Salt Lake City he earned his Ph.D. in philosophy at Harvard in 1942. A natural linguist he served in the U.S. Army as a

Nicholas Rescher • Philosophical Episodes

66

Japanese language instructor during WW II. In 1946 he retired to academia at Yale, where he taught philosophy and linguistics for many years. His dual career is altered by the fact that he served as president both of the C. S. Peirce Society and the Linguistic Society of America. In 1956 Wells published a long (two-part) survey of recent work on the philosophy of Leibniz under the title “Leibniz Today” (The Review of Metaphysics, vol. 10 (1956), pp. 333-49 and 502-525). Written just in time to take brief but appreciative notice of Loemker’s Leibniz edition, Wells’ survey considers only one of the works that concerns us here, namely R. M. Yost, Jr.’s Leibniz and Philosophical Analysis, of whose position regarding Leibniz views of language and its analogies Wells was decidedly critical. * * * It is unfortunate that the early interest in Leibniz manifested by the St. Louis Germanists and propagated through the Journal of Speculative Philosophy never managed to take a permanent hold there. And neither did the Open Court circle and its journal The Monist engendered an ongoing venture in Leibnizian studies. For complex reasons—perhaps associated with the anti-Germanism of the World War I era—neither group managed to establish an enduring academic tradition. It deserves note that over one-third of earliest American Leibnizians were immigrants. This is a token at once of American’s role as “melting pot” and of the substantial point that immigrants have played in American academic culture. And considering the small number of people—fewer than 20—and the fairly modest volume of publications, it really cannot be said that Leibniz had a really substantial presence in academic philosophy in North America by the middle of the 20th century. When I began my entirely self-motivated study of Leibniz in 1949, it was still easily practicable to read everything that American scholarship had contributed to the subject. Nor at this stage did any North American universities offer graduate courses or seminars specifically devoted to the work of Leibniz. All of this changed in the wake of two transformative developments.

67

LEIBNIZ CROSSES THE ATLANTIC

One was the publication in 1956 of Leroy E. Loemker’s G. W. Leibniz: Philosophical Papers and Letters (Chicago: University of Chicago Press, 1956; 2nd ed. Reidel, Dordrecht, 1969). This monumental work which brought into view for Anglophone readers a fuller view of range and depth of Leibniz’s thought. Loemker (1900-85) was a keen student of modern German philosophy who took a special interest in the philosophy of Leibniz. From 1929 until his retirement in the late 1960s—and resettlement in Lakeland, Florida—Loemker had his entire career at Emory University, where he devotedly pursued Leibniz scholarship. He chaired the philosophy department at Emory for many years and also served as Dean of Arts and Sciences there. Apart from his Leibniz anthology, Loemker also published: • “Leibniz and the Crisis of 17th Century Europe,” The Emory University Quarterly, vol. 1 (1945), pp. 51-60. • “Leibniz’s Judgments of Fact,” Journal of the History of Ideas, vol. 7 (1946), pp. 397-410. • “Leibniz’s Doctrine of Ideas,” The Philosophical Review, vol. 55, no. 3 (1946), pp. 229-49. • “A Note on the Origin and Problem of Leibniz’s Discourse of 1686,” Journal of the History of Ideas, vol. 8 (1947), pp. 449-66. • “Boyle and Leibniz,” Journal of the History of Ideas, vol. 16 (1955), pp. 22-43. • “Leibniz and the Herborn Encyclopedists,” Journal of the History of Ideas, vol. 22 (1961), pp. 323-38. • “On Substance and Process in Leibniz,” in William L. Reese, Eugene Freeman (eds.), Process and Divinity: Philosophical Essays Presented to Charles Hartshorne (La Salle, Ill: Open Court Publishing Company, 1946), pp. 403-25.

Nicholas Rescher • Philosophical Episodes

68

The second transformative development the explosion of American studies in the history of philosophy that came to fruition in the last third of the 20th Century in the wake of the expansion of American higher education engendered after WWII by the GI Bill. A goodly number of young scholars now set to work, and dozens of first-rate projects Leibnizian study now poured forth from the academic presses of Northern America. A few of the academic departments that trained significant numbers of philosophy Ph.D’s now began to turn out Leibniz scholars— California, Emory, and Pittsburgh among them. Any by the 1990s Leibnizian studies had gained a modest but secure place in North American higher education. Substantive stimulus to American work on Leibniz was provided by the foundation of the International G. W. Leibniz Society in 1966 and the subsequent launching of the North American G. W. Society in 1900. Both of these scholarly organizations sponsor symposiums and conferences in which America’s now-numerous Leibnizians regularly participate. Appendix One of the extraordinary facets of American Leibniz scholarship in the era under consideration here relates to the great logician and mathematician Kurt Gödel. Paul Erdös, who often visited with Gödel at the Institute for Advanced Studies in the 1940s, reports: “I always argued with him; we studied Leibniz a great deal and I told him: ‘You became a mathematician so that people should study you, not that you should study Leibniz’.”12 In his invited 1944 contribution to Paul Schlipp’s anthology on The Philosophy of Bertrand Russell, Gödel first set out his philosophical views on mathematics, and it was here that he first gave voice to his longstanding interest in each dedication to Leibniz. He lamented that the “incomplete understanding of the foundations” explains why “mathematical logic has up to now remained so far behind the expectations of Peano and others.” Leibniz’s vision that logic “would facilitate theoretical mathematics to the same extent as the decimal system of numbers has facilitated numerical computations” yet remains unre-

69

LEIBNIZ CROSSES THE ATLANTIC

alized. All the same, Gödel saw “no need to give up hope,” for in his view the Characteristica universalis that Leibniz had outlined was not “a utopian project” but a calculus that, “if we are to believe his [own] words,” Leibniz “had [already] developed . . . to a large extent.” Gödel first encountered Leibniz when attending Heinrich Gomperz’ course in the history of European philosophy in 1925-26 at the University of Vienna and he continued reading Leibniz on his own during 1926-28. Later on, accordingly, to Karl Menger, he undertook an intensive study of Leibniz workings in the early 1930’s and returned to an extensive study of his life and work during 1641-46 and continued this off and on for almost a decade.13 Gödel was deeply impressed by Leibniz’s pioneering efforts at the arithmatization of logic represented by Leibniz’s project of a calculus ratiocinatur. To be sure, Gödel’s own efforts in this direction were addressed at the formal (semantical) structure of propositions, while Leibniz’s addressed their substantive content. But Gödel could hardly persuade himself that Leibniz remained on this decidedly different track and was always inclined to suspect that Leibniz had anticipated him in his own project. There is something profoundly ironic about Gödel’s surmise of Leibniz’ anticipations. For Leibniz was in fact the founding father of logicism—the theory that all of pure mathematics (and arithmetic in particular) is subject to axiomatizations—to (finite) proofs on the basis of first principles. And it was exactly this theory that Gödel’s own discoveries definitively destroyed. On the other hand, there was another important area of mathematics—viz. applied mathematics and in particular physics—where Gödel in fact walked in Leibniz’s footsteps. For Leibniz was convinced that the fundamental laws of nature, while rendered not axiomatically provable, were in fact demonstrable certainties that admitted of a priori demonstration, albeit of an infinitely complex sort that assured its rationally cogent validation it through considerations of systemic fitness. And Gödel subscribed fully to this Leibnizian line of thought. Leibniz’s PSR to the effect that every fact has a rational explanation was accepted in toto by Gödel endowed it with enthusiasm as an “interesting axiom.” This principle both encapsulated and substantiated his conviction in the fundamental rationality of the universe which

Nicholas Rescher • Philosophical Episodes

70

was also a the fundamental conviction that provided Gödel with a guiding star throughout his entire life. But there is also another point of deep kinship between the ideas of Gödel and these of Leibniz. Both were in fact deeply convinced of the incompleteness and indeed incompletability of human knowledge. Consider, first the profound implications of Gödel’s incompleteness demonstration. Prior to Gödel it seemed only natural to reason as follows: Of course we humans, finite cognizers that we are, cannot possibly know all facts in detail. But at least we can know the basic facts in which all the rest are implicitly included by way of provability for human premisses by mere logical inference.

However, this seemingly promising ideas was by Gödel’s demonstration of its untenability in ever so limited a domain as arithmetic. And an analogous argument for the inherent incompleteness of human knowledge was developed by Leibniz in an essay “On the Horizon of Human Knowledge” which essentially took the line that all of factual knowledge, being in principle conveyed by language is in principle countable whereas the world’s facts relate to a mathematically unknown and complex manifold that outruns the limits of contentability.14 In consequence, the world involves a subtality and vastness of detail that can never be captured by language. And this situation renders the knowledge of finite beings such as ourselves in principle incomplete and incompatible. Thus while their approaches certainly different in strategy and technique, Gödel and Leibniz were entirely agreed in the essential incompletability of human knowledge. In the late 1940’s Gödel intensified his study of Leibniz. Convinced of the fundamental kinship of their ideas, and persuaded of the outstanding ability of Leibniz as a mathematician, Gödel could not bring himself to believe that Leibniz had not anticipated his (Gödel’s) own work more extensively. He felt sure that Leibniz had in some way anticipated his own demonstration that derivation from first principles were not the sole rational and secure pathway to the demonstration of mathematical truth. But just this is something that Leibniz did

71

LEIBNIZ CROSSES THE ATLANTIC

not—and within the framework of his fundamental commitments could not—do. But there is no question that Gödel looked to Leibniz to supply the assurance of a larger meaningfulness—a deeper understanding of “what it’s all about” that he were unable to extract from his own experience. Hao Wang tells us that it emerged in connection with Gödel that: In philosophy Gödel never arrived at what he looked for—a new view of the world . . . Several philosophers, in particular Plato and Descartes claim to have had at certain moments of their lives an intimate view of this kind, totally different from the everyday view of the world.15

Note here the omission of Leibniz—mention of whom would have brought matters too close to home seeing that he effectively saw the philosophical homestead he sought as effectively prefabricated by Leibniz. Again Wang writes: Gödel’s sympathy with the main lines of Leibniz’s monadology and his interest in realizing some modified form of a universal characteristic (which is, largely through Gödel’s work, seems to be impossible in the strong sense of requiring a decision procedure) . . . [manifests] a faith in the power of axiomatic method and the possibility of a fruitful logic of discovery (or science of logic). Gödel’s respect for Leibniz is comparable to Leibniz’s for Aristotle (in logic) and Plato (in philosophy.)16

As Hao Wang reports: In his conversations with me he [Gödel] commends the Leibnizian conception of science according to which the philosophical task of analyzing concepts is combined with the scientific one of using them. He also speaks of a kind of analysis that yields at the same time a method of proving theorems.17

This seems right on the money except for two things. First instead of “universal characteristic” (characteristica universalis) Wang doubtless meant to say “calculus of reasoning” (calculus ratiocinator). Se-

Nicholas Rescher • Philosophical Episodes

72

cond, and more importantly, it was only in matters of formal knowledge—logic, language, and mathematics—that Leibniz contemplated the finite analytically at issue with calculative decidability. In matters of physics and natural philosophy the decision process will (as Leibniz saw it) generally be of an order of complexity well beyond the finite realm of human powers (and thus practicable of God alone). And so in such matters of understandability that Gödel established from some mathematical facts would—as Leibniz saw it—be only natural not to be expected. However—and this is the critical point— the sort of trans-axiomatic demonstrability that Leibniz envisioned for these truths he characterized as contingent exactly parallels the sort of (trans-axiomatic) systemic rationalizability that Gödel envisioned not only for the fundamental principles of natural philosophy but also for some mathematical facts. So in this regard Gödel was more of a Leibnizian than Leibniz himself. Leibniz, like Gödel assigned to evaluative concepts a fundamental role in the constitution of physical principles. As Hao Wang put it in respect of Gödel: What Gödel calls, probably following Leibniz, positive and negative concepts (or properties) appear to contain a moral element. According to Gödel, “being a positive property is logical.” Hence it would appear that the range of logic includes for Gödel also certain moral considerations. . .18

Conceivably, Gödel seems to envision these positive prospects in terms of consistency, unity, and “God-like” properties such as (presumably) those which like explanatory capacity (power), aesthetic elegance (value: benevolence), and comprehensiveness (knowledge), which can be ascribed alike to the deity and to logical manifolds. A whole host of cognitive value concepts—consistency, coherence, precision, depth, etc. would thus qualify as fundamentally logical. And so in Wang’s preceding statement “normative” or “evaluative” should doubtless be substituted for “moral.” And so it might be thought puzzling that Gödel should view Leibniz as a kindred spirit, seeing that decisively refuted Leibniz’s logicist view of mathematics as a domain all of whose truths could be (finite-

73

LEIBNIZ CROSSES THE ATLANTIC

ly) demonstrated. But he subscribed in toto Leibniz’s neo-Platonic view of physics as a domain all of whose fundamental laws and principles could be validated a priori on principles of systemic fitness and rational order. And so despite his radical departure from Leibniz’s conceptions of logico-mathematical truth Gödel looked to Leibniz as a source of insight and inspiration owing to the fundamental kinships of their fundamentally rationalistic theory of natural science as a manifold of rational order. Why did Gödel feel a deep ideological kinship to Leibniz? The answer is simple. He viewed him as an intellectual percussion in a tradition rooted deep in Greek antiquity—in the teaching of Pythagoras and Plato and Archimedes to view the universe from the vantage point of numbers. Descartes had brought geometry into the domain of arithmetic/algebra. Leibniz, as Gödel saw it, had done the same with logic, preventing its capture by students of language and language and bringing it into the realm of quantitatively exact reasoning. And Gödel saw himself as Leibniz’s heir in this respect, bringing the Leibnizian arithmetization of logic not to its end but to its logical culmination. For Leibniz saw the limits of finite calculation not as bringing the mathemtization of fact to an end but as aspiring a wisdom to a whole new level of complexity and sophistication where effective operation was not possible for fallible humans but by God alone. The deepest truths, so Gödel and Leibniz alike thought, are not absolutely undecided and incalculable but rather only so for our finite axiomatic mechanisms. In larger—and very much larger—scheme of things they indeed are decidable, albeit not by axiomatic calculability—let alone insight or intention—but by a supercalculability that is only at the disposal of a Leibnizian God. Wang points to what seems to be a paradox. How could Gödel, the quintessential ivory tower theoretician, take as his role model Leibniz who was deeply involved in the public, political, and pivotal issues of his day? “How is one to reveal this great difference in their lives with Gödel’s adherence to Leibniz’s general philosophical outlook?”19 And here Wang’s answer runs as follows: “What Gödel found most congenial was probably Leibniz’s conviction . . . to have found a solution to the problem of relating the individual to the universal.”20 But the answer is surely less recondite. What drew Gödel to Leibniz was that

Nicholas Rescher • Philosophical Episodes

74

he more clearly than any other major thinker articulated a scientifically informed commitment to the rational harmony of nature, following this abstract out with a technical facility that provided it with a comprehensive grounding in the science of the day. Style of life and professional modus operandi have nothing to do with it. The crux lies in the combination of conviction and competence. Gödel would certainly never have accepted John von Neumann’s flattering characterization of him as “the greatest logician since Aristotle.”21 He would unhesitatingly have transmitted that encomium to Leibniz. NOTES 1

Kurt Müller, Leibniz Bibliographie: Verzeichnis der Literatur über Leibniz (Frankfurt am Main: Vittorio Kloslerman, 1967).

2

Leroy E. Loemker; G. W. Leibniz: Philosophical Papers and Letters (Chicago: University of Chicago Press, 1956). However, the Anglophone student of Leibniz was not dependent on North American work in Leibniz but also had British contributions at his disposal. Three items were particularly noteworthy here: the LeibnizClarke correspondence already published in England by Clarke himself (London: Knapton, 1717), Robert Latta’s edition of The Monadology: And Other Philosophical Writings (London: Oxford University Press, 1898), and Bertrand Russell’s classic Critical Exposition of the Philosophy of Leibniz (London: Allen S. Unwin, 1899; 2nd ed. 1937). Latta’s opening sentence reads: “In this country, Leibniz has received less attention than any other of the great philosophers” and truer words were seldom spoken. The controversy with Newton cast a long shadow. As far as text translations are concerned, Latta’s offerings had already been overshadowed by Duncan’s anthology.) On the mathematical side, the work of J. M. Child should also be noted.

3

His books include: Reason or Religion (Boston: Walker, Fuller and Company, 1865), Atheism in Philosophy (Boston: Roberts Brothers, 1884), and Ways of the Spirit: and Other Essays (Boston: Roberts Brothers, 1878, ©1877).

4

On Hedge see R. J. Mulvany, “Frederic Henry Hedge, A. A. P Torrey, and the Early Reception of Leibniz in America,” Studia Leibnitiana, vol. 8 (1996), pp. 163-82.

5

Published in Philadelphia by T. B. Lippincott in 1867 and 1868, respectively. He also published several Leibniz translations including: The Journal Speculative Philosophy, No. 47 and 58 (1867/71), tr. “Considerations on the Doctrine of a Universal Spirit,” The Journal Speculative Philosophy 5 (1871), pp. 118-129; and “New System of Nature,” The Journal Speculative Philosophy 5 (1871), pp. 209-19.

6

Gottfried Wilhelm Leibniz, New Essays Concerning Human Understanding, tr. by Alfred Gideon Langley (La Salle, Ill.: Open Court, 1896).

7

Bridgeport, Conn: Joyce & Sherwood, 1903.

75

LEIBNIZ CROSSES THE ATLANTIC

NOTES 8

This book was reprinted in 1902 by Scott, Foresman, & Co, of New York and is included in Vol. I of John Dewey: The Early Works 1882-1898 (Carbondale & Edwardsville: Southern Illinois University Press, 1969-72).

9

Morris, with whom Dewey had studied Leibniz at Johns Hopkins in 1883-84, was responsible for his appointment to be professorship at the University of Michigan.

10

Rescher’s early (pre-1956) publications on Leibniz include: “Contingence in the Philosophy of Leibniz,” The Philosophical Review, vol. 61 (1952), pp. 26-39. Reprinted in R.S. Woolhouse (ed.), G.W. Leibniz: Critical Assessments, Vol. I (London & New York: Routledge, 1994), pp. 174-86; “Leibniz’s Interpretation of His Logical Calculi,” The Journal of Symbolic Logic, vol. 18 (1954), pp. 1-13. German translation in Albert Heinekamp and Franz Schupp (eds.), Leibniz’ Logik und Metaphysik (Darmstadt: Wissenschafftiche Buchgesellschaft, 1988), pp. 175-192; “Monads and Matter: A Note on Leibniz’s Metaphysics,” The Modern Schoolman, vol.33 (1955), pp. 172-175. Reprinted in R.S. Woolhouse (ed.), G.W. Leibniz: Critical Assessments, Vol. IV (London & New York: Routledge, 1994), pp. 168-72; “Leibniz and the Quakers,” Bulletin of Friends Historical Association, vol. 44 (1955), pp. 100-107; “Leibniz’ Conception of Quantity, Number, and Infinity,” The Philosophical Review, vol. 64 (1955), pp. 108-114.

11

For details see Rescher’s web site at: http://www.pitt.edu/~rescher/.

12

Eduard Regis, Who Got Einstein’s Office (New York: Addison Wesley, 1997).p. 64.

13

On Gödel’s studies of Leibniz see John Dawson, Logical Dilemmas: The Life and Work of Kurt Gödel (Wellesley, Mass.: A. K. Peters, 1997), pp. 107, 137, 159, 263, and passim.

14

On the Leibniz part of this story see the author’s “Leibniz’s Quantitative Epistemology,” Studia Leibnitiana, vol. 36 (2004), pp. 210-31.

15

Hao Wang, Reflections on Kurt Gödel (Cambridge, MA: MIT Press, 1987), p. 46.

16

Ibid., p. 261.

17

Ibid., p. 211.

18

Ibid., pp. 194-95.

19

Ibid., p. 229.

20

Ibid., p. 229.

21

Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Gödel (New York: Norton, 2005), p. 174.

Chapter Eight KANT’S NEOPLATONISM (Kant and Plato on mathematical and Philosophical Method) 1. SETTING THE STAGE

P

hilosophers have generally been content to do their work without troubling to explain and justify the processes and procedures that they use in doing it. They think, quite mistakenly, that here the end justifies the means, and product the process. Only a few major philosophers have concerned themselves explicitly and extensively with the methodology of philosophizing. But while this may be the rule, there are some notable exceptions, in particular Plato and Kant. Both of these monumentally significant philosophers have devoted much attention and care to deliberating about their method of philosophizing. And, interestingly, both seek to expound and explain their view of philosophical method by one selfsame strategy: explaining the contrast between rational procedure in mathematics and in philosophy. 2. PLATO Let us begin with Plato—as is often only proper in philosophical deliberation. Plato maintained that philosophy does not establish its contentions by a mathematical-style proof, but that, instead, its methodology is dialectic. As he saw it, the mathematician starts out from purely selfevident certitudes to derive his conclusion therefrom through demonstrations. He moves downwards as it were, from a basis of unquestioned assumptions—axioms and postulates—to what is ever less evident and perspicuous. However, those basic fundamentals themselves lack any rational proof; they serve, as it were, as a gift horse into whose mouth we must not—and need not—look. Their only justifica-

Nicholas Rescher • Episodes

78

tion is their obvious fitness for the project in hand. Those mathematical basics have an air of certainty about them. Plato elaborates the matter as follows: Students of geometry and arithmetic and such subjects first postulate . . . [their materials], regard them as known, and, treating them as absolute assumptions, do not deign to render any further account of them to themselves or others, taking it for granted that they are obvious to everybody. They take their start from these, and, reasoning from this point on, conclude with that for the investigation of which they set out. (Republic 510C-D.)

So much for mathematics. But by contrast Plato has it that philosophical reasoning does not treat its data as certitudes that are not open to question. Philosophy, he maintains, is rooted in the perplexity that arises when things do not fall smoothly into place: it begins not in obviousness and see self-credit certainty but in conflict, tension, and cognitive dissonance. And dialectic accordingly takes the form of an exercise in the reconciliation of apparent contradictions: [For] some things are provocative of thought and some are not. I see as provocative of thought things that impinge upon the senses together with their opposites, while those that do not involve sensation do not tend to awaken reflection do not bring in their opposited. . . . [The former] compel the soul to puzzlement and, by arousing thought, provoke it to ask, whatever then is the one as such, and thus the study of unity will be one of the studies that guide and impel the soul to the contemplation of true being. (Republic, 524d-525A.)

While providing us with some information, the senses are confusing: insight into how actually things stand and what should properly be said about them is something achieved only after much intellectual effort has been expended. As Plato saw it, the philosopher must winnow out the inner tensions of his experience and lay open up to view whatever conflicts and contradictions one may encounter there. His method is not demonstrative but “dialectical,” and in dialectic the inquiry must “advance” from its data [upwards] towards an unconditional basis or principle (archê)”

79

KANT’S NEOPLATONISM

(Repblic, 510B.) Philosophy subjects those seemingly plausible contentions to critical evaluation—and so separates the wheat from the chaff. And so for Plato the deep truths of philosophy become attainable through dialectic but are approached only at the end of inquiry and certainly not given at the outset. In this regard they are unlike the first principles of mathematics encapsulated in its axioms, postulates, and definitions. Just this is why Plato views mathematics as suitable for the young, but philosophy only for the mature who alone can possess the wisdom possibilized by an ample body of experience. In the Divided Line discussion of Book VI of the Republic, Plato vividly contrasts mathematical reasoning (dianoia) with the intelligence the higher knowledge (epistêmê) obtained in philosophy through dialectical inquiry described in the terms that are well worth quoting at length: [In mathematics] the soul is compelled to employ assumptions in its investigations, not proceeding to a first principle because of its inability to extricate itself from the rise above its assumptions. Moreover, it uses images or likenesses [via diagrams. But in philosophy] reason itself lays hold of by the power of dialectic, treating its assumptions not as absolute beginnings but literally as hypotheses, underpinnings, footings, and springboards so to speak, to enable it to rise to that which requires no assumption and is the starting-point of all, and after attaining to that again taking hold of the first dependencies from it, so to proceed downward to the conclusion, making no use whatever of any object of sense, but only of pure ideas moving . . . Here we deal with that aspect of reality and the intelligible, which is contemplated by the power of dialectic, as something truer and more exact than the object of the so-called arts and sciences whole assumptions are arbitrary starting-points. And though it is true that those who contemplate them are compelled to use their understanding and not their senses, yet because they do not go back to the beginning in the study of them but start from assumptions they do not actually possess true intelligence about them, even though the things themselves are intelligibles when apprehended in conjunction with a first principle. (Republic, 510B-511D.)

Nicholas Rescher • Episodes

80

As Plato see it while mathematics rests on unquestioned assumptions, in philosophy there is nothing that deserves to be treated as selfevident and secured on a basis that lies beyond the reach of deliberative investigation. Mathematics proceeds from unquestioned circumstances; whereas philosophy regresses from critically examined plausibilities to the establishment of validated truths. Intuitively apparent certainties are the input of the one while critically consolidated certainties are the output of the other. And a great deal can certainly be said for his view of the matter. After all, one does not prove those axiomatic fundamentals at work in mathematics—they would not be characterized as such if they could be demonstrated on the basis of something yet more fundamental. Their validation is based not on discursive reasoning from prior premises, but some through definition, postulation, or some sort of Descartes-reminiscent clear and distant indication of the mind. Mathematics thus has its undemonstrated demonstrators, secured in place of the very outset of the deliberative processes. But in philosophy there is nothing like this. Here there are at first there are no certainties but only plausibilities—only the problematic dealings of incompatible opinions. And it is through a “dialectical” testing and winnowing of these discordant conflicting concepts that a coherent position emerges in the end through separating securely grasped truth from the chaff of loose thinking. 3. KANT ON THE CONTRAST BETWEEN MATHEMATICAL AND PHILOSOPHICAL INQUIRY Let us now turn from the teaching of Plato to that of Kant. As Kant saw it, the very first domain of inquiry to make good a claim to scientific status was mathematics—and in particular geometry. Thus in the Preface to the second (1787) edition of the Critique of Pure Reason we read: In the earliest time to which the history of human reason extends, mathematics, among that wonderful people, the Greeks, had already entered upon the sure path of science. (CPuR, Bx.)

81

KANT’S NEOPLATONISM

And Kant envisioned the methodological difference between mathematics and philosophy in a manner not far removed from that of Plato. For with Kant “All knowledge arising out of reason is derived either from [the analysis of] concepts or from the construction of concepts. The former is called philosophical, the latter mathematical.”1 Mathematics accordingly has the advantage that it constructs its own objects, whose features are imposed by the human mind on the fabric of experience. Thus Kant has it that mathematics is control of its concepts, which thereby represent the modalities of experiencing rather than products of experience. This puts the mathematician into a position to start out from a certain and assured basis—a basis reflected in the definitions, axioms and postulates of pure mathematics. And given such a basis the mathematician can proceed to elaborate demonstrations that exfoliates the inner substance of those selfconstructed beginnings. He is in the fortunate position of being able to base demonstrative proof on assured first principles. The philosopher, by contrast, is in a far less fortunate position. For he is not in control of his conceptual instrumentalities. They have to be formed with reference to the fruits of our experience. Not—to be sure—that what matters is the content of what substantive experience deliverances regarding the empirical facts. (Philosophy is not natural science.) But rather what is pivotal is a critical analysis of the conditions under which alone observational experience can deliver objective scientific knowledge into our hands. And so we have it once more that while mathematics begins with certainties—with basic definitive and fundamental theses (axioms, postulates)—philosophy ends with them. And while mathematics proceeds analytically from firmly secured basics, philosophy moves synthetically towards them. Kant accordingly rejected the prospect that philosophy is a substantively reality-descriptive discipline that yields demonstrated doctrinal findings. As he saw it, “philosophy is a mere idea of a possible science which nowhere exists in conreto,” and he continues: “We cannot learn philosophy, for where is it, and who is in possession of it, and how should we recognize it?” (CPuR, A838=B806). Instead, he insists “we can at most learn to philosophize” (A837-B805).

Nicholas Rescher • Episodes

82

To be sure, Kant insisted that philosophy is a matter of knowledge based on principles (cognitio ex principiis) (A836=B864). But these principles are only a glint in the philosopher’s eye—something at which he aims and towards which he reaches. For the work at whose realization inquiring reason aims is “the systematic unity of the knowledge provided by the understanding, and this unity is the criterion of truth of its rules;” but this systematic unity is simply an idea— a merely projected unity that must be seen not as a given, established fact but only as a problem to be addressed—an ideal to be pursued. (CPuR, A697 = B 673). But ideal though it is, it relates to the nature of experience-accessible reality and our place within it. As Kant saw it, a treatise on the aim, procedures, and methods of metaphysical deliberation—including a consideration of its conditions for success and the prospect of its realization—is certainly possible. (And presumably actual in the Critique of Pure Reason). But a handbook of metaphysical findings and results lies beyond our reach and outside the prospect of possible realization. The situation here is thus very different from that of mathematics where results and findings abound. Kant accordingly poured scorn John Locke as someone who “goes so far as to assert that we can prove . . .[metaphysical claims] with the same conclusiveness as any mathematical proposition—even though . . . [they] lie entirely outside the limits of possible experience.” (CPur, A855=B883.) The fallacy of taking something as a completed product of cognition in product that is actually no more than some feature of the process of inquiry itself is described by Kant as “lazy reason” (ignava ratio). He lucidly describes it as encompassing “every principle which has us regard our investigation into nature, or any subject, as absolutely complete, inclining reason to cease from further inquiry, as though it had succeeded entirely in the task before it.” (CPuR A689=B717) And this process is as mistaken in philosophy as in the investigation of nature. For in metaphysics there are no securely established results or theorems. There are only problems to be investigated and issues to be deliberated about. There are no established certitudes but only the “regulative ideas” of an ultimate systematization with certitude achievable only “at the end of the day”—a day whose sun may never rise.

83

KANT’S NEOPLATONISM

4. KANT AS A NEO-PLATONIST From his earliest metaphysical work on, Kant envisioned a Platonistically dualistic realty comprising both of a sensible and an intelligible world. Moreover, he agreed with Plato that philosophical cognition of the realities of the intelligible are a work of reason distinct from ordinary cognitive reason—which Kant usually called theoreticall reason—namely a practical reason in terms of matters of comprehension of facts that are of regulation of procedure. There are some dozen references to Plato in Kant’s Critique of Pure Reason, and in particular an extended discussion (A313=B371 – A319=B375) of his theory of ideas or ideas. But in a way Kant turns Plato’s theory against him. For Kant saw philosophy itself not as a body of authentic knowledge (epistêmê) developed by means of dialectic as a useful means of inquiry, but rather as the fondly aspired but unrealizable end-product of an inquiry whose unrealizability is manifest by a “dialectic” which—as far as the proof of philosophical theses is concerned, is destructive rather than constructive in its operation. Ironically the idea of dialectic thus played a virtually opposed role in Plato and Kant. With Plato, dialectic was a matter of testing divergent views against each other to winnow out the truth of things— evolutionary conflicting contentions by testing (elegchô) the strength of their claims is the face of counter-considerations. It is an instrumentality of conformation—of showing how a claim can meet the test of opposition. For Kant, by contrast, dialective shows the equivalency of conflicting claims. It brings to light that every argument in favor of one side can be countered by an equally weighty counterargument in favor of the other. It is in sum an instrumentality for refutation and invalidation. For Kant dialectical confrontation is not the avenue of truth-determination and understanding. As Kant was it, dialectic is merely an avenue to mis-understanding. Here the position of our two philosophers could not be more radically different and discordant. But there is also a very different aspect of the matter. Kant insists in compete consensus with Plato that the task of philosophizing is to provide guidance for the conduct of life.

Nicholas Rescher • Episodes

84

The philosophy which deals with the whole vocation of man is entitled moral philosophy. On account of the superiority which moral philosophy has overall other occupations of reason, the ancients in their use of the term “philosopher” always meant, more especially the moralist, and even at the present day we are led by a certain analogy to entitle anyone a philosopher who appears to exhibit self-control under the guidance of reason, however limited his knowledge may be. (CPuR A839=867.)

And against the background of his position Kant deserves to be ranked as a neo-Platonist on two scores. The first of these, which is not of concern in the context of the present discussion. The other, however, relates to the prominent role of the Platonic Ideas in the framework of Kant’s Critical Philosophy. Kant himself is fully explicit and emphatic in this point throughout the discussion of “the Ideas in General” in Book I of the “Transcendental Dialectic.” And so, as Kant elaborates his position we read: Plato fully realized that our faculty of knowledge fills a much higher need than merely . . . [accounting for] experience. He knows that our reason naturally expires modes of knowledge which so far transcend the bounds of experience that no given empirical object can ever realize them, but which must none the less be recognized as having their own reality, and which are by no means mere fictions of the brain . . . . Plato found the chief instances of his ideas in the field of the practical, that is, in what rests upon . . . . modes of knowledge that are a peculiar product of reason. Whoever would derive the concepts of virtue from experience and make (as many have actually done) what as best can only serve as an example in an imperfect kind of exposition. The Republic of Plato has become proverbial as a striking example of a putatively visionary perfection . . . . But it is not only where human reason exhibits originative causality, and where ideas are operative causes (of actions and their object), namely, in the moral sphere, but also in regard to nature itself, that Plato rightly discerns clear proofs of an origin from ideas. . . . It is, however, putatively in regard to the principles of morality, legislation, and religion—where the experience of the good, it itself made possible only by the ideas, incomplete as their empirical expression must always remain—that Plato’s teaching exhibits its quite peculiar merits. (A314=B371 - A318-B375.)

85

KANT’S NEOPLATONISM

As he insists again and again, the postulative projection of ideals that is the supreme work of creative reason is the pivot of moral worth in human affairs and the basis of a free agent’s claim to respect that lie from the basis of morality. Here, then, there is a salient Kantian endorsement of the Platonic ideas. And for a further—and presently salient—aspect of Kant’s neoPlatonism pervades his discussion of the relationship that obtains between mathematics and philosophy. For he emphatically agrees with Plato that—notwithstanding the eminently prominent significance of mathematics within the sphere of human cognition—it is philosophy that is preeminent and actually stands at the pinnacle of cognition. In just this sense, Kant writes: Whether the world has a beginning [in time] and any limit to its extension in space; whether there is anywhere, an perhaps in my thinking self, an indivisible and indestructible unity, or nothing but what is divisive and transitory; whether I am free in my actions, or like other being, am led by the hand of nature and of fate; whether finally there is a supreme cause of the world, or whether the things of nature and their orderer must as the ultimate objects terminate thought—an object that even in our speculations can never be transcended: these are questions for the solution of which the mathematician would gladly exchange the whole of his science. For mathematics can yield no satisfaction in regard to those highest ends and most closely concern humanity. (A463=B491.)

And Kant then goes on—in much the Platonic manner—to elevate philosophy above mathematics via the decidedly Platonic consideration that the philosopher tolerates no basic unexamined assumption whereas the mathematician proceeds from axioms and postulations that are simply taken for granted as unquestionable and unquestioned givens. Although I leave aside the principles of mathematics, I shall none the less include those [more basis] principles upon which the very possibility and a priori objective validity of mathematics are grounded. These latter must be regarded as the foundation of all mathematical principles.

Nicholas Rescher • Episodes

86

They proceed from concepts to intuition, not from intuition to concepts. (A160=B199.)

And to Kant not only agrees with Plato as to the fundamental contrast between mathematical and philosophical reasoning, but proceeds, just like Plato, to see on this difference the ground and reason for being of the preeminent status of philosophy. On this basis, then, Kant deserves to be regarded as a neo-Platonist of sorts. For not only does he assign to ideas and ideals a key role in the philosophy of knowledge, but he insists in seeing philosophy itself—in the light of an ideal. 5. FINAL COMPARISONS The presently pivotal consideration is that Plato and Kant both agree in thinking that the nature of philosophy is most clearly and instructively revealed by contrasting its procedures and methods of investigation with those of mathematics. And there is substantial agreement in the way in which they implement this idea. For with both Plato and Kant, mathematics proceeds top-down moving from a secure basis (axioms, postulates, definitions) by deductively inferential steps to derived consequences. And by contrast, philosophy is bottom-up, moving from an uncertain manifold of discordant positions to secure an ultimately tenable result. In mathematics security comes at the starting point. In philosophy it is not a fixed and firm beginning but a hoped for (and perhaps unattainable) endproduct. In mathematics the “first principles” indeed come first, but in philosophy they are last. In the terminology of a later age, these thinkers are foundationalists in mathematics but coherentists in philosophy. And his is a position that not only has the imprimatur of these great thinkers of the past but continues to make plausible sense at the present time of day as well.2 The consilience that obtains between Plato’s and Kant’s positions included in particular the following points:

87

KANT’S NEOPLATONISM

• That the method of mathematics is deduction from certitudes (“hypothesized” in Plato, “introduced” in Kant.) But they also agree that this sort of method will not work in philosophy. • That in philosophy, unlike mathematics, the force majeure of stipulation postulation and definitional fiat has no appropriate place. • That therefore the idea of proving or disproving one’s contentions as accomplished facts is unachieved in philosophy. • That the secure basis of assured fact from which our mathematical reasonings can proceed is accordingly lacking in philosophy. • That in philosophy a more circuitous process of constructive or dialectical reasoning is thus required to substantiate one’s claims. And accordingly. • That philosophy can validate its first principles only at the end of inquiry, not at its outset. This is accomplished through dialectical investigation (Plato) or through systematization (Kant.) • That the salient task of philosophy is the pinpoint of systematic knowledge not for its own sake but for that of providing guidance to the conduct of life. The consensus position of the two philosophical giants can thus be put in a nutshell. They both effectively agree—to put it in contemporary words—that a coherentist rather than foundationalist model of substantiation is in order in philosophy. With Plato, the winnowing process at issue is characterized as dialectical. With Kant it is characterized as critical. But both alike see it as characteristic of the difference between mathematics and philosophy, and as essential to securing the higher claims of the latter to cognitive excellence. And with Kant as with Plato philosophizing is not an inquiry that issues in a fixed body of knowledge, but an intellectual project whose greatest utility lies in the training of the mind (paideia)

Nicholas Rescher • Episodes

88

for the serous work of coming to grips with the nature of the world and our place within it. In the end, then, Plato and Kant agree on a fundamental point of philosophical method that is at odds with the mathematicodemonstrative methodology of philosophy found in such philosophers as Spinoza and in Christian Wolff. Both reject the axiomatic approach with its insistence on fundamental truths secured at the outset. Both alike insist that philosophizing—unlike mathematics—is an exercise in rational comparison and assessment when the issue of what is really basic and fundamental comes to view only after the inquiry has gone on for a long time—and certainly not at its start.3 NOTES 1

CPuR, A837=B865.

2

For an elaborate defense of this position see the author’s Philosophical Reasoning.

3

This chapter was presented in a metaphysical series held at SUNY—Stony Brook in April, 2011.

Chapter Nine ON PEIRCE AND UNANSWERABLE QUESTIONS 1. QUESTIONS AND ANSWERS

T

he issue of unanswerable questions has been on the agenda since the medieval scholastic discussion of insolubilia. And it represents a topic that has not lost its interest even down to the present day. Curiosity may kill the cat, but it is the making of an intelligent being. We have questions and we want them answered. But with obtaining information—as with obtaining other desiderata—there are costs. And we are finite beings with only so much of resources like time, energy, and money at our disposal. This means that there is only so much that we can do to get our questions answered. Some questions will have to go unanswered. And some questions are not just unanswerable but unaskable. “When did he stop beating his wife?” (He never had one.) “With how wide a margin did Aaron Burr defeat John Adams for the U.S. Presidency?” (He never ran against him.) It makes no coherent sense to ask questions based on erroneous presuppositions. Instead, what is of real interest is the matter of questions that can appropriately be raised but pose great and perhaps even insuperable difficulties for answering. The very topic of unanswerable questions undoubtedly has its difficulties. The great American philosopher C. S. Peirce wrote: For my part, I cannot admit the proposition of Kant—that there are certain impassable bounds to human knowledge . . . . The history of science affords illustrations enough of the folly of saying that this, that, or the other can never be found out. Auguste Comte said that it was clearly impossible for man ever to learn anything of the chemical constitution of the fixed stars, but before his book had reached its readers the discovery which he had announced as impossible had been made. Legendre said of a certain proposition in the theory of numbers that, while it

Nicholas Rescher • Episodes

90

appeared to be true, it was most likely beyond the powers of the human mind to prove it; yet the next writer on the subject gave six independent demonstrations of the theorem.1

The present discussion will argue that, notwithstanding the plausibility of Peirce’s considerations, there indeed are some impassable bounds to human knowledge. Basic to the present deliberations is the idea of available information. The inquirers at issue are supposed to have at their disposal some adequate means of obtaining secure and reliable information. Thus, for instance, in the present state of information, the question “Was Andrew Jackson the first president of the United States?” is conclusively answerable—in the negative. The question “Did Queen Victoria ever wonder if her grandson, Kaiser Wilhelm, was quite sane?” is not. And for a question to be answerable is for it to be possible to find a conclusive answer to it within the body of available information.2 On this basis there will certainly be unanswerable questions. 2. IMPEDIMENTS INSUFFICIENCY

TO

ANSWERING:

IN-PRACTICE

Initially the schoolmen understood by insolubilia any inherently and inevitably unanswerable questions.3 An instance is afforded by a yes/no question that cannot possibly be answered correctly such as “When you respond to this a question, will the answer be negative?” Consider the possibilities in Display 1. On this basis, that query emerges as meaningless through representing a paradoxical question that cannot be answered correctly. Another instance of a paradoxical question is “What is an example of a question you will never state (consider, conceive of)?” Any answer that you give is bound to be false, though someone else may well be in a position to give a correct answer. But paradoxical questions of this sort are readily generalized. Thus, consider “What is an example of a question no one will ever state (consider, conceive of)?” No one can answer this question appropriately Yes, nevertheless, the question is not unanswerable in principle since there will certainly be questions that individuals and

91

ON PEIRCE AND UNANSWERABLE QUESTIONS

________________________________________________________ DISPLAY 1 When next you answer a question, will the answer be negative? Answer given Yes No

Truth status of the answer False False

_______________________________________________________ indeed knowers-at-large will never state (consider, conceive of). But it is impossible to give an example of this phenomenon. All such illformed questions will be excluded from our purview. Only meaningful questions that have correct answers will concern us here. (There are, of course, also questions that cannot be answered incorrectly. An instance is “What is an example of something that someone has given an example of?” Any possible answer to this question will be correct.) 3. IMPEDIMENTS TO ANSWERING THE UNATTAINABILITY OF INFORMATION The insufficiency of information is the salient impediment to answering a question. And such insufficiency has two distinct versions or modes: the one operative in practice and the other in principle. Let us survey some versions of the former. (i) Information Gaps Information can be unattainable for reasons of contingent unavailability or for reasons of general principle. We simply have no practicable means for determining what Julius Caesar had for breakfast on that fatal Ides of March. Barring the implausible discovery of a record we have no way to find out about this. Whenever the course of events destroys all traces and records of the past—when the winds annihilate all traces of past waves and sanddunes—that past becomes imponderable. Its detail becomes lost to all prospects of cognition. It is not that the phenomena at issue are problematic in themselves, but is just that in the prevailing circumstances

Nicholas Rescher • Episodes

92

all practicable prospects of knowledge has been lost. Thus many questions about the objective feature of concrete reality will be unanswerable because the requisite information has become hidden from our cognitive view. Then too there are issues with the future. Information about the eating habits of the 100th President of the U.S. is nowadays unavailable for reasons of general principle. Barring an inherently infeasible recourse to time travel we have no way of finding out about the doings of this unidentifiable individual. This dual character of information unavailability as sometimes contingent and sometimes inevitable and necessary spills over to deliberations about undecidable propositions and unresolvable questions. The insufficiency infeasibility of question-resolution comes about on either practical or theoretical grounds. And this means that there will be a strong (in theory) and a weak (in practice) sense of each of these conceptions. (ii) Future Contingency In general there is no prospect of securing the data needed to resolve questions about the contingently imponderable future. Thus consider such questions as: • Will there ever come a time when every question actually asked (by some intelligent being somewhere in the universe) one hundred years before will have been answered successfully? • Will there ever come a time in the history of humanity when people no longer value gold? • Will there ever come a time in the history of humanity when people abandon making nuclear power? • Who will be the last-ever person on earth to be called Thomas?

On such matters there is only guesswork and conjecture: there is no prospect of securing here and now the information required for a definitive resolution. It is not that such questions have no answers, but

93

ON PEIRCE AND UNANSWERABLE QUESTIONS

the practicalities of the situation—including the infeasibility of time travel—prevent our getting to it. And this situation prevails in particular with respect to (iii) Future Innovation These disciplines being what they are, there is no question that mathematics will solve heretofore unsolved problems over the next decade. Or that astrophysicists will encounter heretofore undetected phenomena. We know for sure that these things will happen. But we do not—cannot—know what they are. The innovations of the future must await their time—we cannot produce them now. After all, if we could do so then they would not be that which, by hypothesis, they are, to wit: innovations of the future. For reason of principle we cannot presently grasp the detail of future discovery and innovation. The eyes of the body cannot look around physical corners; the eyes of the mind cannot look around temporal ones. 4. MODES OF IN-PRINCIPLE INSUFFICIENCY (i) Postulational Insufficiencies Insufficiency can readily arise in the context of merely postulated information. “A man and woman enter the room. One of them left. The person who remained was female. True or false?” We are simply not told, so there is no way to achieve a tenable answer. (The situation is analogous to obtain in algebra where we are given n equations with n + 1 unknowns.) Given the inevitable limits of textual detail, there will always be informative gaps in situations created by assumptive fact. Suppose that we are given three statements: (1)

Statement (2) is true.

(2)

State (3) is true.

(3)

Statement (1) is false.

Nicholas Rescher • Episodes

94

We have two distinct possibilities: (1)/T → (2)/T → (3)/F → (1)/T (1)/F → (2)/F → (3)/T → (1)/F And the information given us insufficient to disseminate between them: all we know is that at least one of these three statements is true and at least one false. We have no clue as to which is which. The information at hand is insufficient to resolve our questions. To be sure, we can determine that “(2) v (3)” is definitely true and “(2) & (3) definitely false,” so that all is not lost with respect to conclusive verifiability. But resolving the question “Which of those three statements is true and which is false?” lies beyond the reach of the overall available information. In this as in many other situations, the postulationally “given” information is simply insufficient to afford an answer. (ii) Finite vs. Infinite Minds Finite creatures cannot execute infinite search processes. And this can pose problems in our commerce with complex questions. For there will be some infinitistic issues that require an actual survey rather than a mere recourse to general principles. And these are bound to create problems. Let us consider the situation more closely via an example. Some number-theoretic problems admit of a unified general-principle solution. For example How many unit squares can one fit into an n-sided square? Here there is an obvious and straightforward answer, viz. n2. The case becomes more complex when one asks: How many unit circles can one fit into an n diameter circle?

95

ON PEIRCE AND UNANSWERABLE QUESTIONS

The answer is now far more complicated and will have to be split into different cases, depending—for example—on whether n is odd or even. But now one has to realize that there will also be some problems that can only be solved by dealing with an infinite number of subcases, each of which involves distinctive issues characteristic of its own situation. And when this is so, then the correlative question will require a resolution that is itself infinity complex only admitting a solution by addressing distributively and individually an infinite number of cases. And such irremediably infinistic questions will take us outside the range of what we finite creatures working with finite means can possibly manage. And this would now be so for a rather different sort of reason from that standardly contemplated. Then too, consider a symbolic-geared question of the format: Let it be that a sentence L is given in a certain formalized language (such as that of Principia Mathematica). Question: is there some palindromic sentence equivalent to it? Given the vastness of the range of possibilities at issue, this question becomes intractable. Finally consider an open-ended question whose answer-range covers an unspecifiable multitude of alternatives such as • “What are the different ways of stating that rabbits have fur?” • “What are the possible answers to an arithmetical question?” There is simply no practicable way of circumscribing the range of alternatives that is contemplated on such a question. (iii) Vagrancy in Descriptive Terms of Reference One can refer to an item in two distinctly different ways: either specifically and individually by means of naming or identifying characterization (“George Washington, the Father of our Country”), or obliquely and sortally as an item of a certain type or kind (“an American male born in the 18th century”). Now a peculiar and interesting

Nicholas Rescher • Episodes

96

mode of reference occurs when an item is referred to obliquely in such a way that its specific identification is flat-out precluded as a matter of principle by the very way in which the putative reference is effected. This phenomenon is illustrated by claims to the existence of ⎯a correct albeit unverifiable conjecture. ⎯an idea that has never occurred to anybody. ⎯an occurrence that no-one has ever mentioned. —an integer that is never individually specified. With such descriptions those particular items that render (∃u)Fu true are referentially inaccessible: to indicate them individually and specifically as instances of the predicate at issue is ipso facto to unravel them as so-characterized items.4 Here question of the format “what is an example of - - -” inevitably eludes our grasp. We know that such an item exists, but cannot possibly identify it. The concept of an applicable but nevertheless noninstantiable predicate comes to view at this point. This is a predicate F whose realization is noninstantiable because while it is true in abstracto that this property is exemplified⎯that is (∃u)Fu will be true⎯nevertheless the very manner of its specification makes it impossible to identify any particular individual u0 such that Fu0 obtains. Accordingly: F is a vagrant predicate iff (∃u)Fu is true while nevertheless Fu0 is false for each and every specifically identified u0.

Such predicates are “vagrant” in the sense of having no known address or fixed abode: though they indeed have applications these cannot be specifically instanced—they cannot be pinned down and located in a particular spot. Predicates of this sort will be such that: one can show on the basis of general principles that there must be items to which they apply, while nevertheless one can also establish that no such items can ever be concretely identified.5

97

ON PEIRCE AND UNANSWERABLE QUESTIONS

The following predicates present properties that are clearly noninstantiable in this way: ⎯being an ever-unstated (proposition, theory, etc.). ⎯being a never-mentioned topic (idea, object, etc.). ⎯being a truth (a fact) no one has ever realized (learned, stated). ⎯being someone whom everyone has forgotten. ⎯being a never-identified culprit. ⎯being an unpenetrable secret. Noninstantiability itself is certainly not something that is noninstantiable: many instances can be given. The bearing of vagrancy in questions lies in the factor of selffrustration. Thus consider such questions as: —“What is an example of an unknown fact?” —“What is an instance of an every-forgotten declaration?” If we hold something to be a fact we ourselves implicitly claim to know that it is so. So in the circumstances it cannot possibly quality as unknown. If we past declaration of some sort as such we ourselves pinpoint be aware of it. In consequence it obviously cannot be totally forgotten. Such questions are by nature unanswerable. Vagrant predicates afford a wide-open doorway to questions that can not possibly be answered correctly. With facts based on predictive vagrancy, their cognitive inaccessibility lies in their very identifactory characterization.

Nicholas Rescher • Episodes

98

(iv) Imponderable Searches The search for a certain (unquestionably actual) object may carry no guarantee of success. We may have no assurance of the format: • If you don’t find a certain object within D days of search, then you never will. • If you don’t find a number of a certain description among the first N integers, then you never will. The underlying idea in all of these cases is not only that whatever exists admit of cognitive access, but that we can finalize the accordant search-process by specifying in advance when enough is enough. With finite beings of limited capacity questions of the general format asking how much second effort suffices to find something that indeed is findable cannot be resolved. After all, there is just no guarantee for the thesis—If no finite amount of effort suffices to find an x, then it doesn’t exist. The situation here is akin to that of predicate vagrancy. Even when we can say that some quantity is sufficient, we may never be able to say what this quality is. Here too there are bound to be unanswerable questions. 5. ARE THERE SCIENTIFIC INSOLUBILIA? Some factual questions are unanswerable not on the basis of scientific ignorance but on the basis of scientific knowledge. Given that acids turn blue litmus paper red, we must not ask questions that premise things to be otherwise. Given that quantum theory precludes the exact concurrent specification of the location and the momentum of a subatomic particle we must not ask for precise details in these regards. Science itself is an arbiter of what can appropriately be asked. If a transuranic atom is of a type that his a half-life of two years we must not ask why it disintegrated after only two months. Cogent and appropriate questions must not have scientifically illegitimate presuppositions.

99

ON PEIRCE AND UNANSWERABLE QUESTIONS

Our concern will have to be with scientifically legitimate questions that have answers which nevertheless cannot possibly be provided— that is, scientific insolubilia. And within this range there are presumably no questions that are in principle conceivable because any question having this feature would thereby be automatically disqualified from qualifying as authentically scientific. The ramifications of these issues deserve closer scrutiny. Consider some examples of proposed scientific insolubilia: • Why is there anything rather than nothing? Why are there physical things at all? Why does anything exist? • Why is nature an orderly cosmos? Why are there any natural laws (uniformities, regularities) at all? Way are there causal laws to operate as “the cement of the universe”? • Granted that there are (perhaps even must be) things and laws, why are they as they are rather than otherwise? Why were the “initial conditions” thuswise, and why are the laws as they are? (For example, why are the laws so orderly rather than more chaotic?) Notice, first of all, that when we try to answer such “ultimate” questions by the usual device of explaining one thing in terms of another, the former immediately expands to swallow up the latter and the usual form of explanation (subsuming boundary conditions under laws) at once falls within the orbit of the question itself in a way that makes the explanatory process circular. This holistic aspect gives the whole issue a case that is more philosophical than scientific not so much to the discoveries as to the presuppositions of science. In theory, there are four lines of response to such “ultimate questions”: I. They are illegitimate and improper questions, based on defective presuppositions. II. They are legitimate

Nicholas Rescher • Episodes

100

1. but unanswerable: they represent a mystery 2. and answerable a. via a substantively causal route that centers on a substance (God) that is self-generated (causa sui) and is, in turn, the efficient causal source of everything else. b. via a nonsubstantival route that center on some creatively hylarchic principle that has no basis in some preexisting thing or group thereof, a principle that envisions agencies without agents. As such a survey indicates, it transpires that even at best (viz. at II2b) these questions are not really scientific but meta-scientific, or more familiarly meta-physical. And as such the sort of definitive conclusiveness that is at issue with not just giving an answer but actually having an answer is beyond our reach. Such lines of thought point to the conclusion that there is no need to accept the idea of scientific insolubilia—in principle unanswerable questions about the modus operandi of nature. To identify an insoluble problem, we would have to show that a certain inherently appropriate question is such that its resolution lies beyond every (possible or imaginable) state of future science. This task is clearly a rather tall order. Its realization is clearly difficult. But not in principle impossible.

And so the question “Are there non-decidable scientific questions regarding nature’s ways that scientific inquiry will NEVER resolve⎯even were it to continue ad indefinitum” represents an insolubilium that cannot possibly ever be settled in a decisive way. After all, how could we possibly establish that a question Q about some issue of fact will continue to be raisable and unanswerable in every future state of science, seeing that we cannot now circumscribe the changes that science might undergo in the future? And, since this is so, we have it—rather interestingly—that this question itself is selfinstantiating: in being itself a question regarding an aspect of reality

101

ON PEIRCE AND UNANSWERABLE QUESTIONS

(of which of course science itself is a part) that scientific inquiry will never⎯at any specific state of the art⎯be in a position to settle decisively.6 We are cognitively myopic with respect to future knowledge. It is in principle infeasible for us to tell now but only how future science will answer present questions but even what questions will figure on the question agenda of the future, let alone what answers they will engender. In this regards, as in others, it lies in the inevitable realities of our cognitive condition that the detailed nature of our ignorance is—for us at least—hidden away in an impenetrable fog of obscurity. But of course insoluble questions relates to the issue of knowledge whereas the very impredictability of future knowledge renders the identification of noncognitive scientific insolubilia impracticable. The limits of one's information set unavoidable limits to one's predictive capacities. In particular, we cannot foresee what we cannot conceive. Our questions⎯let alone answers⎯cannot outreach the limited horizons of our concepts. To elaborate the prospect of identifying unknowable truth, let us consider once more the issue of future scientific knowledge—and specifically upon the already mooted issue of the historicity of knowledge. And in this light let us consider a thesis on the order of: (T) As long as scientific inquiry continues in our universe, there will always be a time when some then-unresolved (but resolvable) questions on the scientific agenda of the day will be sufficiently difficult to remain unresolved for at least two years. What is at issue here is clearly a matter of fact—one way or the other. But now let Q be the question: “Is T true or not?” It is clear that to answer this question Q we would need to have cognitive access to the question agenda of all future times. And emphasized above, in relation to theses of the always/some format—whose negation would run sometimes/all—are bound to be problematic for finite knowers because of the unusuality that is involved either way. Accordingly, just this sort of information about future knowledge is something that we cannot manage to achieve. By their very nature as such, the discoveries of the future are unavailable at present, and in consequence Q* affords an example of an insolubilium⎯a specific and perfectly

Nicholas Rescher • Episodes

102

meaningful question that we shall always and ever be unable to resolve decisively⎯irrespective of what the date on the calendar happens to read. 7. CONCLUSION As these deliberations indicate, the question “Are there in-principle unanswerable questions?” is one that requires disassembly into a multiplicity of distinct contexts because different contexts demand different answers—as follows: —in the formal disciplines if logic, language, and mathematics: decidedly YES —in the natural sciences: presumably NO —in matters of human cognition and action: decidedly YES —in metaphysics: decidedly YES In regard to the first case, the situation of vagrant predication is definitive. In regard to the second there is the fact that in-principle unanswerability is status-deconstructive: presumably if a question cannot possibly be resolved by scientific methods it is a question of metaphysics and not one of science itself. Then in regard to human affairs there is the fact of inevitable ignorance regarding the detail of our ignorance. Finally, as regards metaphysics there is reason to think that our stance should be reversed, with the question before us transformed to ask if there are any definitively answerable questions. For when the standard for being answered has the high qualification level that we have postulated here—the level of conclusiveness—then it becomes questionable if any answer at all can be secured for the questions of this domain. One important final observation is in order. The inability to answer an in-principle unanswerable question must not be seen as a cognitive limitation. Here as elsewhere it makes no sense to demand the impossible and complain regarding its unavailability. The realm of unan-

103

ON PEIRCE AND UNANSWERABLE QUESTIONS

swerable questions lies beyond the boundaries of knowledge and serves to set limits that constitute us finite creatures as the sort of beings we are. NOTES 1

Charles Sanders Peirce, Collected Papers, ed. by A. Hartshorn et al., Vol VI (Cambridge, Mass: Harvard University Press, 1929). Sect. 6.556.

2

Of course the circumstance that a question admits of one (determinably correct) answer does not prevent its also having another, different one. The question “What is an example of a prime number?” is correctly answered by 3 but also by 7.

3

See Paul Vincent Spade, “Insolubilia,” in The Cambridge History of Later Medieval Philosophy ed. Norman Kretzmann et al. (Cambridge: Cambridge University Press, 1982), 246-53.

4

We can, of course, refer to such individuals and even to some extent describe them. But what we cannot do is to identify them in the sense specified in #7 above.

5

A uniquely characterizing description on the order of “the tallest person in the room” will single out a particular individual without specifically identifying him.

6

And this issue cannot be settled by supposing a mad scientists who explodes the superbomb that blows the earth to smithereens and extinguishes all organic life as we know it. For the prospect cannot be precluded that intelligent life will evolve elsewhere. And even if we contemplate the prospect of a “big crunch” that is a reverse “big bang” and implodes our universe into an end, the project can never be precluded that at the other end of the big crunch, so to speak, another era of cosmic development awaits.

Chapter Ten HEDWIG CONRAD-MARTIUS AND THE SELF TRANSCENDENCE OF PHENOMENOLOGY

H

edwig Conrad-Martius was born in Berlin in February of 1888. She studied philosophy in Munich and Göttingen. Her prospect of an academic career was impeded not only through being a woman but also—and more direly—because she was rendered “non-Aryan” under the Nuerenberg Laws by having a Jewish grandparent. Lacking other sources of income, she lived on her wealthy family’s country estate at Bergzabern. She was a close friend of Edith Stein’s and, though herself Protestant, received a dispensation to serve as her godmother when Stein was received into the Catholic Church. Initially trained in Munich under the influence of Moritz Geiger and Alexander Pfänder, she transferred already before WWI to Göttingen to study with Husserl, Scheler, Reinach, and Theodore Conrad, whom she was to marry. After Dietrich von Hildebrand left there, she chaired the Philosophische Gesellschaft Göttingen. Her thesis—a phenomenological critique of positivism—won her the philosophy faculty’s prize, but because Göttingen’s regulations required Greek, she was awarded her doctorate (with distinction) for this thesis under Alexander Pfänder at Munich. At first trained in phenomenology, Conrad-Martius was increasingly drawn to Aristotle and then under the influence of Edith Stein became interested in the scholastics. Deeply interested in religion, she was over the years increasingly drawn to Christian mysticism. Beginning with her 1920 dissertation, she published some dozen books— including works on space-time and nature. The first World War caused the Conrads considerable personal and economic hardship, and by the time their estate at Bergzabern was back on its feet, the onset of Nazism blocked any prospect for Conrad-Martius to be habilitated for an academic career. Only in the late 1940s was Conrad-Martius—now

Nicholas Rescher • Episodes

106

reaching her 60s—able to obtain a lectureship at the University of Munich. She died in her late 70s in Starnberg. A long series of late-inlife books established her as one of the most productive philosophers of her day. But her long-enforced position outside the academic realm precluded the prospects of having any significant influence. * * * Conrad-Martius’s philosophical position is sometimes described as ontological phenomenology. But this is virtually a contradiction in terms. After all, the heart and core of phenomenology since Brentano is to focus on the phenomena—how things present themselves to the mind, without any intuitive pre-supposition or conjectural postsupposition regarding the material at issue. Description rather than explanation is at the heart of the original phenomenological standpoint. In her critique early of positivism, Conrad-Martius already stressed the limitations of experience as ordinarily understood. As she saw it, in its stress on observation, positivism admittedly only sensory experience as cognitively relevant mode of human experience. In response, she insisted on widening the experiential repertoire to encompass a broadening that allows even religions sensibility with its sense of the divine to penetrate into the very core of our being. But even here the interest in agronomy manifested her early work on The Soul of Plants (Die Seele der Pflanzen) pushed ConradMartius towards a concern for explanatory understanding. Though she always professed faithful adherence to the ideas of Husserl she ongoingly moved away from it in developing her realistic philosophy of nature. And here the crux of Conrad-Martius’s ultimate position lies in its prioritizing focus on the phenomenologically suspect explanatory question of why it is that the phenomena are as is—or indeed why there are any phenomena at all. Over time, scholastic realism captured the core citadel of her thought. Conrad-Martius now demanded a comprehensively renovated phenomenology—one extended from the “phenomena” of description to encompass those of theory (speculation). She effectively sought an inversion of traditional phenomenology, one whose perspective shifted from the experiential apprehension of things to encompass also a se-

107 HEDWIG CONRAD-MARTIUS AND THE SELF TRANSCENDENCE OF PHENOMENOLOGY

cond story endeavor, so to speak, of also explaining the ways by which we conceive and describe them.1 For Conrad-Martius , the paramount aim of metaphysical inquiry is to discern the ultimate origin of the factual reality encompassed in the phenomena at our disposal. For, as she sees it, the phenomena are never self-sufficient but lead on towards a grounding basis for their being as is. This quest for a basis has a dual aspect, being a matter not of causality alone, but of conceptuality as well. For while the being of phenomena does not consist in their being conceived it cannot be detached therefrom. This expanded program could well be seen as a way of deploying its conceptual apparatus of traditional phenomenology to achieve its own supercedence. For it replaced the project of an appearance-based doctrine trying to make sense of the appearance as such to a more speculative theory of being trying to make sense of the reality that manifests itself through them. From the angle of earlier phenomenology Conrad-Martius could thus be seen as a wolf in sheep’s clothing—an old style (or scholastic) ontologist. For having worked her way through phenomenology, so to speak, Conrad-Martius came out at the other end once more and goes beyond the problem of describing the phenomena to that of explaining them one the bases of an underlying productive nonphenomenal reality. All the same, her training in phenomenology had left a permanent imprint. For the initial impetus of phenomenology was the search for a method of understanding that was not grounded in the project of natural science. The early phenomenologists had their intellectual foundation in the negative reaction to a positivistic scientism that saw natural science (the dreaded Naturwissenschaften) as occupying the heartland of the intellectual domain of world-understanding. Like the Geistewissenschaften movement launched earlier on by Dilthey, they looked for an extra-scientific mode of understanding reality as we humans face it. And just this was the basic phenomenological commitment to a natural-science-distinct approach to understanding—something that Conrad-Martius retained from the very outset of her first post-doctoral publication. The ontological realism for which she strived in her tran-

Nicholas Rescher • Episodes

108

scendence of mainstream phenomenology was not the world of modern natural science but that of a naturalism rooted in Aristotle and the scholastics. Conrad-Martius’ early essay “On the Ontology and Phenomenology of External Reality” appeared as Vol. III of the “Annals for Philosophy and Phenomenological Research” edited by Husserl in 1916— the middle of WWI. The initial footnote describes it as forming the basis of her prizewinning 1912 Göttingen dissertation. Written in clear, relatively jargon-free Germany it exhibits a penchant for underscoring reminiscent of Queen Victoria’s epistolary style at its most emphatic. The main thrust of this early monograph is billed as a critique of positivism. Basic to Conrad’s deliberation is the contrast between objective reality and experience. Her key question is whether those realities which the positivist postulate as real actually deserve this ontological prioritization (p. 347). She wonders how—or indeed whether—a naturalistic realism based on aspects such as “external (mind independent) reality”, “objective thinghood”, “naturality”, causality”, etc. is ultimately warranted. Her anti-positivist position stressed that insofar as we have access to actual being (Sein) it is via a conscious epistemologically active mind’s agency (Bewusstsein), and that the reality postulated in a scientific-positivistic view of the world rests on a presumptive conformity here that may or may not be ultimately justified. Whether it in fact is so, Conrad sees as going beyond the limits of her investigation (p. 355), her salient point being that in its postulation of a purportedly mind-independent reality the scientific-positivistic view of the world ignores the problem of epistemological mediation, and seeks to obtain as it were by theft that which could only be secured honestly by intensive deliberative toil. Conrad-Martius’ key complaint is that the natural reality that positivists demand is not authorized by the only cognitive resource they claim to have at their disposal—viz. observation. As Conrad saw it our knowledge of the external world is unavoidably epistemologically mediated since what is given in experiences are not mind-independent realities but phenomena. She insists mind external reality such as we can possibly have it is never an experiential given but an experience-transcending construct. (The construction at

109 HEDWIG CONRAD-MARTIUS AND THE SELF TRANSCENDENCE OF PHENOMENOLOGY

issue here is, to be sure, not a matter of the social contrivance contemplated by present-day social constructivist theories of science, but rather something more like the inherent structuralization of the human intellect contemplated by Kant.) The crux of this critique of positivism—viz. its importance to good objective reality—was an idea that grew in Conrad-Martius’s mind to the point where it unraveled her commitment to phenomenology as well. As Conrad-Martius thus came to see it, a rigorous phenomenology points inexorably to its own transcendence. On the one hand we have no choice but to accept to phenomena at face value. We have to come to terms with them as they are and have no choice but to make the best and the most of this. But on the other hand, we do not need to see them as gift horses into whose mouths we need not look. For those phenomena are not self-explanatory. They do not wear their raison d’être on their own sleeves. The key explanatory question of how and why it is that the phenomena are as they are is one that the phenomena themselves cannot answer. An adequate philosophy cries out for moving beyond phenomenological descriptivity to an underlying reality that transcends the phenomena themselves in its capacity to account for their comprehension. And it is interesting that various important philosophers were even then at work on just this issue—as witness Russell with his “Our Knowledge of the External World,” and Carnap with his “Logische Aufbau Welt”—not to mention Wittgenstein with his Tractatus. In her insistence upon an epistemological intervention between experiential phenomenology and ontological reality, the early Conrad-Martius was by no means a voice crying in the wilderness. Epistemological constructionism was an idea whose time had come. Without exception, however, all of those involved in this movement toward phenomenal constructionism eventually became dissatisfied with it. Russell turned to a metaphysically based scientism, Carnap to neo-pragmatism, Whitehead to a neo-Leibnizian metaphysic, and Wittgenstein turned into the later Wittgenstein. As to Conrad herself, she advanced backwards to Aristotle. In her later, more realistic period she adopted a neo-scholastic Aristotleism which held that man as an integral part of nature dispose over a nature-internal mode of experience that automatically closes the epistemic gap between experi-

Nicholas Rescher • Episodes

110

ence and reality. Nature ensures conformity in theoretical experience even as the signet ring enforces standard uniformity with itself upon the wax—to revert to Aristotle’s own splendid analogy. The gap between experiential phenomenology and natural reality is crossed—or rather abolished—by the fact that man is an inherent part of nature. (If she had been able to read him, Conrad-Martius would have loved C. S. Peirce.) Like others among her phenomenologically inclined contemporaries, Conrad-Martius could not in the end resist the siren call of naturalistic realism. But unlike those who in abandoning naive physicalism looked to a way beyond to biology in psychology or sociology, Conrad-Martius favored a naturalistic realism grounded in the Aristotelian world view that prevailed before the scientific resolution of the 17th century reinforced the Cartesian a barrier between man and nature. * * * It is interesting to note that most of the major movements of 20th Century philosophy came to grief not through attacks from without but through internal issues that grew cancer-like from within as the program matured. The logical positivists could never quite get claim on empirical meaningfulness vs. metaphysical meaninglessness. The ordinary language philosophers could never demarcate acceptable (“everyday”) usage from unacceptable philosophical discourse. And the phenomenologist could never achieve a clear separation between genuinely descriptive, subjective phenomena, and causally contaminated objective characterizations between mere seemings and genuine appearances. Conrad-Martius touched a sore nerve here. However her influence was limited. She had no students; her books came close to being still-born off the press; if any present-day philosophers draw own her writings for their own work I don’t know about them. Her books sit on the library shelves unread. As best I can tell, only a handful of historical scholars have ever heard of her. What then are her claims on our attention? All the same, there is good reason to believe that she counts. She is a significant link in the rise and decline of a substantial philosophical movement, a significant tile in the mosaic of philosophical thought.

111 HEDWIG CONRAD-MARTIUS AND THE SELF TRANSCENDENCE OF PHENOMENOLOGY

And there is another aspect to the matter. Inspection of the relevant directories indicate that in the contemporary world there are some 50,000 professors of philosophy at work with several thousand new PhD’s annually inserted into the group. It seems clear that a profession as large and diversified as ours has enough intellectual talent that some of it can and should be spent on even a lesser magnitude star like Conrad-Martius who does, after all, play a role of some interest within the larger movement of substantial significance we constitute under the heading of phenomenology. The reality of it is that the main ideas of a philosophical star of the second or third magnitude can have greater interest and illustration than minor thoughts of one of the first magnitude. The 100th study of Kant’s “Deduction of the Categories” can add but little to what we already know, while an examination of the relatively unexplored a thinker like Conrad-Martius gives promise to adding something more significant to our understanding of philosophical issues.2 NOTES 1

This aspect of her critique of phenomenology was anticipated by Heinrich Richert in the previous generation. However, he deployed it in a quite different direction.

2

This chapter was delivered as an invited address in a Conference on Munich/Göttingen Phenomenology held at the Franciscan University of Steubenville in May of 2011.

Chapter Eleven THE WAR OF THE WORLDS 1. DUAL REALMS: KANT

T

he idea of distinct worlds was projected into modern philosophy by G. W. Leibniz, building on ancient thinkers ranging from Plato to St. Augustine. In his classic Monadology we read: [Intelligent beings or—as I shall call them—Spirits] compose the City of God, that is, the most perfect state possible, under the most perfect of monarchs. This City of God, this truly universal monarchy, is a moral world (monde), within the natural world, and is the most exalted and the most divine of the works of God. (Monadology, sect’s 85-87).

Leibniz thus clearly contemplated a duality of worlds—a moral world of intelligent beings functioning within, but characteristically different from the wider natural world of physical existence. Immanuel Kant picked up on this word duality in his 1770 inaugural dissertation on the sensible and intelligible worlds (De mundi sensibilis atque intelligibilis forma et principiis). And Kant carried this two-worlds view into the Critique of Pure Reason and also, and especially, into his later moral philosophy. For here we encounter—first off— the world of experience with regard to what alone inquiring reasons can achieve information deserving the name of knowledge. However, man is an amphibious being who lives not only in the realm of knowledge but also in that of action. And here, in the moral domain, we encounter an intelligible world in which a different set of groundrules obtains. All events in the sensible world stand in thoroughgoing connection in accordance with unchangeable laws of nature is an established principle of the Transcendental Analytic, and allows of no exception. . . . . [But] whatever in an object of the senses is not itself appearance, I entitle intelligible. If, therefore, that which in the sensible world must be regard-

Nicholas Rescher • Philosophical Episodes

114

ed as appearance has in itself a faculty which is not an object of sensible intuition, but through which it can be the cause of appearances, the causality of this being can be regarded from two points of view. Regarded as the causality of a thing in itself, it is intelligible in its action; regarded as the causality of an appearance in the world of sense, it is sensible in its effects. We should therefore have to form both an empirical and an intellectual concept of the causality of the faculty of such a subject . . . . (CPuR A536-039. B 564-67.)

As Kant thus saw it, a different mode of causal connection was operative in those two different worlds: There are only two kinds of causality conceivable by us; either causality according to nature or causality arising from freedom. The former is the connection in the sensible world of one state with a preceding state on which it follows according to a rule . . . . By freedom, on the other hand, in its cosmological meaning, I understand the power of beginning a state spontaneously. Such causality will not, therefore, itself stand under another determining it in time, as required by the law of nature. . . . (CPuR A 532-33 = b560-61). The effects of such an intelligible cause appear, and accordingly can be determined through other appearances. But its own causality is not so determined. While the effects are to be found in the series of empirical conditions, the intelligible cause, together with its causality, is outside the series and so may be regarded as free in respect of its intelligible cause. (CPuR A536-37 = B564-65.) All things in the world of sense are contingent, and so have only an empirically conditioned existence. But the non-empirical condition of the whole series . . . . would not belong to it as a member, not even as the highest member of it . . . . the whole sensible world, so far as regards the empirically conditioned existence of all its various members, would be left unaffected . . . . But its ground must be thought as entirely outside the series of the sensible world (as ens extramundanum), and as purely intelligible. (CPuR A560-61 = B588-89.)

And so even in the Critique of Pure Reason, Kant projected the duality of an empirical and an intelligible world-order. But with a crucial dif-

115

THE WAR OF THE WORLDS

ference. For now the non-sensuous world was no longer to be transexperiential but rather opened to human cognition in a way that hinged on a distinction between sensuous and non-sensuous experience. So somewhat along the lines of the distinction between physical and moral sensibility contemplated by the Scottish philosophers. 2. DUAL REALMS: INTUITIVE IDEALISM AMONG THE POST KANTIANS

In the post-Kantian tradition of German philosophy, this idea of variant worlds became a pervasively accepted conception that endorsed for well over a century. Hermann Lotze (1817-1881) Following in Kant’s footsteps, Lotze contemplated two principal realms of human concern: of thought and feeling, of cognition and appreciation—a realm of informative (preeminently scientific) knowledge, and one of action-guiding (preeminently effective) valuation. For Lotze, we humans are amphibians who live and function in these two worlds. The one of them is the world of sensory descriptions (of “I see” or “I hear” etc.), a realm of whose materials provide the grist for our theoretical construal of physical nature which we seek to domesticate cognitively via the process of causal explanation. The other world is that of affective feeling, of pro- and con-reactivity, of positive or negative response—of valuation and evaluation. And while natural science deals with observable fact it leaves aside another dimension—the affectively geared value dimension of “meaning” and human significance. The causal explanation of science—Kant’s causality of nature—is that our prime vehicle for understanding the natural world. But motivational explanation based on value assessment—Kant’s causality of purpose—is our prime vehicle for implementing our concerns with the affective world. And while man is but a small and significant speck of existence, nevertheless within the natural world sentient and especially intelligent beings are the very indispensable pivots of the affective world.

Nicholas Rescher • Philosophical Episodes

116

Accordingly the study of reality has two regions: natural science (Naturerkenntnis) based on observation and inductive generalization, and the ethical apprehension of values (Wertethik) based on the reactive affectivity of intelligent beings. These are different problems but they do not address different domains: reality is one and it has both its procedurally nomic (natural-science accessible) sets and its evaluatively normative scale coordinated to the self-posited purposes of man. Both scientific understanding and normative evaluation are different poles of one single unified power of understanding, akin to the unity of perception/conception/explanation in Leibniz. Wilhelm Dilthey (1833-1911) For Dilthey, there are two ways of conceiving reality, dealing respectively with the cosmos as natural science sees it, and the world (or worlds) we humans see it (or them) as encompassing in world-views (Weltanschaungen). The former is the realm of the natural science (Naturwissenschaft) and is—as best one can tell—unified and uniform; the latter is the realm of the human sciences (Geisteswissenschaften) and is plural and diversified. In studying the latter, we are not concerned with a single and uniform object of concern (as in the qualified realm of the natural sciences) but with a diversity of interpretative perspective. Here the crux is not sense-observation and measurement but the sympathetic or empathetic understanding (Verstehen) needed to enter into the point of view of a given historically formed culture. Experience (Erlebnis) is the fundamental reality of life (Leben) and it provides our only immediate access to reality. And here significance (Bedeutung, meaning) is crucial in its induction of what experience means for us—its possessor. This factor endows all of experience with a value aspect. Just this contextualizes all experience to the condition of its possessor and means that a proper understanding of human dealings and doings can never be properly understood (Versteht) without appropriate contextualizations, something which—in the end, demands an empathetic re-experiencing (Nacherleben).1 Although Dilthey designated both the natural and the humanistic sciences as such, that is as sciences, he was insistent that different modes of in-

117

THE WAR OF THE WORLDS

quiry process were at issue. For the former is a matter of reasoning by inductive generalization from observation, and the latter is fundamentally a matter of reasoning by analogy from the substantive character of immediate experience. With Dilthey there are accordingly two essential sectors to philosophy geared to two aspects of the human condition—viz. a scientific philosophy geared to our presence in the world of nature (“Naturphilosophie”) and a philosophy of life (“Lebensphilosophie”) geared to the affective interiority of human experience—the realms of observation and of feeling, respectivity, of outer-oriented and inner-oriented concerns. These realms constitute the province of the natural sciences (Naturwissenschaften) and that of the humanistic sciences (Geisteswissenchaften), respectively, the latter geared not to observation but to outer-directed empathetic comprehension (Verstehen). And such human life invariably unfolds in an historico-cultural setting, this contextual correlativity is an essential requisite for understanding and explaining human affairs. Accordingly human actions and events cannot be account fur in naturalistic terms, but demand an historically contextualized approach that retraces the affective experience of the agents involved (“Nacherleben” is a crucial component “Verstehen.”) Wilhelm Windelband (1848-1915) Like Lotze before him, Windelband sharply distinguished between the cognitive/scientific and the practical normative domains, between descripting and explaining nature’s phenomena and assessing and shaping the course of human action. As he saw it, cognitive/theoretical deliberations issue factual judgments (Urtheile) and practical/evaluative deliberations issue in normative appraisals (Beurteilungen) often both modes of cognition can be brought to bear, as when our thought process can be described either from the scientific (observational) or from the experiential (effective) point of view. Returning to the ancient Greek dualism between physis (nature) and nomos (custom), Windelband distinguishes between the natural laws at issue in the physical sciences and the human norms that figure in the cultural sciences, the former imposed by nature and the latter by man. The cultural norms are inherently evaluative and fall into three

Nicholas Rescher • Philosophical Episodes

118

regions: the ethical (right/wrong), the evaluative (good/bad), and the aesthetic (beautiful/ugly). And human thought accordingly divides into an observation-based Normal benusslesn at issue with the domain of natural sciences and a normatively geared Wertbewusstsein geared to the implementation of evaluative norms.2 Husserl (1859-1938) The idea of a life-world (Lebenswelt) of human experience in contrast to the envisioning natural world studied by the natural sciences was also prominent in Husserl (1859-1938). Followed in this regard by Heidegger with his “Welt des alltaeglichen Daseins,” Husserl wanted to ground philosophy in ordinary experience, taking the experiential phenomena as is, without trying to get past or beneath them through a science geared to non-experiential (theoretical) mechanisms of explanation. (As far as his acolyte Heidegger was concerned, poetry affords a better entryway into this lifeworld than does science.) With Husserl we essentially have the contrast between a physical cosmos or universe, which in principle may or may not contain sentient let alone intelligent beings, and a world as a realm experientially apprehended by its intelligences. Heed of this distinction led Husserl to the otherwise strange-seeming contention that if there was no consciousness, there would be no world. With all those post-Kantian theorists, the salient contrast was no longer that of a Kantian phenomenal realm explainable and understandable via theoretical/scientific investigation and an underlying transcendental realm of underlying reality—as per a Realm of Appearance in contrast with a Realm of an-sich Reality that grounds the appearances. Instead, their contrast was that between a theory-geared realm of observation in contrast to an experientially accessible realm of human sciences based on experiential participation rather than observation. Along these lines the more idealistically theorists proposed to absent the phenomenal world of science into the human thought world viewing science as itself a human thought-artifact they say things like

119

THE WAR OF THE WORLDS

• “All that is lies in the range of consciousness”: “Alles Seiende liegt innerhalb des Bewusstseins. (Windelband) • “If there were no intelligent beings there would be no world.” (Husserl) 3. FURTHER THEORISTS For C. S. Peirce (1839-1914) reality—God aside—consists basically of two departments: phenomena and signs. The phenomena of the natural domain are the concern of the scientific disciplines at large, and even at a certain level of abstraction of philosophy. The human disciplines focus upon signs. With Peirce signs and the symbolic process are characteristic all definitive features of homo sapiens, and indeed from a certain point of view man is himself a sign. There is, as Peirce sees it, a wider world of nature-at-large but within it and decidedly different from the rest a characteristically human world of symbolization. The sign-mediated interpretation of reality—above all in its artifactual sector—is an indispensible work of humanity. The present phenomena as we apprehend them are almost invariably signs of absent conditions and circumstances. Without the symbolic process meaning would vanish from the cosmos, and intelligence with it. The symbolic realm is a world of meaning within the wider setting of a world of nature, and it is this world which furnishes homo sapiens with his characteristic home. Sigmund Freud (1856-1939) stands prominent among those who have sought to devise a means for explaining human affairs and doings in a ways distinct from that of biological and social science. This is not the place to trace out the somewhat bizarre analgon of psychological mechanisms that figure in Freudian theory. What matters for present purposes is simply that the by-now familiar duality of nature and human science is transmuted by Freud into an analogous duality that contrasts standard sciences with psychoanalysis in a way based on a Dilthey-reminiscent idea of Verstehen that is now, however, shifted from the locus of the explanatory subject to that of the explaining ana-

Nicholas Rescher • Philosophical Episodes

120

lyst because the former is in general quite unaware of what is actually going on. A dualized conception of time was central to the thought of Henri Bergson (1859-1941). On the one hand there is the geometrized time at issue in science, symbolized in physics by t and measures instrumentally by clocks, chronometers, and periodic physical processes. On the other side is the lived time of human experience, the “real duration” (durée réelle) of human experience as we undergo it. These two are fundamentally distinct and serve to define and characterize two distinct order of reality, the physical and observational reality of the scientists and the participatory reality of human life as we experience it. The one is subject to the determinism of impersonal law, the other to the free agency of autonomous human behavior. In line with this diversity, mankind has evolved into a duality of being. On the one side we are cognitive beings of nature’s causally temporalized physical reality, the realm of (scientific) knowledge. On the other side we are affective beings with an intuitive cognition of a different order of being—an immediate and note actually conceptualized grasps of a reality beyond. And thus as Bergson saw it, evolution has so developed as to manage to insert us into a Kant-reminiscent duality of a knowable and deterministic order of nature and an intuitable and indeterministic order of free agency. Thus evolution is creative in that it has ultimately brought to realization an intelligent creature whose thought transcends nature in its leap from a cognitive to an intuitive apprehension of a shift from a deterministic to an indeterministic mode of functioning. In Ernst Cassirer (1874-1945) we find a (not altogether willingly and wittingly) spiritual kinsman of Peirce’s, seeing that for Cassirer too the symbolic process is what characteristically distinguishes mankind from the rest of creation and sets the specifically human sciences apart from the natural. Max Scheler (1874-1928) prioritized the social contextualization of history. (“Alles [historische] Wissen ist . . .durch die Gesellschaft und ihre Struktur Bestimmt.”3) He envisions two cognitive domains, that of impersonal fact and that of personal value. The former is the sphere of natural science, but the understanding of human affairs squarely falls within the latter. And while the operative values are objective and

121

THE WAR OF THE WORLDS

universal, nevertheless different societies and cultures make different selections and different prioritizations among them (much as foods or diseases are universal, but different individuals or societies become involved with different groups of them.) Scheler was thus historical perspectivist par excellence. On his approach our view of the human past fragments into a series of perspectives which themselves turn into a plurality of perspectives of perspectives, and so on. Scheler sought to avert this difficulty by postulating that the historian (somehow as an exception to all the rules!) can survey the whole range of human concerns and empathetically understand each age and culture in its own interests. But just how such an empathetic exceptionlism to value contextuality is to operate—and indeed whether it can ever actually do so—is something that Scheler and his like-minded historicists have never been able to make clear.4 Perhaps the most widely diffused dual-realm theory of the 20th century was launched by English physicist/astronomer Arthur Eddington (1882-1944). In the “two tables” discussion of his best selling book on the Nature of the Physical World5 Eddington contrasted the table as the physicist sees it vs. the table or ordinary life experience. The one is solid and filled with material. The other is largely empty space and replete with electoral phenomenal. He wrote: I have settled down to the task of writing these lectures and have drawn up my chair to my two tables. Two tables! . . . . One of them has been familiar to me from earliest years. It is a commonplace object of that environment which I call the world. How shall I describe it? It has extension; it is comparatively permanent; it is coloured; above all it is substantial. After all if you are a plain commonsense man, not too much worried with scientific scruples, you will be confident that you understand the nature of an ordinary table . . . . Table No. 2 is my scientific table. It is a more recent acquaintance and I do not feel so familiar with it . . . . My scientific table is mostly emptiness. Sparsely scattered in that emptiness are numerous electric charges rushing about with great speed; but their combined bulk amounts to less than a billionth of the bulk of the table itself. Notwithstanding its strange construction it turns out to be an entirely efficient table. It supports my writing paper as satisfactorily as table No. 1. . . . . But there is nothing substantial

Nicholas Rescher • Philosophical Episodes

122

about my second table. It is nearly all empty space-space pervaded, it is true, by fields of force, but these are assigned to the category of “influences,” not of “things”. [And] even in the principle part which is not empty, we must not transfer the old notion of “substance” [since what is at issue is electromagnetic vibration and not “stuff”].

In the face of such a duality of perspectives, the logical positivists of the 1920-40 era launched a movement committed to the methodological unity of science. As they saw it, there is but one allcomprehensive world and one all-comprehending method for its systemic study. The methods for empirical inquiry that function effectively with respect to the natural world—the explanatory subsumption of phenomena under general laws—was necessary and sufficient for work across the board. In effect, for the Eddingtonian duality of a physical world of theoretical entities and an experiential one of ordinary objects, the logical positivists substituted the distinction between the real world and one of illusion and mirage. * * * One important distinction must be drawn at this point, namely that between worlds and world-perspectives. When one insists upon contrasting the physical world of nature with the life-world of human experience, is one talking of different worlds or of different worldperspectives—different ways of looking at one comprehensive reality? Clearly, perspectivalism is the easier option here. After all, one common landscape can be addressed from the angle of the landscape painter, the agronomist, the military engineer, the resources manager. That one single terrain lends itself to description from many distinct avenues of interest. But it is still one terrain. And this analogy rightly suggests that the situation of those “different worlds” is analogous: there is but one world but many would-facets in line with different ranges of concern on people’s dealings with it. The street that is flat for the hiker may not be so for the cyclist. What is at stake depends not just on the item at issue but on people’s modes of interaction with it—i.e. on the nature of the interests at stake.

123

THE WAR OF THE WORLDS

And to be realistic about it there really is no absolute and issuedetached prioritization here—no single option that prevails irrespective of the purposive context at issue. No one perspective, no one interest automatically trumps all the rest, independently of the problem context and without inference to the concerns and questions at stake. Here, as elsewhere, a functionalistic pragmatism coordinate with the particular purposes at hand seems to afford out most sensible and realistic recourse. All the same, for reasons that are not entirely clear the cognitive dualists of the Post-Kantian era preferred to cast their doctrine in the language of worlds rather than that of world perspectives. 4. MAN AND NATURE IN POST-KANTIAN EYES As the preceding considerations indicate, various German postKantian thinkers followed Kant into envisioning a duality of man and nature, conjoining a naturalism knowable to us by the resources of science with a humanism accessible to us in personal experience. Accordingly, the consensus position of the post-Kantian philosophers was that there is a distinctive field of systemic study—the humanistic discipline (Geisteswissenschaften)—concerned with what is peculiarity characteristic of homo sapiens and his works. Additionally—albeit more controversially—they held that the study of his human realm requires methods and procedures distinct from those of scientific inquiry at large—methods which prioritize the empathetic and affective modes of human experiences over the observational. The ruling idea was that the phenomena of the distinctively human realm are sui generis and that their description and explanation correspondingly require conceptually sui generis, resources. Within the natural world they saw a specifically human world whose study requires no specifically humanistic methods. However, on the key question of just what it is that crucially sets man apart from the rest of nature there was no consensus on priority. For throughout this post-Kantian era of dualistic inquiry there was doctrinal diversity with regard to the question of what it is that constitutes the distinctively characteristic feature of man which sets the system study of his doings apart from sciences of nature. Was it

Nicholas Rescher • Philosophical Episodes

124

• affectivity and conscious feeling • valuing and axiological experience • reflexive self-consideration • purposiveness (self-capacity of aims and goals) • deliberative decision (self-legislated) • self-determined rulishness and normativity (Kantian analogy) • rational deliberation • linguistic communication • symbolic thought • imagination (the capacity for supposition, assumption, fiction) Cognition apart, just what is the human capacity that affords our entryway into world the fabric of physical reality? To be sure, two further alternatives also remained: (1) None of the above. Positivism. Unity of science. Rejection of bifurcation by viewing man as just another natural phenomena. (2) All of the above. A complex combination of capacities—all maintained without significant prioritization. There really is no ready explanation for why this last comprehensive (and inherently plausible) alternative was never tried by some major figures in the field, apart from the consideration that funding a single distinctive fact in the human side will be sufficient to effect a split into two distinguishable realms.

125

THE WAR OF THE WORLDS

5. THE PROBLEM OF PERSPECTIVAL CONFLICT Not only can different conditions prevail in different worlds but world perspectives can disagree. How should one to react in the face of discordant rulings from different standpoints of consideration (perspectives?) Where do we stand when out worlds disagree? The starting point here is to acknowledge that the following triad involves no inconsistency whatsoever: • From the standpoint of X-type considerations, P is the case. • From the standpoint of Y-type considerations, Q is the case. • P and Q are logically inconsistent. Perspectival relationship maintains consistency here. Still, there yet remains the reaction of asking: “Yes! But which standpoint is the correct one?” However, this begs the very problematic questions of there being such a thing as one single correct standpoint. In general, this is a questionable proposition. A seemingly more plausible move would be to ask: “But how do matters stand from the synoptic, overall standpoint—one that encompasses both X-type and Y-type considerations.” But here the presumably correct response would be” They stand exactly as in the aforementioned triad.” We are now simply carried back to the starting point and have to confront and accept the there-described situation exactly as is. Given the unsatisfying character of these responses, it is needful to seek alternatives. And cover a considerable range: 1. Equivalentism: To see the various perspectives as equimeritorious and therefore let the discordant rulings cancel each other out. So here one adopts a judgment-suspensive agnosticism with respect to the issue, taking the line that “we just can’t say.” 2. Prioritization. To establish an order of priority among the various perspectives, and then let the ruling of the top-priority perspective prevail.

Nicholas Rescher • Philosophical Episodes

126

3. Combinationism. To search out a complex alternative amalgamating perspective—a “higher point of view”—that somehow combines and amalgamates the discordant perspectives and let it determine the outcome. 4. Perspectivalism. To accept the discord at face value, and let the situation stand as is, resting satisfied to say “From perspective A we have X and from perspective B we have Y, and even though these are incompatible we cannot get beyond this.” The variation of perspectives is seen at the end of the line here. 5. Contextualism. To take the line that in some contexts of deliberation (i.e., with some question issues) the one perspective is appropriate, while with others the other. It would be nice if Combinationism worked and there were always higher-level meta perspective from which all those variant base level perspectives can themselves be adjusted and adjudicated. Kant thought there was and that philosophy—that is, his own critical philosophy—supplied it. (His model was that of a higher court that fixed and set limits to the appropriate jurisdiction of the lesser courts.) However, subsequent developments put paid to this sort of philosophical imperialism, as better experience unfolded to show that any perspectival position was just that—namely a position that was itself just one among others. 6. CONTEXTUALISM’S APPEAL It seems clear that of all these alternatives it is Contextualism that presents the most promising option. For as far as “the appropriate position” goes there simply is no single “one size fits all” optimal overall resolution. The varying circumstances of the particular case must be allowed to determine which stance is appropriate. Thus consider the following range of cases in this light.

127

THE WAR OF THE WORLDS

Case 1. Kelvin vs. the Geologists: In the physics of the 1890s the reason was seen as a thermodynamic burning process. Now while this set the age of the solar system at a great many years, nevertheless looking to the geological strata led geologists and developmental biologists to require a timespan of at least ten times that length. In such a case of as conflict between different scientific disciplines an Equivalentist suspension of judgment would best afford a reasonable course, given our commitment to the idea that the same system must indeed have a particular age. Case 2. Aristotle vs. the Church Fathers. Aristotelian natural philosophy taught the eternity of the universe. The theology of the Church Fathers insisted it was created. The philosophers prioritized the one perspective, the theologians another. A neutral bystander could do little but to make a choice as between agnostic Equalitism and perfecting Prioritization. Case 3. Kant’s theoretical vs. practical philosophy. In Kant’s theoretical philosophy, determinism prevails. In his practical philosophy, there is an accepting emphasis on free will. But overall, as Kant sees it, the practical dimension has primacy from the point of view of human concerns. So his own position was one of Prioritization. Case 4. Eddington’s Two Tables. From the scientific standpoint we have to opt for the physicists’ table. But in the setting of ordinary life affairs, we can accept the table of “the plain man.” Overall, Eddington’s position is one of Contextualism that coordinates one’s position with the themastic domain at issue. To all appearances, then, the best line to take with regard to clashing worlds is that of a Contextualism that sees different approaches as available but lets the appropriate resolution stand on coordinative alignment with the specific conditions of the issue at hand. No single uniform mode of resolution is appropriate across the board—there is no one-size fits all solution. In this situation contextualization affords our best option. And so, on such an approach contextualism can hold

Nicholas Rescher • Philosophical Episodes

128

across the board—both with respect to plural world perspectives and with regard to plural methodologies. But how is one to tell which approach is appropriate in a given situation. What considerations are to be determinative here? The obvious answer lies in the conception of coherence—of harmony, consonance, fitness. One has to undertake a comparative analysis to scrutinize how plausibly each approach handles the case in hand, weighing out the advantages and disadvantages—the positivities and negativities—of each solution to determine the best available cost/benefit adjustment. Thus in the Eddington case, for example, it would be bizarre to adopt an Equivalentist agnosticism, and in the Kelvin case it would be equally absurd to proceed in the matter of combinationism. NOTES 1

However Dilthey insisted on objectivity here. It is no that everybody shares the same values, but rather that anybody can see that a person with a given set of values will function in a certain sort of way.

2

On these matters see especially Wilhelm Windelband’s essay in “Normen und Naturgesetze”, Präludien: Aufsätze und Reden zur Einleitung in die Philosophie (Tübingen: J. C. B. Mohr/Paul Siebeck, 1888; 3rd ed. 1907).

3

Max Scheler, Die Probleme einer Soziologie des Wissens (Muenchen, 1924), p. 48.

4

On this issue see Maurice Mandelbaum, The Problem of Historical Knowledge (New York: Liveright Publishing Corporation, 1938).

5

Arthur Eddington, The Nature of the Physical World,” New York (MacMillan) and Cambridge (Cambridge University Press), 1929. Wilfrid Sellars oft-cited distinction between “the scientific image” and “the manifest image” of things comes straight out of Eddington.

Chapter Twelve WHAT EINSTEIN WANTED 1. EINSTEIN’S DISCONTENT

A

lbert Einstein always thought that the quantum theory in its thenstandard formulation offered no more than a phenomenological observation-descriptive account of reality, bereft of any grounding rationale on the basis of fundamental principles.1 And Einstein disdained as scientifically insufficient and inadequate any theory which (as one recent expositor puts it) “owes its original to [mere] ‘facts of experience’ . . . [since] however compelling these may be, physicists then still did not have a ‘general theoretic basis’ capable of providing a logical foundation for the phenomenology at issue.”2 Einstein was intent upon explanatory understanding and therefore steadfastly rejected any observationality bottom-up, merely phenomenological empiricism. As that just-cited expositor puts it: He remained convinced that his program—his top-down approach, based on maxims of simplicity and naturalness . . . was a promising alternative that in the end would carry the day.3

On this basis Einstein was deeply discontent with quantum theory in its Bohr/Copenhagen version by having what has been characterized as “a methodological discomfort with the nature of its recourse to probabilities.”4 He resisted the introduction of underived probabilities into quantum physics because—as he himself put it—“I still believe in the possibility of a model of reality—that is to say, of a theory which represents things themselves and not merely the probability of their occurrence.”5 He thus viewed the probabilistic description of quantum phenomena as not so much incorrect as incomplete because in admitting probabilities as basic given facts in physics, quantum theory failed to do justice to reality’s descriptive definiteness of condition. As Einstein affirmed in a 1929 address:

Nicholas Rescher • Episodes

130

I admire in the highest degree the achievement of the younger generation of physicists which goes by the name of quantum mechanics, and I believe in the deep level of truth of that theory, but I believe that its restriction to statistical laws will be a passing one.6

Maintaining that “God does not play dice with his universe,” Einstein insisted that probabilities ought not to be introduced into physical theory as underived givens—or, perhaps better, takens—but should be accounted for in nonprobabilistic terms. Accordingly, Einstein told Peter Bergmann in 1949 that “I am convinced that the probability concept must not be introduced into the description of physical reality as primary [i.e. without derivation from plausible nonprobabilistic conditions].”7 As he saw it, probabilities as such are never basic, and his battle-cry was: ad probabilitatem esse deducendam: probability always is—or should be—something derivative. But how derivative, and deducible from what? To answer this question it is—strange to say!—expedient and instructive to go back to the very origin of modern physics in the 17th century, albeit not to Newton but to Leibniz. 2. THE LEIBNIZIAN PROJECT Leibniz regarded physics as an applied mathematics—or perhaps better, an enriched mathematics—one that is enlivened by its enmeshment with matters of existence in the real world. He writes: “There is nothing which is not subordinate to number; Number is thus like a metaphysical figure (numerus quasi figura metaphysica est) and arithmetic is a kind of statics of the universe by which the powers of things are discovered.”8 And as Leibniz saw it, the mathematicizing of nature is subject to certain basic principles. Nature has a vast host of problems to solve in the determination of her modus operandi. And this determination will have to align with an array of fundamental parameters of rational merit as encapsulated in certain basic principles of rational systematization.9 Like Einstein long after him, Leibniz envisioned a rational universe.

131

WHAT EINSTEIN WANTED

__________________________________________________________________________ Display 1 CLASSICAL SCIENTIFIC SYSTEMATIZATION Laws of Nature Inductive Judgment

Causal Explanation

Observations __________________________________________________________________________

The Leibnizian program in physics accordingly sought to dig through to a stratum deeper than that of the Newtonian synthesis. For Newton’s own program in physics was essentially that of the ancient Greek mechanicians and astronomers. With Archimedes and Ptolemy, it asks “What laws of nature can we stipulate to ‘save the phenomena’ by providing an adequate accounting for why our observations are as they are?” And it addresses this question as per the pattern of Display 1.10 There is an elegant equilibrium here. The phenomena instantiate and illustrate the operation of the laws, the laws determine and account for the phenomena. And in this neat arrangement there is both ontological and epistemological closure. However, Leibniz sought to go even further, taking a more ambitious line, one which in effect says: “Fine. Let’s give this program our efforts. But let us then suppose we are successful in getting a grasp on nature’s laws. Then there still remains the question: “Now viewing these laws themselves as our ‘phenomena’ how can we best ‘save’ them—how can we account for these laws themselves?” And so even as standard physics studies nature’s phenomena via observation and experimentation to discern the laws governing nature’s phenomenal modus operandi, so Leibnizian physics studies nature’s laws in thought-experimental deliberation to discern the “archi-

Nicholas Rescher • Episodes

132

______________________________________________________ Display 2 LEIBNIZIAN SCIENTIFIC SYSTEMATIZATION Principles Metainductive Reflection

Functionalistic Explanation Laws of Nature

Inductive Judgment

Causal Explanation Observations

______________________________________________________

tectonic” principles of rational economy and factual efficacy governing nature’s lawful modus operandi. As Leibniz himself put it: We can see the wonderful way in which metaphysical laws of cause, power, and action are present throughout all nature and how they predominate over the purely geometric laws of matter themselves, as I found to my astonishment (admiration) when I was explaining the laws of motion.11

And so as Display 2 shows, Leibnizian physics augments classical physics by superimposing upon it an added cycle of systematization consisting in a meta-inductive step to a set of explanatory principles that make it possible to account for the laws of nature. Even as classical physics seeks to “save the phenomena” by addressing the question of why the observations are as they are, so Leibnizian physics seeks to provide a scientifically cogent and rationally plausible answer to the question of why the laws of nature are as they are.12

133

WHAT EINSTEIN WANTED

As Leibniz saw it, such principles of rational design as those of continuity, of conservation, and of least effort can both guide our researches into nature’s laws and provide a framework for understanding and explaining the results of our investigations: they both serve to explain nature’s mode of operation and provides evidential qualitycontrol for our investigative hypotheses. It was on this basis that Leibniz said such things as: All natural phenomena could be explained mechanically [i.e., scientifically] if we understood them well enough, but the principles of mechanics themselves cannot be so explained . . . since they depend on more substantive [i.e. deeper] principles. (Tentamen anagogicum, GP VII 271 (Loemker 478).)

Leibnizian physics is thus a two-tier affair. It sees the world’s phenomena as explicable by the laws of nature, but has it that these laws themselves are to be explained with reference to fundamental principles of rational coherence. As Leibniz himself put it: All the particular phenomena in nature could be explained mechanically if we were capable enough . . . But I hold, nevertheless, that we must also consider how these mechanical principles and general laws of nature themselves arise from higher principles and cannot be explained by quantitative and geometrical considerations alone.13

What Leibniz ardently wanted was a functional account showing the physical laws of nature as we have them to be the optimal means of satisfying basic principle of operational economy—and so for classic physics to be exhibited as the best solution of a problem of rational design. Considerations of rational intelligibility (“sufficient reason”)— broadly understood to encompass such factors of rational economy at large, conservation, and symmetry [e.g., of action and reaction)— provide the driving impetus of Leibnizian physics. And here, as Leibniz saw it, the prime principles are those listed in Display 3. For what Leibniz emphasized in his physics was not just the lawfulness of nature, but the lawfulness of nature’s laws—their systemic harmonization within a systemic order as geared to principles of rational intelli-

Nicholas Rescher • Episodes

134

_______________________________________________________ Display 3 LEIBNIZIAN PRINCIPLES •

Fertility (variety, abundance, diversity, complexity)14

•

Economy and Simplicity (including matters of minimization and maximization: least effort, economy of operation, greatest efficiency, least time, least action)

•

Continuity (gaplessness, amplitude)

•

Definiteness (specificity, precision, mini-max determinacy)

•

Uniformity (regularity)

•

Consonance (simplicity, uniformity, consistency, regularity)

•

Conservation (equivalence of action and reaction and generally of the causa plena and effectus integer)15

•

Elegance (symmetry, harmony, balance)

________________________________________________________ gibility. The salient and characteristic goal of Leibnizian physics is accordingly oriented to the discovery of deeper physical—or, rather, metaphysical—principles for grounding Nature’s laws. Its key aim is not just the discovery of laws via phenomena but preeminently the explanation of laws via principles. And he set out to deploy such economic and aesthetic principles to account for the explanation of laws. For in Leibnizian physics, the situation is that, first, the laws as best we can discover them be used as a launching-platform for discerning the appropriate principles, and thereupon that these principles can and should be deployed to explain how and why it is that those laws are what they are.16 To be sure, there is circularity here, but it is supportive and substantive, and not vicious. Accordingly, Leibniz has it that: Although all the particular phenomena of nature can be explained mathematically or mechanically . . . it becomes increasingly apparent that

135

WHAT EINSTEIN WANTED

nevertheless the general principles of corporeal nature and of mechanics are themselves of metaphysical rather than merely geometrical form.17

The insistence not just on the lawfulness of nature but on the higherorder lawfulness of nature’s laws is the hallmark of Leibnizian physics. Leibniz insisted that the natural world is designed to function efficiently and economically, and for this reason its investigation must proceed on the principle that “the best hypothesis is that which plans the most phenomena in the simplest way.”18 Rational economy lies at the core: even sufficient reason has its economic dimension. (Why have something be so if one can losslessly dispense with it—i.e., if there is no good reason for its being so?) Leibniz thus envisioned such principles as formative constraints on the laws of nature. For they are not merely or only matters of mathematical elegance but manifest the pressure of rational economy on nature’s modus operandi. Given this gearing to the modus operandi of intelligence, the metaphysics of optimality and the epistemics of rational intelligibility stand coordinate with one another in Leibniz’s thought.19 3.

LEIBNIZ’S IMPLEMENTATION OF HIS PROGRAM THE MECHANICS OF REBOUND

Consider the issue of ball-bouncing in mechanics. And let us start with a billiard-table cushion here. Nature faces the following problem: To propel a ball from point X to point Z by bouncing it off the cushion. Which path is Nature to choose? What impact-point Y is to be appropriate here?

The most “convenient” path is of course the shortest—which is also the fastest when the ball moves at a constant velocity. And it is exactly this path—the one which, as it were, maximized the economy of effort that Nature in fact chooses, with its characteristic feature that the angle of incidence equals the angle of rebound.

Nicholas Rescher • Episodes

136

_____________________________________________________ Display 4 IMPACT INTERACTION

(1) (2)

_____________________________________________________ Again, let it be that a suspended moving elastic object meets a suspended standing one as per the diagram of Display 4. First let it be that the moving object (1) has greater mass then the standing one (2). Then on Cartesian principles (i) they will both move in the direction of the heavier, and (ii) if the moving object has less mass then the standing one, then the later will remain in place while the former bounces back in the direction from which it came. But there are problems here. For so reasons Leibniz, if the difference in masses be only a minuscule amount (∈) in object (1)’s favor then the motion of object (1) after impact will be →, but if object (2) is even minimally the more massive object (1)’s motion after impact will be ←. An infinitesimal difference in input will have a substantial difference in result. This violates Leibniz’s principle of continuity thereby also violates simplicity in specifying a significantly different modus operandi in fundamentally analogous cases. For Leibniz the Principle of Continuity provided for a uniformity of result that insists on the same outcome coming from different directions of approach. Accordingly, this principle was the Archimedean fulcrum that he used to dislodge the principles of Cartesian physics.20

137

WHAT EINSTEIN WANTED

THE OPTICS OF REFLECTION AND REFRACTION As Leibniz saw it, the principle of processual efficiency also governs laws that describe the motion of light. He put the matter as follows in his Discourse on Metaphysics: Snell, who first discovered the rules of refraction, would have waited a long time before discovering them if he first had to find out how light is formed. But he apparently followed the method which the ancients used for catoptrics, which is in fact that of final causes . . . For when, in the same media, rays observe the same proportion between sines (which is proportional to the resistances of the media), this happens to be the easiest or, at least, the most determinate way to pass from a given point in a medium to a given point in another. And the demonstration Descartes attempted to give of this same theorem by way of efficient causes is not nearly as good.21

And the same efficiency principle of time minimization obtains in refraction when rays of light travel from one medium into another— say from air to water. Here nature’s modus operandi obeys “Snell’s Law” which proportions the angles of reflection resistance and refraction to the density of the medium at issue, a relationship that once again maximizes efficacy by minimizing transit time.22 Leibniz ardently espoused this extremal, efficiency-oriented perspective, and he reproached Descartes with having used (in accordance with the Cartesian program) a more clumsy mechanical method in the derivation of Snell’s law, instead of the more elegant a priori principle of least time or distance.23 As he saw it, those Newtonian process-descriptive phenomenological laws of physics are to be derived from deeper, rationally cogent principles. But how did this work out? Here some historical background is relevant. 4. THE LEIBNIZIAN HERITAGE: RATIONAL MECHANICS In the 1740s P. L. M. de Maupertuis enunciated the principle of least action and used it to ground Fermat’s principle and derive Snell’s

Nicholas Rescher • Episodes

138

law in optics. His discussion was soon extended and generalized by Leonard Euler, who thereupon represented the principle as fundamental and applicable to all physical systems and not merely to light. In 1751 Maupertuis’ claims to priority were challenged by J. S. Koenig who cited a 1707 letter from Leibniz to—describing results tantamount to those in Euler’s 1744 paper. This publication created an intense priority dispute. Maupertuis and his supporters demanded that Koenig produce the original of the Leibniz letter, and when Koenig could only produce copies of this and related letters there was a sharp reaction. As president of the Berlin Academy, Euler himself accused Koenig of forgery. And the Academy declared the letter spurious and sustained Maupertuis’ claim to priority for the principle of least action. Koenig however, continued to defend Leibniz’s claim and various eminent figures—including Voltaire and Frederic II of Prussia— took sides in the quarrel, the former defending Koenig and the latter Maupertuis. The matter stood on an indecisive footing for some 150 years until it was settled by modern Leibniz scholars who discovered contemporary copies of those Leibniz letters cited by Koenig in various archives.24 Leibniz’s vision of a physics based on principles certainly found traction. The value of the principle of least action lies in its unifying effect; it provides a basis for the axiomatic development of large sections of physical theory. Here Leibniz’s insights were extended by Maupertuis, and in Lagrange’s Méchanique analytique the principle of least action was shown to be a sufficient basis for the deduction of the laws of mechanics, and the work of Hamilton extended this result to optics and dynamics. Some idea of the power of this principle can be gained from the following except from a paper in which Hamilton presented his results on optics to the Royal Irish Academy in 1824: Those who have meditated on the beauty and utility, in theoretical mechanics, of the general method of Lagrange, who have felt the power and dignity of that central dynamical theorem which he deduced in the Méchanique analytique . . . , must feel that mathematical optics can only then attain a coordinate rank with mathematical mechanics . . . , when it shall possess an appropriate method and become the unfolding of a central idea . . . It appears that if a general method in deductive optics

139

WHAT EINSTEIN WANTED

can be attained at all, it must follow from some law of principle, itself of highest generality, and among the highest results of induction . . . , (This) must be the principle, or law, called usually the Law of Least Action.25

In the hands of the great masters of classical mathematical physics—Euler, Lagrange, Laplace, Gauss, and Hamilton—the Principle of Least Action became the mainstay of rational mechanics. And the work of Gibbs and Mach further amplified its role.26 But from the very outset, Leibniz had already envisioned its significance and that of the general minimax principle from which it derived. However, as the 19th century moved along, other ideas and other paradigms came into prominence and by its end principles like minimax, economy, simplicity, and least action were not greatly in vogue. Moreover, a surprising revival has transpired in the later years of the 20th century. Various capable scientists have found their way back into a Leibnizian state of mind. Simplicity, fertility, and lawful order are back in vogue. Einstein wrote that “experience justifies one belief that nature is the realization of the simplest mathematical ideas that are reasonable.”27 The astronomer Mario Livio proposes a “cosmological aesthetic principle” encompassing such functions as simplicity, symmetry, continuity. The physicist Anthony Zee has the universe continuing in creative terms such functions as “unity and diversity, absolute perfection and boisterous dynamism, symmetry and lack of regularity.”28 And the physicist Freeman Dyson maintains that nature’s simple laws appear to be designed to “make the universe as interesting as possible.”29 Cosmologists Julian Barbour and Lee Smolin see the universe as exhibiting order amidst “extremal variety”.30 The idea of a physical domain subject to the rational efficacy and economy at work in Leibnizian physics is still alive and stirring.31 5. EINSTEIN’S PENCHANT FOR PRINCIPLES But let us now return to Einstein. The Leibnizian distinction between descriptively empirical phenomenological laws and the underlying rational principles that they instantiate and implement actually played a key role in Einstein’s thought. In his oft-cited London Times

Nicholas Rescher • Episodes

140

note of 28 November 1919 he discussed the epistemology of physical theories and emphasized the distinction between “constructive” or merely empirical theories based only on observation and “principle theories” that have a cogent rationale for being as is. And he insisted that those principle theories “have greater logical perfection and security in their foundations.”32 And Einstein went on to maintain: My interest in science was always essentially limited to the study of principles. . . . That I have published so little is due to this very circumstance, as the need to grasp principles has caused me to spend most of my time on fruitless pursuits.33

Writing to Paul Ehrenfest in 1925, Einstein described himself as a “principle-fanatic” (Prinzipienfuchser”).34 Einstein’s principles went beyond anything that constitutes a physical “law” as ordinarily construes (i.e., as a mathematical relationship between physical parameters of some sort, like F = ma or action = reaction). As early as 1919 he wrote: Along with this most important class of theories there exists a second, which I will call “principle-theories.” These employ the analytic, not the synthetic, method. The elements which form their basis and startingpoint are not hypothetically constructed but empirically discovered ones, general characteristics of natural processes, principles that give rise to mathematically formulated criteria which the separate processes or the theoretical representations of them have to satisfy. Thus the science of thermodynamics seeks by analytical means to deduce necessary conditions, which separate events have to satisfy, from the universally experienced fact that perpetual motion is impossible.

Among the fundamental principles of physics at work in Einstein’s thought were “simplicity” and the “economy” of process which harked back to Ernest Mach’s conception of physics, and beyond him to the tradition of rational mechanics.35 As he saw it, “nature is the realization of the simplest conceivable mathematical ideas [that serve for an explanation of certain fundamental facts].”36 And he accordingly affirmed that:

141

WHAT EINSTEIN WANTED

_________________________________________________ Display 5 EINSTEINEAN SCIENTIFIC SYSTEMATIZATION Systemic Basis of Fundamental (Axiomatic) Principles Deduction Rational Insight Guided by “Logical Simplicity”

Deductively Derived Laws Explanatory Reasoning Subsumptively Grounded Observations

NOTE: The diagram is adapted from Einstein’s own 1952 depiction as presented and analyzed in van Dongen 2000, pp. 51-55. ___________________________________________________________________________

I believe that [nature’s] laws are logically simple [his italics] and that trust in this logical simplicity is our best guide, so that it suffices to proceed from only a few empirical data. If nature were not arranged correspondingly to this belief, then we would have no hope at all of achieving any deeper understanding.37

In conversations with Valentin Bargmann, Einstein repeatedly insisted that his efforts in unified field theory were attempts to find the simplest theory in a given class.38 Rational economy via what Einstein himself termed the “logical simplicity” of theories was his guiding star. In his 1933 Herbert Spencer lecture at Oxford, “On the Methods of Theoretical Physics,” Einstein declared “Our experience hitherto justified us in believing that nature is the realization of the simplest conceivable mathematical ideas. I am convinced that we can discover by means of purely mathematical construction the concepts and laws connecting them with each other which furnish the key to the understanding of natural phenomenon.”39

Nicholas Rescher • Episodes

142

______________________________________________________________________ Display 6 Initial State of System Σ X

Final State of System Σ

X X

X

X

X

Transformation Process Π

Ensemble Manifold of Alternative Initial System-State Z Z

Z Z Z Z

Pathway P1 Pathway P2

Final State of System Σ X

__________________________________________________________________________

In a 1952 letter to Maurice Solovine, Einstein gave a diagrammatic sketch of the methodology he advocated for the physical sciences, which in its structure is closely analogous to the Leibnizian systematization of Display 2. (See Display 5). The fundamental kinship between Einstein’s vision of the methodology of systematization in physical science and that of Leibniz becomes readily apparent when one compares the tripartite structure of Displays 5 and 2. And the kin ship at work is all the more strikingly notable when one acknowledges that consideration of economy and simplicity is in each case the driving force of the process of systematization that is at work. 6. EINSTEIN’S APPROACH ILLUSTRATED But how is one to obtain probabilities from nonprobabilistic processes via considerations of simplicity and rational economy? The general idea is implicit in what Einstein wrote to Bohm: “I do not believe in micro- or macro-laws, but only in structure laws that lay claim to a universally binding validity.”40 And the pivotal fact is that when such laws are to serve the interests of simplicity across the entire ensemble of possible state-conditions, a recourse to probabilities can become derivatively necessary. For once one poses a problem to na-

143

WHAT EINSTEIN WANTED

________________________________________________________ Display 7 A

B

+ Ÿ +

______________________________________________________ ture—or indeed once nature sets a problem to itself—the economic factors of the effectiveness and efficiency of a given solution come upon the agenda. And just here it becomes possible for probabilities to enter in, seeing that there are some such optimization problems that are best addressed by probabilistic machinery. To convey a general idea of such a pathway to probability let us consider a simple illustration of a solution of the type familiar from classical rational mechanics which endeavored to show how various laws of nature are as is because conformity to them provides for maximal efficiency-effectiveness-economy of operation. Consider a process Π that takes all constituents of a physical system Σ from an initial state to an end-state as per the top of Display 6. But now let it be that this can be accomplished by one of two pathways P1, and P2, where that initial state can be any one of an ensemble of alternatives Z. (See the bottom half of Display 6). Two lawful modes of transition can be contemplated here: (1) One based on a deterministic law to the effect that every Type 1 constituent of the system effects its state-transit by pathway P1, and every Type 2 constituent of the system effects its state transit by pathway P2.

Nicholas Rescher • Episodes

144

(2) One based on a non-deterministic law that says that any given constituent effects its transit stochastically by P1 with probability p1 and by P2 with probability p2. Now such a transition in the condition of the system can be deemed efficient to the extent that it effects the transition at issue more smoothly—more rapidly or economically—when considered on average across the whole spectrum of the initial-state ensembles. And on this basis, there will be some state-transitions that will operate more efficiently by (2)-style randomness than by (1)-style strict lawfulness. For an example here consider the set-up depicted in Display 7. At issue here is a hypothetical transmission process where there is to be a transfer of the five “units” distributed on side A of a barrier to side B. There are two revolving-door turnstile considerations between the two sides, each of which can allow the passage of one “unit” per second. Now consider two possible and plausible lawful rules for unit transit: I.

Effect transit via the nearest passageway.

II. Effect transit via a passageway selected 50:50 at random. The rule to be adopted is to be general, covering the entire spectrum of alternatives—the “ensemble” range of alternative possibilities for distributing units or the A side of the barrier. It is clear that, in these conditions, rule II would make the transfer of units from such to side B no-one efficient (i.e. faster). For if efficiency to be achieved throughout the entire ensemble of possible initial conditions, then the behaviour of individual constituents may well have to be governed by laws geared to probabilities. It would obviously be more efficient and speedy to have those units pick a gate at random to minimize a traffic jam than to follow a uniformly fixed strict rule. Further, consider also the prospect that those two connective turnstiles rotate at different speeds, say one at twice the rate of the other. Then the optimizing rule for those individual units would not be to effect a transit with one-to-one-randomness as between the two turnstiles but to head for the faster at a two-to-one ratio of probability. For maximum efficiency the operative probability would then have to be

145

WHAT EINSTEIN WANTED

adjusted to the mechanical mode of turnstile operation. Probability would thus become derivative from nonprobabilistic features of the modus operandi of the physical set-up at issue via considerations of efficiency and economy. What we have here is the realization of a mode of operation which, while indeed allowing the individual subunits of a system “to throw the dice” as it were in line with probabilistic variation, this so functions as to realize a process which overall achieves its product in a way that is optimally effective, efficient, and economical. As such illustrational indicate, it can readily prove to the advantage of a system in point of economy, stability, or viability that its components should behave randomly. For rigid regularity involves overload, and randomness helps to keep things on an even keel. Take the analogy of human affairs. Not every passenger should go to the same side of the boat. In evacuating an unevenly occupied building the universalized instruction “Go to the nearest exit” may not be as effective as “Just leave” (by whatever exit you may wish). The salient point of such a condition of things lies in its showing that if certain definite global conditions are to be realized with maximal efficacy in the comportment of a physical system, then its constituent elements may have to conform to probabilistic laws of behavior. On such an approach, probabilities need not enter by unexplained fiat, but can prove to have an explanatory rationale in terms of fundamental principles. And it was apparently just this sort of thing that Einstein had in view. The fact of it is that Einstein had nothing against probabilities as such: it is only elemental probabilities that have no rationale in considerations of principle that he finds objectionable. “That there should be statistical laws that require God to throw dice in each individual case, I find highly disagreeable.”41 Accordingly, probabilities should not just spring into being ex nihilo, but should emerge as part of a solution to a problem of optimization under plausible constraints.42 As he saw it, those physical processes—probabilistic and improbabilistic alike—should have a cogent rationale. He did not hesitate to decline that “When I am judging a theory I ask myself whether, if I were God, I would have arranged the world in such a way.”43

Nicholas Rescher • Episodes

146

7. CONCLUSION The definitive task of Leibnizian Physics—and of the rational mechanics to which it gave rise—was to show that the laws of nature themselves represent solutions to problems of optimization under constraint mediated by considerations of economy and efficiency: in sum, to equip those laws with a rationally cogent explanation for being as is. As this approach developed from Maupertuis to Hamilton, rational mechanics was a realization and elaboration of the Leibnizian vision of physics with its prospect of grounding the laws of nature in underlying principles of economy and efficiency. And Einstein’s position with respect to quantum theory ran along just these lines. For what Einstein wanted was a functional account showing the physical laws of nature as we have them to be the optimal means of satisfying basic principles of rational economy—and so for quantum theory to be exhibited as the best solution of a problem of rational design. In short, Einstein’s great pragmatic desideratum in physics was isomorphic with that of Leibniz. Einstein too was committed to the quest for a Leibnizian physics. The idea of probing behind the laws of nature to consider why they should be what they certainly fascinated Leibniz and impelled his thought in a theological direction. And even Einstein himself was on board here—at least in his more ruminative moments. For he expressed surprise that “despite such harmony of the cosmos as I, with my humble human mind, am able to recognize, there yet are people who say that there is no God.”44 To be sure, Einstein’s God was certainly not personal and anthropomorphic but rather something along the lines of a governing force or power endowing the universe with a harmonious rational order—something akin rather to the cosmic nous of Plato’s Timaeus than to the Judeo-Christian God. But the fact remains that when Einstein made his oft-quoted remark “I believe in Spinoza’s God who reveals himself in the orderly harmony of all that exists”45 he was far from being on target. For his position with regard to the rational methodology of physics was in fact much closer to the optimalism of Leibniz than to the absolute necessitarianism of Spinoza.46

147

WHAT EINSTEIN WANTED

The crux of the matter is that Einstein wanted quantum probabilities to be obtained by derivation under the aegis of rationally cogent basic principles. In specific he was seeking for a higher-level perspective of physical principles that would engender the probabilistic detail of quantum theory as the demonstrably adequate resolution of a problem of optimization under constraints—a projection of the classic standpoint of rational mechanics into the latter-day realm of quantum mechanics.47 And there really seems to be no ultimately compelling reason of fundamental principle why he cannot have his way here.48 REFERENCES Allen, Diogenes, “Mechanical Explanations and the Ultimate Origin of the Universe Accordingly to Leibniz,” Studia Leibnitiana, Sonderheft 11 (Wiesbaden: Franz Steiner, 1983). Barbour, Julian and Lee Smolin, “Extremal Variety as the Foundation of a Cosmological Quantum Theory,” published on the web at http: arxiv.org/hep-th/9203041. Breger, Herbert, “Symmetry in Leibnizian Physics,” in Anonymous (ed.), The Leibniz Renaissance (Firenze: Leo S. Olschki, 1989), pp. 23-42. Calaprice, Alice (ed.), The Expanded Quotable Einstein (Princeton: Princeton University Press, 2000). Duschesneau, Francois, Leibniz et la méthode de la science (Paris: Presses Universitaires de France, 1993). Einstein, Albert, “On Generalized Theory of Gravitation,” Scientific American, vol. 182 (1950), pp. 13-17. Gale, George, “The Physical Theory of Leibniz,” Studia Leibnitiana vol. 2 (1970), pp. 114-127 Gerhardt, C. I. (ed.), Die philosophischen Schriften von G. W. Leibniz, 7 vol.’s (Berlin: Wiedmann, 1875-90). Goldstein, Rebecca, Incompleteness: The Proof and Paradox of Kurt Gödel (New York: Norton, 2005). Gueroult, Martial, Dynamique et métaphysique Leibniziennes (Paris: Les Belles Lettres, 1934) Horgan, John, Rational Mysticism: Spirituality Meets Science in the Search for Enlightenment (New York: Haughton Mifflin, 2003).

Nicholas Rescher • Episodes

148

Jourdain, P. E. B., The Principle of Least Action (Chicago: Carus, 1913). Lanczos, Carnetius, The Variational Principle of Mechanics (New York: Dover, 1986). Livio, Mario, The Accelerating Universe (New York: John Wilem, 2000). Loemker, L. E. (ed.), Leibniz: Philosophical Papers and Letters, 2 vol.’s (Chicago: University of Chicago Press, 1956); 2nd ed. in one vol. (Amsterdam: Reidel, 1970). Mach, Ernst, Die Mechanik in ihrer Entwicklung (Leipzig: Brockhaus, 1901). Mugnai, Massimo, Introduzione alla filosofia di Leibniz (Torino: G. Einaudi, 2001). Norton, John, “Nature is the Realization of the Simplest Conceivable Mathematical Ideas: Einstein and the Canon of Mathematical Simplicity,” in Studies in the History and Philosophy of Modern Physics, vol. 31 (2000), pp. 135-70. Pesic, Peter, Labyrinth: A Search for the Hidden Meaning of Science (Cambridge, MA: MIT Press, 2000). Poser, Hans, “Apriorismus der Prinzipien und Kontingenz der Naturgesetze: Das Leibniz-Paradigma der Naturwissenschaft,” in A. Heinekamp (ed), Leibniz’ Dynamica (Stuttgart: Franz Steiner, 1984; Studia Leibnitiana Sonderheft 13), pp. 164-79. Sommerfeld, Arnold, Eleckdynamics: Lectures in Theoretical Physics, Vol. III [to E. G. Ramberg (New York: Academic Press 1964; German original: Klemm Verlag, 1948). van Dongen, Jeroen, Einstein’s Unification (Cambridge: Cambridge University Press, 2010), pp. 177-78. Wallace, W. M., Soul of the Lion: A Biography of General Joshua L. Chamberlain (Edinburgh: Thomas Nelson & Sons, 1960). Zee, Anthony, Fearful Symmetry (Princeton: Princeton University Press, 1999). NOTES 1

See Jeroen van Dongen, Einstein’s Unification (Cambridge: Cambridge University Press, 2010), pp. 177-78. P. 157. It may be of incident of interest that the writer can himself claim a somewhat curious family connection with Einstein. For there once lived in Adingen, in the Neckar valley in the Swabian region of Germany, one Salomon Pappenheimer (1794-ca. 1870)—a merchant and the richest man in town. He married three times. His first wife died in childbirth. His second wife was Sarah

149

WHAT EINSTEIN WANTED

NOTES

Rescher (1805-1834) of my family, who died enroute to a visit in North America when her ship foundered in a storm. He thereupon married his third and last wife. She was Margot Einstein (1806-1868) of the family of the great Albert. 2

Van Dongen, p 125.

3

Van Dongen, p 174.

4

Van Dongen, pp. 177-78

5

Cited in Van Dongen, p 177.

6

Alice Calaprice (ed.), The Expanded Quotable Einstein (Princeton: Princeton University Press, 2000), p. 246. The original edition (drop “Expanded”) appeared in 1996 and a later revision (change “Expanded” to “New”) in 2005.

7

See van Dongen 2010, pp 154-55.

8

GP VII 184. Citations in this style refer to C. I. Gerhardt (ed.), Die philosophischen Schriften von G. W. Leibniz, 7 vol.’s (Berlin: Wiedmann, 1875-90).

9

The principal secondary sources bearing upon Leibniz’s physics include: Martial Gueroult, Dynamique et métaphysique Leibniziennes (Paris: Les Belles Lettres, 1934); George Gale “The Physical Theory of Leibniz,” Studia Leibnitiana vol. 2 (1970), pp. 114-127; Diogenes Allen, “Mechanical Explanations and the Ultimate Origin of the Universe According to Leibniz,” Studia Leibnitiana, Sonderheft 11 (Wiesbaden: Franz Steiner, 1983); Hans Poser, “Apriorismus der Prinzipien und Kontingenz der Naturgesetze: Das Leibniz-Paradigma der Naturwissenschaft,” in A. Heinekamp (ed), Leibniz’ Dynamica (Stuttgart: Franz Steiner, 1984; Studia Leibnitiana Sonderheft 13), pp. 164-79; Herbert Breger, “Symmetry in Leibnizian Physics,” in Anonymous (ed.), The Leibniz Renaissance (Firenze: Leo S. Olschki, 1989), pp. 23-42; and Francois Duschesneau, Leibniz et la méthode de la science (Paris: Presses Universitaires de France, 1993).

10

The given schematic enfolds, sight unseen, the crucial stage of applicative testing of the laws leading either to confirmation or replacement/revision.

11

GP VII 305. Tr. in L. E. Loemker (ed.), Leibniz: Philosophical Papers and Letters, 2 vol.’s (Chicago: University of Chicago Press, 1956); 2nd ed. in one vol. (Amsterdam: Reidel, 1970), pp. 488-89. (Henceforth cited as simply Loemker.)

12

Leibniz himself then took the further step of adding yet another cycle of systematization that proceeds in theological terms to provide a rational explanation of the explanatory principles themselves. As he put it in a 1679 letter to Christian Philip: For my part I believe that the laws of mechanics which serve as foundation for the whole system [of physics] depend upon final causes, that is to say, on the will of God determined to do what is most perfect ... (GP IV 281-82 (Loemker 273).)

Nicholas Rescher • Episodes

150

NOTES

As Leibniz saw it, the world exists as is because God has chosen to create it that way. And God has so chosen it because that particular world design is optimal. Now here one could, in theory eliminate the middle man and move directly from optimality to existence. In a post-Kantian, not to say post-Nietzechean world, such a sidelining the deity may have a certain appeal. But this view of the matter just was not Leibniz’s—no matter how insistently Bertrand Russell thought it should have been. To be sure, a purely naturalistic Leibnizianism would of course refrain from taking this further, theological step, but for Leibniz himself it was crucial. In any case, for Einstein’s version of exactly this selfsame picture see van Dongen, pp. 51-57. 13

GP IV 391 (Loemker 409).

14

The duly balanced combination of all of these factors is what Leibniz calls harmony, which is for him, the hallmark of perfection.

15

On this principle see especially Leibniz’s letter to de l’Hôpital of 15 January 1696 (GM II 308).

16

Although Leibniz holds that it lies in our power to see how the fundamental principles of natural philosophy can, at least in principle, account for the laws of physics, it is beyond our power to see how they account for nature’s particular detail. This insight is reserved for God alone. On this issue see Hans Poser, “Apriorismus.”

17

“Discourse of Metaphysics,” §18; GP IV 444 (Loemker 315).

18

See the preface to Leibniz’s edition of Nizolius and compare Massimo Mugnai, Introduzione alla filosofia di Leibniz (Torino: G. Einaudi, 2001), esp. pp. 152-63.

19

Many thoughtful people have over the years taken much the same line. Thus in addressing a university convocation in the late 1800’s Joshua L. Chamberlain (Civil War hero, Governor of Maine, and Bowdoin University president) said: Sooner or later . . . .they [our men of science] will see and confess that these laws along whose line they are following, are not forces, are not principles. They are only methods . . . Laws cannot rightly be comprehended except in the light of principles . . . .Laws show how only certain [limited] ends are to be reached; it is by insight into Principles that we discover the great, the integral ends . . . Now the knowledge of these Laws I would call Science but the apprehension of Principles I would call Philosophy, and our men of science may be quite right in their science and altogether wrong in their philosophy. (Quoted in W. M. Wallace, Soul of the Lion: A Biography of General Joshua L. Chamberlain (Edinburgh: Thomas Nelson & Sons, 1960). Pp. 232-33.) The perspective at issue here is in much the same spirit as the more profoundly developed ideas of Leibniz, who did, however, see Principles as still belonging to natural philosophy and thus to science itself.

151

WHAT EINSTEIN WANTED

NOTES 20

See in particular his Critical Thoughts on the “Principles” of Descartes, GP IV 354-92, esp. p. 375 (Loemker 397-98).

21

“Discourse of Metaphysics,” §22, G IV 447-48 (Loemker 317-18).

22

The law in question was stated by Willebrord Snell in 1621.

23

“Tentamen anagogicum,” GP VII 274 (Loemker 478).

24

On the historical issues see P. E. B. Jourdain, The Principle of Least Action (Chicago: Carus, 1913). See also Carnetius Lanczos, The Variational Principle of Mechanics (New York: Dover, 1986).

25

Quoted from the article “Light,” Encyclopedia Britannica, eleventh edition.

26

For an overview of this historical development see Ernst Mach, Die Mechanik in ihrer Entwicklung (Leipzig: Brockhaus, 1901), and also P. E. B. Jourdain, The Principle of Least Action (Chicago: Open Court, 1913).

27

Quoted in Mario Livio, The Accelerating Universe (New York: John Wilem, 2000), p. 34. Einstein speculates that considerations of simplicity alone may determine the laws of nature: “What really intrigues me is whether God could have created the world any differently; in other words; whether the demand for logical simplicity leaves any freedom at all.” Calaprice 2000, p. 221.

28

Anthony Zee, Fearful Symmetry (Princeton: Princeton University Press, 1999), p. 211.

29

Quoted in John Horgan, Rational Mysticism: Spirituality Meets Science in the Search for Enlightenment (New York: Haughton Mifflin, 2003), p. 172).

30

Julian Barbour and Lee Smolin, “Extremal Variety as the Foundation of a Cosmological Quantum Theory,” published on the web at http: arxiv.org/hep-th/9203041.

31

I owe some of these references to William C. Lane.

32

Cited in van Dongen, p. 50.

33

To Maurice Solomon in 1924. See Calaprice 2000, p. 245.

34

See van Dongen, pp 162-63.

35

See Einstein’s “On Generalized Theory of Gravitation,” Scientific American, vol. 182 (1950), pp. 13-17.

36

Van Dongen, p. 52. Compare the ampler discussion of this passage in John Norton “Nature is the Realization of the Simplest Conceivable Mathematical Ideas: Einstein and the Canon of Mathematical Simplicity,” in Studies in the History and Philosophy of Modern Physics, vol. 31 (2000), pp. 135-70; see esp. pp. 136-37.

Nicholas Rescher • Episodes

152

NOTES 37

Letter to Bohm of 24 November 1954. See Van Dongen, 181-82.

38

See van Dongen 2010, p 147.

39

A. Einstein, Ideas and Opinions (New York: Bonanza, 1954; pp. 270-76.) On the relevant issues see John D. Norton, “Nature is the Realization of the Simplest Conceivable Mathematical Ideas: Einstein and the Canon of Mathematical Simplicity,” Studies in the History and Philosophy of Modern Physics, vol. 31 (2000), pp. 13570.

40

Letter to Bohm of 24 November 1954. See Van Dongen p. 181.

41

Calaprice 2000, p. 260.

42

John Norton has reminded me that in other contexts too search problems such as that of the travelling salesman will often be solve most efficiently by probabilistically geared processes.

43

Calaprice 2000, p. 259. Given this perspective on the matter it should be clear that (despite Pesic 2000, pp. 149-50) Einstein did not flatly object to having randomness as such play a role in nature. He objected, rather, to having this transpire without a cogent justificatory rationale.

44

Calaprice 2000, p. 214.

45

Calaprice 2000, p. 204. Also quoted in Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Gödel (New York: Norton, 2005), p. 259. Of course, Einstein rejected the idea of a personal God. See Calaprice 1996, pp. 146-53. Einstein felt a spiritual kinship with Spinoza as a fellow Jew (see Pesic 2000, pp. 14445). And he lacked Gödel’s familiarity with Leibniz’s thought.

46

Spinoza’s necessity was absolute and unconditional; Leibniz’s necessity was axiological and pivoted on an optimality geared to harmony, economy, and elegance to design. And just here Einstein actually took the Leibnizian route: “What really interests me is whether God could have created the word differently; in other words whether the demand for logical simplicity leaves and freedom at all.” (Calaprice 2000, p. 221: my italics). Spinoza’s necessity is unconstrained; Leibniz’s is constrained by conditions of harmony, economy, simplicity, that is, by just those value considerations that Spinoza eschews.

47

Actually, a way of developing relativity theory within the framework of rational mechanics is developed in Arnold Sommerfeld’s Electrodynamics: Lectures in Theoretical Physics, Vol. III [tr. E. G. Ramberg (New York: Academic Press 1964; German original Vorlesungen über theoretische Physik (Wiesbaden: Klemm Verlag, 1945). I owe this reference to my colleague Kenneth Schaffner.]

153

WHAT EINSTEIN WANTED

NOTES 48

This chapter was presented as a Luncheon Lecture at the Center for Philosophy of Science at the University of Pittsburgh in September of 2010 was subsequently published in Logos and Episteme, vol. 2 (2011), pp. 233-252.

Chapter Thirteen GÖDEL’S LEIBNIZ CONSPIRACY 0. COGNITIVE LIMITATION AND REALISM

T

ime and again philosophers have insisted that reality’s complexity outruns the reach of our resources for its cognitive domestication. Plato thought the physical realm we live in to be a world of shadows and held that the full brilliant light of immaterial reality is too bright for our imperfect eyes. St. Thomas taught that the creator’s complex ways are too sophisticated for comprehension by out finite intellects. Leibniz held physical that reality encompasses an unending sophistication of detail that the limited capacity of our intellect cannot manage to encompass other than by analogies. A long tradition in Western thought was prepared to envision a gap between the limited reach of man’s mind and a larger domain of real fact regarding which our knowledge was at best partial and incomplete. On any such view, a clear case for a mind-independent reality is inherent in the very limitations of the human mind. The thought of Kurt Gödel falls squarely within this tradition. 1. GÖDEL STUDIES LEIBNIZ In the 1940’s Gödel’s interests turned increasingly from logic and mathematics themselves to the philosophy of these disciplines, and he became more and more seriously concerned with the views of G. W. Leibniz on these matters.1 He had already made a long-term and detailed study of Leibniz over a period that extended from 1929 to the 1950s.2 (And it is clear that his main secondary source of accurate information about Leibniz’s guiding ideas in logic and mathematics had to be Louis Couturat’s classic la Logique de Leibniz (Paris: Alcan, 1903). In the early 1940s Gödel intensified his study of Leibniz. He then believed that “important writings [of Leibniz] . . . had not only failed

Nicholas Rescher • Episodes

156

to be published, but . . . [been] destroyed in manuscript.”3 Only when he learned after the war about the incredibly vast extent to which the manuscripts of Leibniz had survived could Gödel have realized the truth of the first part of this claim and the falsity of the latter. 2. GÖDEL’S POSITION As Gödel’s study of Leibniz grew broader and deeper he became ever more impressed with the many similarities between his own ideas and those of this great 17th century polymath.4 Indeed he could scarcely get himself to believe that Leibniz had not conceived—in at least embryonic form—the core of the key insights that characterized his (Gödel’s) own position about the foundations of logic and mathematics. Gödel’s own logico-mathematical program gave a salient role to the following considerations: (1) that every logico-mathematical proposition can be correlated with a uniquely corresponding integer. (Gödel numbering). (2) that all proofs (all valid finite demonstrations) can be made to correspond to calculable arithmetical relationships among the numbers allotted to the propositions involved. (3) that nevertheless some arithmetical truths involve noncalculable (i.e., finitude transcending) general relationships. (4) that therefore some arithmetical truths will not be (finitely) provable As Gödel thus saw it, the range of truth—even merely arithmetical truth—outruns the reach of provability. And he proposed to draw the large and wide-ranging conclusion that mathematical truth extends beyond the range of demonstrable relationships and inheres in its own objectively thought-independent condition. Gödel regarded Hilbert’s program as committed to on the thesis “Given any arbitrary mathematical proposition α, there exists a (finil-

157

GÖDEL’S LEIBNIZ CONSPIRACY

ary) proof of α or a (finitary) proof of¬α.”5 But he viewed this thesis as demonstrably false, and construed this fact as betokening a realm of mathematical truth and realty. The upshot looked to be a mathematical Platonism of sorts. 3. GÖDEL’S PLATONIC REALISM As Gödel saw it: “Classes and [other mathematical] concepts may . . . be conceived as real objects . . . existing independently of our definitions and constructions.”6 But although Gödel he was drawn to Platonic realism in mathematics, he never thought that he had built a conclusive case for this position. In the early 1950s he conceded: Of course I do not claim that the foregoing considerations amount to a real proof of this view [i.e., Platonism] about the nature of mathematics. The most I could assert would be to have disproved the nominalistic view, which considers mathematics to consist solely in syntactical conventions and their consequences. Moreover, I have adduced strong arguments against the more general view that mathematics is our own creation. There are however, other alternatives to Platonism.7

All the same, Gödel was convinced that none of these alternatives had anything like as much to be said on their behalf as Platonism did.8 In 1938 he wrote: . . . even if one should succeed in proving [the independence of the continuum hypothesis], this would . . by no means settle the question definitively. Only someone . . . who denies that the concepts and axioms of classical set theory have any meaning (or any well-defined meaning) could be satisfied with such a solution, not someone who believes them to describe some well-determined realty. For in this reality Cantor’s conjecture must be either true or false, and its undecidability from the axioms as known today can only mean that these axioms do not contain a complete description of this reality . . .9

And in his 1951 Gibbs lecture Gödel suggested that his incompleteness theorems furnished strong evidence for an idealist philosophical stance, maintaining that they confront us with a disjunction:

Nicholas Rescher • Episodes

158

Either mathematics is incompletable in [the] sense . . . [that] the human mind (even within the realm of pure mathematics) infinitely surpasses the power of any finite machine, or else there exist absolutely undecidable diophantine problems . . .10

In consequence of such views, Gödel insisted upon an analogous philosophical disjunction whose implications are “decidedly opposed to materialistic philosophy”: Namely, if the first alternative holds, this seems to imply that the working of the human mind cannot be reduced to the working of the brain . . . On the other hand, the second alternative . . . seems to disprove the view that mathematics is only our own creation: . . . So [it] seems to imply that mathematical objects . . . exist objectively] . . . that is to say [it seems to imply] some form or other of Platonism or "realism" as to the mathematical objects.11

Accordingly, in a letter to Gottard Günther dated June 30, 1954, Gödel wrote: When I say that one can (or should) develop a theory of classes as objectively existing entities. I do indeed mean by that existence in the sense of ontological metaphysics, by which, however. I do not want to say that abstract objects are present in nature. They seem rather to form a second plane or level [Ebene] of reality, which confronts us just as objectively and independently of our thinking as nature.12

Gödel was clearly prepared to endorse a dualistic, Plato-reminiscent realism that envisioned the ontological realms of both a concrete (physical) and an abstract (mathematical) sector of reality. It is widely asserted that Gödel’s discovery of the deductive incompleteness of arithmetic—establishing that some arithmetical truths simply cannot be demonstrated—somehow undermines foundations of this field and casts a shadow of uncertainty over arithmetic as a cognitive discipline. Arithmetical truth must now supposedly be deemed as unfolded by human inquirers and ceases to be a matter of objective fact about a mind-independent reality. But, as Gödel himself firmly

159

GÖDEL’S LEIBNIZ CONSPIRACY

maintained, the very opposite is the case. As he saw it, the fact that— no matter how we might twist and turn in our attempts at axiomatization—we will be unable to derive the entire realm of arithmetical truth. He deemed himself to now show that this realm will inevitably outrun the reach of the web we weave by axiomatization bespeaks realism rather than man-controlled relativism. If finite provability is one’s sole standard for rigorous postulation, then Gödel would be led—totally against his inclinations—to the view that—as John von Neumann put it “there is no rigorous justification for (all of) classical mathematics.”13 But such a conclusion was anathema to Gödel. Gödel viewed logico-mathematical demonstration as a region where the mind is in charge. We exert some extent of control over the axioms and continue on sage cognitive ground as long as we follow the delimited rules of proof. But those regions of truth that we cannot reach by these means between a realm of arithmetical fact where our postulational jurisdiction no longer obtains. Here is a Platonic region of reality above and beyond our wish and whim. And it is against this background that one must understand Gödel’s 1975 avowal to Bernays that: I’m pleased that . . . you advocate a cautiously [vorsichtig] Platonistic point of view. To me a Platonism of this kind (also with respect to mathematical concepts) seems to be obvious and its rejection to border on feeble-mindedness [an Schwachsinn zu grenzen].14

And as Gödel saw it, his mathematical Platonism has been foreshadowed—alike in general terms and in substantial detail—in the thought of Leibniz. 4.

LEIBNIZ’S POSITION

In many ways Leibniz’s logico-mathematical program bore a close analogy with that of Gödel. Thus with respect to those four items of Section 2 above we find:

Nicholas Rescher • Episodes

160

(1) that Leibniz’s conception of a universal characteristic (characteristica universalis) envisioned a system for assigning numbers to concepts and propositions in such a way as to reflect their logical interconnections. (2) that Leibniz’s conception of a calculus for reasoning (calculus ratiocinator) envisioned a process for conducting logical inference via calculation with the numbers of the propositions at issue.15 (3) that Leibniz acknowledged that come propositions are surd in that their truth cannot be brought to light by finite calculation. (Leibniz characterized such truths as contingent). (4) that Leibniz in consequence maintained that some truths will not be (finitely) demonstrable. (However as Leibniz saw it such truths would not belong to mathematics proper—that is, pure mathematics—but rather to applied mathematics.) So Leibniz too had it that truth outruns the limits of provability (finite demonstration) and that some other method—distinct from demonstration—is needed by and available for truth-determination. Overall, then, Leibniz maintained the truths of pure mathematics are one and all necessary in that they are finitely analytic, i.e., demonstrable by the principles of abstract logic from propositions that are without substantive content through being either merely definitional/conventional or explicitly tautalogous and redundant. These basic (axiomatic) propositions are certified as his through the fact that they say nothing substantive but merely reflect ways in which the speculative machinery of communication is designed to work. And the truths of pure logic and pure mathematics emerge by formally valid inference from effectively tautologies premises: their truth guaranteed by their lack of any substantive content, they hold good no matter how concrete reality functions—“in every possible world.” Contingent truths, by contrast, have some substantive flesh on their bones. They reflect and depend upon issues of substance and do not root in matters of mere symbolic convention.

161

GÖDEL’S LEIBNIZ CONSPIRACY

To be sure, as Leibniz saw it even contingent truths are demonstrable and can be established as true by analytical proceedings. But in the contingent realm these processes are always infinite—finite demonstration is not feasible here. The verification of a contingent truth requires an infinite process of validation. The laws of nature, for example, fall into this category. Thus an infinite process comparison— made possible even for us via the differential calculus—will show that the optimal (i.e., shortest) cushion-touching path connecting points A and B on a billiard table will be that where the angles of incidence and reflection are equal. With Leibniz such a recourse to optimization (maximization/minimization) is always at issue with the infinalistic demonstration of contingent truths. On this basis, Leibniz was prepared to see some parts of mathematics—applied mathematics, as it were—to be contingent rather than necessary. 5. LEIBNIZ ON INFINITE DEMONSTRATION Moreover, Leibniz’s conception of the objective and thoughtindependent status of truth had deeply Platonic and neo-Platonic rootings. Leibniz subscribed to the ancient Greek idea that mathematics is paradigmatic for knowledge as large, and he as saw calculationreducible reasoning becomes the salient model for rational cognition. But he also saw—as many epistemic mathematophiles do not—that this perspective enjoins two requisites, namely (1) providing a demonstration within some mathematically formalized system, and thus (2) choosing and/or designing particular the system within which we can appropriately operate. The former, intra-systematic functioning is a matter of proof, of finite demonstrability. The latter is a matter of comparison over a potentially infinite range. As Leibniz saw it, all true propositions are analytic and demonstrable. But necessarily true propositions are finitely demonstrable because they obtain under all conditions. By contrast, contingently true propositions obtain only under optimal conditions: they are surd, derivable only by infinitistic means because optimization—a process of infinite comparison—is involved. We finite intelligences can certainly see that such propositions are true, but we cannot

Nicholas Rescher • Episodes

162

establish how this is so. Our cognitive access to infinity is too limited and incomplete for that.16 When Leibniz issued the injunction calculemus and enjoined us to operate our reasonings and resolves our questions by calculating he had in view the limited range of issues that we humans can settle by our limited cognitive resources. But when taking the broader position that cum deus calculat . . . fit mundus17 he was looking to the calculations by which an infinite intellect surveys the range of possibilities to fix upon upon the specific ground-rules to that particular system within which we must operate. We operate intra-systemically by the axiomatic ground-rules that are set for us by the factual circumstances of an actual world. The creator, by contrast, operates trans-systemically by process of comparative optimization that puts those circumstances into place. And his large-scale optimizations move outside the realm of the demonstratively necessary. To be sure, there are many ways of verifying claims regarding a supra-finite range of items: (1) Collectively—as when one can show on general principles that every member of an infinite collection has a certain feature. (Example: “Every real number smaller than five is smaller than 10.) This can actually be accomplished by addressing a single arbitrasively selected but generically typical member of that infinite group. (2) Inductively—by exploiting a serial order among the infinite items and showing both that the initial i0 has a certain property and that if (an arbitrary) in has that property, then so does in+1, the next item of the serial order. (3) Convergently—by exploiting a serial order among the items and showing that the difference between in and in+1 (be it quantitative or qualitative) becomes vanishingly smaller with increasing n, and then presuming continuous uniformity here.

163

GÖDEL’S LEIBNIZ CONSPIRACY

(4) Distributively—by checking that seriatim that each and every member of that infinite collectivity has a certain feature. The first three of these processes are certainly feasible for us finite beings, but the fourth is clearly not. So the situation is not that such beings cannot get any sort of cognitive grip on the infinite, but that such a grip is found to be incomplete. In establishing some facts regarding an infinite collectivity we proceed in (1)-(3) by discursive processes under the aegis of generalities. But when the individualized-inspection determination of (4) is required, we are impotent: for us those features of an infinite collectivity whose determination requires a distributive determination are undeterminable, surd, contingent. However, as Leibniz saw it, even those contingently surd and not finitely demonstrable truths are more-the-less demonstrable—and thereby certain albeit not necessary. However, their demonstration requires a distributive survey of infinitivities that is unrealizable to us.18 And this is so because such a demonstration requires comparing and assessing an infinitude of themselves infinitely complex possibilities with each other to determine what is optimal—and thereby meriting actualization.19 Such an infinitely elaborated comparison among infinitely complex items is more than finite beings can manage. And it rests—in the final analysis—on a companion under the aegis of fundamental principles of value, requiring an optimization which carries the domain of contingent truth beyond any considerations of selfevident redundancy.20 In any venture of coordinating the views of Gödel and Leibniz one has to highlight their common stress on the distinction between finitary and non-finitary processes of reasoning. The point of modern (Hilbertain) meta-mathematics has been the question of what can be achieved by finitary methods. By contrast, both Leibniz and Gödel alike deemed it as only normal, natural, and to be expected that truth—and even merely mathematical truth—outruns the range of finite demonstrability.21 The limited reach of finite methods of verification betoked for Gödel and Leibniz alike the incapacity of limited intellection to secure a comprehensive knowledge of (even merely mathematical) reality as a whole.22

Nicholas Rescher • Episodes

164

As these thinkers saw it, the limitedness of our finite minds betokens a large reality that is independent of us—a region of factuality above and beyond our resources of demonstration. With both alike it transpires that, as Gödel put it, “there are structural laws in the world which cannot be explained causally.”23 When Gödel uttered the shocking dictum “I don’t believe in natural science”24 he clearly did not mean to assert that science is false but only that it is (what else with Gödel?) incomplete: that its truths are not final and definite but rest on an underlying rationale that reaches above and beyond standardly scientific considerations. And when Gödel shocked Noam Chomsky by saying “I am trying to prove that the laws of nature are a priori25he was functioning wholly within the Leibnizian program. For Leibniz viewed these laws as part of the solution of an optimization program, and Gödel apparently viewed the matter in much the same light. 6. GÖDEL’S LEIBNIZ CONSPIRACY As Gödel studied Leibniz via Louis Couturat’s classic La Logique de Leibniz he became convinced that resistance to logicomathematical Platonic realism of his own position was pre-figured in a conspiracy of suppression and silence that had kept Leibniz’s insights from being properly understood and appreciated. One acute Gödel scholar tells us that “his most profound sense of identification was with the über-rationalist Leibniz,”26 and that at the very core of his thought was his “interesting axiom” to the effect that the world is rational27—i.e. always in such a way that its doings are explicable on rational principle—which of course is nothing but Leibniz’s Principle of Sufficient Reason. Gödel’s Leibnizian commitment to the rationality of the real and to the ultimate omnipotence of reason left him deeply estranged from the facile relativism that surrounded him on every side. In drafting a response to a communication from B. D. Grandjean he began with the observation that “Replying to your inquiries I would like to say first that I don’t consider my work [what you call] ‘a facet of the intellectual atmosphere of the early 20th century’ but rather the opposite.”28

165

GÖDEL’S LEIBNIZ CONSPIRACY

Gödel told a skeptical Oskar Morgenstern in 1945 that Leibniz was “systematically sabotaged by his editors.” This is certainly to those conscientious scholars who confronted a labor of Sisyphus—and is ludicrously unjust in the care of Couturat. However he went on to claim for Leibniz (1) various declarations about the scientific importance of developing “a theory of games,” (2) discovery of antonomies of set theory “cloaked in the language of concepts, but exactly the same,” (3) anticipations of Helmholz’s resonance theory of hearing, and (4) the law of the conservation of energy. And while Morgenstern inclined to see such claims as “fantasies,” the fact remains that they are all perfectly true—and far from exhaustive of the scientific, mathematical, and logical discovery that can be ascribed to Leibniz. Much of what we know about Gödel’s belief in a Leibniz conspiracy comes from the Reminiscence of Karl Menger.29 After noting that “Gödel had always been most intensely interested in Leibniz,”30 Menger informs us that during the late 1930s and 1940s Gödel was more and more preoccupied with Leibniz. He was now completely convinced that important writings of this philosopher had not only failed to be published, but were destroyed in manuscript. Once I said to him teasingly, “You have a vicarious persecution complex on Leibniz’ behalf . . . Who had an interest in destroying Leibniz’ writings?” “Naturally those people who do not want man to become more intelligent” he replied. Since it was unclear to me whom he suspected, I asked after groping for a response. “Don’t think that they would sooner have destroyed Voltaire’s writings?” Gödel’s astonishing answer was: “Who ever became more intelligent by reading the writings of Voltaire?” Unfortunately at that moment someone stepped into the room and the conversation was never concluded.31

Gödel was particularly struck by the absence of any reference to Leibniz’s characteristia universalis from any publications dating from his lifetime and well beyond.32 And in general Gödel’s idea of a Leibniz conspiracy rested on two purported considerations: (1) The suppression—or even destruction—of Leibniz’s logicomathematical work, and

Nicholas Rescher • Episodes

166

(2) The failure of some collections of Leibnizian works to contain material that one might expect to find. But these charges are very problematic. By all viable indications Leibniz’s writings were preserved comprehensively and with great case, and were published more and more fully and carefully as the years went on.33 And the occasional coordinate failures of published material looks to be more a product of scholarly carelessness than of malign and conspiritual intent. The long delay—until Couturat’s 1903 book—in a proper appreciation of Leibniz’s logical work is due simply to the fact that until a great deal of logic had been re-developed it was somewhere between difficult and impossible for people to see what he had actually accomplished. Apparently, Gödel thought he had telling evidence for this Leibniz conspiracy, as per the following episode narrated by Karl Menger: I once discussed Gödel’s ideas on Leibniz with a common friend, the economist Oskar Morgenstern. He described to me how Gödel one day took him into the Princeton University Library and piled up two stacks of publications: on one side, books and articles that appeared during or shortly after Leibniz’ lifetime and contained exact references to writings of the philosopher published in collections or series (with places and years of publication, volume and page numbers, etc.); on the other side, those very collections or series. But in some cases, neither on the cited page nor elsewhere was there any writing by Leibniz; in other cases, the series broke off just before the cited volume or the volume ended before the cited page; in still other cases, the volumes containing the cited writings never appeared. “The material was really highly astonishing,” Morgenstern said.34

It would be nice if Gödel’s documentation could be recovered, but it does not appear to be practicable. Insofar as I have been able to check, the references to Leibniz’s publications in his own day are accurate enough as far as they (very incompletely) go. But the issue is also irrelevant. For the severest censor of Leibniz’s work in logic was the man himself, who simply did not publish it. In this regard his own judgment was telling. Que me non nisi editis novit, non novit he wrote” “When does not know me serve via publications, does not

167

GÖDEL’S LEIBNIZ CONSPIRACY

honor me at all?” the vast amount of ground-breaking work that he did in this field was indeed kept out of people’s sight. But for this the man himself was responsible, and not some hostile conspiracy. When he could not persuade an otherwise sympathetic Huygens of the value of symbolic logic, Leibniz gave up and turned attentions elsewhere. As Gödel came to believe, malign forces were astir in the world not only to make men slaves (as per Hitlerian fascism and Stalinique communism) but to render them unthinking as well—forces so powerful as to operate even in democratic societies. As one Gödel scholar puts it “He came to believe that there was a vast conspiracy, apparently in place for centuries, to suppress the truth ‘and make men stupid’.”35 In this regard he felt that those thinkers who, like Leibniz and himself, were persuaded of nature’s fundamental rationality, were destined to have those ideas suppressed and distorted and go “rejected and despised” (as Händel’s Messiah puts it). What is one to say about Gödel’s idea of a Leibniz conspiracy? There is, of course, something paranoic about it. But even paranoia can sometimes prove to be justified. This said, however, the idea of a Leibniz-oriented conspiracy is untenable—for many reasons: 1. Only with Couturat and Russell did working logicians manifest any concern with Leibniz and even Russell—whose Leibniz book contradicted Couturat’s pioneering work did not really understand Leibniz’s logic properly. 2. The failure of secondary-source claims to square with primarysource affirmations is so common a phenomenon as to be probatively indecisive. 3. Effective manipulation would have required one’s knowledge of Leibniz’s work to be of a quantity and quality that was effectively unavoidable. 4. During the generation between the appearance of Couturat’s 1903 and Gödel’s preoccupation with Leibniz beginning in the 1930s there was effectively no serous scholarship on Leibniz’s

Nicholas Rescher • Episodes

168

logic for reasons that were less conspiritual than related to the disruption of the first World War. 5. The forces at work in “dumbing the world down” were not the work of conspiritual intellectuals but the vast sociocultural movement energized by the disasters of the 1914-18 war and the consequent economic disruptions throughout the world. It would seem that in this regard, as in others, Gödel simply had too much confidence in the rationality of the real. The fact of it seem to be that the natural shortcomings of man—both as individuals and as social collectivities—suffice to account for the phenomena that troubled Gödel—no special conspiracy theory was required here. But be this as it may, Gödel was intent on seeing Leibniz and himself as victims of the doctrinal hostility of an uncomprehending world. One very positive effect of Gödel’s Leibniz conspiracy was its contribution to bringing copies of Hannover’s Leibniz manuscripts across the Atlantic. Gödel energized Morgenstern to efforts in this direction which ultimately came into confluence with the cognate efforts of Paul Schrecker of the University of Pennsylvania and ultimately led— with Rockefeller Foundation funding—to securing copies of the Leibniz material for that university. 7. GÖDEL MOVES BEYOND LEIBNIZ—TO HUSSERL Since classical antiquity, philosophers have envisioned two distinct pathways to the ascertainment of truth: the one discursive, by reasoning, and the other intuitive, by insight (be it sensory in the concrete domain or intellectual in the realm of the abstract). The latter, so it was generally held, is the pathway to the ultimate premisses, the former represents the reasoning by which we extend our knowledge beyond them. And the overall structure of knowledge can thus be modelled on Euclidean geometry, with intuitively available connectional definitions, postulates, and axioms on the one side, and theorems on the other. Both Leibniz and Gödel retained this classical perspective. But there was an important difference.

169

GÖDEL’S LEIBNIZ CONSPIRACY

As individually accessible ultimate axioms Leibniz would admit only informatively empty (tautologous and definitionally conventional) premisses. But he was prepared to adopt more elaborate discursive machinery, namely not only finite deduction but also an infinitistic systematization based on normative considerations (via his “principle of perfection”). And just here Gödel was more of a child of his time. Unwilling to trust entirely to his own deeper Leibnizian inclinations, he looked elsewhere for a means of validating the (finitely) indemonstrable and secure ultimate premisses into the bargain. And this led him to adopt the idea of a truth-revelating (Husserlian) intuition and thereby to depart from a more deeply rationalistic Leibniz who was prepared to move from theoretical to normative reality—but no further. As Leibniz saw it, all truth is in principle demonstrable by processes of calculation—empirical truth about the actual world included. But while some of these truths—to wit, the necessary—are demonstrable by inherently finitistic processes others require a distributively infinitistic process of the sort that only an infinite intelligence could manage. This latter category could conceivably include some mathematical propositions in the order that the decimal expansion of pi will never continue a sequence of a thousand 8s. But it would certainly include the proposition that this world of ours, constituted as is, is the very best that is possible. (Hence Leibniz’s dictum cum deus calculat. . . fit mundus.) These finitely incalculable truths cannot be validated by axiomatic derivation from self-evident tautologies, their validation requires the shift to the holistic systemic validation based in normative considerations of fitness within an originally shadowed whole—a process which is the end is one of normative optimization. And Gödel was certainly tempted by Leibnizian optimalism. At one point he affirmed: Our total reality and total experience are beautiful and meaningful—this is also a Leibnizian thought. We should judge [abstract] reality by the little one which we truly know of it. Since that part of it which we know conceptually finally turn out to be so, the real world of which we know so little should also be beautiful.36

Nicholas Rescher • Episodes

170

However, Gödel was still too much of a traditional mathematician to follow Leibniz unhesitatingly down this drastically normative nonstandard pathway. The idea of a synoptic God possessed of a totum simul intellectual vision across a distributively infinite range was— just possibly—something Gödel could come to terms with on his own account, but he realized the hopelessness of selling this viewpoint to the mathematics community of the day, wed as it was to the validation requires proof and proof of a sort manageable by us finite humans. So if one is to accept that mathematical truth outruns possibility, then how might those non-provable truths possibly be validated as such? What service other than demonstration can put at our cognitive disposal a means for validating substantive (non-autologous, nondefinitional, non-conventional) mathematical truths? The quest for such a resource moved Gödel beyond and away from Leibniz and carried him to . . . Edmund Husserl. 37 As Gödel saw it, mathematics confronts us with a very fundamental fact of life, one that inheres in the following line of thought: (1) The number of propositions statable in any axiomatized deductive system is denumerable. (2) Therefor the number of possible propositions in any such system is denumerable. (3) But in mathematics—and certainly in the arithmetic of real numbers—the number of truths is trans-denumerable. (For trans-denumerably many objects are at issue here and each such object is the focus of some unique and idiosyncratic truth.) (4) Therefore some truths are not provable. Clearly if truth cannot be equated with axiomatic provability, there has to be some proof-transcending, demonstration-distinct pathway to truth-establishment. And just here Husserl came to Gödel’s rescue. It would be good to have a terminology suited to two very different senses of the German Anschauung or English intuition, distinguishing

171

GÖDEL’S LEIBNIZ CONSPIRACY

that which can be seen with the eyes of the body from that which can be seen (only) with the eyes of the mind. Perhaps the best we can do here is to use the term inspection for the former, and intellectual intuition for the latter. The Husserlian Wesensschau is a quintessential exemplification of the latter process, in contrast to the Kantian Anschanung which is a quintessential illustration of the former. But it is just this second that is required in the infinitistically realistic mathematics contemplated by Gödel, in contrast to the intellectual inspection mode of Anschauung that is at work in the limits range of finitistic mathematics. And here Husserl came to Gödel’s rescue. As Husserl saw it, we humans possess the capacity for a direct experiential insight into a Plato-reminiscent domain of abstract realty is analogous to, albeit obviously distinct from, our physical insight into the concrete reality about us. And he held that such an insight is even required for comparisons among those sensuously experience particular and those for making universal generalizations regarding them. Gödel believed that a wider understanding of his philosophical standpoint was blocked by willful incomprehensions and prejudices. He held that “even science is heavenly prejudiced in one direction. Knowledge in everyday life is also prejudiced. Two methods to transcend such prejudices are: (1) phenomenology [i.e., Husserl]; (2) going back to other ages [i.e., Leibniz].”38 What Husserlian insight offered to Gödel was “another [i.e. sensedistinct] kind of relationship between ourselves and reality.”39 And the reality at issue was not, of course physico-material reality but the immaterial reality of Platonic abstracta. It is just exactly this insight that is required to provide a pathway to mathematical truth that is distinct from discursive proof and thereby able to provide such possibility with a secure basis. Leibniz was prepared to regard certain mathematical propositions as contingent (in his sense). But Gödel wanted them all to be necessary. And so Gödel turned to Husserl and his Wesensschau. Husserl’s Wesensschau is, in effect, a cognitive apprehension of meanings, and Gödel takes this idea over, lock stock, and barrel by espousing “thought contents which are not derived from a reflection upon . . . symbols representing them, but rather from reflection upon the meanings involved.”40

Nicholas Rescher • Episodes

172

In some late (1961) notes, Gödel recommended Husserl’s phenomenology as providing fruitful direction for metamathematics.41 He maintained that: There exists today the beginning of a science which claims to possess a systematic method for such clarification of meaning, and that is the phenomenology founded by Husserl. . . Here clarification of meaning consists in concentration more intensively on the concepts in question by directing our attention in a certain way, namely onto our own acts in the use of those concepts, onto our own powers in carrying out those acts, etc. In so doing, one must keep clearly in mind that this phenomenology is not a science in the same sense as the other sciences. Rather it is [or in any case should be] a procedure or technique that should produce in us a new state of consciousness in which we describe in detail the basic concepts we use in out thought, or grasp other, hitherto unknown, basic concepts.42

It is clear that he felt an attraction to the standpoint of the Philosophical Investigations because its conception of intellectual insight offered him a proof-apart cognitive pathway to mathematical truth.43 And with intellectual intuition itself viewed as a mode of experience, Gödel was even prepared to consider mathematics as an empirical (i.e., experience based) discipline. If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics. The fact is that in mathematics we still have the same attitude today that in former times one had toward all science, namely we try to derive everything by cogent proofs from the definitions (that is, in ontological terminology, from the essences of things). Perhaps this method, if it claims monopoly, is as wrong in mathematics as it was in physics.44

Husserl had it that in the end, experience is dual, with physical inspection dominant in the realm of the concrete reality of natural science and intellectual intuition dominant for abstract realty of mathematics. And Gödel wrote in 1964:

173

GÖDEL’S LEIBNIZ CONSPIRACY

I don’t see any reason why we should have less confidence in this kind of perception, i.e., mathematical intuition, that in sense perception, which induces us to build up physical theories and to expect that future sense perception will agree with them and, moreover, to believe that a question not decidable not have meaning and may be decided in the future.45

Gödel’s recourse to Husserl need not, however, be construed as an abandonment of Leibniz. For Gödel continued to endorse one of Leibniz’s key ideas on these issues, namely that there are significant questions that cannot be settled formalistically. Only now there came a parting of the ways. For while Leibniz held that the infinitistic resolution at issue is available only to God, Gödel maintained that we humans have a (God-given) power to insight of ultimately enabling us to see what that answer is even where we cannot fully comprehend how and why it is so. And another key difference also looms. Namely that for Leibniz the finitistically undecidable questions relate to matters of contingent fact regarding existence in the natural world, while for Gödel they could also relate to structural facts regarding situations in the realm of mathematical abstracta. Gödel, in sum, was an ontological dualist. With him—as with the Platonic tradition—there were two distinct levels or realms of reality: the physical domain of concrete time-based particulars and the abstractly non-physical domain of mathematical objects and relations. We gain cognitive access to the former via the eyes of the body and into the latter via our intellectual induction managed by the mind’s eye. And Gödel combined an ontology of metaphysical Platonism with a Husserlian epistemology of intellectual intuition that abandons Leibniz’s recourse to innate ideas in favor of a Neo-Husserlian Wesensschau into the distinct nature of things. His position harks back to Neo-Platonism’s proof-independent epibolê that has figured pivotally in Western epistemology since classical antiquity. For Leibniz, finite demonstrations rested on ultimate premisses that were informatively empty—tautologies and definitions. Gödel held that more was needed. Logical machinery such as the axioms of choice—or indeed even the law of excluded middle—were required as

Nicholas Rescher • Episodes

174

substantively informative, inherently nontrivial resources. And these—as he saw it—could come within the realm of our cognition only via an auspicity for intellectual intuition into the realm of abstract reality. Where Leibniz deemed the cognitive ascertainment of the world’s detailed empirical (finitely undemonstrable) fact to be beyond the realm of finite intelligent, Gödel proposed to throw the human mathematicians the lifeline of a Husserlian Wesensschau. In this way Gödel’s God was more anthropophelic than Leibniz’s. And yet in turning to Husserl, however, Gödel did not really abandon Leibniz. He did not follow the Husserl of his later period into accepting the idea that the immaterial reals of mathematics are not only known to consciousness but actually constituted through its activity— that the esse and principi of abstracta stand in accurate coordination with one another (unlike the situation with concreta). However Gödel, like Leibniz, thought that the abstract realm of mathematics was not actually constituted by thought but had a reality of its own that was merely accessed by thought but over which it did not exercise creative control. A PERSONAL POSTSCRPT Some contemporary theorists have been led to Leibniz from Gödel. My own direction of movement has been the reverse. When I was a graduate student in Princeton in 1949-51 I was occasionally in indirect contact with Gödel. For I was then working on my doctoral dissertation on Leibniz and the only person who competed with me for the Leibniz books in Firestone Library was—Kurt Gödel.46 From time to time the one of us would have books called in that that other had charged out. I should, of course, have tried to make something of our common interest, but at the time I simply did not have the nerve. And while I sometimes saw Gödel on the campus, but never got up enough courage to speak to him. However, on one Sunday’s walk I did stop in at Fuld Hall and visited his office on the off chance that he might be there. Of course he wasn’t. But the door was wide open. The office was small and quite bare—with no pictures or decorations, and no couch or other comfortable furniture, just a plain desk, a small table, and a desk-chair, and some rather empty book-

175

GÖDEL’S LEIBNIZ CONSPIRACY

shelves occupied only by a few stacks of reprints. (To my shame, I took one of them—now, unfortunately, long lost.) The contrast of Gödel’s office with that of John von Neumann’s where I visited not long after (when he was in!) was like that between a student’s sparse quarters at a scandinavian university and the mansion of an American university president. REFERENCES Note: This list only resisters material cited here. For a full bibliography of work by and about Gödel see Kennedy 2007. S. Feferman and various collaborators have produced a majestial edition of Gödel’s Collected Works in five volumes published by the Oxford University Press, 1986-2003. Davis, Martin, The Undecidable: Basic Papers (Mineola, NY: Diver Publications, 1956). Davis, Martin, “What Did Gödel Believe and When Did He Believe it?,” in Feferman et. al. 2010, pp. 229-41. Dawson, J. W. Jr., Logical Dilemmas: The Life and Work of Kurt Gödel (Wellesbey, MA: A. K. Peters, 1997). Feferman, Solomon et al., Kurt Gödel: Essays for his Centennial (Cambridge: Cambridge University Press, 2010). Goldstein, Rebeca, Incompleteness: The Proof and Paradox of Kurt Gödel (New York: W. W. Norton, 2005). Kennedy, Juliette, “Kurt Gödel,” Stanford Encyclopedia of Philosophy (13 February, 2007). [This excellent survey provides a very full bibliography.] Menger, Karl, Reminiscences of the Vienna Circle and the Mathematical Colloquium (Dordrecht: Kluwer, 1994).

Nicholas Rescher • Episodes

176

Nagel, Ernest and James R. Newman, Gödel’s Proof, revised ed. (New York: New York University Press, 2001). Tieszen, Richard, Phenomenology, Logic, and the Philosophy of Mathematics (Cambridge: Cambridge University Press, 2005). Van Allen, Mark and Juliette Kennedy, “On the Philosophical Development of Kurt Gödel,” Bulletin of Symbolic Logic, vol. 9 (2003), pp. 475-76. Wang, Hao, “Some Facts about Kurt Gödel,” The Journal of Symbolic Logic, vol. 46 (1981), pp. 653-59. Yourgrau, Palle, A World without time: The Forgotten Legacy of Gödel and Einstein (New York: Basic Books, 2005.) NOTES 1

Gödel told Hao Wang that: “during the war he was interested in Leibniz but could not get hold of the manuscripts of Leibniz. When these manuscripts finally came in after the war, his interested had shifted in other directions.” (Wang 1981, p. 657 n.). But this cannot be entirely accurate. Gödel’s preoccupation with Leibniz continued well into the late 1940’s, even if at a diminished rate.

2

See Van Allen & Kennedy, p. 304. Gödel’s interest in Leibniz extended well beyond mathematics. In a projected (but unsent) reply to a 1975 questionnaire from the sociologist Blanche D. Grandjean, Gödel described his own beliefs as “theistic rather than pantheistic, following Leibniz rather than Spinoza.” (Dawson 1997. p. 6.)

3

Dawson 1997, p. 137.

4

Even if to a lesser extent, various other important 20th century logicians also shared Gödel’s affinity to Leibniz, including Bertrand Russell and Rudolf Carnap. See Awadley & Carus, p. 253.

5

Davis 2010, p. 236.

6

“Russell’s Mathematical Logic,” in Collected Papers (ed.), Feferman et. al., 1900, p. 128.

7

Kurt Gödel, Collected Works III: Unpublished Lectures and Essays, ed. by S. Fefernan et. al (Oxford: Oxford University Press, 1995), p. 321.

8

For a clear and comprehensive account of Gödel’s Platonism see Parsons 2010.

177

GÖDEL’S LEIBNIZ CONSPIRACY

NOTES 9

Davis 2010, p. 235.

10

Davis 2010, p. 239.

11

Davis 2010, p. 239.

12

Davis 2010, p. 239.

13

Stanford Encyclopedia of Philosophy, and “Kurt Gödel,” p. 11.

14

Davis 2010, p. 239.

15

This of basic concepts are represented by prime numbers and complex concepts by multitudes thereof, then the decomposition into primes will reveal the conceptual composition of those complexes and containment relations come down to divisibility. For details see Couturat’s Logique, p. 327.

16

All this is laid out with magisterial clarity in Couturat 1901.

17

GPhil, VII, p. 191, notes.

18

Solius Dei est que totum infinalium Mente comlicatur, nosse certitrediness ominum conteintentium veritatum (Couturat 1901, p. 213 n.)

19

Constat ergo amnes veritales etiam maxime conteingente probationem a priori sein rationem aliquam cur sint potius quam non sint habere. (GPhil. VII, p. 301)

20

For details see Couturat 1901, pp. 220-229. Thus take for example the analogy of a practicing problem along the lines contemplated by Leibniz himself. Thus consider the issue of fitting coins of a given size. It will be a contingent fact that six will never be a suitable number here, because whenever six coins can be fitter in, seven will do so as well. Accordingly sic, being suboptimal will be (contingently) exhibited as an appropriate answer. And world-optimization will make an infinitude of distinct considerations of this given sort.

21

See, for example, Gödel’s 1967 letter to Hao Wang complaining of a “misplaced commitment to finitist metatheory (cf. the discussion in Avigard 2010, pp. 54-55).

22

“What Gödel and Hilbert had in common was an unshakable faith in rational inquiry. But in contrast to Hilbert, Gödel was intensely sensitive to the limitations of formal methods and deemed them insufficient.” (Avigard 2010, p. 57.)

23

Youvgrau 2005, p. 157.

24

See Goldstein, p. 31.

25

Goldstein, p. 32.

26

Goldstein, p. 48.

Nicholas Rescher • Episodes

178

NOTES 27

“Die Welt ist vernünftig.” See Goldstein pp. 20-21, 30-31, 4, 55, and 231.

28

Goldstein, p. 61.

29

Karl Menger, Reminiscence of the Vienna Circle and the Mathematical Colloquium, ed. by L. Golland et al. (Dordrecht: Kluwer, 1994).

30

Ibid.

31

Menger 1994, pp. 122-123.

32

See Dawson 1997. Gödel seems not to have appreciated the fact that Leibniz himself was the severest censor of Leibniz’s work and that he deliberately abstained from publishing many of his ideas and projects. Accordingly he wrote: Qui ni non nisi editis movit, non invit (“Who knows me only via published work does not know me at all”).

33

This is amply attested by Emile Ravier’s magisterial Leibniz Bibliography and by the archival records published in two substantial volumes by Eduard Bodemann.

34

Menger 1997, pp. 223-224. Compare another report. [The Princetonean economist Oskar Morgenstern] had been alerted by Gödel as to the deliberate suppression of Leibniz’s contributions and had tried to argue the logician out of his conviction. Finally, to convince Morgenstern, Gödel had taken the economist to the university’s Firestone Library and gathered together “an abundance of really astonishing material,” in Morgenstern’s words. The material consisted of books and articles with exact reference to published writings of Leibniz, on the one hand, and the very works cited, on the other. The primary sources were all missing the material that has been cited in the secondary sources. “This material was highly astonishing,” a flabbergasted (if unconvinced) Morgenstern admitted. Goldstein, p. 248.

35

Goldstein, p. 48.

36

Stanford Encyclopedia of Philosophy, art. “Kurt Gödel,” p. 36.

37

Gödel’s interest in Husserl went back to at least 1935 when he perused the Vorlesungen zur Phaenomenlogie des Bewusstseins (Dawson 1997, p. 107).

38

Youvgrau 2005, p. 182.

39

Quoted in Parsons 2010, p. 348. On Husserl’s approach to logic and Gödel’s recourse to some of his ideas see Richard Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics (Cambridge: Cambridge University Press, 2005).

40

“On an Extension of Finilary Mathematics . . .” (1958), in Feferman et. al 1990, p. 271-72.

41

Davis 2010, p. 240. And see van Allen and Kennedy 2003.

179

GÖDEL’S LEIBNIZ CONSPIRACY

NOTES 42

“The Modern Development of the Foundations of Mathematics in the Light of Philosophy,” (1961) in Feferman et. al (eds.), 1995, p. 383.

43

See van Allen & Kennedy, 2010.

44

Davis, 2010, p. 240.

45

K. Gödel, “What is Cantor’s Continuum Problem,” in Feferman et. al (eds.), Collected Papers (?), 1990, p. 268.

46

It is, for me, an interesting circumstance that Firestone Library’s copy of Louis Couturat’s classic La logique de Leibniz played a pivotal role alike in Kurt Gödel’s philosophical development and my own.

Chapter Fourteen THE BERLIN GROUP AND THE RAND COOPERATION (A Narrative of Personal Interactions)

A

s a freshman at Queens College in the spring of 1946 I enrolled in a course in Philosophy of Science with Professor C. G. Hempel of whom I already knew something via a recent student of his, Charlotte Knag, my geometry teacher at Flushing High School. During my Queens College days I took all the courses with Hempel that I could and formed a friendly relationship with him. Upon completing undergraduate studies at Queens, I went on to do graduate work at Princeton. Here Hempel had put me in touch with his good friend and collaborator Paul Oppenheim, who had been settled there for about a decade. At Hempel’s suggestion, Oppenheim enlisted me as a collaborator. He had long been interested in the concept of Gestalt—i.e., in the theory and application of the concept of structure in psychology, cognitive theory, and the theory of science. Years before, Oppenheim had cooperated with Kurt Grelling in investigating this topic but their research had been interrupted by the disaster being visited by the Nazis upon all concerned in Europe. My own collaboration with Oppenheim issued in a piece on “Logical Analysis of Gestalt Concepts” published in the British Journal for the Philosophy of Science in 1955.1 However, further collaboration with Oppenheim was aborted by my brief period of military service during the Korean War. Upon discharge from military service in 1954 I went to work in the Mathematics Division at the RAND Cooperation in Santa Monica, California. They hired me at Hempel’s suggestion and I was assigned to a group led by his longtime friend and collaborator Olaf Helmer. Equipped with a lively sense of humor and an inquisitive, openminded spirit, Helmer was an easy-going individual. Notwithstanding his seniority to me in position and in age (by some 18 years), we got on easily as equal partners working in cooperation.

Nicholas Rescher • Episodes

182

While my service at RAND was largely oriented in other directions, I continued to work at some problems that had been engaging the attention of the Berlin Group. In particular, during my time at RAND I was drawn under Helmer’s influence to issues of prediction and futurology. I worked with him and our colleague Norman Dalkey in developing the so-called Delphi Method of expert-interactive prediction.2 (All three of us held Ph.D.’s in philosophy which may have increased our sympathy for eccentric approaches.)3 Because our interests in futuristics went beyond relevancy to RAND’s prime concerns, Helmer and I also pursued our collaboration by periodic evening work sessions held alternatively at our homes. During 1955 we met periodically in the evening or on weekends, either at Helmer’s house on Mandeville Canyon Road or at my house on Bestor Boulevard in Pacific Palisades. Eventually published in 1958 as RAND paper P-1513 entitled “On the Epistemology of the Inexact Sciences,” this paper was re-issued in 1960 as RAND Report R-353 having meantime been published under the same title in Management Sciences, vol. 6 (1959), pp. 25-52. In their book on The Delphi Method: Techniques and Applications (Reading, MA: Addison Wesley, 1975), the editors Harold A. Linstone and Murray Turoff characterized this Helmer-Rescher publication as “a classic paper which was very adequate for the typical technology forecasting applications for which Delphi has been popular” (p. 15).4 This line of work inaugurated a longstanding interest in forecasting on my part, which then resulted in article publications and ultimately in my 1998 book on Predicting the Future.5 During this period I also carried on some investigations in inductive reasoning and the theory of confirmation—a topic which, under the influence of Hans Reichenbach, had preoccupied Hempel and Helmer since the early 1940s. This interest led in the short run to my paper on “A Theory of Evidence”6 and in the long run to my 1980 book on Induction.7 My interest in matters of confirmation and induction were further stimulated by occasional meetings at Rudolf Carnap’s Santa Monica house where Helmer and I and the mathematician L. J. Savage discussed issues relating to the theory of probability and induction. Carnap was by far the most senior of us, but I was impressed by the extent to which he was open-minded and undogmatic, willing to ex-

183

THE BERLIN GROUP AND THE RAND COOPERATION

change ideas with his juniors and even prepared to learn things from them. I want to seize this opportunity to set the record straight on one point. In the course of the Vietnam War, the RAND Corp. became one of the bogeymen to the Liberal Left in American—a symbol of all that was reprehensible about intellectuals in the service of a warmongering establishment. (When I lectured in Oxford in the spring of 1974, one young participant told me of an American colleague who refused to attend because he heard that I had once worked for RAND!) The fact, however, is that what RAND’s studies in those days primarily showed was the effective impracticability of waging a nuclear war. All those war-gaming simulations in which RAND was then engaged pointed towards the desirability of war-avoidance. The prime thrust of RAND’s work in those days was entirely defensive, the prime object being security of the US through an effective defense rather than encompassing any aggressive measures. To the best of my knowledge and recollection, not a single study done at RAND in those days was devoted to matters of aggrandizement and power projection. The large and important contributions that RAND made to American military preparedness in those critical times of the 1950s were concentrated on matters not of aggression but of defense. And RAND was also unjustly charged with further malfeasance. In 2005 George A. Reisch published a book entitled How the Cold War Transformed Philosophy of Science.8 Its principal theses include three contentions: • “An unlikely combination of intellectual and political forces taking root in Cold War anticommunism shaped . . . the research undertaken by leading philosophers.” (Author’s descriptive statement.) • These intellectual and political forces were concentrated in and around the RAND Corporation. “The significance of these personal connections among RAND, operations research, and logical empiricism . . . is that they shaped the [philosophical] profession’s view of itself and its public profile during and after the 1950s.” (Page 351.)

Nicholas Rescher • Episodes

184

• The science-oriented world-view of the RAND-involved philosophers impelled the subject and practitioners away from humanistic concerns—with unfortunate effects. “Had the profession . . . encouraged its brightest lights to supplement their technical work in philosophy with analysis of public issues and debates . . . one cannot but wonder whether . . . a more . . . informed public and possibly a more peaceful, economically stable, and just world would not seem as naïve and dreamlike as they do today.” (Page 388.) Like most conspiracy theories, this view of RAND as an evil democracy-undermining malignly anticommunist octopus sending its ideologically corrupting tentacles out into the wider society overlooks some control thesis-contravening facts. Granted, RAND employed a number of philosophy-trained individuals in those days—also among government-sponsored think-tanks. But most of them were, like myself, refugee immigrants and— • It was not cold-war anticommunism that impelled those philosophers drawn to what Reichenbach called “logical empiricism” to prioritize science, but the prominence of science in the Weimar Germany in which most of them had their cultural foundation. • Their opposition to and distrust of communism was not the product of the McCarthyite hysteria of the 1950s but antedated it as part of their revulsion to totalitarianism in general as product of their experience in Nazi Germany. • Their emphasis on value-free science was not the product of an opposition to values but rather to the confusion of cognitively extraneous values into scientific inquiry. They saw the projects of Hitler’s “Aryan Science” and Stalin’s “Communist Science” as corruptions against which science proper—idiotically unfettered salient inquiry—should be protected.

185

THE BERLIN GROUP AND THE RAND COOPERATION

• These philosophers at RAND were not drawn there by the military-geared mission of the organization, but through a personal relationship. For Olaf Helmer came to RAND by chance (via his wartime encounter with John Williams, who eventually directed RAND’S Mathematics Division), and the others became drawn to RAND through longstanding connections with Helmer, who saw this as a mode of mutual aid to fellow refugees as well as access to a pose of unusually talented theoreticians. • The RAND connection did not impel these philosophers into scientistically anti-humanistic allegiance. Insofar as they has such views—and mostly did not—these long antedated the RAND connection and were formed independently of it. • As a mere drop in a large ocean, those RAND connected philosophers—some dozen in all out of a total of six thousand or so— did not and could not determine the thought orientation of the profession at large. Apart from the inherent diversity of the group itself, there is the fact that it inclined but a dozen individuals in a profession of several thousand idiosyncratic and independent thinkers. They were but one tree in a vast forest of speculation. Moreover— • Given the cultural isolation of academic philosophy in the U.S., it is clear that even if (per impossible) the philosophical profession at large prioritized social reform over rational inquiry— adopting Marx’s injunction that the task of philosophy is not to understand the world but to change it—this would not and could not produce “a more peaceful, economically stable, and just world.” Given the marginal status of philosophy in American life—or for that matter the word at large—the idea of such a massive and monumental potential is ludicrous. But in any case, what rendered the philosophy of science of the 1950s and 1960s a technical, apolitical, and ideologically aseptic enterprise was not the Cold War as such, but a revulsion against totalitarian efforts—mostly by Nazis fascists and Stalinist communists—to enlist

Nicholas Rescher • Episodes

186

science in their totalitarian cause. These science-oriented philosophers felt that science should be done for the sake of understanding and not of politics. “Science should be done scientifically, so let’s keep political predilections and personal ideologies out of it” was effectively their motto. Rather than rejecting human values, they saw unfettered inquiry itself as a prime value. I myself left RAND at the end of 1956 to take up a professorial post at Lehigh University, drawn there by another former Hempel student, Adolf Grünbaum. And after some twenty years at RAND, Helmer left in 1968 to join with Theodore Gordon and RANDites Paul Baran and Arnold Kramish in founding The Institute for the Future⎯a still extant futurology think-tank⎯whose Eastern branch, located in Middletown Connecticut, he headed for a time.1 (I was offered a post there, but could not see my way clear to leave my philosophy professorship.) However, neither of us left RAND because of potentially motivated estrangement from the sort of work being done there. After his mandatory retirement at Princeton in 1976 Hempel, took up a post-retirement appointment at the University of Pittsburgh, whose Philosophy Department faculty I had joined in 1961. For a decade, until his second and final retirement in 1985 we were colleagues. While we never conducted any active collaboration we were on the best of collegial terms—indeed I edited a Festschrift for his 75th anniversary. And we worked in active cooperation to sustain the life of the Department. My own interests during these years included issues in metaphysics and perspectives on philosophical pragmatism, and I am not sure that Hempel altogether approved such radical departures from the tenor of his own earlier sympathies. It is one of the regrets of my life that I did not during these busy years take steps to bring this matter to a more decisive resolution. The reminder of lost opportunities is the disadvantage of retrospection. As regards Olaf Helmer, his unusual longevity made it possible to keep up an occasional friendly contact over the years—unfortunately only via the internet, given the extent of geographical separation. What impressed me deeply throughout my interaction with Oppenheim, Hempel, and Helmer was the inclination of these émigré members of the Berlin Group to look on one another in a profoundly collegial perspective. Our interaction was not just that of investigators who

187

THE BERLIN GROUP AND THE RAND COOPERATION

shared common interests but that of members of a family concerned to support each other in their careers and their professional lives. We were all refugees from Nazi Germany and having shared a difficult past were for this reason (so I think), inclined to the idea of making the present as smooth as possible for one another by mutual aid of some sort. In any case, the clustering of former Hempel students at the University of Pittsburgh and the prominence of its Center for Philosophy of Science can be seen as the prime legacy of the Berlin Group in the USA.9,10 NOTES 1

British Journal for the Philosophy of Science, vol. 6 (1955), pp. 89-106.

2

“On the Epistemology of the Inexact Sciences.” Initially circulated as a RAND paper in the mid 1950s, it was subsequently published in Management Science, vol. 6 (1959), pp. 25-52.

3

The method drew inspiration from the study by Abraham Kaplan, A. L. Skogstad, and M. A. Girshik, “The Prediction of Social and Technological Events,” Public Opinion Quarterly, vol. 14 [1950], 93-110. It was initially explained in Olaf Helmer and N. Rescher, “On the Epistemology of the Inexact Sciences,” Management Science, 6 (1959), pp. 25-52. (This article reprints and internal Rand Corporation paper of 1958, and was the earliest discussion on Delphi published in the open literature.)

4

A comprehensive bibliography of Delphi-relevant writings is given in Linstone and Turoff (op. cit.), pp. 575-605. Of the six items published prior to 1963 specifically dealing with Delphi, I am the author or co-author of three—that is, half of them. For further references see p. 299 ff. of Roger M. Cooke, Experts in Uncertainty (New York: Oxford University Press, 1991). (Chapter 11, entitled “Combining Expert Opinion” is particularly relevant). Good discussions of Delphi are also found in Joseph P. Martino, Technological Forecasting for Decisionmaking (New York: American Elzevier, 1972).

5

“On Prediction and Exploration,” British Journal of Philosophy of Science, vol. 8 (1957), pp. 83-94. Predicting the Future (Albany, NY: SUNY Press, 1998).

6

Philosophy of Science, vol. 25 (1958), pp. 87-94.

7

Oxford, Blackwells, 1980. Germany tr. Induktion: Zur Rechtfertigung des Induktiven Schliessens (München, Philosophia Verlag, 1987).

Nicholas Rescher • Episodes

188

NOTES 8

Published by Cambridge University Press. See also Philip Mirowski, “How Positivism Made a Pact with the Postwar Social Sciences in the United States,” in George Steinmetz (ed.), The Politics of The Politics of Method in the Human Sciences: Positivism and Its Epistemological Others (Durham, NC: Duke University Press, 2005), pp. 142-172. See also Alex Abella, Soldiers of Reason: The RAND Corporation and the Rise of the American Empire (New York: Harvard, 2008), and David A. Hounshell, “The Cold War, RAND, and the Generation of Knowledge, 1946-1962,” Historical Studies in the Physical and Biological Sciences, vol. 27 (1997), pp. 237-67.

9

The Center members who had some training under Hempel include: John Earman, Adolf Grünbaum, Gerald Massey, and Nicholas Rescher. Earman apart, each of us served as Center director for a period of years.

10

This chapter was written for conference on the Berlin Group held in Berlin in November of 2010.

Chapter Fifteen ON INFERENCE FROM INCONSISTENT PREMISSES

T

he expansion of logical devices in many directions is a striking trend of 20th century thought. A striking instance of this is the development of procedures for inference from inconsistent premisses—a procedure for which classical logic made no provision. The crux of traditional logic is truth-preservation: its task is to determine what follows from given premisses, where “given” means given as true. And this requires, among other things, that those premisses must be mutually consistent and compatible. On the subject of what happens with more problematic premisses that are merely given as plausible, and where there can be—and likely are—outright inconsistencies among them, traditional logic is silent. A different, epistemically more enterprising mechanism is called for here. In the second half of the twentieth century, several theoreticians began to address this question, the present writer among them. As he saw it, with inconsistent premisses the question is no longer what conclusions logically follows from these problematic givens, but rather what conclusions optimally cohere with them. So there is now to be a transit from a classical logic of truth to a coherentist epistemology of plausibility. This shift from a logical theory of secure deduction to an epistemological theory of plausible inference is a big step—not so much forward as sideways. Its theory of information processing prepared to deal in inconsistent givens was developed in a substantial series of publications.1 Despite a respectful reception by the reviewers of these publications, the theory is understood less widely than is warranted by its potential utility. So it seems proper to explain once more the rather simple and straightforward line of reasoning that is at work here. And for ready accessibility the general theory is best explained via a particular example.

Nicholas Rescher • Episodes

190

Suppose that three sources of roughly equal reliability provide the following series of collectively inconsistent reports: S1:

p v q; ~(p & q & r)

S2:

~ p v ~r

S3:

q ⊃ ~r; r

Table 1 gives a survey of the entire spectrum of possible alternative states of affairs that can obtain in the light of each of these several reports. Observe that ________________________________________________________ Table 1 p

q

r

+ +

+ +

+ -

+

_

+

+

-

-

S1

S2

S3

Σ

Σ*

x

x √16

x x

0

0

x

√12

√16

x

√16 √16 √16 √16

x

-

+

+

-

+

-

1 5 1 5 1 5 1 5 1 5

-

-

+

x

-

-

-

x

x √12 x

11 30 21 30 11 30 11 30 11 30 20 30 5 30

11 90 21 90 11 90 11 90 11 90 20 90 5 90

NOTE: x = case excluded. In the absence of further information the various possibilities can be treated as equiprobable. Σ* normalizes the overall sum to 1.

________________________________________________________

So looking at those final Table 1 entries as a probability analogous distribution across the spectrum of possibility, we arrive at that Σ* column. On this basis we would have it that pr(p) = 43 90 ≅

1 2≅

.5

191

ON INFERENCE FROM INCONSISTENT PREMISSES

pr(q) = 33 90 ≅ 0.4 pr(r) = 52 90 ≅ 0.6 To be sure, we cannot now make many definite inferences from these initial inconsistent statements regarding the truth-status of the proposition at issue (viz. p, q, r)—apart from excluding p & q & r for which there is universal consensus. But we can use the information they provide to make reasonable conjectures regarding the plausibilities at issue. (For example, that the conjecture that r obtains is substantially more plausible than that q obtains.) And if we had further information about our sources we could of course make good use of it in readjusting our calculation. For instance, if S1 were deemed substantially more reliable than S3, we could readily weight our numbers to provide a corresponding readjustment. This clearly over-simple schematic example should suffice to indicate how plausible reasoning from inconsistent premisses can be conducted. Interestingly, even in with such inconsistent premisses certain for-sure conclusions can be obtained by the methodologies as issue. For example since ~(p & q & r) is secure we have it that ~p v ~q v ~r must definitely be maintained—inconsistency notwithstanding. In deductive logic we conduct inference from premisses that are sufficient to answer the questions at hand. In inductive logic we address questions from which our premissed information is insufficient and where we must accordingly take recourse to probabilities. In inconsistency logic we deal with questions where our premissed information is on overload through making incompatibilities. Here we have a surfeit of information and are driven to dealing with plausibilities (in contrast to probabilities). And so in standard logic we have proofs; in inductive logic estimates, and in inconsistency logic conjectures. Decidedly different sorts of information-management procedure are at work. But even in with worst-case scenarios of outright inconsistent information we are not altogether at sea.

Nicholas Rescher • Episodes

192

NOTES 1

Hypothetical Reasoning (Dordrecht: Reidel, 1964), Aporetics (Pittsburgh: University of Pittsburgh Press, 2009), Conditionals (Cambridge: Cambridge University Press, 2007), The Coherence Theory of Truth (Oxford: Oxford University Press, 1973).

Chapter Sixteen PHILOSOPHY IN THE WORLD OF LEARNING (Aspects of a Two-Percent Solution)

H

ow large a place does philosophy as a field of study occupy in the sphere of academic endeavor and the wider world of learning? At a best estimate provided for by currently available statistics we find that it accounts for • 2% of the professoriate in American higher education • 1.2% of all new academic book titles published in the USA • 2% of overall academic library printspace • 1.5% of all doctorates currently being earned in the USA • 2.5% of the membership of the American Academy of Arts and Science All in all, then, it seems fair to say that philosophy occupies some 2±½ % of the overall realm of present-day academic enterprise in America.1 It is a modest but not yet marginalized endeavor. Its history has been one of decline. In classical antiquity philosophy accounted for easily over 25 percent of space allocated to the written word. With the rise of theology in the middle ages this proportion decreased to some 15 percent. With the emergence of modern science and the unfolding of global exploration, this figure shrank to some 5 percent by the mid-19th century. And now with the expansion of learning and ongoing division of labor and specialization, the proportion has come down to some 2 percent.

Nicholas Rescher • Episodes

194

So one thing is sure: philosophy’s place in the world of learning has been subject to ongoing diminution. On the other hand, it is also safe to say that notwithstanding the large forces that constantly reshape the academic world, philosophy continues to have a nontrivial place. This situation is not due to its position in modern popular culture where philosophy has in fact become increasingly sidelined. Instead it is due entirely to the relatively secure place that the discipline has been able to maintain in higher education. To be sure the “humanities” have become increasingly under pressure here. But they have fought a steady rear-guard action in the ongoing struggle between careerist practicalism and intellectual culture that has prevailed in American academia. To be sure, it should occasion no surprise if philosophy’s present 2% slice of the academic pie were to decline to 1% over the next century. But still, as long as the traditions of academic values continue to have some place in academia itself, philosophy’s concern for the “big questions” regarding the place of homo sapiens in the world’s scheme of things will secure for it some modest Lebensraum. NOTES 1

The preceding data are drawn from the Statistical Abstract of the U.S. (doctorates and higher education), the Statistical reports of UNESCO’s Institute of Statistics and Annual Reports of the American Academy of Arts and Sciences.

REFERENCES Abella, Alex, Soldiers of Reason: The RAND Corporation and the Rise of the American Empire (Cambridge, MA: Harvard University Press, 2008), Allen, Diogenes, “Mechanical Explanations and the Ultimate Origin of the Universe According to Leibniz,” Studia Leibnitiana, Sonderheft 11 (Wiesbaden: Franz Steiner, 1983). Aquinas, Summa contra gentiles. Aquinas, Super libros sententiarum. Aristotle, Magna Moralia. Barbour, Julian and Lee Smolin, “Extremal Variety as the Foundation of a Cosmological Quantum Theory,” published on the web at http: arxiv.org/hep-th/9203041. Beeley, Philip (ed.), “Leibniz on the Limits of Human Knowledge,” The Leibniz Review, vol. 13 (2003), pp. 93-97. Borges, Jorge Luis, El jardin de los senderos que se bifurcan (Buenos Aires: Sur, 1941). Breger, Herbert, “Symmetry in Leibnizian Physics,” in Anonymous (ed.), The Leibniz Renaissance (Firenze: Leo S. Olschki, 1989), pp. 23-42. Burnet, John, Early Greek Philosophy (London: A. and C. Black, 1892). Calaprice, Alice (ed.), The Expanded Quotable Einstein (Princeton: Princeton University Press, 2000). Clarke, Samuel, The Leibniz–Clarke Correspondence (London: Knapton, 1717). Cooke, Roger M., Experts in Uncertainty (New York: Oxford University Press, 1991). Couturat, Louis, Opucules et fragments inédits de Leibniz (Paris: Alcan, 1903). Couturat, Louis, La Logique de Leibniz (Paris: Alcan, 1901).

Nicholas Rescher • Episodes

196

Davis, Martin, “What Did Gödel Believe and When Did He Believe it?,” in Feferman et. al. 2010, pp. 229-41. Davis, Martin, The Undecidable: Basic Papers (Mineola, NY: Dover Publications, 1956). Dawson, J. W. Jr., Logical Dilemmas: The Life and Work of Kurt Gödel (Wellesley, MA: A. K. Peters, 1997). Dewey, John, Leibniz’s New Essays Concerning the Human Understanding: A Critical Exposition (Chicago: S. C. Griggs & Co. 1888), reprinted in 1902 by Scott, Foresman, & Co, of New York and included in Vol. I of John Dewey: The Early Works 1882-1898 (Carbondale & Edwardsville: Southern Illinois University Press, 1969-72). Duschesneau, Francois, Leibniz et la méthode de la science (Paris: Presses Universitaires de France, 1993). Eddington, Arthur, The Nature of the Physical World, (New York, MacMillan and Cambridge, Cambridge University Press, 1929). Einstein, Albert, “On Generalized Theory of Gravitation,” Scientific American, vol. 182 (1950), pp. 13-17. Einstein, Albert, Ideas and Opinions (New York: Bonanza, 1954). Ettlinger, Max W. (ed. and trans.), Apokatastaseôs pantôn an appendix to Leibniz als Geschichtsphilosoph (Munich: Koesel & Puslet, 1921). Feferman, Solomon et al., Kurt Gödel: Essays for his Centennial (Cambridge: Cambridge University Press, 2010). Fichant, Michael, G. W. Leibniz: De l’horizon de la doctrine humaine (Paris: Vrin, 1991). Gale, George, “The Physical Theory of Leibniz,” Studia Leibnitiana vol. 2 (1970), pp. 114-127. Gerhardt, C. I., Die philosophische Schriften von G. W. Leibniz, Vol. VII (Berlin: Wiedmann, 1875-1890). Gödel, Kurt, Collected Works in five volumes published by the Oxford University Press, 1986-2003. This includes “Russell’s Mathematical Logic” and “What is Cantor’s Continuum Problem”.

197

REFERENCES

Goldstein, Rebeca, Incompleteness: The Proof and Paradox of Kurt Gödel (New York: W. W. Norton, 2005). Gueroult, Martial, Dynamique et métaphysique Leibniziennes (Paris: Les Belles Lettres, 1934). Guhrauer, Gottschalk Eduard, Leibniz’ Deutsche Schriften, 2 vols. (Berlin: 1938-40). Halab, L. J., Nietzsche’s Life Sentence: Coming to Terms with Eternal Recurrence (London: Routledge, 2005). Heath, T. L., The Works of Archimedes (Cambridge: Cambridge University Press, 1897). Hedge, Frederic Henry, Reason or Religion (Boston: Walker, Fuller and Company, 1865). Hedge, Frederic Henry, Atheism in Philosophy (Boston: Roberts Brothers, 1884). Hedge, Frederic Henry, Ways of the Spirit: And Other Essays (Boston: Roberts Brothers, 1878, ©1877). Heidegger, Martin, Nietzsche: The Eternal Recurrence of the Same, tr. D. F. Krell (San Francisco: Harper & Row, 1984). Helmer, O. and Rescher, N., “On the Epistemology of the Inexact Sciences,” Management Science, vol. 6 (1959), pp. 25-52. Horgan, John, Rational Mysticism: Spirituality Meets Science in the Search for Enlightenment (New York: Haughton Mifflin, 2003). Hounshell, David A., “The Cold War, RAND, and the Generation of Knowledge, 1946-1962,” Historical Studies in the Physical and Biological Sciences, vol. 27 (1997), pp. 237-67. Huebener, Wolfgang, “Die notwendige Grenze des Erkenntnisfortschritts als Konsequenz der Aussagenkombinatorik nach Leibniz’ unveroeffentlichen Traktat ‘De l’horizon de la doctrine humaine’,” Studia Leibnitiana Supplementa, vol. 15 (1975), pp. 55-71 (see pp. 62-63). Jourdain, P. E. B., The Principle of Least Action (Chicago: Carus, 1913).

Nicholas Rescher • Episodes

198

Kaplan, Abraham, A. L. Skogstad, and M. A. Girshik, “The Prediction of Social and Technological Events,” Public Opinion Quarterly, vol. 14 (1950), 93-110. Kaufmann, Walter, Nietzsche,Philosopher, Psycholigist, Antichrist (Princeton, NJ: Princeton University Press, 1974). Kennedy, Juliette, “Kurt Gödel,” Stanford Encyclopedia of Philosophy (13 February, 2007). Knobloch, Eberhard, Die mathematischen Studien von G. W. Leibniz zur Kombinatorik, Studia Leibnitiana Supplementa, Vol. XI (Wiesbaden, Franz Steiner Verlag, 1973). English translation “The Mathematical Studies of G. W. Leibniz on Combinatorics,” Historica Mathematica, vol. 1 (1974), pp. 409-30. Krell, David F., Nietzsche’s: The Eternal Recurrence of the Same (San Francisco: Harper & Row, 1979). Kroeger, A. E., The Journal Speculative Philosophy, No. 47 and 58 (1867/71), tr. “Considerations on the Doctrine of a Universal Spirit,” The Journal Speculative Philosophy 5 (1871), pp. 118129. Kroeger, A. E., “New System of Nature,” The Journal Speculative Philosophy 5 (1871), pp. 209-19. Lanczos, Carnetius, The Variational Principle of Mechanics (New York: Dover, 1986). Latta, Robert (ed.), Leibniz: The Monadology: And Other Philosophical Writings (London: Oxford University Press, 1898). Leibniz, Gottfried Wilhelm, New Essays Concerning Human Understanding, tr. by Alfred Gideon Langley (La Salle, Ill.: Open Court, 1896). Leibniz, G. W., De l’horizon de le doctrine humain, ed. by Michel Fichant (Paris: Vrin, 1991). Livio, Mario, The Accelerating Universe (New York: John Wilem, 2000). Loemker, L. E. (ed.), Leibniz: Philosophical Papers and Letters, 2 vol.’s (Chicago: University of Chicago Press, 1956); 2nd ed. in one vol. (Amsterdam: Reidel, 1970).

199

REFERENCES

Loewith, Karl, Nietzche’s Philosophy of the Eternal Recurrence of the Same (Berkeley and Los Angeles: University of California Press, 1997). Lukacher, Ned, Time-fetishes: The Secret History of Eternal Recurrence (Durham, NC: Duke University Press, 1998). Mach, Ernst, Die Mechanik in ihrer Entwicklung (Leipzig: Brockhaus, 1901). Magnus, Bernard, Nietzsche’s Existential Imperative (Bloomington: Indiana University Press, 1978). Martino, Joseph P., Technological Forecasting for Decisionmaking (New York: American Elzevier, 1972). Maurice Mandelbaum, The Problem of Historical Knowledge (New York: Liveright Publishing Corporation, 1938). Menger, Karl, Reminiscence of the Vienna Circle and the Mathematical Colloquium, ed. by L. Golland et al. (Dordrecht: Kluwer, 1994). Mirowski, Philip, “How Positivism Made a Pact with the Postwar Social Sciences in the United States,” in George Steinmetz (ed.), The Politics of The Politics of Method in the Human Sciences: Positivism and Its Epistemological Others (Durham, NC: Duke University Press, 2005), pp. 142-172. Moles, Alistair, “Nietzsche's Eternal Recurrence as Riemannian Cosmology,” International Studies in Philosophy, vol. 2 (1989), pp. 21-35. Montgomery, George R., The Place of Values (Bridgeport, Conn: Joyce & Sherwood, 1903.) Mugnai, Massimo, Introduzione alla filosofia di Leibniz (Torino: G. Einaudi, 2001). Müller, Kurt, Leibniz Bibliographie: Verzeichnis der Literatur über Leibniz (Frankfurt am Main: Vittorio Kloslerman, 1967). Mulvany, R. J., “Frederic Henry Hedge, A. A. P Torrey, and the Early Reception of Leibniz in America,” Studia Leibnitiana, vol. 8 (1996), pp. 163-82. Nagel, Ernest and James R. Newman, Gödel’s Proof, revised ed. (New York: New York University Press, 2001).

Nicholas Rescher • Episodes

200

Nietzsche, Ecce Homo (Leipzig: C. G. Naumann, 1888, unpublished until 1908). Norton, John, “Nature is the Realization of the Simplest Conceivable Mathematical Ideas: Einstein and the Canon of Mathematical Simplicity,” in Studies in the History and Philosophy of Modern Physics, vol. 31 (2000), pp. 135-70. Oppenheim, Paul and Nicholas Rescher, “Logical Analysis of Gestalt Concepts” British Journal for the Philosophy of Science, vol. 6 (1955), pp. 89-106. Peirce, C. S., Collected Papers, ed. by C. Hartshorne and P. Weiss, Vol VI (Cambridge, Mass: Harvard University Press, 1929). Pesic, Peter, Labyrinth: A Search for the Hidden Meaning of Science (Cambridge, MA: MIT Press, 2000). Polenz, Max, Die Stoa, 2 vol.’s (Göttingen: Vanderhoeck & Reprecht, 1964). Poser, Hans, “Apriorismus der Prinzipien und Kontingenz der Naturgesetze: Das Leibniz-Paradigma der Naturwissenschaft,” in A. Heinekamp (ed), Leibniz’ Dynamica (Stuttgart: Franz Steiner, 1984; Studia Leibnitiana, Sonderheft 13), pp. 164-79. Regis, Eduard, Who Got Einstein’s Office (New York: Addison Wesley, 1997). Reisch, George A., How the Cold War Transformed Philosophy of Science (Cambridge: Cambridge University Press, 2005). Rescher, Nicholas, “On Prediction and Exploration,” British Journal of Philosophy of Science, vol. 8 (1957), pp. 83-94. Rescher, Nicholas, “A Theory of Evidence,” Philosophy of Science, vol. 25 (1958), pp. 87-94. Rescher, Nicholas, Hypothetical Reasoning (Dordrecht: Reidel, 1964). Rescher, Nicholas, The Coherence Theory of Truth (Oxford: Oxford University Press, 1973). Rescher, Nicholas, Induction, (Oxford, Blackwells, 1980). German tr. Induktion: Zur Rechtfertigung des Induktiven Schliessens (München, Philosophia Verlag, 1987).

201

REFERENCES

Rescher, Nicholas, Predicting the Future (Albany, NY: SUNY Press, 1998). Rescher, Nicholas, Philosophical Reasoning (Malden, Mass. : Blackwell Publishers, 2001). Rescher, Nicholas, “Leibniz’s Quantitative Epistemology,” Studia Leibnitiana, vol. 36 (2004), pp. 210-31. Rescher, Nicholas, Studies in Leibniz’s Cosmology (Frankfurt: ONTOS Verlag, 2006). Rescher, Nicholas, Conditionals (Cambridge: Cambridge University Press, 2007). Rescher, Nicholas, Aporetics (Pittsburgh: University of Pittsburgh Press, 2009). Rescher, Nicholas, “What Einstein Wanted,” Logos and Epistemology, vol. 2 (2011), pp. 233-252. Rey, Abel, le retour éternel et la philosophie de la physique (Paris, Flammarion, 1921). Russell, Bertrand, Critical Exposition of the Philosophy of Leibniz (London: Allen S. Unwin, 1899; 2nd ed. 1937). Rutherford, Donald, Leibniz and the Rational Order of Nature (Cambridge: Cambridge University Press, 1995). Scheler, Max, Die Wissensformen und die Gesellschaft: Probleme einer Soziologie des Wissens (Leipzig: Der Neue-Geist-Verlag, 1926). Simmel, Georg, Schopenhauer und Nietzsche, Ein Vortragszyklus (Leipzig: Duncker & Humblot, 1967). Sommerfeld, Arnold, Electrodynamics: Lectures in Theoretical Physics, Vol. III [tr. E. G. Ramberg (New York: Academic Press 1964; German original Vorlesungen über theoretische Physik (Wiesbaden: Klemm Verlag, 1945). Spade, Paul Vincent, “Insolubilia,” in The Cambridge History of Later Medieval Philosophy ed. Norman Kretzmann et al. (Cambridge: Cambridge University Press, 1982). Stohmann, Walter, Überblick über die Geschichte des Gedankens der ewigen Wiederkunft (München, Kastner, 1917).

Nicholas Rescher • Episodes

202

Tieszen, Richard, Phenomenology, Logic, and the Philosophy of Mathematics (Cambridge: Cambridge University Press, 2005). van Allen, Mark and Juliette Kennedy, “On the Philosophical Development of Kurt Gödel,” Bulletin of Symbolic Logic, vol. 9 (2003), pp. 475-76. van Dongen, Jeroen, Einstein’s Unification (Cambridge: Cambridge University Press, 2010). Wallace, W. M., Soul of the Lion: A Biography of General Joshua L. Chamberlain (Edinburgh: Thomas Nelson & Sons, 1960). Wang, Hao, “Some Facts about Kurt Gödel,” The Journal of Symbolic Logic, vol. 46 (1981), pp. 653-59. Wang, Hao, Reflections on Kurt Gödel (Cambridge, MA: MIT Press, 1987). Warren, J., “Ancient Atomism and the Plurality of Worlds,” Classical Quarterly, vol. 54 (2004), pp. 354-70. Will Dudley, Hegel, Nietzsche, and Philosophy: Thinking Freedom (Cambridge: Cambridge University Press, 2002). Wilson, Catherine, Leibniz’s Metaphysics (Princeton, Princeton University Press, 1989). Windelband, Wilhelm, “Normen und Naturgesetze”, in Präludien: Aufsätze und Reden zur Einleitung in die Philosophie (Tübingen: J. C. B. Mohr/Paul Siebeck, 1888; 3rd ed. 1907). Yourgrau, Palle, A World without Time: The Forgotten Legacy of Gödel and Einstein (New York: Basic Books, 2005). Zee, Anthony, Fearful Symmetry (Princeton: Princeton University Press, 1999).

NAME INDEX Abella, Alex, 188n8, 195 Allen, Diogenes, 147, 149n9, 195 Anaximander, 4 Aquinas, St. Thomas, 23, 24, 25n1, 25n3, 25n5, 155,195 Archimedes, 53n32, 73, 131 Aristotle, 1, 34, 50n9, 71, 74, 105, 108-110, 127 Arnauld, Antoine, 60 Augustine, St., 50n1, 113 Avigard, Jeremy, 177n21, 177n22 Baran, Paul, 186 Barbour, Julian, 139, 147, 151n30, 195 Bargmann, Valentin, 141 Bergmann, Peter, 130 Bergson, Henri, 120 Bernays, Paul, 159 Bignon, Jean-Paul, 38 Bodemann, Eduard, 178n33 Bohm, David, 142, 152n37, 152n40 Bohr, Neils, 129 Borges, Jorge Luis, 48, 195 Breger, Herbert, 147, 149n9, 195 Brantano, Franz, 106 Burnet, John, 48, 50n4, 50n7, 195 Bywater, Ingram, 50n6, 50n7 Cajori, Florian, 62 Calaprice, Alice, 151n27, 151n33, 152n41, 152n43, 152n44, 152n45, 152n46 Cantor, Georg, 157 Carnap, Rudolf, 109, 176n4, 182 Carr, Herbert Wildon, 61 Carus, Paul, 59 Cassirer, Ernst, 120

Nicholas Rescher • Episodes

204

Chamberlain, Joshua L., 150n19 Chandler, A. R., 60-61 Child, J. M., 75n10 Chomsky, Noam, 164 Chrysippus, 34 Clarke, Samuel, 75n10, 195 Collingwood, R.G., 1 Comte, Auguste, 89 Conrad, Theodor, 105 Conrad-Martius, Hedwig, 105-111 Cooke, Roger M., 187n4, 195 Couturat, Louis, 27, 31, 31n1, 52n25, 52n28, 59, 155, 164-167, 177n15, 177n16, 177n18, 177n20, 179n46, 195 Dalkey, Norman, 182 Davidson, Thomas, 58-59 Davis, Martin, 175, 176n5, 177n9, 177n10, 177n11, 177n12, 177n14, 178n41, 179n44, 196 Dawson, J. W. Jr., 75n13, 175, 175n2, 176n3, 178n32, 178n37, 196 Descartes, René, 39, 71, 73, 80, 137 Dewey, John, 61-62, 75n9, 196 Diels, Hermann, 50n11 Dilthey, Wilhelm, 107, 116-117, 119, 128n1 Dionysius, 25n1 Dudley, Will, 52n21 Duncan, George Martin, 59, 75n10 Duschesneau, Francois, 147, 149n9, 196 Dyson, Freeman, 139 Earman, John, 188n9 Eddington, Arthur, 121, 127-128, 128n5, 196 Ehrenfest, Paul, 140 Einstein, Albert, 38, 129-148, 148n1, 149n1, 151n35, 152n39, 152n45, 196 Einstein, Margot, 149n1 Eliot, T. S., 62 Erdmann, Johann Eduard, 58

205

NAME INDEX

Erdös, Paul, 68 Euler, Leonard, 138-139 Fabricius, Johann, 50n1 Feferman, Solomon, 175, 178n40, 196 Fermat, Pierre, 137 Fichant, Michael, 48, 53n29, 53n30, 196 Fichte, J. G., 58 Franklin, Benjamin, 48 Frederic II of Prussia, 138 Fremont, John C., 58 Freud, Sigmund, 119 Gale, George, 147, 149n9, 196 Gauss, C. F., 139 Geiger, Moritz, 105 Gerhardt, C. I., 54n35, 196 Gibbs, Willard, 139, 157 Girshik, M. A., 187n3, 198 Gödel, Kurt, 68-69, 71-73, 75n13, 152n45, 155-175, 176n1, 176n2, 176n4, 176n7, 176n8, 177n21, 177n22, 178n32, 178n34, 178n37, 179n39, 179n45, 179n46, 196 Goldstein, Rebeca, 75n21, 147, 152n45, 175, 177n24, 177n25, 177n26, 178n27, 178n28, 178n34, 178n35 , 197 Gomperz, Heinrich, 69 Gordon, Theodore, 186 Grandjean, Blanche D., 164, 176n2 Grelling, Kurt, 181 Grünbaum, Adolf, 186, 188n9 Gueroult, Martial, 147, 149n9, 197 Guhrauer, Gottschalk Eduard, 50n1, 58, 197 Guldin, Paul, 39, 53n29 Günther, Gottard, 158 Halab, L. J., 48, 52n21. 197 Hamilton, William, 138-139, 146 Händel, G. F., 167

Nicholas Rescher • Episodes

206

Hansch, Michael Gottlieb, 59 Harris, William Torrey, 57 Hartshorne, Charles, 64 Heath, T. L., 53n32, 197 Hedge, Frederic Henry D. D., 57-58, 74n4, 197 Hegeler, Edward, 59 Heidegger, Martin, 49, 51n14, 118, 197 Heine, Henrich, 37 Helmer, Olaf, 181-182, 185-187, 197 Helmholz, H. L. F. von, 165 Hempel, C. G., 181-182, 186-187, 188n9 Heraclitus, 34, 50n5 Hilbert, David, 156, 177n22 Hildebrand, Dietrich von, 105 Hitler, Adolf, 178 de l’Hôpital, Guillaume, 150n15 Horgan, John, 147, 151n29, 197 Hounshell, David A., 188n8, 197 Huebener, Wolfgang, 49, 53n27, 197 Husserl, Edmund, 105, 108, 118-119, 168-174, 178n37, 178n39 Huygens, Christiaan, 167 James, William, 62 Jourdain, P. E. B., 148, 151n24, 151n26, 197 Kant, Immanuel, 40, 48, 52n20, 77-88, 109, 111, 113-115, 123, 126127 Kaplan, Abraham, 187n3, 198 Kaufmann, Walter, 49, 52n18, 52n19, 198 Kelvin, Lord (William Thompson), 127-128 Kennedy, Juliette, 175-176, 176n2, 178n41, 179n43, 198, 202 Klibansky, Raymond, 64 Klopp, Onno, 54n36 Knag, Charlotte, 181 Knobloch, Eberhard, 49, 53n31, 53n34, 198 Koenig, J. S., 138 Korthhold, Christian, 50n1

207

NAME INDEX

Kramish, Arnold, 186 Krell, David F., 52n19, 198 Kretzmann, Norman, 25n1 Kroeger, A. E., 58, 198 Lach, Donald F., 65 Lagrange, J. L. de, 138-139 Lanczos, Carnetius, 151n24, 148, 198 Lane, William C., 151n31 Langley, Alfred Gideon, 60, 62 Laplace, P. S. de, 139 Latta, Robert, 75n10 Leibniz, G. W., 24, 27-31, 33-49, 50n1, 51n15, 52n24, 52n26, 5253n27, 53n29, 53n33, 53n34, 54n36, 54n37, 54n38, 54n40, 54n44, 54n45, 55n48, 57-73, 74n6, 75n9, 75n10, 75n13, 75n14, 113, 116, 130-138, 142, 149n9, 149-50n12, 150n14, 150n15, 150n16, 150n18, 150n19, 152n45, 152n46, 155-175, 176n1, 176n2, 176n4, 177n20, 178n32, 178n33, 178n34, 198 Linstone, Harold, 182,187n4 Livio, Mario, 139, 148, 151n27, 198 Locke, John, 61, 82 Loemker, Leroy E., 57, 66-67, 74n2, 133, 149-50n12, 150n13, 151n20, 151n21, 151n23 Loewith, Karl, 49, 54n46, 199 Lotze, Hermann, 115-117 Lovejoy, Arthur O., 62 Lucretius, Diogenes, 35, 50n5 Lukacker, Ned, 49, 50n4, 199 Luther, Martin, 58 MacDonald, Scott, 25n1 Mach, Ernst, 139-140, 148, 151n26, 199 Magnus, Bernard, 52n19, 199 Mandelbaumm, Maurice, 128n4, 199 Martino, Joseph P., 187n4, 199 Marx, Karl, 185 Massey, Gerald, 188n9

Nicholas Rescher • Episodes

de Maupertuis, P. L. M., 137, 146 Menger, Karl, 69, 165-166, 175, 178n29, 178n31, 178n34, 199 Mirowski, Philip, 188n8, 199 Moles, Alistair, 49, 52n23, 199 Montgomery, George R., 60, 199 Morgenstern, Oskar, 178n34, 165-166, 168 Morris, George S., 62, 75n9 Mugnai, Massimo, 150n18, 199 Müller, Kurt, 57, 74n1, 199 Mulvany, R. J., 74n4, 199 Murray, Bill, 50n3 Nagel, Ernest, 176, 200 Nason, John, 64 Neumann, John von, 74, 159, 175 Newman, James R., 176, 199 Newton, Isaac, 75n10, 130-131 Nietzsche, Friedrich, 36, 37, 51n14, 52n19, 54n46, 200 Northrop, F. S. C., 64 Norton, John, 148, 151n36, 152n39, 152n42, 200 Oppenheim, Paul, 181, 186, 200 Origen, 50n1 Overbeck, Adolph Theobaldus, 45-46, 53n32 Pappenheimer, Salomon, 148n1 Pappenheimer, Sarah Rescher, 148-49n1 Parsons, Terence, 177n8, 178n39 Peano, Guiseppi, 68 Peirce, Charles Sanders, 89-103. 103n1, 110, 119, 120, 200 Pesic, Peter, 148, , 152n43, 152n45, 200 Petersen, Johann Wilhelm, 50n1 Pfänder, Alexander, 105 Philip, Christian, 149n12 Plato, 3, 5, 9, 11, 23, 34, 50n1, 71-73, 77-88, 113, 146, 171 Plotinus, 2-7, 9 Poincaré, Henri, 51n17

208

209

NAME INDEX

Polenz, Max, 50n2, 200 Poser, Hans, 148, 149n9, 150n16, 200 Ptolemy, 130 Pythagoras, 73 Ravier, Emile, 178n33 Regis, Eduard, 75n12, 200 Reichenbach, Hans, 182, 184 Reinach, Salomon, 105 Reisch, George, 183, 200 Rescher, Nicholas, 65, 75n11, 197, 182, 187, 188n9, 200-201 Rey, Abel, 49, 51n15, 52n22, 201 Rickert, Heinrich, 111n1 Robinson, E. G., 60 Rosmini, Antonio, 59 Russell, Bertrand, 52n20, 59, 65, 75n10, 109, 150n12, 167, 176n4, 201 Rutherford, Donald, 49, 201 Savage, L. J., 182 Schaffner, Kenneth, 152n47 Scheler, Max, 105, 120-121, 128n3, 201 Schlipp, Paul, 68 Schrecker, Paul, 63, 168 Scott, Liddell, 50n10 Sellars, Wilfrid, 128n5 Sheldon, Wilmon H., 62 Simmel, Georg, 49, 51n16, 201 Skogstad, A. L., 187n3, 198 Smolin, Lee, 139, 147, 151n30, 195 Snell, Willebrord, 137-138, 151n22 Socrates, 34 Solomon, Maurice, 142, 151n33 Sommerfeld, Arnold, 148, 152n47, 201 Spade, Paul Vincent, 103n3, 201 Spencer, Herbert, 141 Spinoza, 88, 146, 152n45, 152n46, 176n2

Nicholas Rescher • Episodes

210

Stack, G. J., 52n23 Stalin, Joseph, 184 Stein, Edith, 105 Sterns, T. S., 62 Stohmann, Walter, 51n13, 201 Tieszen, Richard, 176, 178n39, 202 Turoff, Murray, 182, 187n4 Toland, John, 54n47 van Allen, Mark, 176, 176n2, 178n41, 179n43, 202 van Dongen, Jeroen, 141, 148, 148n1, 149n2, 149n3, 149n4, 149n5, 149n7, 150n12, 151n32, 151n34, 151n36, 152n37, 152n38, 152n40, 202 Victoria, Queen, 108 Voltaire, F. M. A. de, 138, 165 Wagner, Richard, 59 Wallace, W. M., 148, 150n19, 202 Wang, Hao, 71-73, 74n15, 176, 176n1, 177n21, 202 Warren, James, 51n11, 202 Wells, Rulon S. III, 65-66 Whitehead, A, N., 109 Wiener, Philip Paul, 64 Will, Dudley, 202 Williams, John, 185 Wilson, Catherine, 49, 202 Windelband, Wilhelm, 117-119, 128n2, 202 Wittgenstein, Ludwig, 43, 109 Wolff, Christian, 88 Yost, Robert Morris, 65-66 Yourgrau, Palle, 176, 177n23, 178n38, 202 Zee, Anthony, 139, 148, 151n28, 202

NicholasRescher

Nicholas Rescher

Philosophical Explorations This book continues Rescher’s longstanding practice of publishing groups of philosophical essays that originated in occasional lecture and conference presentations. Notwithstanding their topical diversity they exhibit a uniformity of method in a common attempt to view historically significant philosophical issues in the light of modern perspectives opened up thorough conceptual clarification.

About the Author Nicholas Rescher is University Professor of Philosophy at the University of Pittsburgh where he also served for many years as Director of the Center for Philosophy of Science. He is a former president of the Eastern Division of the American Philosophical Association, and has also served as President of the American Catholic Philosophical Association, the American Metaphysical Society, the American G. W. Leibniz Society, and the C. S. Peirce Society. An honorary member of Corpus Christi College, Oxford, he has been elected to membership in the European Academy of Arts and Sciences (Academia Europaea), the Institut International de Philosophie, and several other learned academies. Having held visiting lectureships at Oxford, Constance, Salamanca, Munich, and Marburg, Professor Rescher has received six honorary degrees from universities on three continents. Author of some hundred books ranging over many areas of philosophy, over a dozen of them translated into other languages, he was awarded the Alexander von Humboldt Prize for Humanistic Scholarship in 1984. In November 2007 Nicholas Rescher was awarded by the American Catholic Philosophical Association with the „Aquinas Medal“. In 2011 Rescher receive the Bundesverdienstkreuz 1. Klasse (First Class Order of Merit) of the Federal Republic of Germany.

ontos verlag

Frankfurt • Paris • Lancaster • New Brunswick 2011. 124 pp., Format 14,8 x 21 cm Hardcover, EUR 69,00 ISBN 978-3-86838-109-2

P.O. Box 1541 • D-63133 Heusenstamm bei Frankfurt www.ontosverlag.com • [email protected] Tel. ++49-6104-66 57 33 • Fax ++49-6104-66 57 34

NicholasRescher

Nicholas Rescher

Free Will An Extensive Bibliography With the Cooperation of Estelle Burris

Few philosophical issues have had as long and elaborate a history as the problem of free will, which has been contested at every stage of the history of the subject. The present work practices an extensive bibliography of this elaborate literature, listing some five thousand items ranging from classical antiquity to the present.

About the author Nicholas Rescher is University Professor of Philosophy at the University of Pittsburgh where he also served for many years as Director of the Center for Philosophy of Science. He is a former president of the Eastern Division of the American Philosophical Association, and has also served as President of the American Catholic Philosophical Association, the Americna Metaphysical Society, the American G. W. Leibniz Society, and the C. S. Peirce Society. An honorary member of Corpus Christi College, Oxford, he has been elected to membership in the European Academy of Arts and Sciences (Academia Europaea), the Institut International de Philosophie, and several other learned academies. Having held visiting lectureships at Oxford, Constance, Salamanca, Munich, and Marburg, Professor Rescher has received six honorary degrees from universities on three continents. Author of some hundred books ranging over many areas of philosophy, over a dozen of them translated into other languages, he was awarded the Alexander von Humboldt Prize for Humanistic Scholarship in 1984. In November 2007 Nicholas Rescher was awarded by the American Catholic Philosophical Association with the „Aquinas Medal“

ontos verlag

Frankfurt • Paris • Lancaster • New Brunswick 2009. 309pp. Format 14,8 x 21 cm Hardcover EUR 119,00 ISBN 13: 978-3-86838-058-3 Due December 2009

P.O. Box 1541 • D-63133 Heusenstamm bei Frankfurt www.ontosverlag.com • [email protected] Tel. ++49-6104-66 57 33 • Fax ++49-6104-66 57 34

NicholasRescher

Nicholas Rescher

Autobiography Second Edition

This revised edition of his Autobiography brings up-to-date Rescher’s account of his life and work. The passage of years since the publication of an autobiographical work makes for its growing incompleteness. Moreover, the passage of time is bound to bring some new perspectives to view. This new edition comes to terms with these circumstances. Since the publication of the previous version Rescher’s philosophical work has made substantial progress, betokened by the publication of over a score of new books that mark an ongoing expansion of his philosophical range. Then too, the internet has brought to light interesting new information about Rescher’s family background and antecedence. Overall the book affords a detailed, vivid, and highly personalized picture of the life and work of someone who counts as one of the most prolific and many-sided contemporary thinkers.

ontos verlag

Frankfurt • Paris • Lancaster • New Brunswick 2010. 419 Seiten Format 14,8 x 21 cm Paperback EUR 49,00 ISBN 978-3-86838-084-2

P.O. Box 1541 • D-63133 Heusenstamm bei Frankfurt www.ontosverlag.com • [email protected] Tel. ++49-6104-66 57 33 • Fax ++49-6104-66 57 34

Ontos

NicholasRescher

Nicholas Rescher

Collected Paper. 14 Volumes Nicholas Rescher is University Professor of Philosophy at the University of Pittsburgh where he also served for many years as Director of the Center for Philosophy of Science. He is a former president of the Eastern Division of the American Philosophical Association, and has also served as President of the American Catholic Philosophical Association, the American Metaphysical Society, the American G. W. Leibniz Society, and the C. S. Peirce Society. An honorary member of Corpus Christi College, Oxford, he has been elected to membership in the European Academy of Arts and Sciences (Academia Europaea), the Institut International de Philosophie, and several other learned academies. Having held visiting lectureships at Oxford, Constance, Salamanca, Munich, and Marburg, Professor Rescher has received seven honorary degrees from universities on three continents (2006 at the University of Helsinki). Author of some hundred books ranging over many areas of philosophy, over a dozen of them translated into other languages, he was awarded the Alexander von Humboldt Prize for Humanistic Scholarship in 1984. ontos verlag has published a series of collected papers of Nicholas Rescher in three parts with altogether fourteen volumes, each of which will contain roughly ten chapters/essays (some new and some previously published in scholarly journals). The fourteen volumes would cover the following range of topics: Volumes I - XIV STUDIES IN 20TH CENTURY PHILOSOPHY ISBN 3-937202-78-1 · 215 pp. Hardcover, EUR 75,00

STUDIES IN VALUE THEORY ISBN 3-938793-03-1 . 176 pp. Hardcover, EUR 79,00

STUDIES IN PRAGMATISM ISBN 3-937202-79-X · 178 pp. Hardcover, EUR 69,00

STUDIES IN METAPHILOSOPHY ISBN 3-938793-04-X . 221 pp. Hardcover, EUR 79,00

STUDIES IN IDEALISM ISBN 3-937202-80-3 · 191 pp. Hardcover, EUR 69,00

STUDIES IN THE HISTORY OF LOGIC ISBN 3-938793-19-8 . 178 pp. Hardcover, EUR 69,00

STUDIES IN PHILOSOPHICAL INQUIRY ISBN 3-937202-81-1 · 206 pp. Hardcover, EUR 79,00

STUDIES IN THE PHILOSOPHY OF SCIENCE ISBN 3-938793-20-1 . 273 pp. Hardcover, EUR 79,00

STUDIES IN COGNITIVE FINITUDE ISBN 3-938793-00-7 . 118 pp. Hardcover, EUR 69,00

STUDIES IN METAPHYSICAL OPTIMALISM ISBN 3-938793-21-X . 96 pp. Hardcover, EUR 49,00

STUDIES IN SOCIAL PHILOSOPHY ISBN 3-938793-01-5 . 195 pp. Hardcover, EUR 79,00

STUDIES IN LEIBNIZ'S COSMOLOGY ISBN 3-938793-22-8 . 229 pp. Hardcover, EUR 69,00

STUDIES IN PHILOSOPHICAL ANTHROPOLOGY ISBN 3-938793-02-3 . 165 pp. Hardcover, EUR 79,00

STUDIES IN EPISTEMOLOGY ISBN 3-938793-23-6 . 180 pp. Hardcover, EUR 69,00

ontos verlag Frankfurt • Paris • Lancaster • New Brunswick 2006. 14 Volumes, Approx. 2630 pages. Format 14,8 x 21 cm Hardcover EUR 798,00 ISBN 10: 3-938793-25-2 Due October 2006 Please order free review copy from the publisher Order form on the next page

P.O. Box 1541 • D-63133 Heusenstamm bei Frankfurt www.ontosverlag.com • [email protected] Tel. ++49-6104-66 57 33 • Fax ++49-6104-66 57 34