Minimal Verificationism: On the Limits of Knowledge 9781501501982, 9781501510571

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Gordian Haas Minimal Verificationism

Epistemische Studien

Schriften zur Erkenntnis- und Wissenschaftstheorie Herausgegeben von/Edited by Michael Esfeld, Stephan Hartmann, Albert Newen

Band 31

Gordian Haas

Minimal Verificationism On the Limits of Knowledge

ISBN 978-1-5015-1057-1 e-ISBN (PDF) 978-1-5015-0198-2 e-ISBN (EPUB) 978-1-5015-0200-2 ISSN 2198-1884 Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2015 Walter de Gruyter Inc., Boston/Berlin Printing and binding: CPI books GmbH, Leck ∞ Printed on acid-free paper Printed in Germany www.degruyter.com

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What is your aim in philosophy? To show the fly the way out of the fly-bottle. Ludwig Wittgenstein

Acknowledgements I am especially grateful for the many comments, criticisms, and suggestions I received over the course of the last years when I was writing this book. Although I benefited enormously from a lot of good advice, I was unfortunately not able to include all of it. I am indebted to so many people that I hope to not offend anyone if I only mention a few of them by name here. I would like to express my appreciation to Wolfgang Spohn, Rudolf Schüßler, and Rainer Hegselmann for offering extensive comments on entire drafts of the manuscript. I profited from numerous discussions with Keith Lehrer in past years, which enhanced my understanding of his theory. Parts of this book were presented on various occasions. I am grateful to all of the participants of these presentations, colloquia, and seminars for many inspiring discussions of my ideas. Niki Rodousakis greatly improved my English. Thanks are also due to the editors, Michael Esfeld, Stephan Hartmann, and Albert Newen for including the book in this series. I am very grateful to Maik Bierwirth of De Gruyter and his staff. I was particularly fortunate to collaborate with Florian Ruppenstein, who offered indispensable support when operating systems refused to do so. Much of this book was written while I was a visiting scholar at U. C. Berkeley for about two years, where Branden Fitelson and Paolo Mancosu created a welcoming research environment in which progress on the book was particularly fruitful. I wish to also express my indebtedness to the Alexander von Humboldt Foundation for generously supporting this visit with a Feodor Lynen Research Fellowship. The criticism of the AGM theory (Section 6.4) partly draws on material from Haas 1999. I first presented the concept of a justification operator (Sections 5.4+5.5) and JuDAS expansions (Sections 7.2.1+7.3.1) in Haas 2003a, while JuDAS revisions (Sections 7.2.2+7.3.2) were first discussed in Haas 2005. Sections 5.1, 5.3, and 6.4 also draw on various other materials of the latter publication. I thank the editors and publishers of those publications for permission to use the material here. Gordian Haas

Contents Introduction: Does This Make Nonsense to You?  1   1   1.1   1.2   1.3   1.4   1.5   1.6   1.7   1.8  

Some Historic Formulations and Their Problems  7   What about Analytic Sentences?  7   Conclusive Verifiability Within One’s Lifetime  8   Conclusive Verifiability in Principle  10   Conclusive Falsifiability in Principle  13   Verifiability or Falsifiability  16   Empirical Import  17   Translatability  22   Summary  32  

2   2.1   2.2   2.3   2.4   2.5  

More Problems Lie Ahead  33   The Problem of Dispositional Terms Spreads Out  33   Another Problem: Particular Sentences  35   Yet Another Problem: The Duhem-Quine Thesis  36   And Another Problem: The Analytic / Synthetic Distinction  41   Summary  47  

3   3.1   3.2   3.3   3.4   3.5   3.6   3.7  

Toward a Solution to the Problems  49   Conditions of Adequacy  49   What You Can and What You Should Not Expect  50   Against Deductive Chauvinism  52   The Discovery of the Subject  55   Counterfactual Conditionals  58   Did We Throw Out the Baby With the Bathwater?  59   Summary  61  

4   4.1   4.2   4.3   4.4   4.5   4.6   4.7   4.8  

Minimal Verificationism  63   The Essence of Verificationism  63   Epistemic Accessibility as a Criterion of Significance  65   The Advantages of the New Criterion  68   O’Connor’s Trick  75   The Choice of an Empirical Basis  76   What Does this Criterion Demarcate?  80   What Is Minimal about Minimal Verificationism?  85   Is Minimal Verificationism a Form of Verificationism at All?  87  

X  Contents 4.9   4.10   5   5.1   5.2   5.3   5.4   5.5  

Setting the Stage  88   Summary  89  

5.6  

Fallibilist Theories of Justification  91   Various Types of Theories of Justification  91   Lehrer’s Theory of Justification  96   Formal Reconstruction of Lehrer’s Theory  100   The Justification Operator  103   Consistency and Compatibility of the Justification Postulates  108   Summary  111  

6   6.1   6.2   6.3   6.4   6.5  

The Standard Theory of Belief Revision: AGM  113   Modeling Epistemic States  113   Axiomatic Characterization of Belief Changes  115   Construction of Belief Change Mechanisms  118   Objections to the AGM Theory  122   Summary  133  

7   7.1   7.2   7.3   7.4   7.5  

Combining Theories of Justification and Belief Revision: JuDAS  135   Modeling Epistemic States  135   Axiomatic Characterization of Belief Changes  138   Construction of Belief Change Mechanisms  148   Some Advantages of the JuDAS Theory  150   Summary  152  

8   8.1   8.2   8.3   8.4  

Lewis’ Semantics for Counterfactuals  153   Varieties of Conditionals  153   Lewis’ Analysis of Counterfactuals  163   Dispositional Terms Analyzed as Counterfactuals  168   Summary  169  

9   9.1   9.2   9.3   9.4   9.5  

Towards a Verifiability-Friendly Semantics for Counterfactuals  171   Objections to Lewis’ Conception of Possible Worlds  171   Objection to Lewis’ Conception of Similarity  180   The Ramsey Test as a Way Out?  182   Problems with the Ramsey Test and Prospected Solutions  184   Summary  186  

Contents  XI

10   10.1   10.2   10.3   10.4  

(Non) Concluding Remarks  187   Is the Criterion of Epistemic Accessibility Epistemically Accessible?  187   Is Epistemic Accessibility a Matter of Degree?  189   Open Questions  191   Summary  193  

References  195   Name Index  205   Subject Index  207  

Figures and Tables Fig. 3.1: Fig. 8.1: Fig. 8.2: Fig. 8.3: Fig. 8.4: Fig. 8.5: Fig. 8.6: Fig. 8.7:

Chronology of Verificationism / Novel Theories  60   Necessity Operator  157   Strict Conditional  157   False Antecedent  159   Strict Conditional with False Antecedent  160   Sequence of Counterfactuals  162   System of Spheres  164   Variably Strict Conditional  167  

Tab. 4.1: Tab. 4.2:

Fine-grained Differentiation  85 Dimensions of Minimality  86  

Introduction: Does This Make Nonsense to You? Some intellectual debates are pointless in that they raise questions that cannot be answered, not even in principle. Following Wittgenstein such questions can be called Scheinfragen (pseudo-questions). While genuine questions may be legitimate subjects of research, any attempts to answer a Scheinfrage would seem to be a waste of time, energy and in some cases of research funds. According to some authors, many of the “great debates”, including large parts of philosophy, are of the latter sort. That is why a demarcation between genuine questions and Scheinfragen is potentially provocative. Consider the following list of sentences, most of which have figured prominently in various philosophical debates. Some of the sentences are perfectly in order while others seem questionable in one way or another. NONSENSE-O-METER: (1) Caesar is babig. (2) Caesar is and. (3) Caesar is less identical than the prime number. (4) Nothingness nothings. (5) The absolute is perfect. (6) God exists. (7) Killing animals is bad. (8) The world sprang into being five minutes ago. (9) I am deceived by a Cartesian demon all the time. (10) The external world exists. (11) The Antarctic Continent already existed before it was discovered. (12) This piece of sugar is soluble. (13) For any substance there exists some solvent. (14) All swans are white. (15) There exists at least one unicorn. (16) The largest dinosaur on exhibit in New York’s Museum of Natural History had a blue tongue. (17) The number of electrons of a helium atom is two. (18) There are mountain ranges higher than 3000m on the far side of the moon. (19) London is the capital of France. (20) There is a book right in front of me.

“Something” is wrong with some of these sentences, namely, it seems impossible to find out whether some of the sentences are true or false. Others from the above list are not flawed in this way. If you do not agree that “something” is wrong with at least some of the above sentences, then this book will be of little to no interest to you, as this assumption is the point of departure for all further considerations.

2  Introduction: Does This Make Nonsense to You? Different terms have been introduced by various authors to denote sentences that are defective in the above way, i. e., “meaningless”, “illegitimate”, “spurious”, “pseudo-proposition”, etc. I will line up with those who use the terms significant / insignificant to distinguish these two types of sentences. For the time being, I will use these terms in a broad and rather vague sense. Later, I will provide a more precise explication of these terms. Note, however, that the demarcation significant / insignificant should not be confused with the distinction true / false or known / unknown. There are true sentences that are significant, e. g., “London is the capital of Great Britain” as well as false sentences that are significant, e. g., “London is the capital of France”. What matters is that it is possible to determine whether these sentences are true or false, and that is why these two sentences are significant. For a sentence to be significant, it is not of relevance, however, whether its truth value has actually been determined. For instance, consider the two sentences “The number of U. S. states is even” and “The number of U. S. citizens is even”. The former sentence is known to be true yet we do not know whether the latter one is as well. Nevertheless, the latter sentence—just like the former—is significant because its truth value can, in principle, be determined. According to Wittgenstein, a Scheinfrage cannot be answered. Instead, it has to be exposed as being a Scheinfrage, that is, we have to come to understand that it cannot be answered. Once we realize that a question cannot be answered, we should stop looking for an answer to it or even avoid raising the question in the first place. To determine whether a question is a Scheinfrage we need a criterion to demarcate significant from insignificant sentences. Formulating such a criterion of demarcation has been a key issue of the philosophy of science for nearly three decades. At first glance, it seems as though linguistics readily provides such a criterion. Some of the above “sentences” are not well-formed according to the rules of the English language, in other words, they are not even proper sentences. This might suggest that determining which sentences are significant is a linguistic task. Some of the insignificant sentences listed above are not lexically wellformed, that is, they are not composed of proper words (e. g. “Caesar is babig”) while others are syntactically not well-formed, that is, they do not conform to grammatical rules (e. g. “Caesar is and”). This seems to suggest that a sentence is significant if and only if it is lexically and syntactically well-formed. However, the sentence “Caesar is less identical than the prime number” is lexically and syntactically well-formed. However, it has been pointed out that the logical structure of this sentence is defective despite being well-formed. Thus, the sentence is insignificant, proving that the suggested criterion is inadequate. Anoth-

Introduction: Does This Make Nonsense to You?  3

er popular example is Chomsky’s “Colorless green ideas sleep furiously.” Such sentences can be taken as an indication that the demarcation significant / insignificant does not supervene on linguistic concepts. Natural languages like English are imperfect. Their rules allow for the formation of sentences that are insignificant. Therefore, it is not a linguistic but an epistemological task to formulate a criterion that demarcates significant from insignificant sentences. Verificationism has been an attempt to formulate such an epistemological criterion of demarcation. Since the 1930s, verificationism has been one of the ground pillars of the philosophy of the Vienna Circle and logical empiricism in general. Influenced by the young Wittgenstein, philosophers like Carnap, Schlick, Waismann, Hempel and Ayer have assumed verificationist principles of one sort or another to demarcate “good science” from “bad metaphysics”. This antagonism to metaphysics was usually presented in a very polemic way. An objective dispute has thus been made more difficult—if not impossible—right from the outset. Surely, the best-known formulation of a verificationist principle is the notorious claim that the meaning of a sentence consists in the method of its verification:1 If there is no way of telling when a proposition is true, then the proposition has no sense whatever; for the sense of a proposition is the method of is verification. In fact, whoever utters a proposition must know under what conditions he will call the proposition true or false; if he cannot tell this, then he also does not know what he has said. A statement which cannot be conclusively verified is not verifiable at all; it just lacks all sense […]. [italics GH]

According to this criterion, a sentence would be literally meaningless if it is not “conclusively verifiable [by observation]”. Hence, a metaphysical sentence like “the absolute is perfect” would be just as meaningless as “Caesar is less identical than the prime number” or even “Caesar is babig”. Taken seriously this would mean that a metaphysician produces sounds without, however, articulating anything meaningful, comparable to what a musician does. As music, however, the sounds of the metaphysician might be of questionable value. That is why logical empiricists sometimes describe the metaphysician as an “unmusical musician”. Such a crude verificationist principle, let alone the intolerable polemics accompanying it, is unacceptable for several reasons, which we will consider in due course. The logical empiricists therefore eventually replaced  1 This is an early formulation of this principle from Waismann 1930/1977, p. 5. Cf. also Schlick 1936, p. 341 and Schlick 1932/1938. This formulation is rejected, e. g., by Ryle 1936.

4  Introduction: Does This Make Nonsense to You? this verificationist principle with more moderate versions. Different philosophers have proposed different principles, and some have even advocated different criteria at different times. That is, the history of verificationism is not marked by a single verificationist principle. Rather, we should think of verificationism as a family of criteria. Several of these verificationist principles are reviewed in this volume. They all amount to the claim that a sentence (statement / belief or the like) is in some sense insignificant if it does not stand in a certain relation to experience: A sentence which does not stand in such-and-such a relation to experience is in such-andsuch a way insignificant.

On the one hand, verificationist principles differ with regard to the relation that should obtain to experience. On the other, they differ in terms of the alleged form of insignificance. Such a broad characterization of verificationism is assumed, for instance, by Misak 1995. Misak is thereby able to subsume various historical positions (e. g., pragmatistic theories) as well as Popper’s falsificationism under the common concept of verificationism, thus demonstrating interesting parallels between these different approaches. None of the verificationist principles proposed by the logical empiricists is satisfactory. Each and every one of their principles is flawed in one way or another. The logical empiricists failed to overcome these problems and to develop an adequate explication of verificationism. This led to a general abandonment of verificationism in the early 1960s. The history of verificationism is a history of failure. Given the great level of self-confidence with which logical empiricists have mostly confronted their opponents, their own failure to adequately explicate verificationism seems almost tragic. Today, verificationism is mostly regarded as an outdated historical view. The term “verificationism” almost became a dirty word used only by some diehard adherents of scientism. The unpopularity of verificationism and the many unsuccessful attempts to flesh it out in detail notwithstanding, most analytically oriented philosophers still seem to agree that “something” is wrong with sentences like “Nothingness nothings”. Yet if we want to claim that such sentences are, in some sense, insignificant, then we ought to elucidate how precisely they differ from sentences that we consider to be significant. Hence, it does not come as a surprise that occasional attempts were made to rehabilitate verificationism, even after the heyday of logical empiricism. Contemporary philosophers who have been associated with a verificationist position include Michael Dummett, David Wiggins, Christopher Peacock and Cheryl Misak.

Introduction: Does This Make Nonsense to You?  5

Verificationism is also the subject of the present study. Although I acknowledge that verificationism failed in all its historical versions, I want to understand how precisely insignificant sentences differ from those we consider to be significant. In this volume, I show how later developments in formal epistemology, philosophy of science, and logic can substantially contribute to a solution to some of the key problems of verificationism. I combine verificationism with several theories that are—in my opinion—immediately relevant to the debate on verificationism, though they were only developed after its failure. In view of these potential improvements, I argue that a weak form of verificationism is still tenable. Such an approach could be called minimal verificationism, as it involves a weakening of traditional verificationist principles in various respects, while maintaining their core idea. I also propose a first formulation of such a minimal principle of verification. Although this proposal should not be considered a final answer to the questions the debate has raised, it may provide a reasonable foundation for further investigations into verificationism. Though it should go without saying, I would like to point out that I intend to avoid any of the polemics that are all too familiar from the past. Such objectivity may have only become possible due to the passing of several decades. Part of these efforts is my intent to refrain from proposing minimal verificationism as a criterion of meaning, as this would commit us to accuse the metaphysician of talking nonsense. Instead, I argue that minimal verificationism should best be seen as a criterion that demarcates the realm of possible inquiry, thus helping us avoid unanswerable questions without stigmatizing them as nonsense. This positions minimal verificationism in a long-standing philosophical tradition that has sought to determine the limits of knowledge. The aim of this inquiry into verificationism is systematic and not historical. Nevertheless, it is best to begin by reviewing the major stages of the historical debate on verificationism (Chapter 1). Because the various verificationist principles that have been proposed were all motivated by the specific shortcomings of their respective predecessors, this review provides a good understanding of the intricate problems verificationism faces (Chapter 2). These problems naturally result in a list of conditions that any adequate verificationist principle must fulfill. Next, it is important to understand from a more fundamental perspective how these problems arise. A small number of principles that cause the problems of verificationism are identified (Chapter 3). In the constructive part of the book, I abandon these outdated principles the logical empiricists subscribed to and replace them with formal theories that became available only after the fall of verificationism in the early 1960s. These theories are fairly diverse and were not formulated with verificationism in mind. It is therefore crucial to first find a way

6  Introduction: Does This Make Nonsense to You? to implement these theories within a verificationist framework before they can actually be put to work. A precise notion of epistemic accessibility will turn out to be this “missing link”. This notion allows us to formulate a verificationist principle which I call minimal verificationism (Chapter 4). Within the relatively flexible framework of minimal verificationism, we can then apply various theories of contemporary epistemology, philosophy of science, and logic: Firstly, we profit from fallibilist theories of epistemic justification (Chapter 5). Secondly, a theory of belief revision turns out to be of considerable importance (Chapter 6). Subsequently, both of these theories are combined into a unified epistemological theory (Chapter 7). Finally, formal semantics for counterfactuals help to overcome the problems of verificationism (Chapter 8). A critical survey of the latter, however, reveals that its ontological commitments are at odds with a verificationist approach. Thus, it is inevitable to seek a verifiability-friendly counterpart of it (Chapter 9). Some general remarks conclude this inquiry into verificationism (Chapter 10).

1 Some Historic Formulations and Their Problems The many different verificationist principles that have historically been proposed by various philosophers were all motivated by the specific shortcomings of their respective predecessors. Therefore, these criteria are best understood by looking at the historical course of the debate on verificationism. The debate was initiated by Ludwig Wittgenstein’s Tractatus logico-philosophicus, first published in 1921.2 It was the logical empiricists, however, who sought to provide a detailed account of and to defend a verificationist principle of meaning. Carnap 1931/1959, 1963 might be taken as denoting both the beginning and the end of these attempts. Misak 1995 presents a comprehensive overview of the history of verificationism, including the predecessors and successors of the logical empiricists.3 A number of papers by logical empiricists has been collected by Ayer 1959. In a series of papers, Hempel 1950, 1951, 1965b4 presented a concise review of some important verificationist proposals. Stegmüller 1970, 1975 are very readable presentations in German. In this chapter, I will review the major stages of the historical debate on verificationism. This provides a good understanding of the intricate problems a verificationist principle faces.5

1.1 What about Analytic Sentences? Logical empiricists were convinced that a sentence, which cannot be verified, has no meaning. The verification of a sentence roughly consists in observations, which establish the truth or falsehood of the given sentence. The truth of logical and mathematical sentences, however, is not established by way of observations. Logical empiricists certainly did not want to claim that these sentences or any other analytically true or false sentences are meaningless. Therefore, theories of meaning by logical empiricists are typically bifurcated. Sentences, which are verifiable, are said to be empirically meaningful (or significant). An arbitrary  2 See Wittgenstein 1921/2014. 3 Most notably, Misak discusses verificationist ideas within pragmatism. For a further discussion on that subject, cf. also Putnam 1995 and Schantz 1998. Stekeler-Weithofer 1995 discusses this issue from an even broader historical perspective than Misak, including such varied philosophers as Plato, Aristotle, Hume, Kant, and Wittgenstein. However, he does not address the post-Wittgensteinian debate on verificationism. Cf. also Martin-Löf 1995. 4 For a discussion on the related issue of operationism by the same author, cf. Hempel 1965c. 5 The discussion on the historical debate on verificationism in this chapter is reminiscent of Hempel’s presentation.

8  Some Historic Formulations and Their Problems sentence is said to be cognitively meaningful (or significant) if, and only if, it is either (i) analytically true or false or (ii) empirically meaningful (or significant). Taking the analytic / synthetic distinction for granted, logical empiricists focused exclusively on characterizing empirically meaningful sentences in order to determine the realm of cognitively meaningful sentences.6 Consequently, a correct and precise formulation of a verificationist principle is the key objective for an empiricist criterion of cognitive meaning. Various attempts have been made to formulate a verificationist principle of meaning.

1.2 Conclusive Verifiability Within One’s Lifetime To prevent an all too common misunderstanding right from the start, it must be emphasized that verificationism does not claim that a sentence has empirical significance only if it is verified. Otherwise, a sentence like “the number of books on my desk is odd” would be meaningless, since I have not counted the books on my desk. For a sentence to be empirically significant, it is not necessary for it to have actually been verified, but only that it is verifiable, that is, it must be possible to verify the sentence. Sometimes, a sentence, which has not yet been verified, is readily verifiable, as in the case of the number of books on my desk. It is not a requisite for a sentence to have empirical significance that it is verifiable in the here and now.7 Otherwise, a sentence like “the number of trees in London’s Hyde Park is odd” would be meaningless for me because I am not in London right now and thus not in a position to count the trees in Hyde Park in the here and now. Hence, a first proposal for a verificationist principle which has at least some credibility might be that a sentence is empirically significant if, and only if, it can be verified by me within my lifetime. Perhaps it should not even be a requirement for me to be able to verify the given sentence myself.

 6 As is well known, the analytic / synthetic distinction was seriously called into question by W. V. O. Quine later on in his seminal essay Two Dogmas of Empiricism. Quine’s criticism and its potential bearing on verificationism will be discussed in Sec. 2.4. 7 That verificationism is not meant to require any empirically significant sentence to be verified or at least to be verifiable in the here and now has been pointed out, e. g., by Schlick 1936, Sec. 2 referring to a potential objection raised by C. I. Lewis 1934, pp. 130ff, who himself comments on a passage by Russell 1914, p. 112.

Conclusive Verifiability Within One’s Lifetime  9

1. ATTEMPT (verifiability within one’s lifetime):8 Sentence p has empirical meaning iff the speaker (or his research community) can make observations within his lifetime, which would conclusively verify p. This first proposal of a verificationist principle is, however, much too restrictive. Objection 1: According to this criterion, sentences about the remote past or distant future would be meaningless. For example, consider the following two sentences:9 (1.1) (1.2)

The largest dinosaur on exhibit in New York’s Museum of Natural History had a blue tongue. There will be at least 100 skunks within a 40-mile radius of Lethbridge exactly 100 years from now.

Despite the fact that both of these sentences are clearly meaningful, neither can be conclusively verified by me or by any of my fellow beings within my lifetime. Hence, this empiricist criterion of meaning is too narrow.10 Objection 2: To address another problem of this proposal, consider the following sentence:11 (1.3)

There are mountain ranges higher than 3000m on the far side of the moon.

Logical empiricists discussed this sentence in the 1930s, when it was impossible to verify it. However, it has in fact been possible since the 1960s to launch rockets to the moon. Hence, the sentence was verifiable within the lifetime for some logical empiricists but not for others. This already is an unwanted consequence  8 This particularly strict criterion of meaning is mentioned, e. g., by Hempel 1950, Sec. 2 and Hempel 1965b, Sec. 2. 9 The first example is discussed, e. g., by Hempel 1950, Sec. 2. Misak 1995, p. 71 discusses a 50year version of the second example. Depending on the age of the speaker, this may make a crucial difference in the present context. This indicates another difficulty, since the 50-year version of the sentence is meaningful intuitively if, and only if, the 100-year version is meaningful. 10 These shortcomings of a criterion of meaning as verifiability within one’s lifetime have been discussed by Ryle 1936, Ayer 1936/1946, Chap. 1, Pap 1949, Chap. 13, Russell 1948, Part 6, Chap. 4. This criterion was already abandoned by Schlick 1932/1933. 11 Cf., e. g., Schlick 1932/1933, p. 8 and Ayer 1936/1946, Chap. 1.

10  Some Historic Formulations and Their Problems of the proposal. Worse still, engineers could have made more rapid progress in constructing rockets. Clearly, we do not want to say that this might have changed the meaningfulness of the sentence, say, for Friedrich Waismann (†1959). But according to the proposed criterion, the meaningfulness of a sentence would depend on such highly contingent matters. Objection 3: The situation gets more complicated still when it comes to sentences like:12 (1.4)

The Antarctic Continent already existed before it was discovered.

Not only can this sentence not be verified by me or by my fellow beings, it cannot be verified by any human being. Nevertheless, it seems to be a perfectly meaningful sentence. The verifiability-within-lifetime criterion of meaning is therefore much too restrictive. Because of the absurd consequences of this principle of verification, logical empiricists time and again emphasize that it is not practical verifiability by the speaker within his lifetime or by any other human being, but that it is verifiability in principle that is required for empirical significance.13

1.3 Conclusive Verifiability in Principle The key task for verificationism therefore seems to be a general characterization of the class of all sentences that are verifiable in principle. This can be achieved in two stages. First, the subset of all those sentences that are verifiable in principle by direct observation is characterized; these are called observation sentences. Second, the set of all sentences that are verifiable in principle is characterized as the set of all those sentences that can be justified on the basis of observation sentences. Consider the following set of definitions:14 DEFINITION 1.1 (observable characteristic): A property or a relation of physical objects is an observable characteristic iff under suitable circumstances, its presence or absence in a given instance can be ascertained through direct observation (e. g., green, soft, liquid, longer than, but not: radioactive, better electric conductor).

 12 Cf. Russell 1948, Part 6, Chap. 4 for this and similar examples. 13 Cf., e. g., Schlick 1932/1933, p. 8. 14 Cf. Hempel 1950, Sec. 2.

Conclusive Verifiability in Principle  11

DEFINITION 1.2 (observation predicate): A term is an observation predicate iff it designates an observable characteristic (e. g., “green”, “soft”, “liquid”, “longer than”, but not: “radioactive”, “better electric conductor”). DEFINITION 1.3 (observation sentence): A sentence is an observation sentence iff it asserts of one or more specifically named macroscopic objects that they have, or that they lack, some specified observable characteristic (e. g., “The Eiffel Tower is taller than the buildings in its vicinity”, “The pointer of this instrument does not cover the point marked ‘3’”, but not: “This piece of uranium is radioactive”). The notion of an observation sentence is supposed to be an explicatum of the vague idea of a sentence being verifiable in principle by direct observation. In turn, precisely those sentences that are justifiable on the basis of observation sentences are verifiable in principle. Since logical empiricism in its early stage was exclusively concerned with conclusive verifiability, the only legitimate form such justification might take was logical entailment. Furthermore, the evidential basis had to be finite. Hence, a sentence is verifiable in principle if, and only if, it is logically implied by a finite set of observation sentences. Since any given sentence would be entailed by an inconsistent set of observation sentences, we need to restrict the evidential basis to consistent sets of observation sentences. An additional minor amendment is needed to exclude analytic sentences from having empirical significance since they, too, are entailed by any set of observation sentences. Thus, the idea that a sentence is empirically significant if, and only if, it is verifiable in principle can be spelled out as follows. 2. ATTEMPT (conclusive verifiability in principle): Sentence p has empirical meaning iff p is not analytic and there is a finite set of observation sentences o1, o2, …, on, such that {o1, o2, …, on} ⊬ ⊥ and {o1, o2, …, on} ⊢ p.

This criterion—which may be regarded as the classical formulation of a verificationist principle—does better than the first proposal with respect to the problems discussed in the last section. For instance, consider the sentence “The largest dinosaur in New York’s Museum of Natural History had a blue tongue.” The term “having a blue tongue” is an observation predicate, while “the largest dinosaur in New York’s Museum of Natural History” is a definite description of a physical object. Therefore, the respective sentence is an observation sentence.

12  Some Historic Formulations and Their Problems Thus, being verifiable in principle, it is empirically significant according to the proposed criterion.15 Similarly, for sentences like (1.2) about the distant future, there are observation sentences describing logically possible evidence that would imply the sentence under consideration, thereby revealing its empirical significance. Even if mankind in fact had never launched a rocket to the moon there would still be observation sentences describing logically possible evidence implying the sentence (1.3). Thus, this sentence, too, is empirically significant according to the proposed criterion. Eventually, under a plausible reading of sentence (1.4), its empirical significance can be shown along the same lines.16 Nevertheless, the proposed conclusive-verifiability criterion is seriously flawed. Objection 1: The main shortcoming concerns sentences of universal form. If a universal sentence quantifies over an infinite domain, it will not be entailed by any finite set of observation sentences. For instance, consider the following sentence: (1.5)

All swans are white.

This sentence has the form (∀x) (Fx ⊃ Gx), where F and G be observation predicates. Despite being supported and perhaps even justified by the observation sentences Fa1 ∧ Ga1, Fa2 ∧ Ga2, …, Fan ∧ Gan, the universal sentence is not logically implied by this nor by any other finite set of observation sentences. Hence, universal sentences would be deprived of meaning by the proposed criterion since they are not conclusively verifiable, not even in principle. Sentences expressing general laws are of universal form quantifying over infinite domains. Quite contrary to commonsense, these sentences would therefore become meaningless. This is the case even for sentences like “Copper is an electric conductor”, whose superficial grammatical structure do not involve any universal quantification at all, since their logical structure is something like (∀x) (copper x ⊃ conductor x). Given the importance of general laws for scientific theories, this

 15 Cf. Hempel 1950, Sec. 2. 16 Hempel 1950, Sec. 2 claims that sentences like (1.4) are empirically significant according to the implication-by-observation-sentences criterion. But this might depend on the modal disambiguation of such sentences. There is a possible world w where we gather conclusive evidence for the existence of the Antarctic Continent before it was discovered in the actual world. At least according to this interpretation, the sentence (1.4) is empirically significant. But there is no possible world w where we gather conclusive evidence for the existence of the Antarctic Continent before it was discovered in w. We cannot discover the Antarctic Continent before we discover the Antarctic Continent. For more on possible world semantics, cf. Chap. 8.

Conclusive Falsifiability in Principle  13

problem constitutes a major drawback for the proposed criterion of meaning. Thus, the conclusive-verifiability criterion has been proven to be too narrow in this respect. Objection 2: Another problem with this criterion is that nonsensical sentences can be “smuggled in”. Let p be any sentence that is meaningful according to the proposed criterion. Let n be any sentence failing the criterion. Let n, for instance, be metaphysical nonsense like “Nothingness nothings.” According to this assumption, there is a finite set of observation sentences implying p. The same set of observation sentences also implies the logically weaker sentence p ∨ n. According to the proposed criterion the sentence p ∨ n is therefore meaningful. Thus, there might be meaningful sentences with nonsensical components. In this respect, the proposed criterion therefore seems to be too wide. Objection 3: An adequate criterion of meaning should meet the following two conditions: (i) if sentence p is meaningful, then its negation ¬p is meaningful, too; (ii) if sentence p is meaningful, then any sentence that is logically equivalent to p is meaningful, too.17 While the proposed criterion obviously satisfies the second condition of adequacy, it does not fulfill the first one. This is readily shown by the following reductio argument. For a contradiction, let us assume that the first condition of adequacy is fulfilled and consider an existential sentence of the form (∃x) Fx, where F might be any observation predicate. This existential sentence is logically implied by the observation sentence Fa, where a be the name of any physical object. Therefore, the sentence (∃x) Fx is meaningful according to the proposed criterion. Thus, by the first condition of adequacy, its negation ¬(∃x) Fx is meaningful, too. In turn, the sentence (∀x) ¬Fx being equivalent to it has to be meaningful, too, by the second condition of adequacy. As shown before, the latter however is not the case. From this contradiction it follows that the proposed criterion of meaning does not satisfy the first condition of adequacy.

1.4 Conclusive Falsifiability in Principle The fact that general laws would be deprived of meaning because they are not conclusively verifiable is surely the most damaging consequence of the previous criterion. Therefore, one might instead try to regard conclusive falsifiability in principle as the criterion of meaning. Thus, a sentence has empirical signifi 17 Consider the seemingly stronger requirement (i′) Sentence p is meaningful if, and only if, its negation ¬p is meaningful. Obviously, (i) and (i′) are equivalent given (ii).

14  Some Historic Formulations and Their Problems cance if, and only if, it can, in principle, be refuted conclusively by a finite number of observations. Amendments analogous to those of the previous criterion are in order here. Hence, the following would be a precise formulation of a principle of falsificationism: 3. ATTEMPT (conclusive falsifiability in principle):18 Sentence p has empirical meaning iff ¬p is not analytic and there is a finite set of observation sentences o1, o2, …, on, such that {o1, o2, …, on} ⊬ ⊥ and {o1, o2, …, on} ⊢ ¬p.

In other words, a sentence is falsifiable if, and only if, its negation is verifiable. The greatest merit of this criterion as compared to the previous proposal is that it can be met by general laws. For example, consider again a universal implication of the form (∀x) (Fx ⊃ Gx), where F and G be some observation predicates. The observation sentence Fa ∧ ¬Ga implies the sentence ¬(∀x) (Fx ⊃ Gx), thereby falsifying (∀x) (Fx ⊃ Gx). Although universal sentences are not conclusively verifiable, they are conclusively falsifiable by a finite number of observation sentences even if they quantify over an infinite domain. Therefore, general laws are not deprived of empirical significance by the criterion of falsifiability— at least not all of them.19 This major improvement notwithstanding, the new proposal faces challenges, which are somehow mirror symmetrical to those of the previous criterion. Objection 1: The first problem concerns sentences of existential form. If an existential sentence quantifies over an infinite domain, its denial will not be entailed by any finite set of observation sentences. For instance, consider the following sentence:

 18 Although this formulation of a principle of falsificationism is attributable to Hempel 1950, Sec. 2, it was Karl Popper in his seminal work The Logic of Scientific Discovery, who propagated falsifiability as the criterion of demarcation instead of verifiability by observational evidence. Cf. Popper 1935/1959, Sec. 1–7 and 19–24. Cf. also Popper 1945, Vol. 2, p. 282ff and Popper 1963, pp. 183ff. However, Popper did not regard falsifiability as a criterion of meaning but as a criterion demarcating empirical science, on the one hand, from logic and mathematics as well as metaphysics, on the other hand. Cf. also Sec. 4.6 for the latter aspect. 19 If a general law is not of a purely universal form but also involves some existential quantification, it will not be falsifiable. Thus, some general laws would still be meaningless under the new criterion. Cf. the next section for a discussion of problems concerning sentences with mixed quantifiers.

Conclusive Falsifiability in Principle  15

(1.6)

There exists at least one unicorn.20

This sentence takes the form (∃x) Fx, where F be an observation predicate. The negation of this sentences ¬(∃x) Fx is logically equivalent to the sentence (∀x) ¬Fx. Despite being supported and perhaps even justified by the observation sentences ¬Fa1, ¬Fa2, …, ¬Fan, the sentence (∀x) ¬Fx is not logically implied by this nor by any other finite set of observation sentences. Hence, the existential sentence (∃x) Fx is not conclusively falsifiable and would therefore become meaningless under the proposed criterion. Thus, the conclusive-falsifiability criterion has been proven to be too narrow in this respect. Given the tremendous importance of general laws for the sciences, it might at first seem worthwhile to trade the meaningfulness of existential sentences for that of universal sentences, but this is a Pyrrhic victory. Not only are sentences of a purely existential form important in various nonscientific contexts, sentences containing existential quantifiers also play an important role in the sciences. This will become clear in the next section. Objection 2: The falsifiability criterion, too, cannot prevent nonsensical sentences from being “smuggled in”. Let p be any sentence that is meaningful according to the proposed criterion. Let n be any sentence failing the criterion. Let n, for instance, be metaphysical nonsense like “Nothingness nothings.” According to this assumption, there is a finite set of observation sentences implying ¬p. The same set of observation sentences also implies the logically weaker sentence ¬p ∨ ¬n which is equivalent to ¬(p ∧ n). Thus, the sentence p ∧ n is meaningful according to the proposed criterion since it is conclusively falsifiable. Hence, there still may be meaningful sentences with nonsensical components. In this respect, the falsifiability criterion seems to be too broad as well. Objection 3: Recall that an adequate criterion of meaning should fulfill the following two conditions: (i) if sentence p is meaningful, then its negation ¬p is meaningful, too; (ii) if sentence p is meaningful, then any sentence which is logically equivalent to p is meaningful, too. Like the previous proposal, the falsifiability criterion obviously satisfies the second condition of adequacy while it does not fulfill the first one. The latter is readily demonstrated by the following reductio argument. For a contradiction, let us assume that the first condition of adequacy is met and once more consider a universal sentence of the form (∀x) (Fx ⊃ Gx), where F and G be some observation predicates. As shown before, this sentence is conclusively falsified by the observation sentence  20 See, e. g., Hempel 1965b, Sec. 2.

16  Some Historic Formulations and Their Problems Fa ∧ ¬Ga, where a be the name of some physical object. Therefore, the sentence (∀x) (Fx ⊃ Gx) is meaningful according to the proposed criterion. Thus, according to the first condition of adequacy, its negation ¬(∀x) (Fx ⊃ Gx) is meaningful, too. In turn, the sentences (∃x) ¬(Fx ⊃ Gx) and (∃x) (Fx ∧ ¬Gx) being equivalent to it have to also be meaningful according to the second condition of adequacy. As previously shown, the latter is not the case. From this contradiction it follows that the falsifiability criterion of meaning does not satisfy the first condition of adequacy, either.

1.5 Verifiability or Falsifiability Given the problems of the previous two proposals, one might suggest regarding a sentence that is verifiable or falsifiable as being meaningful. Thus, a sentence has empirical significance if, and only if, it in principle can be conclusively verified or falsified by a finite number of observations. With analogous amendments as before, a precise formulation of this principle would read as follows: 4. ATTEMPT (verifiability or falsifiability): Sentence p has empirical meaning iff p is not analytic and there is a finite set of observation sentences o1, o2, …, on, such that {o1, o2, …, on} ⊬ ⊥ and either {o1, o2, …, on} ⊢ p or {o1, o2, …, on} ⊢ ¬p.

While not being verifiable, universal sentences are falsifiable. Similarly, existential sentences are not falsifiable but verifiable. Therefore, both types of sentences are meaningful under the proposed disjunctive criterion. Obviously, the new criterion also meets the condition of adequacy according to which the negation of a meaningful sentence has to be meaningful. Despite these merits, the new proposal is still open to similar objections like the previous two criteria of meaning. Objection 1: The first problem concerns sentences with mixed quantifiers. If sentence p involves a universal and an existential quantification both of which are over an infinite domain, then neither p nor its negation ¬p will be implied by a finite set of observation sentences. For example, consider the following sentence:

Empirical Import  17

(1.7)

For any substance there exists some solvent.21

This sentence takes the form (∀x) [Fx ⊃ (∃y) Gxy], where F and G be observation predicates. The universal quantification prevents this sentence from being logically implied by any finite set of observation sentences. The negation of this sentence being equivalent to (∃x) [Fx ∧ (∀y) ¬Gxy] is not entailed by any finite set of observation sentences, either, since it also involves a universal quantification. Hence, sentences like (1.7) with mixed quantifiers would be deprived of meaning by the proposed criterion since they are neither conclusively verifiable nor conclusively falsifiable. This even applies to some sentences whose superficial grammatical structures do not involve mixed quantifiers. For instance, consider the sentence “All men are mortal”. Only its logical structure reveals that a universal and an existential quantification is involved since it means something like “For every human being there is a finite period of time after its birth within which it dies.”22 Thus, the verifiability-or-falsifiability criterion is still too narrow. Objection 2: Another persisting problem with the new proposal is that nonsensical sentences can be “smuggled in”. Let p be any sentence which is meaningful according to the proposed criterion. Let n be any sentence failing to fulfill the criterion. Let n, for instance, be metaphysical nonsense like “Nothingness nothings”. Since p meets the disjunctive criterion by assumption, it must either be verifiable or falsifiable. In case p is verifiable, the sentence p ∨ n will be meaningful. In case p is falsifiable, the sentence p ∧ n will be meaningful. Thus, there will be a meaningful sentence with nonsensical components in either case. Hence, the proposed criterion still seems to be too broad.

1.6 Empirical Import All aforementioned proposals require some possibility of conclusive or complete verification or falsification: (1) conclusive verifiability within lifetime, (2) conclusive verifiability in principle, (3) conclusive falsifiability in principle, (4) conclusive verifiability or falsifiability in principle. These diverse requirements are then spelled out in terms of logical entailment by a finite set of observation sentences. Arguably, the most important lesson to be learned from the discussion on these criteria is that there are types of meaningful sentences whose  21 See, e. g., Hempel 1950, Sec. 3. 22 This was pointed out by Stegmüller 1970, Vol. 2, Chap. 3, Sec. 2d.

18  Some Historic Formulations and Their Problems truth or falsehood is not made logically certain by any finite number of observation sentences. Nevertheless, observation sentences seem to support, confirm and perhaps even justify these sentences in some sense. Instead of requiring a sentence or its negation to be logically implied by observation sentences, it would therefore seem more promising to consider some weaker form of support by observation sentences as the criterion of meaning. Ayer’s requirement of empirical import is one attempt among others to flesh out this idea:23 We say that the question that must be asked about any putative statement of fact is not, Would any observation make its truth or falsehood logically certain? but simply, Would any observations be relevant to the determination of its truth or falsehood? And it is only if a negative answer is given to this second question that we conclude that the statement under consideration is nonsensical. To make our position clearer, we may formulate it in another way. Let us call a proposition which records an actual or possible observation an experiential proposition. Then we may say that it is the mark of a genuine factual proposition […] that some experiential proposition can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.

Based on the terminology introduced earlier, Ayer’s criterion of meaning can be reformulated as follows: 5. ATTEMPT (empirical import): Sentence p has empirical meaning iff there is a set of subsidiary hypotheses H and an observation sentence o, such that H ∪ {p} ⊢ o while H ⊬ o.

An epistemic version of this principle may contribute to its rationale. Think of the subsidiary hypotheses H as a corpus of background knowledge. A hypothesis p provides some empirical import to the corpus H if, and only if, its addition to H would allow deriving some observable consequence o which is not entailed by the background knowledge alone. A hypothesis is said to have empirical import simpliciter if it provides empirical import relative to some background corpus. Thus, Ayer’s principle amounts to the claim that a sentence is meaningful if, and only if, it has empirical import. This proposal surely overcomes most of the difficulties the previous criteria faced. It is not worth discussing these seeming improvements in any detail, however, since they are achieved at much too high a price. When Ayer first published his principle in the first edition of Language, Truth and Logic in 1936, he

 23 See Ayer 1936/1946, Chap. 1. Cf. also Ayer 1936/1937.

Empirical Import  19

did not impose any restrictions on the permissible subsidiary hypotheses. It is readily seen that in this case, any sentence whatsoever meets the criterion.24 Let n be an arbitrary sentence. Let n, for instance, be metaphysical nonsense like “Nothingness nothings”. Let o be an arbitrary observation sentence. Let o, for instance, be “The Eiffel Tower is taller than the buildings in its vicinity”. Choose the sentence h ≔ n ⊃ o as the sole subsidiary hypothesis. Obviously, the observation sentence o is derivable from n and h while not being entailed by the subsidiary hypothesis h alone. Thus, the arbitrary sentence n would be meaningful according to the proposed criterion. As it stands, Ayer’s criterion is much too inclusive. Ayer accepted this criticism as valid. In the introduction to the second edition of Language, Truth and Logic published in 1946, he therefore proposed an emended version of his principle: I propose to say that a statement is directly verifiable if it is either itself an observationstatement, or is such that in conjunction with one or more observation-statements it entails at least one observation-statement which is not deducible from these other premises alone; and I propose to say that a statement is indirectly verifiable if it satisfies the following conditions: first, that in conjunction with certain other premises it entails one or more directly verifiable statements which are not deducible from these other premises alone; and secondly, that these other premises do not include any statement that is not either analytic, or directly verifiable, or capable of being independently established as indirectly verifiable. And I can now reformulate the principle of verification as requiring of a literally meaningful statement, which is not analytic, that it should be either directly or indirectly verifiable, in the foregoing sense.

This criterion of meaning is quite complicated indeed. Moreover, it is redundant in certain aspects. At the bottom line, however, the decisive difference to Ayer’s first proposal is a recursive restriction of the permissible subsidiary hypothesis. This recursive characterization does not involve any vicious cycle, although this might not be apparent according to Ayer’s own formulation. In order to gain a better understanding of the proposal, I suggest considering a semi-formal reformulation of it. Let us first define two auxiliary concepts.

 24 This type of objection was first raised by Berlin 1938/1939, p. 234. D. Lewis 1988 added some minor clarification to this criticism without diminishing its force. Cf. also Scheffler 1963, p. 41 and Foster 1985, p. 14.

20  Some Historic Formulations and Their Problems DEFINITION 1.4 (directly verifiable sentence): Sentence d is directly verifiable if, and only if, there is a set O of observation sentences and an observation sentence o, such that O ∪ {d} ⊢ o while O ⊬ o.25

DEFINITION 1.5 (permissible subsidiary hypothesis): (i) All analytic sentences are permissible subsidiary hypotheses. (ii) All directly verifiable sentences are permissible subsidiary hypotheses. (iii) If H is a set of permissible subsidiary hypotheses and d is a directly verifiable sentence, such that H ∪ {h} ⊢ d while H ⊬ d, then h is a permissible subsidiary hypothesis. (iv) There are no permissible subsidiary hypotheses besides those mentioned by (i)–(iii). With these two auxiliary concepts at hand, we can restate Ayer’s new proposal in perfect analogy with his first proposal. 6. ATTEMPT (empirical import):26 Sentence p has empirical meaning iff there is a set of permissible subsidiary hypotheses H and a directly observable sentence d, such that H ∪ {p} ⊢ d while H ⊬ d.

In contrast to Ayer’s first proposal, not every sentence will do as a subsidiary hypothesis. Only those sentences that correspond to Definition 1.5 are permissible subsidiary hypotheses. On the other hand, the implied sentence no longer has to be an observation sentence. Any sentence which is directly verifiable according to Definition 1.4 will do. Thus, Ayer’s new proposal is more restrictive in one sense while being more inclusive in another. Objection 1: Unfortunately, the new criterion is still far too inclusive. Church 1949 proved that Ayer’s modified principle is open to nearly the same objection as his original version. Let o1, o2, o3 be three observation sentences, none of which implies either of the other two. In this case, it can be shown that any given sentence or its negation is meaningful according to the revised criterion.

 25 Note that, in particular, every observation sentence d ≔ o is directly verifiable. This is readily seen by letting O ≔ ∅. 26 Note that according to Ayer’s characterization, every directly verifiable sentence is also indirectly verifiable. This is readily seen by letting H ≔ O and d ≔ o. Therefore, the disjunctive form of his criterion of meaning is redundant. The first disjunct can simply be omitted.

Empirical Import  21

Let n be an arbitrary sentence. Let n, for instance, be metaphysical nonsense like “Nothingness nothings”. Consider the sentence ¬o1 ∧ o2 ∨ o3 ∧ ¬n. The following two cases have to be dealt with separately: Case (i): ¬o1 ∧ o2 ∨ o3 ∧ ¬n ⊢ o2: It immediately follows in this case that ¬n together with o3 implies o2. Furthermore, o3 being directly verifiable is a permissible subsidiary hypothesis and o2 is a directly verifiable sentence. Therefore, ¬n is a meaningful sentence according to the proposed criterion, because o3 alone does not imply o2 according to the assumptions. Case (ii): ¬o1 ∧ o2 ∨ o3 ∧ ¬n ⊬ o2: The sentence ¬o1 ∧ o2 ∨ o3 ∧ ¬n is directly verifiable, because with o1 it implies o3 while o1 ⊬ o3 according to the assumption. Thus, the sentence ¬o1 ∧ o2 ∨ o3 ∧ ¬n is a permissible subsidiary hypothesis. Furthermore, n and ¬o1 ∧ o2 ∨ o3 ∧ ¬n together imply the directly verifiable sentence o2. According to the assumption, o2 is not implied by the subsidiary hypothesis alone. Hence, n qualifies as meaningful according to the proposed criterion. It has thus been shown that for an arbitrary sentence n, either n or ¬n is meaningful. Ayer’s revised criterion of meaning is therefore still far too inclusive. Objection 2: Just like most of the previous verificationist principles, Ayer’s proposal cannot prevent nonsensical sentences from being “smuggled in”. Let p be any sentence which is meaningful according to the proposed criterion. Let n be any sentence failing the criterion. Let n, for instance, be metaphysical nonsense like “Nothingness nothings.” According to the assumption, there is a set of permissible subsidiary hypotheses H and a directly observable sentence d such that H ∪ {p} ⊢ d while H ⊬ d. Obviously, the molecular sentence p ∧ n together with the same set of permissible subsidiary hypotheses H will also imply d while H alone does not entail the directly observable sentence d. Thus, the sentence p ∧ n is meaningful according to Ayer’s criterion since it has empirical import.27 Hence, there may still be meaningful sentences with nonsensical components. In this respect, Ayer’s principle also seems to be too inclusive.

 27 Cf. O’Connor 1949/1950, Sec. 2 for an example of this and another type of molecular sentence which meets Ayer’s criterion of meaning despite containing a nonsensical component. Cf. also Hempel 1950, Sec. 2.4.

22  Some Historic Formulations and Their Problems

1.7 Translatability Although the proposals we discussed so far are quite heterogeneous, they all attempt to spell out a verificationist principle in terms of some deductive relationship to observations or rather to observation sentences. That is, all these criteria—including Ayer’s proposal—accord a sentence p empirical meaning if, and only if, p stands in some deductive relation to observation sentences. Given the overwhelming shortcomings of this type of principle, it does not come as a surprise that logical empiricists sought a fairly different type of criterion to demarcate meaningful from nonsensical sentences. The basic idea is to first construct an artificial language that allows expressing precisely those sentences that the logical empiricists considered as meaningful. Call such an artificial language an empiricist language Le. A sentence of the ordinary language will be regarded as meaningful if, and only if, it is translatable into that empiricist language. 7. ATTEMPT (translatability):28 A sentence p has cognitive meaning iff p is translatable into the empiricist language Le. Unlike the previous proposals, this criterion is not bifurcated in that it deals with analytic and empirically significant sentences in a unified way. There has not, however, been a single empiricist language logical empiricists would have agreed upon. Instead, a number of different empiricist languages were proposed. At the bottom line, an empiricist language Le can be characterized as a first order predicate language whose predicates include only certain observation predicates and those predicates that are definable from observation predicates by purely logical means. Complemented in this way, the translatability criterion of meaning avoids all problems the previous proposals faced. The sentences (1.1)–(1.4) can readily be translated into an appropriate empiricist language. Therefore, according to the translatability criterion, sentences about the remote past and distant future are meaningful. Furthermore, the meaningfulness of a sentence does not depend on contingent matters like the practical possibility to verify it.  28 This type of criterion originates from Carnap 1936/1937, Chap. 4. Although he himself did not explicitly state this kind of criterion, Carnap has been credited with it, e. g., by Hempel 1950, Sec. 3.

Translatability  23

Universal and existential sentences as well as sentences with mixed quantifiers can be translated into an empiricist language Le, even if they quantify over an infinite domain, because Le is a first order predicate language and no restriction to finite domains has been imposed. Therefore, these types of sentences are not generally precluded from being meaningful. In particular, general laws are meaningful according to the translatability criterion as long as they do not involve any predicates that cannot be translated into Le. The new proposal also prevents nonsensical sentences from being “smuggled in” as is the case for most of the previous criteria Let n be any sentence failing the criterion. Let n, for instance, be metaphysical nonsense like “Nothingness nothings.” Since n cannot be translated into the empiricist language Le, no molecular sentence m containing n as a component (e. g., p ∨ n, p ∧ n) can be translated into Le, either. Thus, there are no meaningful sentences with nonsensical components. Suppose a sentence p of the ordinary language is translatable into the sentence pL of the empiricist language Le. The sentence ¬p will then be translatable into the sentence ¬pL which is also a sentence of the empiricist language. Hence, unlike some of the previous proposals, the translatability principle ensures that the negation of every sentence p that is meaningful according to the proposed criterion will qualify as meaningful, too. Finally, in contrast, for instance, to Ayer’s empirical import criterion of meaning, the translatability principle does not allow any given sentence to be cognitively meaningful. The sentences “Nothingness nothings” and “The absolute is lazy”, for example, contain terms which cannot be defined in an empiricist language. Thus, the translatability criterion will classify these sentences as meaningless because they cannot be expressed in an empiricist language. Despite these improvements the new proposal offers, the translatability criterion of cognitive meaning has serious shortcomings. The first problem concerns so-called dispositional terms. Dispositional terms are expressions such as “soluble”, “fragile”, “is a good electric conductor”, “electrically charged” and “magnetic”. In other words, dispositional terms are terms that express the disposition of one or more objects to respond in a certain way under certain circumstances. Call the circumstances in question the test conditions. That a piece of sugar is soluble in water, for instance, means that it would respond by dissolving under the test conditions of being placed in water. It is crucial to note that an object may or may not have a disposition, even if the test conditions do not obtain. A glass is fragile even if it stands on a table and is not exposed to any shocks. Similarly, a piece of iron is not fragile even if it lies on a table and is not exposed to any shocks. At first, the class of dispositional

24  Some Historic Formulations and Their Problems terms might seem smaller than it actually is. The logical structure of some concepts reveals them as dispositional terms although their superficial grammatical structure conceals this fact. The concept of temperature is a case in point. That “an object x has a temperature of c degrees centigrade” means something like “if a thermometer is in contact with x, then it registers c degrees on its scale”. Thus, the concept of temperature is dispositional, although this is not obvious at first glance. For a sentence containing a dispositional term to be meaningful according to the translatability criterion, the dispositional term must be definable by purely logical means in terms of observation predicates. More specifically, it must be defined by means provided for by first order predicate logic. This, however, cannot be accomplished. Given the importance of dispositional terms for everyday language and the sciences alike, the fact that the new proposal qualifies all sentences containing such terms as nonsense, is detrimental. To envisage how this difficulty arises, consider, for instance, a sentence involving the dispositional term “soluble in water”: (1.8)

x is soluble in water.

Due to the dispositional term involved, the logical structure of this sentence has a conditional form: (1.9)

If x is placed in water, then x will dissolve.

Indeed, “is placed in water” and “dissolves” are observation predicates, but it is the implicit conditional structure in the dispositional term that presents an obstacle to the translation of this sentence into an empiricist language. The “if… then…” clause of sentence (1.9) has to be reconstructed as a material implication within an empiricist language, since this is the only conditional a first order predicate language provides for. Using the symbol “⊃” to denote the material implication, the sentence (1.8) would thus have to be translated into an empiricist language as follows: (1.10)

x is placed in water ⊃ x dissolves.

More generally, a dispositional term D that expresses the disposition of an object x to give the response R under the test conditions T would have to be defined in first order predicate logic as follows:

Translatability  25

(1.11)

∀x(Dx ≡ (Tx ⊃ Rx)).

This definition of dispositional terms is misguided though. A key feature of the material conditional is that it is true if the antecedent is false. Thus, if the test conditions T do not obtain for object x, then the sentence Tx ⊃ Rx will be trivially true. Therefore, the definiendum Dx has to be true, too, according to Definition (1.11). This means that any object for which the test conditions do not obtain will have the disposition in question, no matter what. A stone that does not happen to be placed in water would thus be soluble in water. A piece of iron would be fragile if it is not exposed to any shocks. In the case of the concept of temperature, the puzzling consequence of Definition (1.11) would be that an object that is not in contact with a thermometer has a temperature of c degrees centigrade for every value of c. Thus, objects could have multiple temperatures at the same time. I take it that these highly problematic consequences are evidence enough to show the inadequacy of Definition (1.11).29 This, in turn, means that the translatability criterion of cognitive meaning would render meaningless every sentence containing a dispositional term, unless we come up with a more appropriate way to define dispositional terms using the limited resources provided for by a first order predicate language. Carnap 1936/1937 tried to introduce dispositional terms within the framework of a first order predicate language by what he called reduction sentences.30 Definition (1.11) breaks down only in cases where the test conditions do not obtain. That is why it is tempting to begin an analysis of a dispositional term by simply assuming that the relevant test conditions do obtain. If an object x is placed in water, it is safe to say that it is soluble in water if, and only if, it dissolves: (1.12)

If x is placed in water, then x is soluble in water if, and only if, x dissolves.

Analyzing the involved “if… then…” clause once again as a material conditional, one can translate sentence (1.12) into a first order predicate language as follows: (1.13)

x is placed in water ⊃ (x is soluble in water ≡ x dissolves).

 29 The problem concerning dispositional terms has already been pointed out by Carnap 1936/1937, Sec. 7 himself. 30 Cf. also Carnap 1935, 1938, Sec. 3.

26  Some Historic Formulations and Their Problems More generally, let D be an arbitrary dispositional term, which expresses the disposition of an object to give response R under the test conditions T. An arbitrary object x which is subjected to the test conditions T will have disposition D if, and only if, it gives the response R. Thus, the following sentence containing the dispositional term D is true: (1.14)

∀x(Tx ⊃ (Dx ≡ Rx)).

This is called a bilateral reduction sentence for the dispositional term D.31 The vocabulary of an empiricist language Le only includes observation predicates and those predicates that are definable from observation predicates by purely logical means. As shown by the inadequacy of Definition (1.11), this would preclude all dispositional terms from an empiricist language. In order to avoid this severe limitation, one might try to give a weaker characterization of an empiricist language. Consider an empiricist language that allows introducing complex predicates not only by defining them from observation predicates, but also by relating them to some observation predicates by means of reduction sentences.32 Call such a language an extended empiricist language L+e . This weaker characterization of an empiricist language corresponds to a more inclusive criterion of cognitive meaning: 8. ATTEMPT (translatability): Sentence p has cognitive meaning iff p is translatable into the extended empiricist language L+e . Even in its revised version, the translatability criterion of cognitive meaning is fundamentally misguided and misses the point much more than any of the previous proposals. Let us first examine two objections that have been raised

 31 In general, a predicate is introduced by a pair of reduction sentences one of which states necessary conditions for the application of the predicate while the other states sufficient conditions. In the special case of a dispositional term, however, these conditions can be expressed by a single bilateral reduction sentence which is equivalent to the conjunction of the corresponding pair of reduction sentences. 32 Like other logical empiricists, Carnap first subscribed to the view that all extra-logical vocabulary of an empiricist language needs to be introduced by explicitly defining it either in phenomenological terms or in terms of observation predicates. Cf. Carnap 1928 and Carnap 1931, respectively. Carnap 1936/1937 later abandoned this principle by allowing for the possibility to introduce new predicates by means of reduction sentences as well.

Translatability  27

against specific formulations of a translatability criterion before making a more fundamental objection against this type of criterion. Objection 1: To introduce dispositional terms into an empiricist language by means of reduction sentences along the lines of schema (1.14) amounts to a partial definition of these indispensible concepts only. 33 A reduction sentence defines a dispositional term D for all those objects x for which the test conditions T obtain. For these objects the reduction sentence states necessary and sufficient conditions for D to hold. For all objects x for which the test conditions T do not obtain, the dispositional term D is simply not defined by its reduction sentence. Thus, according to the revised version of the translatability criterion, it would be nonsense to say of a piece of sugar and a stone, neither of which is placed in water, that the former is soluble in water while the latter is not. Schemes (1.11) and (1.14) are both inappropriate to introduce dispositional terms into an empiricist language, because neither can handle the case of nonobtaining test conditions. Schema (1.11) at least defines a dispositional term for all objects, but the consequence is that every object for which the test conditions do not obtain will have the disposition in question. Schema (1.14) only avoids this unacceptable consequence by refraining from defining dispositional terms for this class of objects altogether. Hence, the revised version of the translatability criterion of cognitive meaning still falls short of adequately integrating dispositional terms into an empiricist language.34 Objection 2: Let us consider a strategy that might help reduce and in some cases even overcome the problem the fact poses that reduction sentences have the character of partial definitions only. Many dispositions can be tested in more than one way. The disposition of being magnetic is a case in point. One way to find out whether an object is magnetic is to place iron filings next to it and see whether these are attracted by the object. Another way to determine whether an object is magnetic is to see whether the north pole of a compass is attracted by one side of the object while the south pole is attracted by the opposite side. Dispositions that can be detected by more than one test have been called multiple or broad dispositions. A predicate D designating a multiple disposition can be introduced into an empiricist language by a set of bilateral reduction sentences instead of a single one:

 33 Therefore, reduction sentences are sometimes referred to as “partial definitions” or “conditional definitions”. 34 A particularly clear formulation of this objection can be found in Pap 1963, p. 560f.

28  Some Historic Formulations and Their Problems (R1) (R2) ⋮   (Rn)

∀x(T1x ⊃ (Dx ≡ R1x)) ∀x(T2x ⊃ (Dx ≡ R2x))

∀x(Tnx ⊃ (Dx ≡ Rnx)).

Each reduction sentence (Ri) corresponds to one way in which the disposition in question can be tested.35 If a dispositional term D is introduced by a single bilateral reduction sentence, say (Ri), then D will only be defined for those objects x that meet the test condition Ti. For all other objects, it is simply meaningless to say that they have or that they lack disposition D. This is the problem with single bilateral reduction sentences as pointed out above. If a dispositional term D is introduced by a set of bilateral reduction sentences (R1), (R2), …, (Rn) instead, then the dispositional term will be defined for all objects x which fulfill at least one of the test conditions T1, T2, …, Tn. In many cases, this will considerably reduce the class of objects for which the dispositional term D cannot be meaningfully applied. In some cases, the problem posed by reduction sentences as partial definitions might even be overcome completely. In cases in which T1 ∨… ∨ Tn is an analytically true sentence, every object x fulfills at least one of the test conditions, thereby ensuring that the dispositional term D can be meaningfully applied to it. In this special case, the set of bilateral reduction sentences (R1), (R2), …, (Rn) can be turned into an explicit definition. For most dispositional terms, however, this strategy will at best somewhat weaken the above objection and is thus far from being satisfactory. What makes it worse is that the introduction of multiple bilateral reduction sentences for one and the same predicate creates a new problem. If we introduce a new predicate into a language, we have to characterize its meaning in terms of the vocabulary that is already understood in the language. Apart from characterizing the meaning of the new term—either fully or partially—this process should be non-creative36 in the sense that it should have no empirical implications. That is, the introduction of the new term, call it D, must not allow to prove new theorems, more specifically, no new theorems formulated in the original vocabulary alone. The rationale for this condition of adequacy is as follows. Suppose p is a sentence that can be formulated without D. Suppose further that p is not a theorem prior to the introduction of D into the language. That is to say, p is an empirical sentence which is either true or false, depending  35 Carnap 1936/1937, p. 450ff explicitly allows the introduction of a single dispositional term by such a set of bilateral reduction sentences. 36 This term has been coined by Suppes 1957, p. 154.

Translatability  29

on what the world looks like. If p were provable in the language once we introduced the term D, the sentence p would suddenly be analytically true no matter what the world looks like. This creation of pseudo analytic sentences by introducing a new term that the sentence in question does not even contain would obviously be absurd. Therefore, the introduction of new terms into an empiricist language has to be accomplished by some non-creative means. This non-creativity requirement for the introduction of new terms is met by both explicit definitions and single bilateral reduction sentences. In contrast, the introduction of a new term by a set of more than one bilateral reduction sentences does create pseudo analytic sentences. For example, consider a dispositional term D that is introduced by two bilateral reduction sentences, say (R1) and (R2) of the above schema. It is readily seen that (R1) and (R2) jointly imply the following sentence: (1.15)

∀x(T1x ∧ T2x ⊃ R1x ≡ R2x).

Despite being an empirical sentence that does not even contain the new predicate D, sentence (1.15) is turned into a pseudo analytic truth once we introduce the term D into the empiricist language by (R1) and (R2). Let D, for instance, be the dispositional term “magnetic”. Sentence (1.15) may then be taken as stating that all objects x, which lie next to both iron filings (T1) as well as a compass (T2), will pass the iron filing test (R1) if, and only if, x passes the compass test (R2). This sentence is certainly true, but it is an empirically and not an analytically true sentence. Nevertheless, by introducing D by more than one bilateral reduction sentence, we set up a language according to which it would be selfcontradictory do deny sentence (1.15). Hence, introducing multiple bilateral reduction sentences cannot solve the problem of dispositional terms.37 Thus, there are types of respectable terms that can be adequately integrated into an empiricist language neither by definitions nor by (sets of) reduction sentences. Dispositional terms are the most well-known example of this type of term. The vocabulary of advanced scientific theories, however, also includes theoretical terms like “absolute temperature”, “gravitational potential” and “electric field”. These terms are similarly resistant to incorporation into an empiricist language.

 37 This peculiarity of sets of two or more bilateral reduction sentences concerning the same term has been discussed by Hempel 1952, Sec. 6 and Hempel 1965b, Sec. 4. Cf. also Hempel 1965a, Sec. 9 and 10.3.2, Winnie 1965 and Peijnenburg 1996, Chap. 3, Sec. 3.

30  Some Historic Formulations and Their Problems Because a first order empiricist language fails to accommodate for these types of concepts, the translatability criterion renders every sentence that contains one of these indispensible terms meaningless. As was the case for some of the previous proposals, the translatability criterion of cognitive meaning is thus too restrictive in one important respect. Objection 3: Apart from failing to identify some sentences as meaningful that we—or, for that matter, the logical empiricists—would intuitively regard as meaningful, the translatability criterion is fundamentally misguided in a way in which none of the previous proposals has been, namely, it is ad hoc. Although the logical empiricists advocated the artificial language L+e , it is anything but inevitable to opt for this specific language. All sorts of artificial languages can be constructed at will. Different languages are suitable for different purposes. More often than not, an artificial language reflects the philosophical bias of the person constructing it. According to the translatability criterion of meaning, a sentence of the ordinary language is qualified as meaningful if, and only if, it is translatable into some artificial language; call this the reference language of the criterion. Various artificial languages might be considered as a reference language. Which sentences of the ordinary language are regarded as meaningful by the translatability criterion crucially depends on the choice of reference language. In particular, no metaphysical sentence will be qualified as meaningful if we happen to choose L+e as the reference language. By contrast, one might construct a metaphysical language—call it L+m—which allows to formulate any metaphysical sentence you can think of. If we choose L+m as the reference language of the translatability criterion, any metaphysical sentence of the ordinary language will be qualified as meaningful. Carnap himself regarded the construction of an artificial language L to be a matter of choice:38 [T]he rules of L are not given, and the problem is how to choose them. We may construct L in whatever way we wish. There is no question of right or wrong, but only a practical question of convenience or inconvenience of a system form, i. e. of its suitability for certain purposes. [italics GH]

That Carnap 1936/1937 explicitly allowed for the coexistence of several artificial languages is also highlighted by the fact that he himself proposed several such languages in the very same essay. Yet if one acknowledges a multitude of artificial languages, the choice of a specific one as a reference language needs to be justified. Otherwise, the choice will be arbitrary and the resultant translatability

 38 See Carnap 1936/1937, p. 4.

Translatability  31

criterion will be ad hoc.39 More specifically, the translatability criterion proposed by the logical empiricists will be ad hoc unless an argument in favor of L+e as the only legitimate choice for a reference language is given. It would obviously be question-begging to justify the choice of L+e as the reference language of the translatability criterion by claiming that L+e allows for the formulation of precisely those sentences that are meaningful, since this assumes what is at issue between the empiricist and the metaphysician. Carnap’s reference to the convenience of an artificial language in the above quotation does not suffice either to justify L+e as a reference language. Even if we granted that L+e was the most convenient language to be used, this would not legitimize the choice of L+e as the reference language of the translatability criterion. It is important to recall that the logical empiricists’ proposal of a criterion of meaning was not primarily a linguistic endeavor. Rather, they proposed and defended such a criterion as a bulwark against metaphysics. The logical empiricist intended to propose a criterion of meaning that is not met by metaphysical sentences and to thereby discredit metaphysics. To shoulder this burden, it will not suffice for the translatability criterion to refer to an artificial language, which is only legitimized by way of being more convenient than other languages. A metaphysical sentence of the ordinary language is not proven to be meaningless or spurious in any other sense just because it fails to be translatable into the most convenient artificial language. Unless the choice of L +e as the reference language is justified in a more stringent sense, the translatability criterion is ad hoc. As it stands, the criterion is rather a lame duck than a bulwark against metaphysics. Could this ad hoc character of the translatability criterion be avoided by giving a more appropriate justification in favor of L+e as the reference language? What Carnap had in mind when he proposed artificial languages like L+e seems pretty obvious. He tried to construct languages that would allow for the formulation of precisely those sentences that are verifiable, more specifically, sentences that he considered to be verifiable.40 If Carnap succeeded in this respect,  39 Some sentences will not be considered controversial by the empiricist and the metaphysician. That is, there are some sentences (e. g., “Paris is the capital of France”) that are regarded as meaningful by both the empiricist and metaphysician alike, while there are other sentences (e. g., “Caesar is and”) that are regarded as meaningless by both. It seems reasonable to require an adequate reference language to allow for the formulation of sentences whose meaningfulness is uncontroversial, while not allowing the formulation of sentences whose nonsensical status is not called into question. But even with this constraint, the choice of a reference language will be seriously underdetermined. 40 Cf., e. g., Carnap 1936/1937, Sec. 27.

32  Some Historic Formulations and Their Problems that might well constitute a justification in favor of L+e as a reference language, which goes beyond considerations of convenience and is not question-begging, either. In this case, a metaphysical sentence would be spurious, at least in the sense of not being verifiable if it does not fulfill the translatability criterion. Combined with the further conviction of the empiricists that a sentence is meaningful if, and only if, it is verifiable, a metaphysical sentence could be shown to be meaningless by demonstrating that it fails to fulfill the translatability criterion. This would indeed discredit metaphysics just the way logical empiricists initially intended. Further arguments are certainly required to show that L+e —or rather some language of this type—singles out the verifiable sentences and that a sentence is meaningful if, and only if, it is verifiable. Without any justification for the empiricists’ choice of a reference language, the translatability criterion of meaning remains ad hoc.

1.8 Summary – –

–

– – – –

A sentence is cognitively meaningful if, and only if, it is either analytic or verifiable. Neither the practical possibility to verify a sentence in the here and now nor within the lifetime of the speaker matters. For a sentence to be meaningful, it is sufficient to be verifiable or falsifiable in principle. Some proposals of a verificationist principle are too restrictive (e. g., Attempts 1, 7 and 8) while others are too inclusive (e. g., Attempts 5 and 6). Still others are too restrictive and too inclusive at the same time (e. g., Attempts 2, 3 and 4). General laws cannot be verified conclusively. An adequate verificationist principle has to require some weaker form of support by observation sentences than logical entailment. The translatability criterion of meaning is ad hoc. All attempts at fleshing out a verificationist principle of meaning have failed for various reasons.

2 More Problems Lie Ahead In the previous chapter, we discussed some of the most well-known verificationist principles and their respective problems. In this chapter, we will review some additional problems that in one way or another, are of a more general nature. The discussion of these two chapters will naturally lead to a number of conditions that any adequate verificationist principle has to fulfill. This list of conditions of adequacy will be the guideline for all subsequent chapters.

2.1 The Problem of Dispositional Terms Spreads Out The problem of dispositional terms discussed in Section 1.7 was first raised as an objection to translatability criteria of cognitive meaning. Typically, this problem has been discussed with respect to that type of criterion ever since. Nevertheless, it must be pointed out that dispositional terms also pose a serious problem for other verificationist principles.41 Any verificationist principle has to be formulated relative to some object language. As the logical empiricists were limited to the formal methods available at the time, all empiricist criteria of meaning assume that some classical logic underlies the object language, that is, either propositional logic or first order predicate logic. However, the discussion in Section 1.7 revealed that the resources provided for by classical logic are insufficient to adequately formalize sentences containing dispositional terms. Recall, the logical structure of sentences containing dispositional terms like “soluble” has a conditional form: (2.1)

x is soluble in water.

This sentence means something like: (2.2)

If x is placed in water, then x will dissolve.

The material implication has proven to be inadequate to formalize that type of conditional.42 Thus, not being able to analyze the involved conditional it is im 41 Hempel 1950, Sec. 4 mentions that in passing, too. 42 Neither is the logical implication nor any other strict conditional more suited for that purpose. This will become clear in Chap. 8 where we consider David Lewis’ so-called variably strict conditionals as a possible solution to the problem of dispositional terms.

34  More Problems Lie Ahead possible to formalize sentences like (2.2) in predicate logic at all. That is why dispositional terms pose a problem for translatability criteria of cognitive meaning (cf. Section 1.7). By the same token, a formalization of the form p ⊃ q in propositional logic has to be dismissed. This does not, however, mean that we cannot formalize sentences containing dispositional terms in classical logic at all. Rather, it means that we are left with a sentence constant p as the only way to represent such sentences in classical logic. Since this coarse grained formalization does not reflect the conditional structure of dispositional terms at all, it is to be expected that it will prove to be inadequate, too. Nevertheless, we should examine in some detail the difficulties that will arise with regard to some of the verificationist principles we discussed in the previous chapter. Although sentences like (2.2) containing dispositional terms may well consist of observation sentences, they themselves are not observation sentences. Furthermore, being formalized as a sentence constant p, their truth or falsehood is independent of the truth value of other atomic sentences. In particular, p can be false while an arbitrary set of observation sentences is true. That is to say, there is no finite set of observation sentences o1, o2, …, on such that {o1, o2, …, on} ⊢ p. Hence, p does not meet the requirement of conclusive verifiability in principle as discussed in the previous chapter (cf. Attempt 2). Not being analytic, either, sentences containing dispositional terms would have to be regarded as meaningless. Thus, dispositional terms pose a problem for the criterion of conclusive verifiability in principle, just as they did for translatability criteria of meaning. If sentences containing dispositional terms are not verifiable in principle, they will be even less verifiable within a lifetime. Thus, dispositional terms also pose a problem for the requirement of conclusive verifiability within lifetime (cf. Attempt 1). If we have to formalize a sentence containing a dispositional term as a sentence constant p, it will also be meaningless according to the requirement of conclusive falsifiability in principle (cf. Attempt 3). Since the truth value of p is independent of that of other atomic sentences, ¬p can be false while an arbitrary set of observation sentences is true. Thus, there is no finite set of observation sentences o1, o2, …, on such that {o1, o2, …, on} ⊢ ¬p. Being neither verifiable nor falsifiable, sentences containing dispositional terms also fail to be meaningful according to the disjunctive criterion of empirical meaning (cf. Attempt 4). Hence, dispositional terms pose a serious problem not only for translatability criteria, but for most verificationist principles that have been proposed by logical empiricists. Certainly, Ayer’s criterion of empirical import would qualify

Another Problem: Particular Sentences  35

sentences containing dispositional terms as meaningful (cf. Attempts 5 and 6). But this is only because his principle fails to exclude any sentences. This was the main shortcoming of Ayer’s proposal.

2.2 Another Problem: Particular Sentences One of the most striking objections to verificationist principles is surely that universal sentences are not conclusively verifiable. As pointed out in Section 1.3, this would result in general laws becoming meaningless according to conclusive-verifiability criteria of meaning (cf. Attempts 1 and 2)—an altogether inacceptable consequence. Recall, the problem with universal sentences is that they refer to infinitely many instances and can therefore never be exhausted by our observations which are always finite in number. That is why universal sentences are not implied by any finite set of observation sentences. It was Karl Popper in The Logic of Scientific Discovery, who pointed out that particular sentences are open to basically the same objection. 43 Carnap acknowledged this criticism: “Now a little reflection will lead us to the result that there is no fundamental difference between a universal sentence and a particular sentence with regard to verifiability but only a difference in degree.” 44 He discusses the problem using the following example:45 Take for instance the following sentence: “There is a white sheet of paper on this table.” In order to ascertain whether this thing is paper, we may make a set of simple observations and then, if there still remains some doubt, we may make some physical and chemical experiments. Here as well as in the case of the law, we try to examine sentences which we infer from the sentence in question. These inferred sentences are predictions about future observations. The number of such predictions which we can derive from the sentence given is infinite; and therefore the sentence can never be completely verified.

A particular sentence containing a universal term such as “is a sheet of paper” transcends what can be ascertained by a single observation or a finite number of observations. To be a sheet of paper is to be a thing that shows a certain lawlike behavior, that is, to give certain responses if subjected to certain tests.46 It is crucial to note that the number of such potential tests is infinite. That is why  43 Cf. Popper 1935/1959, Chap. 5, Sec. 25. 44 See Carnap 1936/1937, p. 425. 45 See Carnap 1936/1937, p. 425. 46 Note the obvious similarity to the problem of dispositional terms that we discussed in Sec. 1.7 and 2.1.

36  More Problems Lie Ahead sentences containing a universal term implicitly refer to infinitely many instances just like universal sentences. A particular sentence implies infinitely many possible observations of which we can only make finitely many. Thus, particular sentences can be verified conclusively no more than universal sentences. For another example to illustrate the same point, suppose you look at an object that appears to be a pyramid. Hence, you believe that the following sentence is true: “This object has the shape of a pyramid.” However, that sentence also makes predictions about how the object will appear under other perspectives. No matter how many perspectives you have actually observed, there will always be infinitely many—indeed, innumerable many—other perspectives that you have not observed. Therefore, it is impossible for you to conclusively verify the sentence in question. Consequently, particular sentences would become meaningless according to a criterion of meaning that requires some sort of conclusive verifiability. Since this is clearly an inadequate classification, particular sentences pose a problem for verificationist principles just like universal sentences do.

2.3 Yet Another Problem: The Duhem-Quine Thesis With the exception of Ayer’s criterion of empirical import, all verificationist principles discussed in the previous chapter presuppose what might be called verification atomism. That is, they all assume that individual sentences taken in isolation are capable of being verified or falsified. The underlying idea of verification atomism can be described schematically as follows: To verify or falsify a sentence p, we deduce some observable consequence o from the sentence. If o then is actually observed, p is verified (or at least confirmed or justified to some degree). If o is not observed, p is falsified. At no point are sentences other than p and its observable consequences involved. As is well known, W. V. O. Quine criticized verification atomism in his seminal essay Two Dogmas of Empiricism. Verification atomism is (a weak form of) what Quine addresses as one of the two “dogmas of empiricism”. The other socalled dogma is the analytic / synthetic distinction. In this section, we deal with criticisms of verification atomism. The potential bearing of Quine’s criticism of the analytic / synthetic distinction on verificationism will be discussed in the next section. Although Quine 1951 is best known for criticizing verification atomism and outlining a holistic conception of theory testing, he was not the first to do so. Pierre Duhem argued along the same lines in his 1906 monograph The Aim and Structure of Physical Theory well before logical empiricism even origi-

Yet Another Problem: The Duhem-Quine Thesis  37

nated.47 Therefore, this doctrine became known as the Duhem-Quine thesis in the later philosophical literature.48 Duhem and Quine object to verification atomism by pointing out that no theory or hypothesis implies observational consequences if taken by itself. Rather, the hypothesis at issue entails observational consequences only if joined by a whole group of auxiliary hypotheses such as boundary conditions and theories justifying the use “of physical instruments, e. g. the thermometer, the manometer, the calorimeter, the galvanometer, and the saccharimeter […].”49 But if isolated hypotheses do not imply observational consequences, then hypotheses cannot be verified or falsified one by one, either. For instance, consider the following example:50 EXAMPLE 2.1 (celestial mechanics): In the 19th century, astronomers observed the path of the planet Uranus to test whether it conformed to the path predicted by Newton’s law of gravitation. By itself, Newton’s law does not predict anything that could be observed by the unaided eye. A telescope was needed to observe Uranus’ path. Thus, Newton’s law makes predictions that are actually observable only in combination with a theory about the functioning of the telescope. At least implicitly further assumptions were made to predict what would be observed through the telescope. For instance, it was assumed that light travels through space in a straight line and that no unknown planet disturbs Uranus’ path. The observed path did not conform to the predicted one. From that it was concluded that some yet undiscovered planet disturbs Uranus’ path. Le Verrier could even calculate the position of this unknown planet. It was observed soon after and given the name Neptune. The aim was to test Newton’s law of gravitation (p) against observations. To accomplish this, some observable consequence (o) had to be deduced from the theory to see whether it would conform to the actual observations or not. The  47 The original French title is La Théorie Physique: Son Objet et Sa Structure. Quotes are from the English translation by Philip P. Wiener. Cf. Part 2, Chap. 6 for Duhem’s argument against verification atomism, most parts of which have also been reprinted in Duhem 1998. Cf. also Lowinger 1941, p. 132ff. 48 Quine 1991 admits that he was not aware of Duhem’s writings when he first published Two Dogmas. In later reprints of his paper, he credits Duhem in a footnote, stating that Hempel and Frank had drawn his attention to this point. 49 See Duhem 1906, p. 183. 50 Cf. the brief remark on the discovery of Neptune in Duhem 1906, p. 195.

38  More Problems Lie Ahead point, however, is that Newton’s law taken by itself does not imply anything that is observable. Rather, the theory at issue had to be combined with several auxiliary hypotheses of the background knowledge (h1, h2, …, hn) to imply a prediction that could actually be observed, namely, a prediction of what would be seen through the lens of a telescope. Thus, the situation can schematically be represented as follows: (2.1) (2.2)

p⊬o p ∧ h1 ∧ h2 ∧ … ∧ hn ⊢ o

Observing that the actual path of Uranus is different from the predicted one amounts to observing ¬o. According to (2.1), ¬o does not, however, imply ¬p. That is, it is not inevitable to dismiss Newton’s law of gravitation in light of the new evidence. Nevertheless, modus tollens allows us to conclude from ¬o and (2.2) the truth of ¬(p ∧ h1 ∧ h2 ∧ … ∧ hn) which in turn is equivalent to ¬p ∨ ¬h1 ∨ ¬h2 ∨ … ∨ ¬hn. Observing that the actual path of Uranus is different from the predicted one shows that at least one of the hypotheses used to deduce the prediction must be false. That is, either Newton’s law of gravitation or some of the auxiliary hypotheses is false. The experiment does not determine which of these hypotheses is false. Thus, as far as logical consistency is concerned, we can sustain our belief in any of the involved hypotheses, provided we give up belief in some of the others. Historically, astronomers decided to stick to their belief in Newton’s law while giving up the assumption that there is no unknown planet disturbing Uranus’ path. To sum up, several hypotheses are needed to deduce an observable prediction. Therefore, in case the actual observations conflict with the prediction, the falsification of the hypotheses is underdetermined in that the experiment only shows that some hypothesis is false without showing which one. Thus, it is not a single hypothesis that is falsified, but a set of hypotheses. Similarly, in case the actual observations conform to the predictions, it is not just a single hypothesis, but the set of all involved hypotheses that is verified (or confirmed / justified). In other words, verification and falsification atomism fails to adequately describe example 2.1. Rather, verification and falsification is a holistic process, sets of theories are jointly verified or falsified. Quine puts it almost poetically: “[O]ur statements about the external world face the tribunal of sense experience not individually but only as a corporate body.” 51

 51 See Quine 1951, p. 38.

Yet Another Problem: The Duhem-Quine Thesis  39

Example 2.1 shows that there are theories that cannot be verified or falsified in isolation, that is, verification atomism fails at least in some contexts. The Duhem-Quine thesis claims, however, that it fails systematically. To support this broader claim, it does not suffice to simply refer to some examples. A more general argument is needed to support the Duhem-Quine thesis. Duhem and others have appealed to the so-called theory-ladenness of observation to support their holistic theses.52 The theory-ladenness argument: Just like example 2.1 involves the use of a telescope to make the relevant observations, most experiments in physics and other sciences involve the usage of rather complicated instruments of all sorts: Microscopes, spectrometers, cloud chambers, thermometers, voltmeters, etc. Physical theories that are themselves nothing but empirical hypotheses explain how these instruments function. To interpret the readings of these instruments and to justify their usage in the first place, we must refer to these fallible theories. For instance, when we read a voltmeter, our actual observation will be something like “the needle of this instrument covers the point marked ‘3’ on its dial”. From this we conclude something like “a voltage of 3V is applied to this instrument”. To justify this conclusion, we must to refer to a physical theory about how the voltmeter functions. Hence, observations are theory-laden each time they involve one or more instruments. Now, if we want to test a given theory against observations that can only be made with the help of one or more instruments, its verification or falsification will become a holistic matter for the same reasons as in example 2.1. It is only if we combine the respective theory with auxiliary hypotheses about how the instruments involved function that we can deduce predictions about what will actually be observable, namely, predictions about the readings of the instruments. Therefore, contradicting observations will only demonstrate that the theory at issue or some of the—likewise fallible—hypotheses about the instruments must be false. It is not an isolated hypothesis but the set of all involved hypotheses that is falsified. Similarly, observations that conform to the predictions will not just verify (or confirm / justify) the theory we want to test but the entire set of hypotheses. In sum, most scientific theories can only be tested against observations if we use more or less complicated instruments. Observations through instruments are theory-laden. Therefore, scientific theories can only be verified or falsified holistically.

 52 Cf., e. g., Duhem 1906, p. 183ff.

40  More Problems Lie Ahead The theory-ladenness argument is sufficient to show that verification atomism fails not only in some cases, but with respect to most scientific theories. Duhem restricted his holistic claim to theories in physics while Quine is well known for extending holism to any given sentence.53 The theory-ladenness argument is insufficient to back up the latter, since its scope is limited to contexts that involve the usage of instruments. A Quineian sort of universal holism calls for an even more general argument. Quite surprisingly, Quine 1951 does not offer a profound argument for his dramatic extension of holism. At best, an argument can be reconstructed from a very brief remark he made on hallucination.54 The hallucination argument: The atomistic claim that a hypothesis taken by itself can be verified or falsified is most plausible with respect to sentences about what is directly observable with unaided senses. For instance, the sentence “there is a red book lying on the desk” is itself an observation sentence. Therefore, we do not have to combine it with any auxiliary hypothesis to imply a prediction that can then be tested against actual observations. Rather, it seems as though we could test the sentence taken by itself against observations. We simply look at the desk. If we see a red book lying on it, the sentence is verified. If we do not see a red book on the desk, the sentence is falsified. It seems that no other sentences get involved at any point. Since atomism is most plausible with respect to observation sentences, it would be a strong—though not conclusive— argument for universal holism, if we demonstrated that even the verification and falsification of observation sentences is a holistic matter. Sense perception is a reliable belief forming process under normal circumstances. However, the starting point for the holist is to point out that sense perception is not a reliable belief forming process if certain deceiving conditions obtain. For instance, it is unreliable if you are hallucinating, if you took drugs, if you are in a so-called hall of mirrors, if the light is deceiving, etc. Now suppose I believe that a red book is lying on the desk (p) prior to actually looking at it. Hence, I predict that I will see a red book when I look at the desk (o). At least implicitly, I make the assumption that none of the deceiving conditions obtain under which visual perception is an unreliable belief forming process (h1, h2, …, hn). Only if we combine p with the auxiliary hypotheses h1, h2, …, hn does it entail o. Thus, verification and falsification once again becomes a holistic matter.  53 For a discussion of the similarities and differences between Duhem and Quine, cf. Gillies 1998. 54 Cf. Quine 1951, p. 40.

And Another Problem: The Analytic/Synthetic Distinction  41

The conclusion from that discussion is that no sentence can be verified or falsified in isolation. Verificationist principles that presuppose this kind of atomism are misguided. An adequate verificationist principle has to be compatible with the Duhem-Quine thesis, that is, it has to be holistic. Quine addresses verification atomism as (a weak form of) one of the two “dogmas of empiricism”. The other dogma is the analytic / synthetic distinction. Let us now turn to his discussion of the latter.55

2.4 And Another Problem: The Analytic/Synthetic Distinction As pointed out in Section 1.1, most empiricist criteria of meaning are bifurcated in that they regard an arbitrary sentence as cognitively meaningful if, and only if, it is either (i) analytically true or false, or (ii) empirically meaningful. So far, we have only dealt with various attempts to spell out the concept of empirical meaningfulness in terms of some form of verifiability or falsifiability. That is, we have exclusively been concerned with the second disjunct of the above principle. It is about time we take a closer look at the first disjunct, too. It is by way of this disjunct that most criteria of cognitive meaning refer to the analytic / synthetic distinction. This reference also echoes with several criteria of empirical meaning, e. g., Attempts 2, 3, 4 discussed in the previous chapter. By Definition 1.5(i), Ayer’s criterion of empirical import also refers to the analytic / synthetic distinction. As is well known, this distinction has been called into serious question by W. V. O. Quine in Two Dogmas of Empiricism. While we discussed the other so-called dogma—verification atomism—in the last section, I will summarize Quine’s rather complex argument against the analytic / synthetic distinction in this section and discuss its potential bearing on verificationism. The starting point for Quine’s attack on the analytic / synthetic distinction is the following characterization of analyticity.56 DEFINITION 2.1 (analyticity): Sentence p is analytically true iff: (i) p is logically true or

 55 Cf. Curd and Cover 1998 for further reading on the Duhem-Quine thesis. Chap. 3 collects several contributions on that debate along with a substantial commentary by the editors on each paper. 56 Cf. Quine 1951, p. 23.

42  More Problems Lie Ahead (ii) p can be turned into a logically true sentence by putting synonyms for synonyms. An example of the first kind of analytic sentence is: (2.1)

No unmarried man is married.

The following is an example of the second kind of analytic sentence: (2.2)

No bachelor is married.

Although (2.2) is not logically true, it can be transformed into the logically true sentence (2.1) by replacing “bachelor” with the synonymous term “unmarried man”. This characterization of analyticity “lean[s] on a notion of ‘synonymy’ which is no less in need of clarification than analyticity itself.” 57 Thus, understanding the notion of synonymy is essential for understanding the analytic / synthetic distinction. Quine considers various ways of analyzing the former and dismisses all of them. Thus, his criticism of the latter has the form of a reductio argument. Firstly, one might try to analyze synonymy in terms of definitions. Two terms are synonymous if, and only if, one term can be defined in terms of the other one. For instance, “bachelor” and “unmarried man” are synonymous because “bachelor” can be defined as “unmarried man”. But “definition— except in the extreme case of the explicitly conventional introduction of new notations—hinges on prior relationships of synonymy.”58 This includes even explications in the Carnapian sense. Thus, on pain of circularity one must not try to analyze synonymy in terms of definitions. Secondly, one might try to analyze synonymy in terms of interchangeability salva veritate. Two terms are synonymous if, and only if, they are interchangeable in all contexts without change in truth value. For instance, “bachelor” and “unmarried man” are synonymous because both terms can be interchanged in all contexts without changing the truth value.59 At this point, we need to distinguish whether we are dealing with an extensional or an intensional language. A language is called extensional if, and only if, any two coextensive predicates are  57 See Quine 1951, p. 23. 58 See Quine 1951, p. 27. 59 Of course occurrences within words or quotation marks as, e. g., in the sentence “‘Bachelor’ has less than ten letters.” need to be exempt from this requirement.

And Another Problem: The Analytic/Synthetic Distinction  43

interchangeable salva veritate. A language is called intensional if, and only if, it is not extensional. “[I]nterchangeability salva veritate, if construed in relation to an extensional language, is not a sufficient condition of cognitive synonymy […].” For instance, the terms “creature with a heart” and “creature with a kidney” are perhaps coextensive. Thus, they would be interchangeable salva veritate relative to an extensional language. Nevertheless, the two terms are by no means synonymous. On the other hand, if we assume an intensional language, then interchangeability salva veritate is in fact a sufficient—as well as a necessary—condition of synonymy. The reason for this is that an intensional language will contain the modal adverb “necessarily” or some other particle to the same effect. This allows us to form sentences of the following sort: 60 (2.3)

Necessarily, all and only bachelors are bachelors.

If two terms are interchangeable in all contexts without change in truth value, then they must, in particular, be interchangeable in such intensional contexts. For instance, when we replace the second occurrence of “bachelors” in (2.3) with “unmarried men”, then the sentence will still be true: (2.4)

Necessarily, all and only bachelors are unmarried men.

The truth of (2.4) indeed ensures the synonymy of the terms “bachelor” and “unmarried man”. However, “[t]he above argument supposes we are working with a language rich enough to contain the adverb ‘necessarily’, this adverb being so construed as to yield truth when and only when applied to an analytic statement. […][B]ut such a language is intelligible only if the notion of analyticity is already clearly understood in advance.”61 Thus, it would once again lead to circularity if we tried to analyze the notion of analyticity in terms of synonymy and then went on to analyze the latter in terms of interchangeability salva veritate relative to an intensional language which presupposes the notion of analyticity. Hence, interchangeability salva veritate is not an adequate criterion for synonymy, regardless whether we assume an extensional or an intensional language.62  60 See Quine 1951, p. 29. 61 See Quine 1951, p. 29f. 62 Similarly, Quine diagnoses that the introduction of so-called “[s]emantical rules determining the analytic statements of an artificial language are of interest only in so far as we already

44  More Problems Lie Ahead Finally, Quine discusses whether the analytic / synthetic distinction can be backed up by the verification theory of meaning. He assumes the following three definitions:63 DEFINITION 2.2 (meaning): The meaning of a sentence is the method of its verification. DEFINITION 2.3 (synonymy): Two sentences are synonymous iff they have the same meaning.64 DEFINITION 2.4 (analyticity): A sentence is analytically true iff it is synonymous with a logically true sentence. Note that Quine assumes a particularly strong form of verificationism with Definition 2.2 according to which verifiability is not only taken to be a criterion of meaningfulness, but for which meaning is identified with the method of verification.65 Taken together, these three definitions allow us to characterize analyticity as follows: DEFINITION 2.5 (analyticity): A sentence is analytically true iff the method of its verification is the same as that of a logically true sentence. Qua this definition, the analytic / synthetic distinction might be backed up by a verificationist principle. “So, if the verification theory can be accepted as an  understand the notion of analyticity; they are of no help in gaining this under-standing.” To support his claim, Quine discusses two forms of semantical rules. The first explicitly refers to the concept of analyticity. Thus, this type is clearly unavailing for analyzing this very concept. The second form of semantical rule avoids such direct circularity only by appealing to an unexplained phrase “semantical rule of language L” which “is as much in need of clarification, at least, as ‘analytic for [language L]’”. However, at the very best, the introduction of semantical rules would determine the analytic statements for artificial languages only. Thus, we do not have to discuss Quine’s argument concerning semantical rules in detail since this strategy of backing-up the analytic / synthetic distinction is a non-starter when it comes to natural languages. Cf. Quine 1951, Sec. 4. 63 Cf. Quine 1951, p. 35. 64 Note that unlike the notion of synonymy we have dealt with so far, this is an account of synonymy for sentences only. However, Quine points out how a concept of synonymy for other linguistic forms can easily be derived from this notion of synonymy for sentences. Cf. Quine 1951, p. 35. 65 This distinction will be discussed further in Sec. 4.6.

And Another Problem: The Analytic/Synthetic Distinction  45

adequate account of statement synonymy, the notion of analyticity is saved after all.”66 Unfortunately, this way out of the problem does not work according to Quine, because verificationism—or rather the strong version Definition 2.2 assumes—fails. Quine indicates two reasons for believing that verificationism is untenable: (i) All historical attempts at spelling out a verificationist principle have failed. (ii) The verification atomism these attempts presuppose has to be rejected. In light of our somber discussion of various verificationist principles in the previous chapter, the first of these claims has to be conceded. Furthermore, as revealed in the previous section, Quine also made a strong claim for verification holism. Hence, the analytic / synthetic distinction cannot be backed up by the verification theory of meaning. To sum up Quine’s reductio argument against the analytic / synthetic distinction: The key for understanding analyticity would seem to be the notion of synonymy. However, all prima facie plausible ways to analyze this notion fail. That is, synonymy can be neither spelled out in terms of definitions nor interchangeability salva veritate, nor by reference to the verification theory of meaning. From this, Quine concludes that the analytic / synthetic distinction itself has to be abandoned as “some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth[s] which are synthetic, or grounded in fact.”67 Of course, Quine’s reductio argument is not conclusive in that it does not take into account all possible ways of spelling out synonymy but only certain plausible ways of doing so. Nevertheless, it must be granted that Quine’s argument is compelling. Numerous philosophers have criticized Quine’s criticism of the analytic / synthetic distinction. Some of the more prominent ones include, for instance, Grice and Strawson 1957 and Putnam 1976. Nevertheless, it seems fair to say that none of them has been able to come up with a convincing analysis of the concept of analyticity. Although this is not to say that it is impossible for an adequate account of the analytic / synthetic distinction to be developed, it does not come as a surprise that this distinction has been regarded with a great deal of suspicion by philosophers ever since. However, one important qualification needs to be added to what seems to be Quine’s own conclusion from his argument. Recall that according to Definition 2.1, there are two kinds of analytic sentences: (i) Logically true sentences, and (ii) sentences that can be turned into logically true sentences by putting synonyms for synonyms. Having undermined the notion of synonymy, one has  66 See Quine 1951, p. 35. 67 See Quine 1951, p. 20.

46  More Problems Lie Ahead to give up the belief in the second class of alleged analytic sentences. This however, leaves the first class of analytic sentences, that is, logically true sentences, untouched. Logically true sentences can still be upheld as being fundamentally different from other sentences in that their truth does not depend on matters of facts. Although the first class of analytical sentences is not affected by his reductio argument Quine clearly seems to give up the belief in any analytic sentences whatsoever when he outlines his counter-suggestion of an “empiricism without dogmas”.68 That means throwing the baby out with the bathwater. Thus, the analytic / synthetic distinction needs to be given up, except for logically true sentences. This qualification will become relevant later on.69 As pointed out, most empiricist criteria of meaning refer to the analytic / synthetic distinction. Therefore, the rejection of the distinction poses a further problem for those theories. An adequate principle of verification must not refer to or depend on a concept of analyticity over and above that of logical truth.70

 68 Cf. Quine 1951, p. 39f, e. g., “[N]o statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed […].” 69 Cf. the discussion of (CA11) and (CA17) in Sec. 4.3, as well as the frequent reference to deductive closure by various postulates in Chap. 5–7. 70 One might wonder whether this condition of adequacy adds anything to the various conditions we have discussed so far. Recall that Quine acknowledges that the analytic / synthetic distinction could be backed up by the verification theory of meaning if the latter were tenable. Therefore, a criticism of verificationism that is based on its reference to the analytic / synthetic distinction is not independent of other criticisms of verificationism: (i) On the one hand, if verificationism solves all other problems, then the analytic / synthetic distinction would be intelligible after all. In that case, referring to it would not pose a problem for verificationism. (ii) On the other hand, if verificationism does not solve the other problems, no further criticism is needed to demonstrate its untenable nature. At first glance, it would therefore seem that a criticism of verificationism that is based on its reference to the analytic / synthetic distinction is either a non-starter or superfluous. On closer inspection, however, we find that this is not quite true. According to Definition 2.2, we have to assume a particularly strong form of verificationism to back up the analytic / synthetic distinction. There may well be a form of verificationism that solves all other problems while being too weak to back up the analytic / synthetic distinction. It would not be superfluous to require such a criterion to not refer to the analytic / synthetic distinction. Actually, we shall discuss such a verificationist theory in Chap. 4. Thus, the requirement to not refer to the analytic / synthetic distinction is in fact an addition to the list of conditions of adequacy for the construction of a principle of verification.

Summary  47

2.5 Summary – – – – –

Most verificationist principles that have been proposed by logical empiricists fail to qualify sentences containing dispositional terms as meaningful. Just like universal sentences, particular sentences are not verifiable conclusively. A verificationist principle has to be compatible with the Duhem-Quine thesis, that is, it has to be holistic. A verificationist principle must not refer to an analytic / synthetic distinction over and above the logical / non-logical distinction. Numerous objections have been raised against verificationism. Each and every verificationist principle that has been proposed historically is flawed in one way or another.

3 Toward a Solution to the Problems 3.1 Conditions of Adequacy The previous two chapters presented a number of objections that have been raised against all formulations of a verificationist principle proposed by the logical empiricists. These objections give rise to a list of conditions that an adequate principle of verification must fulfill. Let us call a sentence significant if it meets the verificationist criterion under consideration and insignificant if it fails to meet it.71 The conditions of adequacy for a verificationist principle can then be formulated as follows: CONDITIONS OF ADEQUACY (CA1)

Some sentence about the remote past has to be significant.72

(CA2)

Some sentence about the distant future has to be significant.

(CA3)

The significance of sentences must not depend on highly contingent matters like the pace of technological progress.

(CA4)

Some sentence that cannot be conclusively verified by any human being has to be significant.

(CA5)

Some universal sentence quantifying over an infinite domain has to be significant.

 71 The logical empiricists, of course, regarded verifiability as a criterion of meaning. That is to say, they considered a sentence that is verifiable (not verifiable) as significant (insignificant) in the sense of being meaningful (meaningless). Other senses in which a sentence might be regarded as significant (insignificant) if it is verifiable (not verifiable) will be discussed in Sec. 4.6. 72 Taken literally, this condition could be satisfied by a criterion that classifies exactly one sentence about the remote past as significant, while we obviously want an adequate criterion to classify more than one such sentence as significant. However, it would be difficult to formulate (CA1) in a more ambitious way without already being confronted with the twists and turns of constructing a criterion of significance. Therefore, we shall leave (CA1) as it is. This underlines the status of the conditions of adequacy as formulating only some necessary conditions that an adequate criterion of significance has to fulfill. Even jointly the conditions of adequacy will do no more then filter out some inadequate criteria rather than uniquely characterize one criterion. In other words, the conditions of adequacy should not be seen as stating sufficient conditions for constructing an adequate criterion of significance. For this purpose, it is in order to formulate (CA1) as well as some of the other conditions of adequacy in a rather weak way.

50  Toward a Solution to the Problems (CA6)

Some existential sentence quantifying over an infinite domain has to be significant.

(CA7)

Some sentence with mixed quantifiers quantifying over an infinite domain has to be significant.

(CA8)

Some particular sentence has to be significant.

(CA9)

No molecular sentence containing an insignificant component must be significant.

(CA10) If a sentence is significant, then its negation has to be significant. (CA11) If a sentence is significant, then any sentence that is logically equivalent to it has to be significant. (CA12) Some sentence has to be insignificant. (CA13) Some sentence containing a dispositional term has to be significant.73 (CA14) A verificationist principle has to be non-creative, that is, it must not lead to the creation of pseudo analytic sentences. (CA15) A verificationist principle must not be ad hoc. (CA16) A verificationist principle has to be compatible with the DuhemQuine thesis, that is, it has to be holistic. (CA17) A verificationist principle must not refer to an analytic / synthetic distinction over and above the logical / non-logical distinction.

3.2 What You Can and What You Should Not Expect Not only does verificationism face a great number of problems, but these problems are fairly diverse, too. Thus, the corresponding list of conditions that an adequate verificationist principle must fulfill is very challenging. The logical empiricist did not manage to resolve these problems. Although they proposed increasingly refined criteria, they did not in the end succeed in fleshing out verificationism adequately. Each and every of their principles is flawed in one way or another. This led to a general abandonment of verificationism in the  73 More precisely, there should not only be a significant sentence containing a dispositional term, but actually a significant sentence containing a dispositional term of which the test conditions do not obtain. Cf. the discussion of dispositional terms and reduction sentences in Sec. 1.7.

What You Can and What You Should Not Expect  51

early 1960s. This development was certainly more likely to occur due to the disappearance of its main proponents around that time. Despite some improvements, the history of verificationism is a history of failure. Given the great deal of self-confidence with which logical empiricists typically confronted their opponents, their own failure to adequately explicate verificationism seems almost tragic.74 Verificationism today is mostly regarded as an outdated historical view. The term “verificationism” almost became a dirty word used only by some diehard adherents of scientism.75 Notwithstanding the unpopularity of verificationism and the many unsuccessful attempts to flesh it out in detail, most analytically oriented philosophers still seem to agree that “something” is wrong with sentences like “Nothingness nothings”. Yet if we claim that such sentences are, in some sense, insignificant, we ought to elucidate how precisely these sentences differ from those we are prepared to regard as significant.

 74 For a more optimistic assessment of the history of verificationism, cf. Lutz 2010 with the telling title: Criteria of Empirical Significance: A Success Story. However, Lutz arrives at his positive conclusion without even addressing the problems we have reviewed in the previous two chapters. That is, he does not at all discuss to what extent historical criteria of empirical significance meet the above listed conditions of adequacy. In his technically sophisticated paper, the author merely demonstrates that a number of equivalence and entailment relations hold between various criteria of significance. Some of these relations are obvious while others are unexpected and illuminating. From the fact that different criteria of significance “form a coherent whole”, Lutz concludes that “[t]he equivalences also provide a positive justification rather than a defense, because now the arguments in favor of each individual formulation turn out to be arguments for the same criterion.” That is why he arrives at his positive conclusion. The power of this kind of reasoning is, however, limited as long as the author does not address the well-known problems of the criteria he discusses. Furthermore, most of Lutz’ results depend on the implausible assumption that the observational basis establishing a sentence’s significance may include infinite sets of quantified observational sentences. If we want to consider a sentence empirically significant if, and only if, its truth value can be determined by observations, then Lutz’ conception of an “observational basis” is inappropriate because we never observe what is described by an infinite set of quantified observational sentences. Apparently, the author has some other explicandum in mind. For this reason, too, Lutz’ findings have little bearing on what we are focusing on. Cf. also Sec. 9.1 where the author discusses a more stringent observational basis. 75 Weintraub 2003 puts it this way: “Hardly anyone advocates verificationism nowadays. It is so disreputable a doctrine, that one need[s] only identify a verificationist basis for a philosophical position so as to be able to reject it without further ado.” Friedman 1999 adds about logical positivism in general that it “now often serves more as an intellectual scapegoat than as an honorable philosophical opponent” making a veritable effort himself to protect it by way of a substantial reinterpretation.

52  Toward a Solution to the Problems In the remainder of this book, I will show how later developments in formal epistemology, philosophy of science, and logic can substantially contribute to a solution of some of the key problems of verificationism. I will combine verificationism with several theories that are—in my opinion—immediately relevant to the debate on verificationism, though they became available only after its fall. In view of these potential improvements, I will argue that a weak form of verificationism is still tenable. Such an approach could be called minimal verificationism, as it involves a weakening of traditional verificationist principles in various respects, while maintaining their core idea. I will also propose a first formulation of such a theory of minimal verificationism. Although I do think that some substantial progress can be made by applying new techniques to the debate on verificationism, you should not expect to find a solution in this book to all problems of verificationism. You should not expect to find a full-fledged theory of verificationism. You should not expect to find a criterion of verifiability that will readily classify any given sentence as either significant or insignificant. In other words, you should not expect to find an ultimate solution to problems that have been unsuccessfully tackled for decades by some of the most talented philosophers of the 20 th century. Nonetheless, you can expect to find an analysis of the problems of verificationism from a more fundamental perspective and you can expect to understand the path we need to follow to find solutions to these problems. To put it metaphorically, you should not expect a solution but rather a roadmap to a solution of the problems of verificationism. You can also expect to take initial steps toward such a solution in this book. But there still is a long way to go. It will, however, be useful to have a roadmap for the journey.

3.3 Against Deductive Chauvinism Arguably, the most important and revealing problem of verificationism is the one that concerns universal sentences (CA5). This problem is important in its own right because sentences expressing general laws are of universal form. Since the latter are indispensible for the sciences, it is essential for a criterion of verifiability to correctly ascertain the status of universal sentences. The problem of universal sentences is furthermore important because it represents a whole cluster of problems concerning not only universal but also existential sentences, sentences with mixed quantifiers, particular sentences and sentences about the remote past and distant future (CA1, 2, 5–8). A solution to the problem of universal sentences will thus set the stage for a solution to these other problems, too. Since the problem with negations (CA10) arises only as a conse-

Against Deductive Chauvinism  53

quence of the aforementioned problems, it will also disappear once these have been resolved. Recall, the problem with universal sentences quantifying over an infinite domain is that they are not logically implied by any finite set of observation sentences. Observing a number of positive instances may well support, confirm and even justify a general law—especially in the absence of negative instances. But no finite number of observations will ever suffice to verify a universal sentence conclusively, no matter how many instances we observe. Thus, universal sentences would be considered insignificant according to any principle that establishes conclusive verifiability as a criterion of significance (cf. Attempt 2 in Chapter 1). This altogether inacceptable consequence shows that an adequate criterion of significance must require something weaker than conclusive verifiability, that is, something weaker than logical entailment by a finite set of observation sentences. I take the following three observations to be indisputable. Firstly, universal sentences are significant, more precisely, some universal sentences quantifying over an infinite domain are significant. Secondly, universal sentences quantifying over an infinite domain are not verifiable conclusively, that is, they are not logically implied by any finite set of observation sentences. Thirdly, universal sentences—including those quantifying over an infinite domain—can nevertheless be justified. To be logically implied by some evidence is one way in which a sentence can be justified. Structures of epistemic justification are not, however, limited to relations of logical entailment. Our justificatory practice is much richer than logic and includes inductive reasoning, inferences to the best explanation and coherentist forms of justification as well. Admittedly, logic describes a particularly important part of our justificatory practice because logical entailment is the only form of justification that is truth preserving. By focusing exclusively on this relation, however, logical empiricists ignored other forms of justification altogether (cf., e. g., Attempts 1–4 in Chapter 1). This one-sided approach leads to the absurd consequence that universal sentences are classified as insignificant. Although a universal sentence might be justifiable by finitely many observation sentences in “some sense”, it is not logically implied by them. Consequently, the requirement of conclusive verifiability must be replaced by a requirement of justifiability. Thereby, we allow universal sentences to be significant while still holding on to the idea that a sentence is insignificant if it is not justifiable at all—not even in principle. Certainly, the relevant notion of justification needs further explication, but it will have to be a fallibilist concept of justification if it is to be applicable to universal sentences. I will have more to

54  Toward a Solution to the Problems say about the notion of justification relevant for a criterion of significance in subsequent chapters. Already Carnap 1936/1937 noted that universal sentences are not verifiable conclusively while being justifiable in some weaker sense, a sense for which he uses the terms “testable” and “confirmable”:76 If verification is understood as a complete and definitive establishment of truth then a universal sentence, e. g. a so-called law of physics or biology, can never be verified […]. We cannot verify the law, but we can test it by testing its single instances […]. [W]e may speak here of gradually increasing confirmation of the law.

As a result he, too, gave up the idea that a significant sentence has to be verifiable conclusively while still holding on to the idea that a sentence has to be justifiable (confirmable): 77 “Every synthetic sentence must be confirmable” […]. [I]t seems to me that [this requirement] suffices as a formulation of the principle of empiricism […].

Therefore, it is only consistent that beginning with Hempel 1945, logical empiricists tried to provide formal accounts of the concept of confirmation.78 Although these proposals do not identify confirmation with logical implication, they still typically try to explicate the concept in terms of deductive relationships. That is, the empiricist notions of confirmation supervene on deductive relationships just as Ayer’s criterion of empirical import did (cf. Attempts 5 and 6 in Chapter 1). These approaches were not particularly successful. This led Hempel to conclude that one should give up the attempt to spell out a criterion of significance in purely deductive terms:79 I think it is useless to continue the search for an adequate criterion of testability in terms of deductive relationships to observation sentences.

 76 See Carnap 1936/1937, Sec. 3. 77 See Carnap 1936/1937, Sec. 27. 78 Cf. Hempel 1945, Sec. 9. In Sec. 7 of the same paper, Hempel suggests that the problem with theoretical terms can also be solved by replacing logical entailment with some weaker notion of confirmation: “[F]rom observation sentences, no merely deductive logical inference leads to statements about […] theoretical constructs […]. [S]tatements […] such as ‘This piece of iron is magnetic’ or ‘Here, a plane-polarized ray of light traverses a quartz crystal’ can be confirmed, but not entailed, by observation reports […].” An extensive attempt to explicate the notion of confirmation was made by Carnap 1950. 79 See Hempel 1950, Sec. 3. Cf., e. g., Fitelson 2006 for a contemporary attempt to explicate the notion of confirmation without reducing it to deductive relationships.

The Discovery of the Subject  55

Although the empiricists’ failure to spell out confirmation in terms of deductive relationships does not in any strict sense prove that such a reduction is impossible, there can be little doubt that this is a dead end. Nowadays, there seems to be general agreement among epistemologists that it is far more promising to seek an adequate explication of the concept of justification (confirmation or the like) beyond deductive relationships. To be sure, deductive relationships are one factor when it comes to justification, but the concept of justification does not supervene on these structures. Impressed by Frege’s discovery of modern logic and the new possibilities it opened up for philosophical analyses, logical empiricists got hooked on what might be called deductivism. They subscribed to the claim that either justification is to be identified with deductive entailment or that the former at least supervenes on the latter. As a consequence, they also paired their verificationism with that form of deductivism. The problem with universal sentences shows that the combination verificationism plus deductivism is untenable. Hence, at least one of these positions needs to be abandoned. What happened historically, though, is that both of these positions were discarded. But this may have been premature as it might be possible to keep one of the two. I certainly do not want to argue in favor of deductivism. But I do think it is worth taking a closer look whether verificationism is a viable option if we do not combine it with deductivism. Verificationism without deductivism will thus be one of the guidelines for the formulation of an adequate criterion of significance in subsequent chapters. Many theories of justification have been offered on the epistemological market in the last 40 years or so that analyze the concept of justification without reducing it to deductive relationships. We can build on these theories to formulate a more adequate criterion of significance. Namely, we should first replace the requirement of conclusive verifiability by a requirement of justifiability and then spell out the respective notion of justification by one of these existing theories of justification. This is the strategy I will pursue to overcome the problem of universal sentences and related problems. At least to my knowledge, these more recent theories of justification have not been implemented in a verificationist framework before. The next section should shed some light on the question why this has not been done before.

3.4 The Discovery of the Subject Theories of epistemic justification that do not reduce justification to deductive relationships have been proposed by a number of authors over the last decades.

56  Toward a Solution to the Problems These proposals are quite diverse. We will learn more about these different types of theories in Chapter 5. Typically, these theories do not explicate the concept of justification as a two-place relation holding between a sentence p that we wish to justify and some (sentence(s) describing) evidence e. Rather, these theories take other contextual elements into account as well. Certainly, the epistemic state A of the epistemic subject S is the most important contextual element when it comes to analyzing the notion of justification. While some evidence e might justify p for subject S given its epistemic state A, the very same evidence e might not justify p relative to the epistemic state A′ of another subject S′. Depending on the specific theory of justification, the epistemic state is further analyzed into its various components, such as the sentences accepted by the subject in the state under consideration and an epistemic preference relation of one form or another. Thus, contemporary theories of epistemic justification typically construe the relation of justification as a multi-place predicate. This tendency reflects the development in other epistemological debates like the debate on explanation, for instance. By implementing such a theory of justification in a verificationist framework, our criterion of significance will also refer to and thus ultimately depend on the epistemic state of the subject. This is remarkable in three ways. Firstly, by explicitly referring to the epistemic state of the subject, we avoid an atomism about verification / justification root and branch, thus complying with the Duhem-Quine thesis (CA16). Recall, according to Duhem and Quine, the verification of a theory is a holistic process because the theory under consideration only implies observable consequences if we combine it with auxiliary hypotheses. Hence, the theory and the auxiliary hypotheses involved can only be jointly verified or falsified. When we will formulate a criterion of significance in the next chapter, we can do justice to the holistic nature of this process by referring to the full epistemic state—part of which will be the auxiliary hypotheses referred to by the Duhem-Quine thesis. Secondly, when we formulate a criterion of significance that refers to the epistemic state of the subject, we have to ensure that it refers to the correct state. As pointed out in Section 1.2, the logical empiricists made it quite clear that it is not verification but verifiability that matters for a sentence’s significance. For a sentence to be significant, it is not necessary that it has actually been verified. Otherwise, a sentence like “the number of books on my desk is odd” would be insignificant if I did not, in fact, count the books on my desk.

The Discovery of the Subject  57

Rather, for a sentence to be significant, it suffices that it is possible to verify it.80 This distinction translates as follows into our new framework where verification / justification has been relativized on an epistemic state. The question whether a sentence p has actually been justified by a subject S translates into the question whether p is justified relative to the current epistemic state A of S. This is the question that does not matter for the significance of p. What matters is the question whether it is possible for S to justify p. This question now has to be rephrased into whether p is justified relative to some epistemic state A′ that S could be in. Now, what are the epistemic states a subject “could be in”? Surly, an irrational subject could be in all kinds of epistemic states relative to which it might be able to justify any given sentence. Hence, as empiricists, we want to impose certain constraints on the permissible epistemic states we wish to consider when it comes to the significance of a sentence. I take it that the fundamental idea of verificationism is that a synthetic sentence is significant if, and only if, it can be justified by some observations (cf. Attempt 2 in Chapter 1). Given a subject S is currently in the epistemic state A, this idea suggests that we have to look at all those epistemic states A′ that could be formed from the state A by a rational belief revision induced by certain observations. The basic idea for a criterion of significance will then be that a sentence is significant if, and only if, it is justified relative to some of those epistemically accessible states. I will elaborate on this proposal in the next chapter. For now I would like to underscore that it is not the current epistemic state, but certain epistemic states after some belief revision that matter for a sentence’s significance. Hence, we need a theory of rational belief revision in order to formulate an adequate criterion of significance. Fortunately, such theories are available on the epistemological market today as well. These theories were developed much later, though, than most of the non-reductionist theories of justification we alluded to in the previous section. Since the latter cannot be implemented within a verificationist framework without the former, it does not come as a surprise that nonreductionist theories of justification have not been used to back up verificationism in the past. On closer examination in Chapter 6, we shall find that theories of justification and belief revision are not independent of each other. Thus, what is actually required to improve verificationism is not a theory of justification and a theory of belief revision, but rather a combined theory of justification and belief revision. We have just begun exploring such a unified epistemological approach. In Chapter 7, we will review these attempts.

 80 Cf., e. g., Schlick 1936, Sec. 2.

58  Toward a Solution to the Problems Thirdly, the reference to the epistemic state of the subject means that our criterion of significance will not be an objective but a subjective one. At first, this might be surprising and seem counterintuitive. But the subjective character of significance is an immediate consequence of the Duhem-Quine thesis and has to be accepted as such. As mentioned above, the verification / justification of a theory is, according to Duhem and Quine, a holistic process because the theory under consideration only implies observable consequences if we combine it with auxiliary hypotheses. The most natural—if not inevitable—is to interpret these auxiliary hypotheses as part of the background knowledge, that is, as the beliefs of someone, either as those of an individual epistemic subject or as the collective beliefs of some research community. In neither case will the notion of verification nor the derived notion of significance be an objective one. Hence, it is misleading to speak of the significance or insignificance of a sentence p as a property of this sentence. Rather, we should say that a sentence p is significant or insignificant relative to an epistemic state A. In other words, significance construed as a one-place predicate will be subjective. Objectivity can only be regained if we make dependency on the epistemic state explicit by construing significance as a two-place predicate. As we shall see in Section 9.1, a solution to the problem of dispositional terms (CA13) will also call for a subjective character of a criterion of significance.

3.5 Counterfactual Conditionals Dispositional terms posed another intricate problem for verificationism (CA13, 14). Recall from Section 1.7, the logical structure of sentences containing dispositional terms has a conditional form. The conditional involved cannot, however, be analyzed adequately within classical logic. If we tried to analyze it by a material conditional, then any given object would have the disposition in question if the relevant test conditions do not obtain. Thus, a stone, for instance, would have to be considered soluble in water if it is not actually placed in water. Obviously, such an analysis is as misguided as is Carnap’s attempt to introduce dispositional terms by reduction sentences. It is not too difficult to see where to seek a solution to this problem. If we attribute a disposition to an object when the relevant test conditions do not, in fact, obtain, then we do not refer to an actual but to a counterfactual situation. For instance, if we say of an object x that it is soluble in water when in fact x is not placed in water, then we express that x would dissolve if x were placed in water. Here, we are referring to a counterfactual situation. We state what would happen in a non-actual situation. Thus, the conditional involved is clearly a

Did We Throw Out the Baby With the Bathwater?  59

counterfactual conditional and needs to be analyzed as such—a fact Hempel 1950 was already well aware of:81 [C]ounterfactual conditional[s] […] would provide an answer to the problem of defining disposition terms if it were not for the fact that no entirely satisfactory account of the exact meaning of counterfactual conditionals seems to be available at present. Thus, [this] way out of the difficulty has the status of a program rather than that of a solution.

However, the limited recourses provided by classical logic are insufficient to account for the semantics of counterfactual conditionals. That is why Hempel expressed disappointment that no satisfactory semantics for counterfactual conditionals was available at the time he published his essay back in 1950. However, this situation has greatly improved since. Counterfactual conditionals are of crucial importance to many philosophical issues. Therefore, analytic philosophy has focused on the study of their semantics in the last decades. Many promising attempts have been made to give a formal semantics for counterfactuals correctly reflecting their peculiar properties. Among these, the theory put forth in David Lewis’ seminal monograph Counterfactuals in 1973 stands out as the major breakthrough. This most influential proposal will be reviewed in Chapter 8. To formulate a more adequate criterion of significance, we can build on this theory as well. At least to my knowledge, this has not been done before. Unfortunately, though, a critical discussion of Lewis’ theory in Chapter 9 will reveal that its philosophical commitments are at odds with a verificationist approach. Thus, it will be necessary to seek a verifiability-friendly alternative to Lewis’ semantics for counterfactuals. The so-called Ramsey test will prove to be a suitable starting point to accomplish this.

3.6 Did We Throw Out the Baby With the Bathwater? The discussion in this chapter made clear where we have to seek solutions to most of the problems verificationism faces, namely, the problem concerning sentences about the remote past (CA1) and distant future (CA2), the problem concerning universal (CA5) and existential sentences (CA6), sentences with mixed quantifiers (CA7) and particular sentences (CA8), the problem concerning negations (CA10), the problem concerning dispositional terms (CA13, 14), and the problem posed by the Duhem-Quine thesis (CA16).

 81 See Hempel 1950, Sec. 4.

60  Toward a Solution to the Problems

Lewis’ semantics 1973 Improved theories of justification Belief revision since 1985 Heyday of verificationism 1930–1963

Unified theories 2005

t

Fig. 3.1: Chronology of Verificationism / Novel Theories

In order to overcome these problems we need (i) a non-reductionist theory of justification, (ii) a theory of belief revision, (iii) a theory combining these two approaches, and (iv) a formal semantics for counterfactual conditionals. These are the main ingredients of the theory of minimal verificationism I am about to develop in the rest of this essay (see Figure 3.1). Great efforts have been undertaken to understand the notions of epistemic justification, belief revision, their interconnections and counterfactual conditionals. Many promising theories have been proposed in all of these subject areas. Unfortunately, these theories share the fate of most philosophical theories, namely, they cannot claim to provide final answers to the problems being treated. The ultimate solutions need to still be found. Insofar as the ingredients of our theory of minimal verificationism are imperfect, it cannot provide ultimate answers to the problems of verificationism, either. Nevertheless, considerable progress has been made in these subject areas since the time of the logical empiricists. New and improved theories have become available in all of these fields in the last decades. We can benefit from these insights when formulating a criterion of significance. By building a criterion of significance on these novel theories, we can hope to improve verificationism considerably. In view of these potential improvements, the abandonment of verificationism appears premature. Half a century following its decline, it might be about time to revisit this unfashionable view.

Summary  61

3.7 Summary –

– –

– – – –

The objections that have been raised against verificationism lead to a diverse list of conditions that any adequate principle of verification must fulfill. The quest for an adequate criterion of significance can benefit from later developments in formal epistemology, philosophy of science, and logic. The requirement of conclusive verifiability needs to be replaced by a requirement of justifiability. The relevant notion of justification will be fallibilist, holistic, and will not supervene on deductive relationships. Due to its reference to the epistemic state of the subject, an adequate criterion of significance will have to build on a theory of belief revision. A formal semantics for counterfactual conditionals is needed to analyze dispositional terms. We can improve verificationism considerably by building on novel theories of justification, belief revision, and counterfactual conditional. Although you should not expect to find ultimate solutions to the problems of verificationism in this book, it seems premature to abandon verificationism altogether.

4 Minimal Verificationism 4.1 The Essence of Verificationism Now that we have understood that modern theories of justification and belief revision along with a formal semantics for counterfactuals can help overcome the problems of verificationism, the obvious task is to elaborate a precise formulation of a principle of verification that will allow us to apply these novel theories while holding on to the core idea of verificationism. It is not as clear as it might seem at first glance what this “core idea” actually is. The discussion of some historic versions of verificationism in Chapter 1 has already shown that different philosophers advocated different criteria, and that some authors supported different formulations at different times.82 When we look at some of the more informal characterizations that were proposed, the diversity grows even larger. Some logical empiricists even used different formulations to characterize verificationism within the same breath. More often than not, these characterizations are only seemingly equivalent to each other: [F]or an elementary sentence S containing the word an answer must be given to the following question, which can be formulated in various ways: 1. What sentences is S deducible from, and what sentences are deducible from S? 2. Under what conditions is S supposed to be true, and under what conditions false? 3. How is S to be verified? 4. What is the meaning of S?83 If there is no way of telling when a proposition is true, then the proposition has no sense whatever; for the sense of a proposition is the method of is verification. In fact, whoever utters a proposition must know under what conditions he will call the proposition true or false; if he cannot tell this, then he also does not know what he has said. A statement which cannot be conclusively verified is not verifiable at all; it just lacks all sense […].84 Stating the meaning of a sentence amounts to stating the rules according to which the sentence is to be used, and this is the same as stating the way in which it can be verified (or falsified). The meaning of a proposition is the method of its verification.85

 82 Cf. Cordes 2011 for a review of Carnap’s changing criteria of significance. 83 See Carnap 1931/1959, p. 62. 84 See Waismann 1930/1977, p. 5. 85 See Schlick 1936, p. 341.

64  Minimal Verificationism Given the great diversity of formulations logical empiricists have used to characterize verificationism, it is difficult, if not impossible, to give a non-controversial answer to the question what the essence of verificationism actually is. Before I propose a criterion of significance in the next section spelling out what I take to be the core idea of verificationism, let me try to explain its rationale first. The following characterization by Hempel according to which a sentence is significant if, and only if, it can be known, proves to be a viable starting point: 86 [T]he testability criterion of meaning is not logically entailed by the principle of empiricism […]. According to the latter, a sentence expresses knowledge only if it is either analytic or corroborated by empirical evidence; the former goes further and identifies the domain of cognitively significant discourse with that of potential knowledge; i. e., it grants cognitive import only to sentences for which—unless they are either analytic or contradictory—a test by empirical evidence is conceivable. [italics GH]

If there is no chance—not even in principle—to determine whether a sentence is true or false, we are better off not wasting any cognitive resources on determining its truth value. That is why a sentence is only significant if there is at least some chance of knowing whether it is true or false. We are, however, well advised to slightly loosen this alleged criterion of significance. Knowledge implies holding a justified (true) belief. Thus, the possibility to know that p implies the possibility to justifiably believe that p, while the converse does not hold in general. As pointed out in Section 3.4, we ought to relativize the notion of significance on an epistemic state / subject. From the perspective of the epistemic subject, however, having a justified belief that p and knowing that p are indistinguishable. That is why significance should not only be granted to those sentences that can possibly be known, but to every sentence for which it is possible to justifiably believe it. If the latter is the case, then—judged from the perspective of the subject—there may be a chance of knowing at some point whether the sentence is true or false, which in turn is the conditio sine qua non that makes an investigation into the subject matter worthwhile. Thus, as a first formulation for a criterion of significance, we can say that a sentence p is significant for an epistemic subject S if, and only if, it is possible for S to have the justified belief that p. To analyze the involved modality “possible” correctly, we have to bear in mind that theories of justification typically relativize justification on an epistemic state. As pointed out in Section 3.4, we have to ensure they refer to the correct epistemic state when explicating the notion of significance. The question whether a sentence p is justified relative to  86 See Hempel 1950, Sec. 1.

Epistemic Accessibility as a Criterion of Significance  65

the current epistemic state of S is the question whether p has actually been justified. This question is irrelevant for a sentence’s significance. What matters is the question whether it is possible for S to justify p. This question now has to be rephrased as to whether p is justified relative to some epistemic state S could be in. In Section 3.4, I suggested that the relevant epistemic states S could be in are those that can be formed from its current state by a rational belief revision induced by some observations. Hence, as a second, somewhat more precise formulation for a criterion of significance, we can claim that a sentence is significant if, and only if, it is justified relative to some of those epistemically accessible states.

4.2 Epistemic Accessibility as a Criterion of Significance Next, let us specify this criterion of epistemic accessibility in a rigorous way while making sure to frame it in such a way to be able to adequately implement theories of justification, belief revision and counterfactuals within it. Some of the latter theories we are about to apply impose some very moderate constraints on the object language.87 Henceforth, we shall thus assume the following “usual” properties of the logic underlying the object language L: A sentence p is logically valid iff it is a consequence of the empty set. The consequence relation ⊢ satisfies: (1) If p is a truth-functional tautology then ⊢p. (2) Modus ponens. If ⊢p→q and ⊢p then ⊢q. (3) Not ⊢⊥, that is, ⊢ is consistent. (4) Deduction theorem. ⊢p→q iff p⊢q. (5) Compactness. If p is deducible from a set A, then p is deducible from a finite subset of A. Some proofs for theorems we

 87 The reason for alluding to an object language here is, of course, that the criterion of significance we are about to propose will be applicable to sentences. Alternatively, one could try to formulate a criterion that applies to some other entities, such as propositions, statements, beliefs, or even terms. However, sentences seem to suggest themselves as the objects of our criterion, not only because most verificationist principles take that form (cf. Attempts 1–8 in Chap. 1), but there is also very little contention about their precise nature. Furthermore, the theories of justification, belief revision, and counterfactuals that we will apply later are likewise all based on sentences. By formulating our criterion of significance for sentences, we can thus ensure a smooth and easy compatibility with these theories as well. Even Ayer seems to acknowledge that one may refer to sentences, although he himself prefers to formulate his principle of verification (primarily) for statements. Cf. Ayer 1936/1946, Preface to the second edition. Note also that we may use any given criterion of significance that is formulated for sentences to derive criteria that are applicable to other entities. Cf., e. g., Carnap 1936/1937, Sec. 17.

66  Minimal Verificationism will later draw on further require the language L to contain at least three logically independent sentences. Besides these ordinary properties, we shall assume that the object language L also contains a binary sentential connective ⟥→, called counterfactual conditional. A sentence p ⟥→ q will be read as: “If it were the case that p, then it would be the case that q”. Recall, our preliminary formulation for a principle of verification was this: A sentence is significant if, and only if, it is justified relative to some epistemically accessible state, where a state is called accessible if it can be formed from the current epistemic state by a rational belief revision induced by some observations. Let A be the current epistemic state of the subject S. The belief revision of A by a sentence p will then be denoted by A*p, while the iterated belief revision [(A*p1)*p2…]*pn will be denoted by A*. Furthermore, let Js(A) denote the set of all sentences that can be justified relative to the epistemic state A. Building on that terminology, we can now characterize epistemic accessibility as a criterion of significance by the following sequence of definitions: DEFINITION 4.1 (accessible state): An epistemic state A′ is epistemically accessible from a state A iff there is a finite set of observation sentences o1, o2, …, on such that A′= A*.

DEFINITION 4.2 (accessible sentence): Sentence p is epistemically accessible from a state A iff there is some accessible state A′ such that p ∈ Js(A′).

DEFINITION 4.3 (significant sentence): Sentence p is epistemically significant relative to an epistemic state A iff p or its negation are epistemically accessible from A. Combining Definitions 4.1–4.3, we obtain our criterion of significance as epistemic accessibility: DEFINITION 4.4 (criterion of significance):88 Sentence p is epistemically significant relative to an epistemic state A iff there is a finite set of observation sentences o1, o2, …, on such that Js(A*) ∩ {p, ¬p} ≠ ∅.  88 You might wonder whether Def. 4.4 could be “simplified” by replacing the sequence of belief revisions A* with a single revision on the corresponding conjunction A*(o1 ∧…∧ on). There is little doubt, however, that these two procedures do not yield the same results universally. For one reason, cf. Sec. 7.4 where we criticize the so-called superexpansion

Epistemic Accessibility as a Criterion of Significance  67

Note the similarity of this definition with the second attempt to formulate a criterion of significance in Chapter 1. Instead of requiring that there is a finite set of observation sentences that logically implies the sentence p, we now require a finite set of observation sentences that triggers a belief revision, resulting in an epistemic state relative to which the sentence p (or its negation) is justified. Note also the striking resemblance of the accessibility criterion with a characterization of verificationism by Ayer:89 The criterion which we use to test the genuineness of apparent statements of fact is the criterion of verifiability. We say that a sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express— that is, if he knows what observations would lead him, under certain conditions, to accept the proposition as being true, or reject it as being false. [italics GH]

Interestingly, this quote already reveals the dependency of the notion of significance on the epistemic subject / state, which we pointed out above.90 Definition 4.4 reduces the notion of significance to the notions of justification, belief revision and counterfactuals, which figure in the accessibility criterion by means of the operators Js, * and ⟥→, respectively. All of these notions are rather complex and need to be explicated themselves. It could thus be objected that little has been gained by reducing one unclear notion to a bunch of other unclear notions. Unlike the notion of significance, however, the notions of justification, belief revision and counterfactuals have been thoroughly investigated in recent years. Considerable progress has been made in understanding their semantics since the era of the logical empiricists. Many promising theories have been proposed to analyze these philosophically important notions, some of which will be reviewed in subsequent chapters. By building our principle of verification on these novel theories, we can hope to improve our understanding of the notion of significance as well. Definition 4.4 shows in a rigorous way how this implementation can be accomplished.91  and subexpansion postulates, both of which would be immediate consequences of such an identification. 89 See Ayer 1936/1946, Chap. 1. 90 Cf. also Spohn 2012, Sec. 17.2 for a similar principle in ranking theory. 91 The precise nature of epistemic states and the accessibility relation will not become clear until the operator * is fleshed out in subsequent chapters. Nevertheless, let me make a few general remarks in passing here. Intuitively, every epistemic state is certainly accessible from itself. Formally, we can ensure this by allowing for empty sets of observation sentences as inputs. Furthermore, the accessibility relation as characterized by Definition 4.1 is obviously

68  Minimal Verificationism The theory we are about to develop by fleshing out the accessibility criterion could be called minimal verificationism, as it involves a weakening of traditional verificationist positions while holding on to their guiding principle.

4.3 The Advantages of the New Criterion Certainly, it is of utmost interest to see whether the accessibility criterion does any better with respect to the problems of verificationism discussed in the first two chapters. At this point, however, we are not yet in a position to carry out such an evaluation unambiguously. The accessibility criterion was designed to incorporate other theories. The operators Js, * and ⟥→ referred to by the criterion are like blank spaces which need to be filled in by specific explications of the corresponding concepts. Thus, Definition 4.4 is more like a blueprint for the construction of a criterion of significance rather than the actual criterion itself. Since the complemented criterion can only be as good as its weakest part, we cannot assess the merits of the accessibility criterion before we have filled in its blanks. In subsequent chapters, we shall review some of the theories that may be used to flesh out the accessibility criterion. But even after complementing our principle of verification with theories of justification, belief revision and counterfactuals, we will still not be in a position to readily decide for any given sentence whether it is significant or not. It is the dependency of the notion of significance on an epistemic state that precludes us from doing so. This dependency must be accepted as an inevitable consequence of the Duhem-Quine thesis. The essentially subjective nature of significance is a fundamental obstacle for the epistemologist to classify any given sentence as significant or insignificant. It rather takes an epistemologist and an epistemic subject for that kind of  transitive. At least, if we confine ourselves to belief changes that are induced by new inputs, there is no reason why the accessibility relation should in general also be symmetrical. Thus, if we wish to add some flavor of modal logic to our way of talking we could speak of the epistemic states and the accessibility relation as jointly constituting a reflexive, transitive frame—a system colloquially known as S4. The philosophical rationale that one might give for such a modal system based on epistemic accessibility would certainly be similar to the one for intuitionist logic. Therefore, it would be worthwhile to explore the relation of the two systems. Suppose a sentence is significant relative to some future epistemic state, that is, relative to some accessible epistemic state. Due to transitivity, the sentence will then also be significant relative to the current epistemic state. The converse will, however, not hold if the accessibility relation is not symmetrical. Hence, the realm of significance shrinks monotonically over time. Presumably, this is not what Lao Tse had in mind when he said: “The more you know, the less you understand.”

The Advantages of the New Criterion  69

classification. Without specifying an epistemic state it will thus be even more difficult to provide general answers to the question whether the accessibility criterion successfully overcomes the problems of verificationism. Having said this, I nevertheless want to highlight some potential improvements the accessibility criterion brings. Let us begin with what I take to be the most serious problem of verificationism, namely, the problem concerning universal sentences and its related problems: (CA5) (CA6) (CA7)

Some universal sentence quantifying over an infinite domain has to be significant.92 Some existential sentence quantifying over an infinite domain has to be significant. Some sentence with mixed quantifiers quantifying over an infinite domain has to be significant.

 92 This formulation of (CA5) is actually elliptic now that we have understood that the concept of significance has to be relativized on an epistemic state. We should instead formulate it with reference to an epistemic state A as well. Since the variable A would then need to be within the scope of some quantifier, this specification gives rise to an ambiguity as we can either bind A with an existential or a universal quantifier. In the former case, the resultant condition is rather weak: (CA5′) There has to be a universal sentence p and an epistemic state A such that p is significant relative to A. In the latter case, we need to distinguish between two subcases because the involved universal and existential quantifiers do not commutate. The condition could either become as strong as: (CA5′′) For all epistemic states A there has to be a universal sentence p such that p is significant relative to A. Or the condition could be interpreted even stronger as: (CA5′′′) There has to be a universal sentence p such that for all epistemic states A the sentence p is significant relative to A. Since we cannot rule out the existence of some seriously deviant epistemic states relative to which virtually no sentence would be significant, we are well advised to reject the latter two interpretations as being too strong. Therefore, I suggest resolving the ambiguity of condition (CA5) by interpreting it according to (CA5′). The weakness of (CA5′) once again underlines the status of the conditions of adequacy as formulating only some necessary conditions that an adequate criterion of significance has to fulfill. Even jointly, the conditions of adequacy will do no more than filter out some inadequate criteria rather than uniquely characterize one criterion. In other words, the conditions of adequacy should not be seen as stating sufficient conditions for constructing an adequate criterion of significance. For this purpose it is in order to disambiguate (CA5) according to (CA5′). Cf. also the corresponding remark about condition (CA1) in Sec. 3.1. Some of the other conditions of adequacy give rise to similar ambiguities that should be resolved accordingly. I thank Rainer Hegselmann for drawing my attention to these ambiguities that were not resolved in an earlier draft of this essay.

70  Minimal Verificationism Recall, the problem with universal sentences quantifying over an infinite domain is that they are not verifiable conclusively as they are not logically implied by any finite set of observation sentences. By spelling out the operator Js in Definition 4.4 by some fallibilist theory of justification, we lower the relevant epistemic standard to something that can be met by universal and existential sentences and sentences with mixed quantifiers alike. At the same time, we hold on to the empiricist idea that knowledge of non-analytic sentences must derive from experience by relativizing the relevant notion of justification on an epistemic state that some observations have brought about. Essentially, the same problem arose with particular sentences. Thus, this problem can be resolved along the same lines: (CA8)

Some particular sentence has to be significant.

The problem in connection with negations emerged as an immediate consequence of the problem with universal and existential sentences: (CA10)

If a sentence is significant, then its negation has to be significant.

By resolving the latter problems, the problem with negations thus evaporates all on its own. Furthermore, by admitting significance to a sentence if the sentence itself or its negation is epistemically accessible, Definition 4.4 eliminates the problem with negations root and branch. The main reason for giving the accessibility criterion this kind of disjunctive character is not an avoidance of the problem with negations, as this problem should disappear automatically. It is rather the idea of “potential knowledge” that has guided us here. Not knowing the truth value of a sentence in the current epistemic state, there may be some hope of knowing the sentence’s truth value at some point if the sentence itself is epistemically accessible, but equally so if its negation is accessible. Duhem and Quine urged the holistic character of verification and falsification: (CA16)

A verificationist principle has to be compatible with the DuhemQuine thesis, that is, it has to be holistic.

Verification atomism fails because theories imply observable consequences only if we combine them with auxiliary hypotheses. It is most natural, if not inevitable, to interpret these auxiliary hypotheses as part of someone’s background knowledge, that is, as elements of the epistemic state of a subject. Our

The Advantages of the New Criterion  71

criterion of significance accounts for the holistic nature of verification by explicitly referring to the epistemic state A of the subject. The role of the epistemic subject needs to also be discussed with respect to another cluster of problems. The difficulties concerning sentences about the remote past and distant future, as well as the unwanted dependencies on contingent matters and mankind all resulted from some criteria’s reference to the epistemic subject and the factual limitations that come along with it: (CA1) (CA2) (CA3) (CA4)

Some sentence about the remote past has to be significant. Some sentence about the distant future has to be significant. The significance of sentences must not depend on highly contingent matters like the pace of technological progress. Some sentence that cannot be verified conclusively by any human being has to be significant.

At first glance, it might seem as though the accessibility criterion faces the same kind of problems because it also makes reference to the epistemic subject. It is crucial, however, to note that it is in fact not the epistemic subject, but only the epistemic state of the subject that figures in Definition 4.4. Unlike the epistemic subject itself, the epistemic state is an abstract entity. As such, it is not subjected to factual limitations as nasty as mortality. For instance, suppose that the verification of a sentence p requires making an observation o that can only be made in 200 years. Then p would be insignificant according to the verifiabilitywithin-lifetime criterion (cf. Attempt 1 in Chapter 1). In contrast to this, p could well be significant according to the accessibility criterion, because the observation sentence o can trigger a belief revision of the current epistemic state, just as any observation sentence could that describes an observation within the lifetime of the given subject. Furthermore, the lowering of the epistemic standard from conclusive verifiability to some form of fallible justification will certainly also help in overcoming this cluster of problems. Dispositional terms posed another intricate problem for verificationism. Their logical structure implicitly involves a conditional that must not be analyzed as a material implication. The attempt to introduce dispositional terms within classical logic by means of so-called reduction sentences led to the problem of pseudo analytic sentences: (CA13) (CA14)

Some sentence containing a dispositional term has to be significant. A verificationist principle has to be non-creative, that is, it must not lead to the creation of pseudo analytic sentences.

72  Minimal Verificationism As pointed out above, the conditionals involved in dispositional terms have to be analyzed as counterfactual conditionals. We acknowledge this by assuming an object language that provides for a binary sentential connective ⟥→ to represent such conditionals. Admittedly, on its own, the sheer introduction of a formal operator to represent counterfactuals in the object language is nothing but cheap talk—just like the introduction of the other operators. We will, however, go to great lengths to elaborate a formal semantics for the operator ⟥→ in subsequent chapters. It should be clear from the outset that we will have to transcend classical logic to achieve this. Fortunately, there will be no need for reduction sentences. Hence, we will be able to ensure that our principle of verification is non-creative, as desired. The theories we are about to review to flesh out Definition 4.4 typically assume so-called extensionality postulates ensuring that logically equivalent sentences are “treated the same way”. These postulates will in turn guarantee that if a sentence is significant, then all sentences that are logically equivalent to it will also be significant: (CA11)

If a sentence is significant, then any sentence that is logically equivalent to it has to be significant.

As you can see from the extensionality postulates, we will subsequently distinguish between sentences that are logically valid and those that are not. Hence, we will not comply with Quine’s strict rejection of the analytic / synthetic distinction. However, I have argued above that we only have to steer clear from an analytic / synthetic distinction that exceeds the logical / non-logical distinction. We should feel free to rely on the latter distinction, as it is not undermined by Quine’s critique in any way: (CA17)

A verificationist principle must not refer to an analytic / synthetic distinction over and above the logical / non-logical distinction.

Neither Definition 4.4 nor any of the theories we will implement within it refer to an analytic / synthetic distinction over and above the logical / non-logical distinction. Thus, the accessibility criterion will meet (CA17) as well. Note, furthermore, that there is no way to comply with Quine’s total rejection of the analytic / synthetic distinction while at the same time satisfying (CA11), as this condition of adequacy itself refers to the concept of logical equivalence. As pointed out at the beginning of this section, Definition 4.4 is more like a blueprint for the construction of a criterion of significance rather than the actual

The Advantages of the New Criterion  73

criterion itself. Before filling in its blanks and specifying an epistemic state, it is therefore impossible to determine whether a given sentence is significant or not. From a purely epistemological perspective it is thus also difficult to give a substantial answer to the question whether the accessibility criterion excludes any sentence from being significant: (CA12)

Some sentence has to be insignificant.

Compare this situation to a steam engine that we construct to lift heavy weights. While the actual engine is capable of serving this purpose, the blueprint for its construction cannot lift any weights. Similarly, the purpose of a criterion of significance is to expose certain sentences as insignificant. While the actual accessibility criterion may well be capable of serving this purpose, Definition 4.4 being only the blueprint for its construction, cannot expose any sentence as insignificant. Although we cannot demonstrate of any specific sentence that it is insignificant, let us try to understand how the actual accessibility criterion may be able to do so. Consider, for instance, some of the sentences we listed in the introductory section. A clear-cut example of a sentence that we would intuitively classify as insignificant is “Caesar is less identical than the prime number.” Now, in my current epistemic state, I do not believe this sentence to be true. Even less do I justifiably believe it to be so. Furthermore, it seems safe to claim that there are no possible observations that would make me believe this sentence to be true in the future, either. In other words, none of the epistemic states that are accessible for me will contain the sentence in question. Therefore, the sentence will not be justified relative to any of my epistemically accessible states (nor its negation). It is along these lines that the actual accessibility criterion will classify the sentence in question as insignificant relative to my epistemic state. By the same token, the criterion will also render insignificant any sentence that is lexically or syntactically not well-formed, that is, sentences like, e. g., “Caesar is babig” or “Caesar is and.” Consequently, the actual accessibility criterion can easily satisfy condition (CA12). Such sentences contrast with clear-cut examples of sentences that we would intuitively classify as significant like, e. g., “There is a book right in front of me.” Presumably, in your current epistemic state you believe this sentence to be true and you will do so justifiably according to any plausible fallibilistic theory of justification. Because the sentence in question is thus justified relative to some epistemic state that is accessible for you, the accessibility criterion will classify it as significant relative to your epistemic state.

74  Minimal Verificationism For a more controversial example, let us consider some sentence that philosophical skepticism has challenged, e. g., a sentence like “The external world exists.” Taken as a philosophical claim, we learned from the debate on skepticism that no observation (past or future) could ever demonstrate such a sentence to be true (or false). Hence, none of the epistemic states that are accessible for me will put me in an epistemically better position to judge the sentence than my current state. According to the accessibility criterion, this means that in this particular case, the question whether the sentence is significant or not boils down to the question whether or not the sentence is justified relative to the current epistemic state. Different explications of the concept of justification might answer the latter question differently, presumably reflecting different explicanda, that is, corresponding to divergent pre-theoretic standards of justification. The same applies to some of the other sentences listed in the introductory section, e.g., to the sentences “I am deceived by a Cartesian demon all the time.” and “The world sprang into being five minutes ago.” The status of such sentences will thus crucially depend on how we spell out Definition 4.4 by a specific theory of justification. Since it seems correct that the status of such sentences depends on nothing but the standard of justification we implement, this indeterminacy of Definition 4.4 should be seen as a point in favor of the accessibility criterion. To demonstrate that Definition 4.4 is not void, we actually do not even have to show that the actual accessibility criterion satisfies condition (CA12). Rather, it suffices to show something weaker, namely, that there is some combination of a justification operator Js, a revision operator * and an epistemic state A, such that some sentence is insignificant according to Definition 4.4. Once we have introduced all the relevant theories, we can demonstrate in a rigorous way that this is actually the case.93 The translatability criterion of significance was ad hoc because we could not see any reason why it should be virtuous for a sentence to be translatable into some artificial language that some logical empiricist construed at will:

 93 In anticipation of some terminology and theories we will introduce later, let the epistemic state be Cn(∅), let the justification operator be Jsmin and let the revision operator be the socalled JuDAS revision. Then it holds for arbitrary o1, …, on ∈ L: Js(A*) = Cn(∅). Thus, according to this criterion, a sentence would be significant if, and only if, it is either valid or contradictory. Surely, this criterion is far too restrictive and we should not flesh out the accessibility criterion this way. However, this criterion does the trick of demonstrating that the accessibility criterion is not void, that is, it may well exclude sentences from being significant.

O’Connor’s Trick  75

(CA15)

A verificationist principle must not be ad hoc.

Note, however, that the earlier principles of verification we discussed did not suffer from the same shortcoming. For the epistemic subjects we are it is quite understandable that it is a desirable property for a sentence to be verifiable— much more than being translatable into some artificial language. Similarly, it seems desirable for a sentence to be epistemically accessible, for if it is not, then—judged from the perspective of the epistemic subject—there cannot be any hope of determining the sentence’s truth value at some point. But in this case it is pointless to even investigate into the subject matter. Thus, epistemic accessibility is a minimum requirement for an inquiry to be worthwhile. Sentences that are epistemically accessible are thus in some sense more virtuous than sentences that are not. That is why the accessibility criterion is not ad hoc. Of the many problems of verificationism, we have now reviewed all but one with respect to the accessibility criterion. The problem with molecular sentences will be discussed in the next section and will result in another modification of Definition 4.4: (CA9)

No molecular sentence containing an insignificant component must be significant.

4.4 O’Connor’s Trick As we have just seen, the accessibility criterion avoids most of the problems verificationism faces, thus complying well with the conditions of adequacy put forth earlier. As it stands, the criterion does not ensure, however, that no molecular sentence containing an insignificant component will be significant, that is, it does not yet meet (CA9). To get around this difficulty as well, we can apply a technique that O’Connor 1949/1950 introduced to resolve the same problem for Ayer’s second criterion of empirical import (cf. Attempt 6 in Chapter 1). This method can actually be used to improve any purported criterion of significance in this regard. Suppose we wish to set up condition C as a criterion of significance. Instead of simply saying that a sentence p is significant if, and only if, p satisfies condition C, we should rather say something like this: p is significant if, and only if, p satisfies condition C with the proviso that if p is a molecular sentence, then all its components have to satisfy condition C as well. Admittedly, that is a sloppy way to put it, but it is straightforward how to turn this idea into a proper recursive definition for any given language L. Suppose, for instance, ¬,

76  Minimal Verificationism ∧ and ⟥→ are the only (primitive) sentential connectives in L. Given the original criterion C, we then first define a new property C¯ as follows: DEFINITION 4.5 (O’Connorization): Let p, q ∈ L be arbitrary. (i) If p is atomic then p has C¯ iff p satisfies C. (ii) ¬p has C¯ iff ¬p satisfies C and p satisfies C¯. (iii) p ∧ q has C¯ iff p ∧ q satisfies C and p, q both satisfy C¯. (iv) p ⟥→ q has C¯ iff p ⟥→ q satisfies C and p, q both satisfy C¯.

Subsequently, we can define significance in terms of the new criterion C¯: A sentence p is significant if, and only if, p satisfies condition C¯. This amended definition ensures that significance is admitted to a sentence only if it and all its components satisfy the original condition C. By “O’Connorizing” our accessibility criterion along these lines, we can thus avoid the problem with molecular sentences as well. Now that we learned once and for all how to comply with (CA9), I shall henceforth keep referring to the original Definition 4.4 in order to simplify matters.

4.5 The Choice of an Empirical Basis Definition 4.4 reflects the empiricist conviction that all knowledge of synthetic sentences must derive from experience by accounting only for observation sentences as possible causes of belief revisions. It is difficult to see how to prevent insignificant sentences from being classified as significant by the accessibility criterion, if we allowed any sentence whatsoever as input sentences, including insignificant sentences themselves. Hence, it is crucial for our principle of verification to restrict the permissible input sentences to observation sentences. In Chapter 1, I gave the following characterization of observation sentences according to Hempel: DEFINITION 4.6 (observation sentence): A sentence is an observation sentence iff it asserts of one or more specifically named macroscopic objects that they have, or that they lack, some specified observable characteristic. An “observable characteristic” refers here to a property or a relation of physical objects whose presence or absence can be ascertained through direct observation. The notion of an observation sentence is an explicatum of the vague idea of a sentence being verifiable in principle by direct observation. These sentences

The Choice of an Empirical Basis  77

are often referred to as forming the empirical basis (of knowledge). In the Vienna Circle’s so-called debate on protocol sentences (Protokollsatzdebatte), various empiricists offered several alternative proposals for an empirical basis. Let me exemplify some of these proposals without delving into the details of this debate: Observation sentence (Hempel):94 A red die is lying on the table. Confirmation (Schlick):95 Here now red borders on brown. Protocol sentence (Carnap style):96 Squarish red body next to longish brown body. Protocol sentence (Neurath style):97 Otto’s protocol at 3:17 o’clock: [At 3:16 o’clock Otto said to himself: (at 3:15 o’clock there was a red die lying on the table perceived by Otto)]. Empirical bases can chiefly be classified as phenomenalist and physicalist. The former refer to perceptions and experiences of the observing subject, e. g., “(impression of) red”. The latter refer to physical objects and their properties, e. g., “red die”. Phenomenalist bases can make a plausible claim to be infallible, thus offering the possibility to establish a rock-solid foundation of knowledge. Due to the privileged epistemic access of only one subject, phenomenalist bases are inappropriate as a foundation for the sciences, however, as these are crucially based on the possibility of an intersubjective verification. Furthermore, phenomenalists have failed to show how sentences about physical objects can eventually be justified in terms of a phenomenalist basis. Physicalist bases, like observation sentences, on the other hand, correspond much more to the actual practice of both scientists and ordinary people alike, as they can be verified intersubjectively. Also, there are obviously no obstacles in principle to justify sentences about physical objects in terms of a physicalist basis. It is out of question, however, that a physicalist basis is a fallible basis. Moreover, it is also clear that all empirical knowledge will become  94 Cf. Hempel 1950, p. 42f. 95 Cf. Schlick 1934, p. 96f. The German term used by Schlick is Konstatierung. 96 Cf. Carnap 1931, p. 437f. 97 Cf. Neurath 1932/1933, p. 207.

78  Minimal Verificationism fallible if we found it on a fallible basis. This inevitable consequence was considered the greatest disadvantage of physicalist bases by most of the logical empiricists.98 In connection with the problem of universal sentences, I argued in Section 3.3 that empirical beliefs can only be justified in some fallibilist sense anyway. Nowadays, it is generally accepted among epistemologists that empirical beliefs are—more or less—universally fallible. Thus, what seemed to be the greatest disadvantage of a physicalist basis is something we have to accept on independent grounds at any rate. In our discussion on the translatability criterion we learned earlier that Carnap considered the construction of an appropriate empiricist language a matter of choice:99 [T]he rules of L are not given, and the problem is how to choose them. We may construct L in whatever way we wish. There is no question of right or wrong, but only a practical question of convenience or inconvenience of a system form, i. e. of its suitability for certain purposes. [italics GH]

For Carnap this decision extends to empirical bases. He explicitly regards the construction of an empirical basis a matter of choice which should be guided by pragmatic considerations. There is no choice that is right or wrong, but only bases that are more or less convenient:100 [I]t seems to be preferable to choose the primitive predicates from […] the observable thing-predicates. These are the only intersubjectively observable predicates. In this case, therefore, the same choice can be accepted by the different members of the language community. […] The choice of primitive predicates is meant here as the choice of a basis for possible confirmation. [italics GH]

For the reasons outlined above, I opt for a physicalist basis. But apart from this, I do not have to make an original contribution to the debate on protocol sentences. Thus, I shall not take a stand on which specific choice of a basis is best. As far as I can see, the criterion of epistemic accessibility is compatible with different choices. I will keep using the term “observation sentence” in a roughly Hempelian sense, however, as I consider this a reasonable choice once we have dismissed infallibilism and with it the need to choose an overly cautious basis.  98 Cf., e. g., Schlick 1934, p. 82f. 99 See Carnap 1936/1937, p. 4. 100 See Carnap 1936/1937, p. 12. Carnap 1932/1933 already argued that Neurath’s conception of a protocol sentence and his own do not contradict each other.

The Choice of an Empirical Basis  79

You should feel free, however, to replace this term in the following with your preferred choice of an empirical basis.101 Note, observation sentences being fallible should not enjoy a privileged epistemic status over and above being the only permissible input sentences. In particular, we have to ensure that they can also be rejected by the epistemic subject.102 The standard theory of belief revision that we shall review in Chapter 6 to spell out the operator * will not allow for this. This is one of the reasons why we will construct an alternative theory of belief revision in Chapter 7.103

 101 Here, a remark on what is commonly referred to as “knowledge by testimony” seems to be in order. We know many things not because we have made the relevant observations ourselves, but because someone else has made them and reported them to us. In such cases, my belief could be justified schematically as follows: P1 “If S asserts that p, then it is reasonable to believe that p.”, P2 “S asserts that p.”, therefore C “It is reasonable to believe that p”. Although it is out of question that large portions of our knowledge are in fact derived in this way, we are well advised not to allow for this kind of indirect justification within our principle of verification. To understand why, let us distinguish two cases: (i) S believes that p because he made observations o1, …, on that justify p, (ii) S believes that p for some empiricistically inacceptable reason (for the sake of simplicity, we are ignoring a third case where S believes p by testimony himself). In the first case, I could, in principle, have made the observations o1, …, on myself. Since the accessibility criterion does not only account for actual observations but for all observations that are possible in principle, the first case would not extend the realm of significance. In other words, we could reconstruct the justification of S within our own epistemic system. Thus, the first case is already included in our principle of verification. In the second case, we should not allow for an indirect justification in our principle of verification because some insignificant sentences would otherwise be classified as significant. In sum, in one case we do not have to, while in the other we should not allow for knowledge by testimony in our criterion of significance. There are at least two ways we could accomplish this. We could either block justifications by testimony by excluding sentences of the type P1 from epistemic states or we could preclude sentences of the type P2 from being permissible input sentences. For several reasons, I suggest following the second approach. If we settle for observation sentences as the empirical basis, this becomes a free ride if we notice that linguistic activities such as “asserting that p” are no observable characteristics, that is, no relations of physical objects (while moving the lips in certain ways clearly is). 102 From the standpoint of a Quineian sort of universal holism outlined in Sec. 2.3, it is quite clear that no kind of physical basis can enjoy a privileged epistemic status. Otherwise, it was Neurath 1932/1933, p. 209ff who first pressed this point. 103 Cf. the discussion of the so-called success postulates in Sec. 6.4.1 and the proposed improvements in Sec. 7.2.1+7.2.2.

80  Minimal Verificationism

4.6 What Does this Criterion Demarcate? Just like any other criterion of significance, our criterion of epistemic accessibility classifies sentences into so-called “significant” and “insignificant” ones. We have undertaken considerable effort to ensure that every sentence will end up in the right category. In other words, we have worked hard to find a criterion that has the correct extension. So far, little has been said on what the criterion of epistemic accessibility actually demarcates. What is epistemic accessibility a criterion of? Finding a criterion that has the right extension might be the technically more challenging task, but these efforts are pointless if we do not know what it is that we want to demarcate by this criterion. Therefore, it is vital to discuss what we mean when we call a sentence “significant” before developing our criterion further. Once again, let us begin the discussion by reviewing some historic proposals. In the early stage of logical empiricism, its proponents identified the meaning of a sentence with the method of its verification: (4.1)

The meaning of a synthetic sentence is the method of its verification.

Consequently, they also subscribed to the claim that a sentence has meaning only if there is some method to verify it: (4.2)

A sentence is meaningful if, and only if, it is verifiable or analytic.

Often, both of these assertions can be found in texts from that period. A good example of this is the quote from Waismann 1930/1977 given in Section 4.1, another one is that by Carnap 1936/1937:104 Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible.

Later on, logical empiricists backed out from the claim (4.1) while holding on to (4.2) as can, for instance, be seen in the following quote by Hempel 1950, who elaborates on the translatability criterion discussed in Chapter 1:

 104 See Carnap 1936/1937, Sec. 1. Cf. Schlick 1936, p. 341+344 for yet another example of a text that states both (4.1) and (4.2).

What Does this Criterion Demarcate?  81

[T]he criterion […] qualifies a sentence as cognitively meaningful if its non-logical constituents refer […] to observables. But it does not make any pronouncement on what “the meaning” of a cognitively significant sentence is […].105

Just like the logical empiricists, Popper considered it a task of eminent importance to state a criterion that will allow distinguishing between empirical sciences and metaphysics:106 [I] take it to be the first task of the logic of knowledge to put forward a concept of empirical science, in order to make linguistic usage, now somewhat uncertain, as definite as possible, and in order to draw a clear line of demarcation between science and metaphysical ideas […].

He referred to that as the problem of demarcation (Abgrenzungsproblem):107 The problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as “metaphysical” systems on the other, I call the problem of demarcation.

For Popper it was the possibility to falsify a sentence rather than its verifiability that served that purpose: (4.3)

A sentence is empirical scientific if, and only if, it is falsifiable.

Although Popper takes falsifiability as a criterion that demarcates science from metaphysics, he did not claim that this demarcation coincides with that between sense and nonsense. In sharp contrast to the logical empiricists, he considered the latter identification an arbitrary linguistic stipulation: 108 Note that I suggest falsifiability as a criterion of demarcation, but not of meaning. Note, moreover, that I have already […] sharply criticized the use of the idea of meaning as a criterion of demarcation […]. Falsifiability separates two kinds of perfectly meaningful statements: the falsifiable and the non-falsifiable. It draws a line inside meaningful language, not around it.

Thus, Popper’s conception of a criterion of demarcation is in some sense weaker than the claims made by the logical empiricists. Let us clarify the precise sense

 105 See Hempel 1950, Sec. 5. 106 See Popper 1935/1959, Sec. 4. 107 See Popper 1935/1959, Sec. 4. Cf. also Popper 1963, p. 185. 108 See Popper 1935/1959, Sec. 6. Cf. also ibid. Sec. 4 and Popper 1963, p. 183–187.

82  Minimal Verificationism in which Popper’s proposal is weaker by looking at the following three sentences: (4.4) (4.5) (4.6)

A sentence is empirical scientific if, and only if, it is significant. If a sentence is empirical scientific or analytic, then it is meaningful. If a sentence is neither empirical scientific nor analytic, then it is not meaningful.

If we take “significant” here as a generic term that could either mean “verifiable” or “falsifiable”, then Popper and the logical empiricists will agree on (4.4) and (4.5), while only the empiricists will endorse (4.6). It is in this sense that Popper’s conception of a criterion of demarcation is weaker than the empiricist criterion of meaningfulness. Take, for instance, the following sentence which is presumably neither verifiable nor falsifiable nor analytic: (4.7)

I am deceived by a Cartesian demon all the time.

Logical empiricists and Popper ban sentences like this from science, but only the former stigmatize such sentences as meaningless. Note, however, that even without stigmatizing sentences as meaningless, a Popperian criterion of demarcation is not as weak as it might seem at first glance. Combined with the empiricist conviction that all knowledge of synthetic sentences must derive from experience, it implies that sentences like (4.7) cannot be known to be true or false. Thus, if a sentence does not meet a Popperian criterion of demarcation and is not analytic, either, it can still be deemed as raising an unanswerable question, even if we do not consider it meaningless. At least at a later stage of logical empiricism, its proponents seem to have agreed that an avoidance of such unanswerable questions is the principal reason for introducing a criterion of significance. Some unambiguous evidence for that can be found in Feigl 1963:109 It is today generally agreed among logical empiricists that the criterion of factual meaningfulness is to be construed as a norm proposed for the purpose of avoiding unanswerable questions. [The] requirement of confirmability in principle eliminates pseudoproblems, i.e., problems which by their very construction can be recognized as absolutely insoluble.

 109 See Feigl 1963, p. 236f.

What Does this Criterion Demarcate?  83

Popper’s example of a criterion of demarcation shows that it is perfectly possible to accomplish this goal without the need to construe it as a criterion of meaning. It is a matter of particular concern for me to point out that I propose epistemic accessibility as a criterion of demarcation in a roughly Popperian sense, thus committing myself to only the weakest of the aforementioned claims. Although one might try to install epistemic accessibility as a criterion of meaning along the same lines the logical empiricists did with their criteria of verifiability, I have no intention to engage in such endeavors. I do not see any argument that could back the empiricist claim (4.6) in a way that does not beg the question. That is to say, I agree with Popper that it is nothing but an arbitrary verbal stipulation to define “meaningless” as “neither empirical scientific nor analytic”.110 Furthermore, it is the fact that a criterion of demarcation has mostly been put forth in the disguise of a criterion of meaning that must be held responsible for a great deal of the polemics that accompanied the debate on verificationism all too often. Namely, it is one thing to point out to an opponent that some of his claims are not empirical scientific and raise unanswerable questions, while it is quite another to accuse him of talking nonsense, or even calling him an “unmusical musician”. It is one thing to consider an attempt to determine the truth value of, say, sentence (4.7), a waste of time and energy, while it is quite another thing to claim that this sentence is just as meaningless as, say, “Caesar is and”. Although I am siding with Popper here, we need to point out some differences between his proposal and mine. First of all, there is the obvious difference that Popper takes falsifiability to be the criterion of demarcation whereby I am proposing epistemic accessibility as such a criterion. This difference does not have to be discussed here, as we have dealt with it at some length already, and I hope to have made my point. What is more interesting here is a minor divergence from Popper concerning the question what the criterion of significance is a criterion of. This difference concerns the status of analytically (logically) true sentences. Popper’s and my criterion seem to put these sentences on opposite sides when drawing the line of demarcation. Since logically true sentences are not falsifiable, they end up on the side of metaphysics according to Popper’s proposal. In contrast to this, the criterion of epistemic accessibility puts logically true sentences on the side of science. This difference is trivial, however, and

 110 Cf. Popper 1935/1959, Sec. 4.

84  Minimal Verificationism should not be misunderstood as a criticism of Popper’s view. Both criteria could easily be supplemented by further differentiations telling science, metaphysics, and logic apart, thus making it quite clear that all of them have a different status. In the case of our proposal, we can actually introduce an even more finegrained differentiation along the lines of the original criterion of epistemic accessibility. For a given sentence p, let us look at all epistemic states A that are accessible from the current state according to Definition 4.1. Relative to some of those states p will be justified, while relative to some others its negation may be justified. Table 4.1 shows the different combinations that could occur. Note that certain combinations are impossible because we will introduce it later as a rationality constraint on epistemic states that they have to be consistent. The shaded areas correspond to those sentences that are significant according to the criterion of epistemic accessibility. Table 4.1 shows that these sentences include not only the verifiable, falsifiable, and decidable sentences, which could properly be addressed as the empirical scientific ones, but also the analytically true and false sentences. For this reason, I prefer to regard the criterion of epistemic accessibility as a criterion of inquirability rather than of empirical science: (4.8)

A sentence is inquirable if, and only if, it is epistemically accessible.

Unlike Popper’s criterion, epistemic accessibility singles out all sentences whose truth value could possibly be known while excluding all sentences that raise unanswerable questions. Combining (4.8) with Definition 4.4, we obtain our general characterization of minimal verificationism: DEFINITION 4.7 (criterion of inquirability): A sentence p is inquirable relative to an epistemic state A iff there is a finite set of observation sentences o1, o2, …, on such that Js(A*) ∩ {p, ¬p} ≠ ∅.

This definition characterizes the entire realm of possible inquiry. A more finegrained classification could be introduced along the lines suggested by Table 4.1, if desired. Definition 4.7 puts minimal verificationism into a long-standing philosophical tradition that has attempted to determine the limits of knowledge—more accurately, the limits of possible knowledge. Rationalists and empiricists discussed this topic in the 17th and 18th century, while Kant made the most resolute

What Is Minimal about Minimal Verificationism?  85

attempt to determine the limits of knowledge in his Critique of Pure Reason.111 That is why Popper sometimes calls the problem to formulate a criterion of demarcation the “Kantian problem”. ¬p ∈ Js(A) p ∈ Js(A) For all A For some A For no A

For all A

For some A

For no A

×

×

Analytically True

Decidable

Verifiable

Falsifiable

Insignificant

×

Analytically False

Tab. 4.1: Fine-grained Differentiation

4.7 What Is Minimal about Minimal Verificationism? The term “minimal verificationism” indicates that my proposal is in some sense minimal and in some sense verificationist. Both of these aspects might need further clarification. In this section, I will elaborate on the sense in which my proposal is minimal and turn to the question whether it is at all a verificationist one in the next section. Now, in which sense is minimal verificationism minimal? The principle of epistemic accessibility involves a weakening of traditional verificationist principles in various respects. Thus, the question should rather be in which senses is minimal verificationism minimal? A first sense in which minimal verificationism is minimal concerns the stringency of the justificatory relationship, that is, the stringency of the relation that must hold between any significant sentence and a set of observation sentences. The verificationist principles we discussed in Chapter 1 typically restrict the justificatory relationship to logical entailment. It is crucial to our position, however, that we relax this requirement by allowing for fallible forms of justification as well. In fact, we do not even require that these need to supervene on deductive relationships as some other traditional principles of verification did.

 111 Cf. Kant 1781/1998.

86  Minimal Verificationism

Justificatory relationship

Objective vs. subjective

Verifiable vs. falsifiable

Demarcation

Traditional theories

Logical entailment

Objective

Verifiable / falsifiable

Meaning (-fulness)

Minimal verificationism

Also fallible justification

Subjective

Verifiable or falsifiable

Inquirability

Strong

Weak

Tab. 4.2: Dimensions of Minimality

A second sense in which minimal verificationism is minimal concerns the question whether significance is objective or subjective. Traditional verificationist principles take significance to be objective, thus construing the notion “significance” as a one-place predicate. In contrast to this, we accepted it as a consequence of the holistic nature of verification that significance is essentially subjective. A sentence is significant or insignificant relative to an epistemic state only. Objectivity can only be regained by making this dependency explicit, thus construing the notion “significance” as a two-place predicate. This relativization amounts to another dimension in which minimal verificationism weakens traditional verificationist positions. A third sense in which minimal verificationism is minimal concerns the question whether a significant sentence needs to be verifiable or falsifiable. Most principles we discussed in Chapter 1 require of a significant sentence to be verifiable while it is the possibility to falsify a sentence that is constitutive for a sentence’s significance according to falsificationism. In Chapter 1, we also encountered one criterion that is weaker than either of these requirements, as it admits significance to every sentence that is verifiable or falsifiable. By requiring of a significant sentence that it or its negation is epistemically accessible we gave our criterion of significance this kind of disjunctive character as well. Thus, in this regard, minimal verificationism is as weak as possible, too. Finally, a fourth sense in which minimal verificationism is minimal concerns the question we just discussed in the previous section, namely, what the criterion of epistemic accessibility demarcates. While some of the earlier verificationist principles identified the meaning of a sentence with the method of its verification, most of the principles proposed by logical empiricists only identify

Is Minimal Verificationism a Form of Verificationism at All?  87

meaningfulness with verifiability. Although the latter identification is slightly weaker than the former, we still found it too strong to be eligible. I wanted to commit myself only to the much weaker claim that verifiability—or rather epistemic accessibility—demarcates the realm of possible inquiry. Hence, minimal verificationism is not just minimal in one sense, but in at least four different ones (see Table 4.2).

4.8 Is Minimal Verificationism a Form of Verificationism at All? Although it might be granted that verification in the sense of a logical entailment by observation sentences is too strong of a requirement for significance and should indeed be replaced by some fallibilist form of justification, it could be objected that this amounts to abandoning verificationism rather than weakening it. Thus, it could be criticized that the term “minimal verificationism” is a misnomer as the term “verification” simply means conclusive establishment of truth. Once we abandon this conclusiveness requirement, it is misleading to stick to the term “verificationism” at all. In other words, it could be objected that minimal verificationism is too minimal to still deserve the name “verificationism”. Ordinary language, however, stands against that kind of criticism. Before the logical empiricists started publishing in English using the term “verification”, they published in German, thus originally using the German term “Verifikation”. Therefore, it is of some interest to see how this term was used in the German language before the logical empiricists picked it up. In German literature, the term can be found as early as in Zedler 1746:112 Verificiren, Lat. […] auch verificare, heißt, etwas beweisen, bekräfftigen, bewähren, erweislich darthun, bestätigen, gut sprechen, und vor Recht halten. Daher kommt Verification, Lat. Verificatio […] ein Beweisthun, die Beweisung, Darthuung, Bekräfftigung, Bewährung […].

Still before the ordinary usage of the term “Verifikation” could have possibly been influenced by the way the logical empiricists coined it in the 1930s, the 1923 edition of the German encyclopedia Brockhaus defined it as “Beglaubigung, Erweis der Richtigkeit”.113 With the possible exception of the terms “Beweisthun” and “Beweisung”, none of the terms given as synonyms for “Verifika 112 Cf. Blume 2001. 113 Cf. Brockhaus 1923.

88  Minimal Verificationism tion” in either of these quotes suggests a conclusive establishment of truth. Thus, at least until the logical empiricists turned up the German term, “Verifikation” was used for more than one and a half centuries in a way that is perfectly compatible with our use of it in “minimal verificationism”. Moreover, not even the logical empiricists themselves always identified verification with a conclusive establishment of truth. This can, for instance, be seen in the following quotes by Carnap and Ayer, respectively: If by verification is meant a definitive and final establishment of truth, then no (synthetic) sentence is ever verifiable […].[italics GH]114 […] I adopt what may be called a modified verification principle. For I require of an empirical hypothesis, not indeed that it should be conclusively verifiable […].115

At any rate, as long as there is an agreement on the merits of the proposed criterion of significance, the question whether the name “minimal verificationism” is well chosen is a trivial one. The accessibility criterion weakens traditional principles of verification in various respects while holding on to their core idea. I find the term “minimal verificationism” expressing both of these aspects well, but if you prefer some other term like, for instance, epistemic accessibilism, I am fine with that as well—or how about accessism for its catchy resemblance to “exorcism”?

4.9 Setting the Stage First, we have understood that modern theories of justification and belief revision, along with a formal semantics for counterfactuals, can somehow help overcome the problems of verificationism. Now we have formulated a criterion of significance that shows how exactly these novel theories ought to be implemented in a verificationist framework. Next we should spell out the operators Js, * and ⟥→ that are involved in Definition 4.7 by specific theories of justification, belief revision, and counterfactuals, respectively. Fortunately, all three of these concepts have been studied intensively in the last decades—quite unlike the concept of significance itself. In the remainder of this essay, we shall review

 114 See Carnap 1936/1937, Sec. 1. 115 See Ayer 1936/1946, Preface (to first edition). In Chap. 1, Ayer also distinguishes between a strong and a weak sense of the term “verifiable” where only the strong sense corresponds to a conclusive establishment of truth.

Summary  89

some of the theories that have been proposed to explicate these concepts. However, it would go far beyond the scope of the present inquiry to provide a comprehensive overview of these rather complex debates. The best we can do is to exemplify some of the proposals that have been made. For this it would certainly make sense to select “the best” one from each of the three different types of theories, if it were not for the fact that it is highly controversial which one this should be. Thus, what we will actually do is select theories from the epistemological market that (i) have some credibility, (ii) are suitable for an implementation in a verificationist framework, and (iii) suit each other. These criteria will reduce the number of possible theories considerably. In the rest of this essay, I will thus present one plausible combination of theories of justification, belief revision, and counterfactuals to spell out the accessibility criterion. May other epistemologist come and propose better theories or better combinations thereof. By formulating the accessibility criterion in the modular way as we did, we are presenting a stage on which various plays can be put on.

4.10 Summary –

–

–

–

– – – –

The bottom line of the many different verificationist principles that have been proposed seems to be that a sentence is insignificant if there is no possibility whatsoever to determine whether the sentence is true or not. This idea is spelled out by the accessibility criterion according to which a sentence is significant if, and only if, the sentence or its negation is justified relative to some epistemically accessible state, where a state is called accessible if it can be formed from the current epistemic state by a rational belief revision induced by some observations. This form of minimal verificationism leads the way to a solution of the problems discussed, thus complying well with the conditions of adequacy for the construction of a principle of verification. Once we have dismissed infallibilism, it seems preferable to opt for a physicalist basis like, e. g., Hempel’s observation sentences. These sentences must not enjoy a privileged epistemic status. Epistemic accessibility should best be seen as a criterion that demarcates the realm of possible inquiry. Minimal verificationism is minimal in several respects. Our technical use of the term “verificationism” is in line with ordinary language. The accessibility criterion shows in a rigorous way how modern theories of justification, belief revision, and counterfactuals can be employed in a

90  Minimal Verificationism principle of verification. Different combinations of such theories might be proposed to flesh out minimal verificationism.

5 Fallibilist Theories of Justification Logical empiricism in its early stage was fundamentally misguided when it regarded some form of conclusive verifiability / falsifiability as a criterion of significance. If one makes the mistake of narrowing the notion of justification down to logical entailment by a finite set of observation sentences, then the problem with universal sentences and its related problems become inevitable. One of the most important lessons to be learned from the history of verificationism is that the notion of conclusive verifiability must be replaced by some more inclusive notion of justification. In the previous chapter, I suggested epistemic accessibility as a criterion of significance. This criterion shows that and how such a notion of justification can be incorporated in a principle of verification. However, the notion of justification itself being rather complex, it urgently needs further explication. Fortunately, the analysis of justification has been a focus of analytic philosophy.

5.1 Various Types of Theories of Justification Many theories of justification have been proposed in the last 40 years or so. We can—and should—try to profit from these insights by building our principle of verification on one of those existing theories. Not all theories of justification are, of course, equally suitable for our purposes. In this section, I will provide an overview of the different theories that have been proposed by various authors. This will allow us to understand which characteristics to look for in a theory of justification that we aim to implement in a verificationist framework. The semiformal theory proposed by Keith Lehrer shows all of these characteristics and is thus well suited for our purposes. This theory will be presented and formally reconstructed in Sections 5.2 and 5.3. However reasonable the choice of Lehrer’s theory may be, it can be challenged just like any other choice of a specific theory could. Therefore, we are well advised not to limit ourselves to a single theory of justification. To attain this flexibility on a formal level, we will carry on by introducing a so-called justification operator that will be characterized axiomatically as weak as possible. This will ensure that our principle of verification is compatible with a vast range of theories of justification instead of being relativized to a specific one. Let us first gain a better understanding of the different types of theories of justification that have been proposed before taking a closer look at a specific one. Theories of justification can be classified into different types, some of which we have already encountered in Section 3.3.

92  Fallibilist Theories of Justification Infallibilism vs. Fallibilism: Theories of justification can chiefly be classified into infallibilist and fallibilist ones. Infallibilist theories establish an epistemic standard according to which a belief is justified only if every possibility of error has been precluded. In other words, if a belief is justified then it is necessary that the belief is true. Fallibilist theories, on the other hand, establish a weaker standard according to which a belief may well be justified, even if not every possibility of error has been precluded. Despite being justified, a belief can thus be false. The philosophical tradition is marked by the hegemony of infallibilist theories, the epistemic ideal of rationalism being a prominent case in point. Although fallibilist theories of justification were not seriously considered until the 20th century, there is general agreement among contemporary epistemologists that infallibilism establishes an unrealistically high standard of justification. Consequently, fallibilism has become a mainstream view. For our purpose it is crucial to focus on fallibilist theories of justification. By narrowing justification to logical entailment by some finite set of observation sentences, several of the verificationist principles discussed in Chapter 1 hang onto an infallibilist standard of justification (cf. Attempts 1–4). In Section 3.3, we understood that this unrealistically high standard of justification causes the problem concerning universal sentences. In the case of universal sentences, we can never exclude the possibility of error altogether, because we can only verify a finite number of its infinitely many instances. Consequently, universal sentences can at best be justified in a fallibilist way. The problem with universal sentences and its related problems (cf. CA1, 2, 5–8, 10 in Chapter 3) can thus be overcome only if we replace the notion of conclusive verifiability with a fallibilist notion of justifiability. To explicate the latter we can aim at implementing some existing theory of justification—some fallibilist theory of justification.116 Reductionism vs. Irreducibilism: Theories of justification can further be classified into reductionist and non-reductionist ones. While not identifying justification with logical implication, some theories of justification nevertheless reduce justification to deductive relationships. In other words, some theories— including some fallibilist ones—explicate the notion of justification in such a way that it supervenes on deductive relationships. Other theories of justification

 116 In Sec. 3.4, we learned that a theory of justification can only be implemented in a verificationist framework if we combine it with a theory of belief revision. In Chap. 7, we shall see how such a combination can be achieved. In Haas 2005, Sec. 7.3, I argued that only fallibilist theories of justification are feasible for such a combination. Thus, the intended combination of a theory of justification with a theory of belief revision constitutes another reason why we should focus on fallibilist theories.

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more resolutely abandon what has been called deductivism in Section 3.3. These theories neither identify justification with logical implication nor do they try to reduce the former to the latter. The theories of confirmation proposed by some empiricists are reductionist approaches, while virtually all contemporary theories of justification are non-reductionist. Empiricist attempts to reduce justification to deductive relationships were not particularly successful. This led at least Hempel to conclude that one should give up the attempt to spell out a criterion of significance in purely deductive terms. 117 In Section 3.3, we agreed with him that reductionist theories of justification are inappropriate for overcoming the problems of verificationism. Hence, when looking for an adequate theory of justification we should confine ourselves to non-reductionist approaches. Foundationalism vs. Coherentism: Another major distinction for classifying theories of justification is that between foundationalist and coherentist approaches. Epistemic foundationalism is characterized by two claims: (i) there is a class of so-called basic beliefs that are justified and whose justification does not depend on other beliefs; (ii) all other beliefs can be justified by these basic beliefs. Metaphorically said, the basic beliefs form an epistemic foundation upon which the entire edifice of justified beliefs rests. Coherentist theories, on the other hand, do not single out a class of basic beliefs as enjoying a privileged epistemic status. The justification of every belief depends on other beliefs. A belief is justified if it “coherently fits” into the system of all beliefs. At first glance, epistemic foundationalism seems to be the more attractive view as it conforms to everyday life experience and effectively prevents us from getting caught up in an infinite regress of justification. Coherentism, on the other hand, has the unpleasant taste of circular reasoning. Therefore, it is not surprising that the history of philosophy has primarily been characterized by foundationalist approaches. This is highlighted by the fact that philosophical views as disparate as rationalism and empiricism both favored foundationalist theories of justification, although they certainly disagreed on which beliefs to regard as basic. The problem with foundationalism, however, is that there is not a single choice of a set of basic beliefs that simultaneously fulfills (i) and (ii). One basically has the choice between a meager epistemic basis and a rich one. In the former case, one might be able to fulfill condition (i) but not (ii), while in the latter case, it is the other way round.118 Philosophers only took the less appeal 117 Cf. the corresponding quote by Hempel given in Sec. 3.3. 118 Since Sellars 1963 coined the term “the myth of the given”, epistemic foundationalism has been harshly criticized, BonJour 1985 offering a particularly extensive argument against it.

94  Fallibilist Theories of Justification ing position of coherentism into consideration because foundationalists failed to demonstrate the compatibility of their two principal claims. Starting with the logical empiricists Hempel and Neurath, as well as some British idealists and Blanshard, many philosophers including Rescher, Sellars, Harman, BonJour and Lehrer advocated epistemic coherentism in the 20th century. We should favor coherentist theories of justification over foundationalist ones when trying to overcome the problems of verificationism for two reasons. Firstly, we have made it quite clear that we ought to steer clear from infallibilism. But if there are no infallible beliefs it is difficult to see which beliefs could form an epistemic foundation stable enough to even set off foundationalism. In other words, foundationalism does not go well with fallibilism. By opting for the latter, we have already pre-settled for coherentism.119 Secondly, by building our principle of verification on a coherentist theory of justification, we do justice to the Duhem-Quine thesis. That is to say, condition (CA16) stated in Section 3.1 clearly calls for a coherentist approach. Internalism vs. Externalism: Finally, theories of justification can be classified into internalist and externalist ones. Every theory of justification states one or more conditions that must hold for a belief to be justified. We speak of an internalist theory if these conditions are such that it is necessarily within the cognitive grasp of the epistemic subject itself whether they hold or not. We speak of an externalist theory if this is not necessarily within the cognitive grasp of the subject. An example for an externalist condition is the requirement that a belief is justified only if it has in fact been formed by a reliable process. On the other hand, the requirement that a belief is justified only if the epistemic subject believes that it has been formed by a reliable process is an internalist one. Traditional theories of justification tend to be internalist while contemporary epistemologists have proposed both internalist and externalist theories. Contemporary theories of justification that are usually regarded as internalist include Chisholm 1989, BonJour 1985, Pollock 1986, Foley 1987, while externalist theories were, for instance, proposed by Armstrong 1973, Goldman 1979, 1986, Dretske 1981, Nozick 1981, Plantinga 1993. This distinction, however, is not as clear-cut as it might seem at first glance because there are also theories that combine internalist and externalist elements. Keith Lehrer’s theory of justification that we shall study in the next two sections is an example of such a combined approach (although many authors consider Lehrer to be an internalist). Which type of theory is most suitable depends on what you intend to do with it.  119 Although fallibilism and foundationalism do not match well, they are not fully incompatible, either. This can be seen, e. g., by Chisholm’s 1989 fallibilist foundationalism.

Various Types of Theories of Justification  95

Typically, an interest in the notion of justification evolves from an interest in the notion of knowledge as knowing that p implies having the justified true belief that p. In that context, the so-called Gettier problem poses the main difficulty for (purely) internalist theories, while the fact that knowledge and epistemic rationality can fall apart represents a serious drawback for (purely) externalist theories.120 We are, however, not interested in an analysis of knowledge here. Therefore, I will put these problems aside and will not take a stance on which type of theory of justification is best suited for analyzing the notion of knowledge. The need to formulate an adequate verificationist criterion of significance is what prompted our interest in a theory of justification. This framework imposes specific constraints on the choice of a suitable analysis of justification, differing from those imposed by an analysis of knowledge. In Section 3.4, we first understood that a theory of justification can only be implemented in a verificationist framework if we combine it with a theory of belief revision. The previous chapter has demonstrated how the principle of epistemic accessibility combines these two types of theories. Furthermore, the next two chapters will show that these theories are not independent of each other. Consequently, we cannot develop a theory of justification and a theory of belief revision separately from each other and then go on to combine the two in a principle of significance. Rather, we have to combine both theories on a more fundamental level. More specifically, a theory of belief revision has to rely on a theory of justification because justificational structures will crucially influence the way we revise our beliefs. However, justificational structures will influence the belief revisions of a subject only insofar as these structures are cognitively accessible to the subject. Not even an ideally rational subject can possibly be influenced by justificational structures outside its cognitive grasp. For this reason, externalist theories of justification are flat out irrelevant to our endeavor—whatever merits they may have for other purposes. Hence, we should focus on internalist theories of justification and on the internalist aspects of those theories that combine internalist and externalist elements.

 120 The problem posed by Gettier 1963 demonstrates that it does not suffice for knowing that p to have a justified true belief that p. Some additional condition is needed where internalist conditions seem inadequate to do the trick. A rather comprehensive overview of the efforts that have been made to resolve the Gettier problem in the first decade after it emerged can be found in Shope 1983. Cases in which knowledge and epistemic rationality fall apart according to an externalist theory of justification are cases where the externalist conditions hold while the epistemic subject has every reason to believe that they do not hold.

96  Fallibilist Theories of Justification In sum, an adequate criterion of significance has to replace the notion of conclusive verification by a more inclusive notion of justification. The latter should then be explicated by an existing theory of justification. For that purpose, we should look for a theory that is fallibilist, non-reductionist, coherentist and non-externalist.

5.2 Lehrer’s Theory of Justification Keith Lehrer proposed a theory of justification that neatly meets all the demands we have formulated in the previous section for a theory to be suitable for our purposes: it is fallibilist, non-reductionist, coherentist, as well as nonexternalist. In this section, Lehrer’s semi-formal theory of knowledge will be briefly reviewed before a formal reconstruction of it is presented in the next section. The present section contains nothing new for the reader who is already familiar with Lehrer’s proposal. All other readers are referred to the very clear original publications for a more detailed presentation and motivation of Lehrer’s analysis of the notions of “knowledge” and “justification”.121 The starting point for Lehrer’s theory is the classical analysis of knowledge as justified true belief. Because of the well-known Gettier examples, he regards these conditions as necessary conditions only. In order to attain a set of conditions which are jointly sufficient for knowledge, Lehrer adds a fourth condition, namely the requirement that the belief under consideration must be justified in a way that is not defeated. According to Lehrer, a subject S knows that p if, and only if, S has the undefeated justified acceptance that p. It is worth mentioning that Lehrer prefers the term “acceptance” over the commonly used term “belief” because it can thereby better be expressed that it is acceptance with the objec-

 121 Lehrer has developed and modified his theory over a period of several decades. He first presented it comprehensively in Lehrer 1974. Significant modifications were introduced by Lehrer 1990. Lehrer 1986, 1989 are brief and concise presentations of his ideas. Further modifications to his proposal were added in Lehrer 1997, 2000. Numerous articles that critically analyze Lehrer’s theory, along with replies by Lehrer, are found in the three anthologies Bender 1989, Brandl et al. 1991 and Olsson 2003. The following presentation of Lehrer’s theory is chiefly based on Lehrer 1986, 1989, 1990. The later amendments by Lehrer 1997, 2000 include a modified definition of the so-called ultrasystem and the replacement of the former acceptance system by a so-called evaluation system which encompasses the acceptance system as well as some other structures. Since these amendments are quite irrelevant for what follows, they have been omitted in favor of the simpler and thus clearer earlier version of Lehrer’s theory.

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tive of obtaining truth and avoiding error that is constitutive for knowledge rather than mere belief which is usually not directed toward a particular goal. Acceptances, however, play approximately the same role in Lehrer’s theory as beliefs typically do. Note further that the truth condition can be skipped in Lehrer’s analysis of knowledge as it will be implied by his explication of an undefeated justification. Hence, an explication of what an undefeated justification is supposed to be is obviously the key task for Lehrer’s theory. Lehrer himself explicates the notions of “justification” and “knowledge” by a series of semi-formal definitions. Before we look into these slightly puzzling definitions, it will be helpful to outline the underlying idea which is fairly simple. As fallibilists, we are not of the opinion that a belief is justified only if it is absolutely certain. Nevertheless, we have the clear and distinct intuition that not all beliefs are equally reliable. The justified beliefs are those that have a high degree of reliability and thus appear to be particularly reasonable from the perspective of the epistemic subject. To assess the relative reasonableness of a belief p, we have to compare it with other beliefs in terms of their reasonableness. But to which other belief should we compare a belief? At first glance, one might think that we have to compare a belief with its negation and require of any justified belief that it is more reasonable than its negation. Obviously, that requirement is far too weak. Consider a fair lottery with 100 tickets, 51 of which win. Now, the hypothesis that ticket number n wins will be more reasonable than its negation. However, we would not regard this hypothesis as justified since it is only minimally more reasonable than its negation. As it is too weak of a requirement to compare a belief with its negation only, one might think that we have to compare it with all other beliefs. Thus, at second glance, one might consider a very strong requirement according to which a belief is justified only if it is more reasonable than any other belief (or rather, at least as reasonable). However, it is easy to see that this requirement is too restrictive. For instance, my belief that there are mountains that are higher than 8000m is justified although I have other beliefs that are even more reasonable, like, for instance, my belief that there is a red book lying on the table in front of me. While it is too weak to require of a justified belief that it be more reasonable than its negation only, it is in turn too restrictive to require that it be more reasonable than any other belief. Consequently, we have to find a golden mean between these two extremes. The following proposal has a particularly high intuitive appeal: A belief p is justified if, and only if, it is more reasonable than any other statement c that conflicts or competes with p. Yet, which statements compete with each other? It makes sense to say that a statement c competes with a belief p if, and only if, c is negatively relevant for p. More precisely, c

98  Fallibilist Theories of Justification competes with p if, and only if, p is more reasonable on the assumption ¬c than on the assumption c. This is the idea underlying Lehrer’s analysis of “S knows at time t that p”. L1. S is justified in accepting that p on the basis of system X at t if and only if all competitors of p are beaten or neutralized for S on X at t. L2. c competes with p for S on system X at t if and only if it is more reasonable for S to accept that p on the assumption that c is false than on the assumption that c is true on the basis of X at t. L3. p beats c for S on X at t if and only if c competes with p for S on X at t and it is more reasonable for S to accept that p than to accept that c on X at t. L4. n neutralizes c as a competitor of p for S on X at t if and only if c competes with p for S on X at t, the conjunction of c and n does not compete with p for S on X at t, and it is as reasonable for S to accept the conjunction of c and n as to accept c alone on X at t. L5. A system X is an acceptance system of S at t if and only if X is a set of statements of the form “S accepts that p” attributing to S just those things S accepts at t with the objective of accepting p if and only if p is true. L6. S is personally justified in accepting that p at t if and only if S is justified in accepting that p on the basis of the acceptance system of S at t. L7. S is justified in accepting that p at t in a way that is undefeated if and only if S is justified in accepting p at t on the basis of every system that is a member of the ultrasystem of S at t. L8. A system M is a member of the ultrasystem of S at t if and only if either M is the acceptance system of S at t or results from the acceptance system of S at t by eliminating one or more statements of the form “S accepts that q” when q is false, replacing one or more statements of the form “S accepts that q” with a statement of the form “S accepts that not q” when q is false, or any combination of such eliminations and replacements. L9. S knows at t that p if and only if S is justified in accepting that p at t in a way that is undefeated.

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Although some redundant definitions have been omitted, this presentation of Lehrer’s analysis of knowledge resembles the series of semi-formal definitions he himself gives in Lehrer 1989, 1990.122 Only Definition (L8) of the ultrasystem given here differs significantly from Lehrer’s own presentation.123 This series of definitions might be a bit confusing at first sight. Therefore, let me point out once again the basic idea underlying it: A belief p is (personally) justified if, and only if, p can beat or neutralize all competitors (on the basis of the acceptance system). The competitors of p are those statements that are negatively relevant for p. To beat a competitor c simply means that p is more reasonable than c. The possibility to also neutralize competitors allows us to come to terms with indirect and remote competitors of a belief p that we wish to justify. Such competitors may be highly reasonable, making it impossible to beat them. Thus, they have to be excluded as irrelevant competitors. An example may illustrate such a situation: I believe that there is a book in front of me (p). The statement that people sometimes dream that there is a book in front of them when there is none (c) is negatively relevant for p. Thus, c is a competitor of p. Because c is highly reasonable, too, it may be impossible for p to beat c. In order to nevertheless justify p, one can neutralize c as a competitor of p by the belief that I am not dreaming now (n).124

 122 The numbering of the definitions has been adjusted to the slightly modified version. 123 In contrast to (L8), the original definition of the ultrasystem reads: “A system M is a member of the ultrasystem of S at t if and only if either M is the acceptance system of S at t or results from eliminating one or more statements of the form, ‘S accepts that q’, when q is false, replacing one or more statements of the form, ‘S accepts that q’, with a statement of the form, ‘S accepts that not q’ when q is false, or any combination of such eliminations and replacements in the acceptance system of S at t with the constraint that if q logically entails r which is false and also accepted, then ‘S accepts that r’ must also be eliminated or replaced just as ‘S accepts that q’ was.” (Lehrer 1990, p. 149 and p. 194 (n. 11)); italics GH. Cf. also Lehrer 1988, 1997. In Haas 2003b, I have argued that the additional constraint introduced by Lehrer’s original definition can be skipped without loss, that is, the ultrasystem may as well be defined by the simpler (L8). This simplification has been endorsed by Lehrer 2003. However, in the following we will only rely on Lehrer’s analysis of (personal) justification, that is to say, we will refer to Definitions (L1)–(L6) only. Hence, there is no need to argue in favor of the simplified definition of the ultrasystem here. 124 One merit of Lehrer’s theory that is worth mentioning is a neat solution to the so-called lottery paradox. Cf. Lehrer 1990, p. 129f.

100  Fallibilist Theories of Justification

5.3 Formal Reconstruction of Lehrer’s Theory Lehrer himself only presents his theory in the semi-formal version we reviewed in the previous section. To ensure a high degree of precision when we implement his proposal within a verificationist theory, it is therefore indispensible to give a formal reconstruction of it first. Fortunately, how to accomplish this is fairly straightforward. Lehrer explicates the notion of (personal) justification as part of his analysis of knowledge. In the present verificationist context, we are not interested in knowledge, however, but in justification only. Thus, we can fully ignore (L7)–(L9) from the above list of definitions focusing exclusively on Lehrer’s Definitions (L1)–(L6). Unlike other authors, Lehrer bases his analysis of justification not on a relation “p1 is at most as reasonable as p2”, but on the more complex relation “p1 on the assumption p2 is at most as reasonable as p3 on the assumption p4”. This idiosyncrasy of Lehrer’s theory is highlighted by Definition (L2). If we also take into account that this relation depends on the acceptance system A of the epistemic subject, we see that Lehrer bases his analysis on a 5-place relation of reasonableness “relative to A p1 on the assumption p2 is at most as reasonable as p3 on the assumption p4”. This relation shall be denoted as follows:125 p1|p2 ≤A p3|p4: “relative to A p1 on the assumption p2 is at most as reasonable as p3 on the assumption p4” The relations