A Priori Knowledge: Toward a Phenomenological Explanation 9783110325645, 3937202927, 9783937202921, 9783110325034

Table of contents :
Table of Contents
Introduction
1. A Priori, Analyticity,and Implicit Definition
Empiricism, Analyticity, and the A Priori
Reductive and Non-Reductive Conceptions of Analyticity
Implicit Definition, Logical Truth, and the Recalcitrant A Priori
Problems with Implicit Definition
BonJour’s Objection
Fodor and Lepore’s Objection
Horwich’s Objection
Hale and Wright’s Defence of the Traditional Connection
Logic and Convention
Coda
2. Realism about Logic
Introduction
Logical Principles, Justification, and Epistemic Relativity
Objective Truth
Resnik’s Attack
Wittgenstein on the Necessity of “1 inch = 2.54 cm” and Logical Inference
Dummett’s Objection
Rule Following Considerations and the Adoption of a Convention
Summarising Remarks
Wright’s Attack
Conclusion
3. Objective Knowledge
Introduction
What the Tortoise Said to Boghossian
What Boghossian would say to the Tortoise
Rule-circular Arguments
The Side-Argument
Rejecting the Side-Argument
First Horn: Simple Internalism and Rational Insight
Second Horn: Epistemic Responsibility and the Lack of EpistemicIrresponsibility
Realism, the A priori and Rational Insight
Boghossian’s Argument against Relativism
Epistemological Realism about Justification
Conclusion
4. Phenomenology and Rational Insight
Naturalism and Justification
Phenomenology, Justification, and Eidetic Seeing
Is Holism a Possibility for the Empiricist?
Intuition of Essences and the Analytic/Synthetic Distinction
Husserl’s Conception of the Analytic/Synthetic Distinction
Eidetic Variation
Passive Synthesis and Concept Constitution
Knowledge of Reality and Conceptual Truth
Absolute vs Relative Objectivity
Are Conceptual Truths True?
Conclusion
References

Citation preview

Tommaso Piazza A Priori Knowledge Toward a Phenomenological Explanation

PHENOMENOLOGY & MIND Herausgegeben von / Edited by Arkadiusz Chrudzimski • Wolfgang Huemer Band 10 / Volume 10

Tommaso Piazza

A Priori Knowledge Toward a Phenomenological Explanation

ontos verlag Frankfurt I Paris I Ebikon I Lancaster I New Brunswick

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

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2007 ontos verlag P.O. Box 15 41, D-63133 Heusenstamm nr. Frankfurt www.ontosverlag.com ISBN 10: 3-937202-92-7 ISBN 13: 978-3-937202-92-1 2007 No part of this book may be reproduced, stored in retrieval systems or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use of the purchaser of the work Printed on acid-free paper ISO-Norm 970-6 This hardcover binding meets the International Library standard Printed in Germany by buch bücher dd ag

Table of Contents Introduction

v

1. A Priori, Analyticity, and Implicit Definition Empiricism, Analyticity, and the A Priori Reductive and Non-Reductive Conceptions of Analyticity Implicit Definition, Logical Truth, and the Recalcitrant A Priori Problems with Implicit Definition BonJour’s Objection Fodor and Lepore’s Objection Horwich’s Objection Hale and Wright’s defence of the traditional connection Logic and Convention Coda

1 3 5 8 10 13 23 31 46 52

2. Realism about Logic Introduction Logical Principles, Justification and Epistemic Relativity Objective Truth Resnik’s Attack Wittgenstein on the necessity of ‘1 inch = 2.54 cm’ and logical inference Dummett’s Objection Rule Following considerations and the adoption of a convention Summarising Remarks Wright’s Attack Conclusion

57 60 64 65 75 79 84 87 89 109

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3. Objective Knowledge Introduction What the Tortoise Said to Boghossian What Boghossian would say to the Tortoise Rule-circular Arguments The Side-Argument Rejecting the Side-Argument First Horn: Simple Internalism and Rational Insight Second Horn: Epistemic Responsibility and the Lack of Epistemic Irresponsibility Realism, the A priori and Rational Insight Boghossian’s Argument against Relativism Epistemological Realism about Justification Conclusion

111 115 117 119 122 123 123 126 131 132 134 135

4. Phenomenology and Rational Insight Naturalism and Justification Phenomenology, Justification, and Eidetic Seeing Is Holism a Possibility for the Empiricist? Intuition of Essences and the Analytic/Synthetic Distinction Husserl’s Conception of the Analytic/Synthetic Distinction Eidetic Variation Passive synthesis and Concept Constitution Knowledge of Reality and Conceptual Truth Absolute vs Relative Objectivity Are Conceptual Truths True?

138 145 150 156 157 164 168 174 177 179

Conclusion

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References

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Introduction Do we know anything a priori, that is to say independently of experience? Do we know a priori anything objective concerning reality? Do we know logic? Do we know it a priori? This book is devoted to critically analysing these problems, to inquiring into existing answers to these questions, and to suggesting a plausible way out of the difficulties my analysis will hopefully bring to the fore. Addressing the general question about whether we do know anything a priori involves addressing two distinct sub-questions. The first one concerns the very nature of the statements allegedly known a priori, that is to say concerns the question whether these statements do express the kind of things that can in principle be known, and the question concerning what kind of knowledge one acquires when knowing them. The second subquestion deals with the way, if these statements do express the kind of things that can in principle be known, they can, and indeed are (at least sometimes and locally), known a priori. Contemporary empiricism has delivered a unified answer to both questions with the notion of analyticity. In accordance with this traditional answer, all a priori statements are analytic statements. As synthetic statements, analytic statements are truth-apt (indeed, true) statements. Therefore, a priori statements are the kinds of things that can be known. However, unlike synthetic statements, analytic statements do not have cognitive content, they do not say anything about reality. This feature of analytic statements is due to the fact that their truth, on the empiricist reading of the notion of analyticity, is entirely due to the meanings of their constituting expressions. So, a priori knowledge is not any kind of knowledge of reality. However, the distinctive nature of analytic truth yields a satisfactory account of our knowledge of it. For a natural suggestion is that if the truth of a statement is entirely determined by the meaning of its constituting expressions, then its truth can be known simply by understanding the statement. Accordingly, the truth of an analytic statement can be known merely by understanding it, therefore a priori. This empiricist solution has exerted a considerable influence among empirically minded philosophers; in fact it avoids the intuitive drawbacks of Mill’s solution according to which alleged pieces of a priori knowledge, like mathematical and logical knowledge, is empirical and inductive in nature. Mill’s solution is consistent with the empiricist prin-

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ciple according to which every piece of knowledge of reality stems from and is justified on the basis of experience. However, this solution has the unpalatable feature of imposing a conception of mathematic and logic as just contingently true, for just beliefs in contingent statements can be justified, to a degree sufficient for knowledge, by inductive and empirical means. The solution based on analyticity allows the empiricist to defend her epistemological principle without loosing the necessity of mathematical or logical statements. If mathematic and logic say nothing about reality, in fact, to admit that our mathematical or logical knowledge is a priori is not to admit that our knowledge of reality has sources other than our experience of it. The viability of this empiricist solution clearly depends on the very notion of analyticity called into question. Notoriously, the empiricist notion of analyticity is not Kant’s notion. However, admitting that Kant’s notion constitutes an improvement on such notion is probably not that far from the truth. Kant held that an analytic statement is one characterized by the fact that its predicate term expresses a concept which is contained by the concept expressed by its subject term. Kant’s analyticity has been found wanting for two reasons. It is too narrow, for it applies just to statements of the subject-predicate form: statements like (K1) Everything is spatio-temporal or is not spatio-temporal is not analytic according to Kant’s definition, because its predicate concept is not contained in its subject concept. Secondly, it is too wide, for a statement like (K2) Every daughter of a professional philosopher is a professional philosopher is false, and a fortiori not analytic, yet the concept [professional philosopher] expressed by the predicate term is actually contained by the concept [daughter of a professional philosopher] expressed by the subject term. However, Kant notoriously also held that analytic statements are not ampliative with respect to our knowledge of reality, while synthetic statements are; for this reason he also claimed that the a priori epistemological status of analytic statement is not problematic: given the containment theory, to know an analytic statement it is sufficient to possess

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both its predicate- and the subject-concept, and to be acquainted with the principle of non-contradiction. Both features are preserved within the empiricist notion of analyticity, because according to this notion analytic statements do not say anything about reality. Given the wider nature of the empiricist conception with respect to its applicability just to statements of the subject-predicate form, however, the epistemology of analytic statement is not anymore Kant’s. Rather, we might say, it is Frege’s. Frege held that a statement is analytic when it is either a substitutional instance of a logical principle – much in the way “it rains → it rains” is a substitutional instance of the principle “p → p” – or can be reduced to a substitutional instance of a logical principle with the aid of definitions – much in the way “every bachelor is an unmarried man” can be reduced to “every unmarried man is unmarried”. If, pace Quine, the question whether two expressions of a natural language are synonymous is not intractably unintelligible, and if a competent speaker of a natural language is indeed in a position to answer such a question whenever it arises concerning two distinct expressions, the question about how analytic statements can and are known reduces to the question about how predicate and propositional logic is known. Though Frege considered the latter epistemological task as completely unproblematic – convinced, as he was, that logical principles are simply self-evident – it is clearly vital for a sound empiricist theory of the a priori to provide such an account. Unless we are told how logic is known, we cannot stay content with the contention that a priori knowledge of analytic statement is unproblematic because, at bottom, it reduces to knowledge of logical truths. A simple suggestion is that logical principles are known either because they are implicit definitions of the logical constants they contain, or because they are deducible from such principles. This is the contemporary proposal I shall consider at the beginning of the first chapter. The basic idea is that the meaning of certain expressions – in the case at issue the meaning of the logical constants – is determined by constraining those expressions to have whatever meaning is required for the truth or the correctness of certain basic contexts that contain them. It follows that no one understanding such context (sentences or rules of inference) can fail to appreciate that they are true (valid), if they perform the role of implicit definitions. So long as they do, understanding what they mean coincides with (because it requires) appreciating that they are

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true (valid). More than this, the theory seems to make good sense of the traditional suggestion according to which logical principles are selfevident. Since accepting such principles is constitutive of the capability of understanding what they say, it follows that no one fully understanding what they say can fail to appreciate that what they say is true. An empiricist should welcome this account for a third important reason. Take the following statement: (H) If something is entirely coloured of red it is not, at the same time and under the same respect, entirely coloured of green. (H) is not the instantiation of a logical principle, nor it is reducible to the instantiation of a logical principle if synonymous are substituted by synonymous. The meaning of “red”, in fact, is not the same as the meaning of the (conjunctive) predicate “not green and not blue and not gray …”. Given the potential infinity of colour discriminating expressions, the meaning of any colour term “c” could not be grasped in the first place if it were equivalent to the infinite conjunction of the negative predicates constructed out of each colour expression other than “c”. Accordingly, statements like (H1) are to be counted as synthetic under the standard (Fregean) empiricist notion of analyticity. The problem is that synthetic a priori knowledge is not consistent with the empiricist epistemological principle. In contrast with analytic statements, synthetic statements are about reality. So, the admission of a priori knowledge of synthetic statements entails that experience is not the only source of knowledge and justification. The notion of implicit definition seemingly makes it available to the empiricist a plausible way out. As it makes available a notion of logical truth according to which logical principles are just definitions of a devised sort of the logical constants they contain, it seemingly makes available the view that statements like (H1) are just definitions of a devised sort of the color predicates they contain, therefore acceptable from an empiricist epistemological point of view. The first chapter of this book will be devoted to taking into consideration several criticisms, advanced by L. BonJour, J. Fodor and H. Lepore, and by P. Horwich, against P. Boghossian’s idea that meaning coincides with conceptual role, and against the idea that the meaning of certain expressions is implicitly defined by the resolve to accept as true given contexts featuring these very expressions. In accordance with a

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presupposition shared within the contemporary debate, both criticisms will be considered as striving against one and the same epistemological suggestion concerning logical knowledge and knowledge of statements like (H)1. Fodor and Lepore have objected to Boghossian’s proposal that the conceptual role semantic is the hostage of a dilemma between two unpalatable options. The unqualified identification of meaning and conceptual role entails the violation of the compositionality of meaning. If the identification is unqualified, every transition accepted within a language constitutes a conceptual role. So, for instance, does the transition from “x is a brown cow” to “x is dangerous”, constituting a conceptual role for the expression “brown cow”. However this conceptual role is not a function of the conceptual role of “brown” and “cow”, because neither the transition from “x is a cow” to “x is dangerous”, nor the transition from “x is brown” to “x is dangerous” are legitimate. If meaning is identified with conceptual role, this means that the meaning of “brown cow” is not a function of the meaning of “brown” and of the meaning of “cow”. The natural alternative is to qualify the identification of meaning and conceptual role by narrowing the scope of meaning-constituting inferences to analytic inferences. However, according to Fodor and Lepore, the analytic/synthetic distinction has been convincingly rejected by Quine. So, this second alternative also proves unviable. It follows that conceptual role semantics itself must be rejected. Against Fodor and Lepore’s suggestion I shall point out that Quine’s arguments are correctly understood as being directed against the notion of synonymy. Accordingly, such arguments do not have any immediate bearing on the suggestion that the meaning of the logical constants is constituted by the conceptual roles specified by their introduction and elimination rules. So long as it is conceded that we should allow for the advertised correspondence between rules of inference and axiom schemata, Quine’s argument then has a direct bearing just on the suggestion that those analytic statements which are reducible to logical principles by means of definitions can be know a priori. However, this objection 1

My suggestion as to the equivalence of the implicit definitional approach and the conceptual role semantics is apparently taken for granted in the literature. An example is seen in Horwich 1998: “For simplicity I am focusing on the case in which implicit definition proceeds by regarding a sentence […] as true. But this discussion carries over in an obvious way to the case of implicit definition in which certain rules of inference are regarded as valid” (p. 133).

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can be resisted also in its qualified variety. To do so I will rehearse Boghossian’s characterization of Quine’s attack against synonymy – both in its error theoretic and non factualist varieties– and will show how it can be resisted in both its varieties. Horwich’s objection is directed against the notion of implicit definition. According to Horwich, the main problem of the traditional connection – the thesis that implicit definition explains a priori knowledge – is that it is undermined by the Wittgensteinean conception of meaning needed to make good sense of the model of implicit definition. Horwich contends that the model actually explains how certain expressions receive a meaning only provided that we know that the required meaning exists, that it is unique, that our resolve to accept as true the implicit definer determines that the expression comes to possess that meaning, and that we are able to explain why it is so. The identification of meaning with use helps coping with the four problems, yet at the cost of undercutting the connection with (a priori) knowledge. Since a meaning is constituted by the regularity of use centred on the resolve to accept as true the implicit definition, it constitutes a possibility that, besides our resolve, the content thereby constituted turns out to be false. Hale and Wright have recently rehearsed the point that a wittgensteinean conception of meaning is indeed needed for making sense of the model of implicit definition. However, they also suggest that the wittgensteinean conception doesn’t impede establishing the traditional connection. I will end the first chapter by critically assessing Horwich’s argument, and Hale and Wright’s replies to it. I will not dwell upon the question whether the wittgensteinean conception of meaning is indeed needed to make sense of implicit definition. A major problem concerns the relation between meaning and reference fixing. If an implicit definition performs the role of determining a meaning for an uninterpreted expression, it is arguably by constraining the identity of its reference to be such that it makes the implicit definition true. This is why the existence problem matters: the defined expression, if reality doesn’t cooperate, may suffer from reference failure. Hale and Wright grant the point when they require an implicit definition not to be arrogant, that is to say not to entail fresh existential commitments whose fulfilment could be ascertained just by additional epistemic work. Borrowing from the early debate issuing from Prior’s provocative proposal of “tonk” as a legitimate logical constant, Hale and Wright assert that an implicit definition (or a set of rules) is not arrogant, and may

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be accepted as true (respectively, valid) a priori, only if it is conservative and in harmony: that is to say, if the addition to a language of the new expression (together with the linguistic apparatus which defines it) does not allow one to derive something which is underivable within the same language without the new expression. The elimination rule of an expression is not in harmony with the introduction rule if it licenses from a context containing the expression the inference of more (or less) than is required to introduce such context. In this case then it is possible to prove statements not containing that expression which it was not possible to prove before, and this amounts to a non-conservative extension of the language2. The first thing to notice is that Hale and Wright’s proposal is meant to apply both to implicit definitions provided by simple sentences, and to implicit definitions provided by pairs of rules. As it is clear, however, harmony cannot constraint implicit definitions of the first kind. Accordingly, the relevant question is about whether an implicit definition of that sort can be safeguarded from reference failure by some other condition. The most natural proposal, however, is that such implicit definitions be transformed in corresponding so-called Carnap-conditionals, whose meaning constituting role is safeguarded from reference failure by their conditional formulation. If #F is an implicit definition of “#”, the corresponding Carnap-conditional is If ∃xFx, then F# is true.

2

“The introduction rule states the conditions under which a conclusion with that operator dominant can be inferred. It describes, if you like, the obligations that have to be met by the speaker in order to be justified in asserting the conclusion in question. The corresponding elimination rule states what the listener is entitled to infer from the speaker’s assertion. Clearly, these mutual obligations and entitlements have to be in balance. The listener must not be allowed to infer more than is required to have been “put in” to the justification of the assertion. Likewise, the speaker must not be able to get away with less than is required when one is giving the listener entitlement to make certain inferences from what has been asserted”, Tennant 2005, p. 628-629.

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As Horwich remarks, the Carnap-conditional is uninteresting from an epistemological point of view. In particular, advocating the epistemological role of implicit definitions of the conditional form does nothing to show, as intended by the theory, that their consequents are known a priori. There remain to be analyzed implicit definitions framed in terms of introduction and elimination rules. First of all, it might be suggested that all implicit definitions are to take this form if they are both not to be arrogant and to convey substantial a priori knowledge. This move would in fact prevent the foregoing problem from arising. However, take in consideration implicit definitions of individual terms, or predicates, framed in terms of introduction and rules. If the rules are in harmony, then no fresh existential commitment has been introduced by their adoption. In particular, it means that whatever existential commitments are ratified within a language after the introduction of the new expression must have been ratified before. It seems to follow that no new knowledge is made available once it is introduced by means of the new expression through an implicit definition of it. Since no new knowledge has been introduced, the same knowledge must have been available before. This result does seem to stand in clear opposition to the idea that implicit definition plays a primary role in the epistemology of the a priori. There remains the case of the logical constants. If a pair of harmonious introduction and elimination rules implicitly defines a logical constant, are we thereby justified in believing that these rules are valid (that the corresponding conditionals are true)? Unfortunately, harmony and conservative extension guarantee the validity/truth of these rules/conditionals, only against the backdrop of our accepting the validity/truth of other rules/conditionals whose status cannot be in turn explained by implicit definition. Two distinct reactions to this circularity are available. The first one is to endorse conventionalism, and justify the adoption of the conservative extension and harmony constraint not in the light of their conductivity to validity/truth, but rather as natural desiderata, in the light of the function they are to perform, for the adoption of certain conventions. If the conventional rules of inference just play the function of facilitating the exchange of information, and logical truth is a by-product of such rules, it is easy to see how non-conservative extension and harmony suffice to vindicate the view that implicit definition conveys a priori knowledge.

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The shortcoming, however, is that it is a priori knowledge just of conventional truths. The second alternative is to welcome the circularity at issue as unavoidable, and argue that it does not stand in the way of justifying our rules of inference. Since Dummett’s paper on the Justification of Deduction, such justification is alleged to be necessarily circular, that is to say necessarily to employ the very rules of inference whose validity is under dispute. I shall leave open the issue about whether such a justification is enough to ensure objective a priori knowledge of the validity of such rules. I will take up the issue in the third chapter, when discussing a recent proposal of Boghossian. The second chapter will be devoted at assessing the questions whether logical truth can coherently be conceived as objective truth, and whether, so conceived, it can be known along the circular pattern described by Dummett, and recently developed by Boghossian. Before taking into consideration an influential, negative answer to this question, I will firstly pause to stress the connection between the idea that logical truth is objective and several pressing questions in general epistemology, most importantly the objectivity of normative epistemological principles. To show this I will rehearse a very general argument put forward by L. BonJour, and much in the same vain by P. Boghossian, to the effect that an anti-objectivist construal of logic entails strongly unpalatable forms of epistemic relativism and scepticism. Objective truth can be characterized as a property that sentences (or propositions) possess independently of our holding them to be true. Along with Dummett’s characterisation, objective truth has been identified with a non-epistemic property. According to a recent proposal of Wright, however, evidence transcendence should be seen just as a sufficient, but not as a necessary condition for objectivity. According to Wright even an evidentially constrained truth-predicate may be shown to deserve a realist – objectivist – interpretation if (a) it satisfies Cognitive Command, (b) it allows for a Socratic resolution of the Euthyphro Contrast and (c) the facts allegedly reported by true sentences within the area perform a Wide Cosmological Role. The idea that logical truth is objective has been attacked in both senses of the notion. M. Resnik, on the one side, has put forward an argument (echoing Benacerraf’s argument against mathematical Platonism), according to which realism and objective truth should be rejected in the case of logic. The argument concludes with the rejection of objec-

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tive logical truth from the premise that the same method of enquiry – the method of reflective equilibrium – may ratify completely different logics. The argument can be resisted by showing that it proves too much. Take scientific theories. As it is well known, it constitutes a possibility that scientific theories be underdetermined by evidence. Resnik’s argument, then, can be run even in the case of scientific theories, preventing a realistic interpretation of their content. Unless it is possible to explain, by resorting to some alleged asymmetry between both cases, why underdetermination by data should motivate, in the case of logic, while not in the case of physics, antirealism, it seems to follow that antirealism should not be conceded, or that it should be extended to science as well. More than this, however, there is a natural reply to the claim that, in the indicated sense, logical truth is not objective. Shapiro has put forward such a reply in a recent article. I will further develop it, in the form of the following argument: if a proposition, say P, is, according to rule R, a logical consequence of Q and S, then R cannot be truth-preserving unless, given the truth of Q and S, P is true as well. Since P might be taken to be an objective sentence (proposition), whose truth or falsehood we may have independent means to ascertain, the validity of rule R must answer to the objective truth of P, and in this sense, must be held to be objective as well. It is not something that it is at our liberty to dignify with the status of a logical rule of inference. Whether it is, depends on its being a fact that, whenever an argument features true premises and takes its main step according to the rule, the conclusion comes out true. This argument might be resisted along a broadly wittgensteinean interpretation of logical necessity. Roughly, it could be maintained that the argument does not take into account the fact that our ordinary standards of truth assessment, when a conventional decision is agreed upon as to the logical status of a rule of inference, are subjected to an appropriate conceptual modification, in a way that a contrast between what the rule of inference requires to be true, and what, by employing our ordinary criteria of truth assessment, we find out to be true, is ruled out a priori. According to the proposal, there is no question of our having adopted a rule of inference that enables us to infer conclusions which, by ordinary, non-inferential criteria, turn out to be false. When we propose to regard a determinate principle as a rule of inference, we implicitly commit ourselves to regard any situation which seems to be of the indicated sort as one where we have committed a mistake in applying our non-inferential criteria of truth assessment, either in regarding the premises as true, or in

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regarding the conclusion as false. The proposed counter parallels Wittgenstein’s reconstruction of the necessity of claims like “1 inch = 2.54 centimetres”. In the Remarks on the Foundations of Mathematics, Wittgenstein maintains that, by dignifying the claim of the special status of a necessary truth, we rule out the possibility that a measurement tells against it. The conventional decision affects a modification on the notion of correct measurements, to the effect that, whenever a measurement, by ordinary criteria, has been carried out properly and has given, as a result, a different ratio between inches and centimetres, then it must be supposed that a mismeasurement has undetectably taken place. Against Wittgenstein’s line of thought Dummett has replied that, if, on the one side, we have ordinary criteria of correct measurement, and, on the other side, we have a new criterion of correctness of measurement (roughly the new criterion according to which a mismeasurement must have taken place if the result is returned that the ratio “1 inch = 2.54 centimetres” is not correct), then the new one has to answer to the ordinary ones, and, when correct, it has to be correct for it “corresponds” to the old criteria. It might be replied that Dummett’s argument does not take into account what is the moral of the rule following considerations: a conflict between old and new criteria is excluded – and, conversely, the notion of the new criterion complying with the old ones devoid of any clear content – when it is recognized that, according to the rule following considerations, there is not a determinate pattern of use to which a thinker, by accepting the old criteria, commits herself and against which a new criterion could be seen to entail something like a conflict. In fact the acceptance of the convention according to which “1 inch = 2.54 centimetres” expresses a necessary truth just constitutes a way of fixing one possible interpretation of the old criteria and of the moves which are necessitated by their acceptance. This reply seems to be flawed by the following considerations: if the acceptance of the old criteria does not commit to a determinate pattern of use, it might be questioned, why does the conventional agreement to regard “1 inch = 2.54 centimetres” as necessary? Should not the rule following considerations apply to the latter case, as they supposedly apply to the former? Is not, in the end, the conventional decision to regard “1 inch = 2.54 centimetres” as necessary nothing but the acceptance of a new rule – the rule according to which a couple of measurements must not be regarded as having been carried out properly unless they produce

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results, respectively in the imperial and in the metrical system, standing in the ratio which has been chosen? I think that all these questions should be answered in the affirmative and that the reply based on the rule following considerations, eventually, should be rejected. Wright, on his part, has tried to deny that logical truth should be held to be objective. His argument is not based on the fact that logical truth cannot be held to transcend evidence. His attack is based on the fact that, according to him, logical truth is not able to satisfy the criterion of Cognitive Command. Roughly, Cognitive Command holds that the truth predicate finding application within a discourse is an objective truth predicate if it is a priori certain that every disagreement about some statement in the discourse can be explained by the supposition that at least one of the disputants committed a cognitive mistake. Wright considers the case of a disagreement about the necessity of the conclusion of what is normally regarded as a logically valid argument. If such a disagreement has to be interpreted as cognitive, Wright urges, then either prejudicial assessment of data, ignorance or mistake has to be attributed at least to one of the disputants. However, Wright contends, no such possibility can be countenanced. Accordingly, logical truth fails Cognitive Command, and is thereby shown to deserve an antiobjectivist interpretation. My reply to Wright’s suggestion will be twofold. On the one hand, I will refine an argument put forward by Shapiro, to the effect that logic’s lack of objectivity threatens to ramify into discourses traditionally regarded as objective by Wright’s own lights. According to Wright, a discourse A disputationally supervenes upon a discourse B, when every disagreement about the truth-value of some sentences in A depends on some disagreement about the truth value of some sentences in B. The premise is that, in Wright’s sense, mathematics and space-time theory disputationally supervene on logic. As long as mathematics and space time theory can defensibly be held to satisfy Cognitive Command, they cannot but supervene upon discourses that satisfy it as well. In fact, if the premises are conceded that (a) A exhibits Cognitive Command, and (b) that A disputationally supervenes upon B, then B too must exhibit Cognitive Command. Were it not so, it should be conceded that even if every disagreement in A, satisfying Cognitive Command, is always explained by cognitive shortcomings, it nonetheless depends on disagreements in B, which are not always explained by cognitive shortcomings.

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Independently of the fortune of the preceding argument, however, I will propose an additional argument. The general thought which underlies it is that, if we allow for the conclusion that disagreement about logic is not constrained to be cognitive in nature, something like a global form of antirealism should derive from the acceptance of the Cognitive Command as a condition for objectivity; with the consequence of emptying the condition of any significance in relation to the realist/antirealist divide. I will conclude the first half of the second chapter by maintaining that the current literature does not seem to provide compelling a reason not to regard logical truth as objective truth, either in the sense of mindindependent truth, or in Wright’s sense of an objective cognitive domain. In the third chapter I will consider a recent epistemological account of objective, logical knowledge. A result of the first chapter is that the attribution of a meaning-constituting function to introduction and elimination rules for a logical constant provides the materials for a rulecircular (pragmatic) justification of our logical beliefs. Boghossian has recently attempted to show how such an account could be specified. Boghossian addresses the problem about how we know, if we do, that the rules of inference we employ are valid. His claim is that such knowledge has to be accounted for in terms of arguments which employ in one of their steps the very rule whose validity the argument is suppose to prove. One problem with arguments of this sort is that every rule can be proven valid if the use of such rule is admitted as a legitimate move in the proof. Boghossian’s strategy is to show that not every rule can be legitimately employed in a proof attempting to show that this very rule is valid. The proposal is that just meaning-constituting rules may be employed to that effect. The rationale for such a restriction is epistemological in nature, and concerns the theory of justification. On the one hand, Boghossian claims that Internalism, the theory according to which a belief that p is justified if it is entertained on the basis of self-consciously entertained good reasons, makes inferential transition of justification impossible. The demands of internalism, he contends, are too strong: the Lewis Carroll regress argument shows that, even if we knew of a particular inference that it is truth-preserving, our use of it could never be internalistically acceptable. As a consequence, Boghossian proposes the weaker internalist account according to which a belief that p is justified if it is entertained on the basis of a responsible epistemic practice. Inferring according to a meaning-constituting rule of in-

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ference is not an irresponsible epistemic practice: if a subject fell short of the disposition to infer in accordance with that rule, she would not possess the concept it constitutes, therefore she could not entertain any propositional attitude toward the very rule, let alone prove it valid. An assumption of Boghossian’s argument is that Externalism does not provide the correct account of justification. Accordingly, I shall assume that it does not. However, I will argue two points that seem to counter Boghossian’s strategy. The first is that he incorrectly derives from the claim that inferring according to R is not epistemically irresponsible the claim that inferring according to R is epistemically responsible. At best, a meaning constituting inferential practice cannot be assessed as epistemically responsible or irresponsible deployment. Accordingly, I will deny that rule-circular arguments employing meaning constituting rules of inference do provide internalistically acceptable justification even in the weaker sense envisaged by Boghossian. Secondly, I shall deny that the Carrollian regress problem makes inferential transition of warrant impossible even under the hypothesis that we directly know, of particular rules of inference, that they are valid. This conclusion depends on two undefended assumptions concerning the nature of the transition of warrant, in particular on the assumption that knowledge that R is truth preserving justifies one in inferring through R only because such knowledge constitutes an additional premise for a further inference. Boghossian does nothing to show that this is the right picture, and it is consequently open to his opponent to simply deny it. I will conclude the second chapter by diagnosing the dialectical situation. The failure of Boghossian’s rule-circular manoeuvre leaves undefended the claim that we do have objective logical knowledge. More than this, Boghossian’s regress argument does not show that that direct accounts of logical knowledge are useless, because it does not show that they fail to make good sense of inferential transition of justification. In the light of the envisaged urgency of an account of objective logical knowledge in order to dispel relativist and sceptical epistemological conclusions, I will devote the third chapter to an analysis of an alterative picture of a priori justification based on the Husserlean concept of eidetic insight. Contemporary epistemologists, however, manifest a distinguished tendency to equate rational insight, or, by using a broadly corresponding husserlean terminology, eidetic insight, to wishful thinking. A typical criticism (endorsed by Boghossian, for instance) is that unless a natural-

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istic acceptable explanation is given of how the faculty of rational insight (or eidetic seeing) is supposed to work, and give us access to necessary structures of reality, no such faculty should be accepted. A typical rationalistic reply, one that roughly constitutes the structure of the present work, is that rational insight seemingly constitutes the only viable alternative satisfactorily to reconstruct pieces of objective knowledge whose aprioricity fairly no one would be disposed to challenge. As we have seen, neither implicit definition, nor rule-circular justification, seems to constitute viable alternatives. As a consequence, unless one is disposed to accept that we actually engage in a fully responsible epistemic practice, by deploying rational insight, one should have to admit that we lack objective knowledge of logic and, via the indicated link between logic and the notion of epistemic justification, that we lack objective knowledge of the world. Though, in my opinion, effectively supplying some warrant for the conclusion that rational insight should be admitted, such considerations do not exhaust the arguments an Husserlean objectivist or a contemporary rationalist could deploy to defend her position. I think that, contrary to the customary presentation of the dialectical situation, two main concerns come to the fore. The first one is related to the phenomenological level of description of cognitional acts (eidetic seeing, as based on eidetic variation, included); the second is related to a broadly phenomenological analysis of concept formation and possession, and, as closely related to it, to the broadly phenomenological conception of conceptual analysis and conceptual truth. The first concern arguably comes to the following line of thought. When adopting a phenomenological point of view – one, to be sure, that can be taken in full abstraction from a literal interpretation of the various phenomenological epoches – an epistemologist undertakes to describe the subjective modes of giveness of the objects of cognitional acts. Justification, in this perspective, becomes a notion which hinges at the way things present themselves to the subject of cognitional acts. A perceptual belief, for instance, is justified as long as perceptual experience exhibits certain traits which are appreciable at the level of the phenomenological description of Erlebnisse: the perceived object manifests itself through a multiplicity of phases, which are coherent with one another, displaying an uninterrupted continuity and a distinguished tendency to motivate expectations which, in the subsequent unfolding of the perceptual experience, are fulfilled. The actual perception of a tree, for instance, moti-

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vates expectations as to the characteristics the object would show if perceived from another standpoint; and the subsequent perception of the other side of the tree, if performing a fulfilling function, may eventually accrue some – reflectively appreciable – warrant for the belief that in front of the perceiver there is a tree which is so-and-so. A typical counter against the phenomenological treatment of the epistemic notion of justification is that, as long as it exclusively concentrate on the description of the structures of cognitional acts, it completely disregards that justification should be analysed in terms of a belief being gathered in a way which is reliable (externalistic condition) and, more than this, positively known to be reliable (internalistic condition). The latter claim, however, calls for a suitable explanation as to why one should think that beliefs gathered by means of perceptual experience are reliable: and the answer that is typically returned is that there is a causal relation between the state of affairs the belief is about and the content of the belief which enables us to suppose that the obtaining of certain epistemic conditions enhances the probability of the belief’s being true. Accordingly, an epistemologist could be tempted to disallow for a phenomenological order of explanation of our justifiably forming perceptual beliefs about the world, and to require a treatment of the notion to relate both to the reliability of our epistemic norms and our knowledge thereof. Yet, the phenomenologist has at her disposal the following reply: it is true that a belief, unless it is acquired in a way a subject knows to be conducive to truth, can hardly be epistemically justified. It is also true that the phenomenological characterisation of perceptual warrant more or less extensionally coincides with the internalistic treatment thereof. Yet, no clear account of our possessing a warranted belief about the reliability of perception can be mounted by resorting to the postulation of a suitable causal chain leading from the object to the subject. In fact, the phenomenologist could urge, causation is not something we could have some ground to suppose as operating at a perceptual level unless by resorting to the deliverances of perception itself, and to the information about the world it is normally taken to encode. That perception is reliable, in so informing us about there being causal relations which sustain the claim that perception is reliable, however, is nothing that perception, in turn, could noncircularly help us to believe. As a consequence, it could be argued that any belief about the reliability of perception, should either be disallowed, or, if accepted, that it should be accepted on the basis of a phenomenological description of the structure of perceptual experience.

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Since it is normally accepted, I will urge that, unless one is prepared not to accept it in the case of perceptual justification, and, as a consequence, to reject the notion of perceptual reliability, there do not seem to be compelling reasons to reject a phenomenological account of a priori knowledge based on the description of the structure of eidetic experience. I have already insisted on this point when discussing Cognitive Command and stressing, in defence of the objectivity of logic, that there are no better reasons to regard disagreements about sense perception’s reliability as cognitive, than there are to see logical disagreements as cognitive. The reason why should now become apparent. What I have been proposing, in fact, is nothing but a generalisation of the phenomenological notion of justification, which, in the case of logic as in the case of perception, just comes to the requirement to take at face value the phenomenological structure of cognition and evidence. Since such structures exhibit features which are constitutive both of perceptual acts and of intellectual or rational acts of insight – every cognitional act begins with a rough prehension of its object, and, following the Leitfaden attached to its content, ends up, if successful, with a full apprehension of it – there seems to be no reasons for granting perception, and not acts of eidetic seeing, a distinguished right to posit their own objects. Before passing at the second part of the third chapter, I will consider a possible reply, which is based on the Quinean notion of the web-of-beliefs. According to the reply in question, it could be conceded that the reliability of perception cannot satisfactorily be reconstructed by resorting to the deliverances of perception. The belief that perception is mostly reliable, however, contrary to the belief that rational insight or eidetic seeing is reliable, could be seen as credible in that it depends on its being conducive to the maximization of the coherence amongst the beliefs in the web. It is the overall structure of the web which rationally motivates the acceptance of the reliability of perception. As against this, I will deploy an argument, which has been put forward, amongst others, by BonJour, Wright, Resnik and Shapiro, to the effect that the very notion of coherence amongst the beliefs in the web hinges at the underived acceptance of a logic by means of which questions as to the coherence, incompatibility, maximization of simplicity of the system must be assessed. The main result of the argument, as a consequence, would seem to be that unless some positive account is given about our entitlement to make use of some logic to assess questions related to the coherence of the web, no clear explanation could be given why we should regard perception, on

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the basis of the characteristic of the web, as reliable. On the other side, if such an account could be given, it should be independent of the characteristics of the web, and there would be enough room to take into account means to justify our epistemic practices which are independent of holistic considerations. More than this, I think that a phenomenological account of concept acquisition and concept possession may illuminate the very functioning of eidetic insight. The rough idea is this: the process of eidetic variation seems to be the hostage of two separate objections; they pull towards opposite directions, but their disjunctive presentation seemingly leaves no room for a rational reconstruction which is capable of jointly securing the distinct claims according to which (a) the deliverances of eidetic seeing constitute pieces of objective knowledge about reality, which (b) are justified a priori. Eidetic seeing is the result of a process of eidetic variation. By arbitrarily varying in imagination instances of a determinate kind – say, material things – we eventually come to know what all the instances have in common and what, therefore, constitutes their essence – alternatively, a set of properties a material thing, being what it is, could not but possess. On the one side, however, it has been replied that as long as eidetic seeing constitutes an extrapolation – and is a function – of all the instances that have entered the variational multiplicity, its epistemic deliverances should be seen as possessing a merely inductive, revisable and probabilistic character. On the other side, it might be replied that eidetic seeing is not a process of inductive generalisation. The high price of preserving the a priori status of eidetic variation, however, is the trivialization according to which it should be equated to a process whereby we clarify the content of our concepts. Otherwise, the criticism goes, it would be impossible to understand how a subject could be attributed the capability of selecting appropriate instances and allowing for their insertion into the variational multiplicity. The subject, so to say, should be attributed to have the possession of the very concepts whose content, and defining traits, is clarified by means of eidetic variation. I think that the second horn of the dilemma should be chosen. In a sense, it could be right that eidetic variation constitutes a process whereby we make clear to ourselves the content of the formal and material concepts we possess and deploy in our ordinary cognitive practice. What shouldn’t be allowed, however, is the move that is normally taken immediately thereafter; the move according to which both analytic and synthetic a priori propositions, in Husserl’s sense, should be equated, given

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the way they are supposedly justified, to non-factual, uninformative and linguistic conceptual truths. Not, at least, if something of the sort of the phenomenological reconstruction of concept constitution is allowed to enter the picture. Much in the opposite direction, in fact, it could be had that the way both formal and material concepts have been acquired, motivate the conclusion that, by clarifying their content, we simply display pieces of objective knowledge. The process of eidetic variation, in fact, can be taken to be directed by the very epistemic principles which are operative in the way the concepts, whose content is clarified, have been acquired. The idea is that, independently of whether one chooses to call such propositions synthetic or analytic, the concepts we clarify by eidetic variation do not constitute just revisable and conventional means of categorization, but answer to salient traits of reality and consequently can be recognized as founding a kind of truth which should be regarded as objective, informative truth about the world. As a consequence, I will be proposing to equate this kind of informative truth about the world with what synthetic a priori propositions, in Husserl’s sense, do express. In so doing I will defend Husserl’s characterization of the analytic/synthetic divide – mainly concerned on the nature of the concepts which possess an essential occurrence in the proposition – and propose the husserlean notion as a suitable reconstruction of the kantian/empiricist notion on the basis that both notions encode knowledge about the world. In the end, I shall try to defend the general claim that conceptual truth may be regarded as objective and informative truth about reality, by arguing against Conventionalism, in both Ayer’s and Carnap’s formulation.

A Priori, Analyticity, and Implicit Definition Empiricism, Analyticity, and the A Priori Empiricism is the philosophical tradition according to which all knowledge human can have of the external world stems from, and is justified in the light of, the outcome of external experience. Call this epistemological principle (EMP). Contemporary empiricists – the philosophers who joined during the Twenties and Thirties of the last century the socalled Wiener Kreis – pleaded for a different characterisation of the tradition which their movement (Logical Empiricism) was making explicit reference to. Instead of characterising Empiricism by means of EMP they preferred to identify, though tentatively, their position with the refusal of synthetic a priori knowledge. Contemporary empiricism does not deny, as traditional empiricism does, that there are forms of justification that are not experiential. However, it counts as a form of empiricism because it still sticks to EMP. One major problem for EMP was constituted by logic and mathematics. Mathematical and logical statements appear to be necessary statements. They do not simply state, for instance, that 2 + 2 equals 4. The statement at issue seemingly states that 2 + 2 necessarily equals 4, that it must do so. Same story for the truth of logic: it is not simply the case that for every proposition p, the conjunction of p and ¬p is false. Rather such conjunction is necessarily false, it must be false. To know a logical and mathematical statement, so it seems, is to have a justified true belief in a necessary statement. The problem for EMP derives from the observation that its endorsement is inconsistent with the admission of logical and mathematical knowledge. If, in accordance with EMP, experience is the sole source of justification, logic and mathematic cannot be known. For experience cannot justify, to a degree sufficient for knowledge, a belief in a necessary statement. Experience can only tell us that something is such and such, not that it must be such and so. Accordingly, the un-

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conditional acceptance of EMP commits the empiricist to deny that we have any true mathematical or logical knowledge. A traditional reaction to this unpalatable upshot has been to deny that logic and mathematics are necessary. J.S. Mill, for instance, has notoriously maintained in his System of Logic that geometrical and mathematical statements are inductive generalizations of experience, and as such, that they are not necessary. As far as logic is concerned, Mill’s solution is that logical statements are necessary, though only verbally so. As we are about to see, the position on a priori knowledge taken by the contemporary empiricists constitutes a generalization of the latter position. Like Mill for logic, the Logical Empiricists have maintained that logical, mathematical and geometrical statements are indeed necessary. However, they have denied that such statements convey knowledge about reality. They are indeed known a priori; however such admission doesn’t commit to the denial of EMP. The principle just states that all knowledge about reality, or the world, stems from and is justified in the light of experience. Alternatively, it just states that every belief about reality can be justified on the basis of experience. According to the Logical Empiricists, logical and mathematical statements are analytic statements. No clear unique account has ever been given as to what kind of property analyticity is supposed to be. Among the most influential characterisations of this property we can list the following: a statement is analytic iff (i) it lacks cognitive content, (ii) it is formally true, (iii) it owes its truth solely to the meanings of its constituting expressions, (iv) it is tautological. The common trait of all these characterisations is that an analytic statement does not state contingent matters of fact concerning reality. Its truth, as a consequence, is not the result of the obtaining of corresponding matters of fact. Analytic truth, on the contrary, somehow results from the linguistic apparatus that is used to express it, and is thereby to be qualified just as linguistic or conventional truth. As BonJour has put it, analytic truth is “very roughly, merely a product of human concepts, meanings, definitions, or linguistic conventions”1.

1

BonJour 1998, p. 28.

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So long as analytic statements are characterised as failing to have any direct bearing on reality, EMP is not put in danger by the admission that analytic statements are known – justifiably believed to be true – on the basis of non experiential sources of justification. A clearly acceptable account of this source needs just to mention the nature of analytic truth: since it is derivative on linguistic meaning, or concepts, the general suggestion is that full mastery of these meanings, or proper possession of these concepts, suffice for appreciating their truth. The account will vary according to whether analyticity is conceived in reductive or in non-reductive terms. Reductive and Non-Reductive Conceptions of Analyticity According to reductive accounts of analyticity, a statement is analytic if it is reducible to some other kind of statements. Kant’s and Frege’s conceptions of analyticity are examples of this sort. According to Kant a statement of the subject-predicate form is analytic if it is reducible to a statement of the form ABC is A. According to Frege, a statement is analytic if it is reducible to a truth of logic. From an epistemological point of view, reductive strategies let the justification we have for believing an analytic statement depend on the justification we have to believe the corresponding statement in the reductive class. Kant, for instance, famously claimed that our justification for accepting an analytic statement just depends on our knowledge of the principle of contradiction. For any analytic statement, in fact, this statement is reducible to a statement of the (identical) form ABC is A. Appreciating that such a statement is true just presupposes that, along with the principle of non-contradiction, any statement of this form cannot be false. Frege, on his part, claimed that our justification for accepting an analytic statement depends on the justification we have for accepting the purely logical principles and definitions from which it is derivable. Naturally enough, the empiricist cannot simply resort to a reductive analysis of analyticity when trying to account for the a priori justification we have for accepting analytic statements. Such accounts are necessarily incomplete, for they make essential reference to the justification we have for accepting the statements in the reductive class, and such jus-

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tification, on pains of circularity, cannot be accounted for by noticing that those statements are analytic. This move would result in the unhelpful observation that such statements are knowable a priori because they are knowable a priori. Both Kant and Frege believed that the justification we have for accepting the statements in the reductive class is of an unproblematic sort. Frege, in particular, believed that logical statements are self-evident statements, not in need of any particular defence. They are simply to be accepted as far as they are understood. Such a defence is however unsatisfactory for the empiricist. On the one hand, it fails to discriminate the empiricist position from its rival rationalist one. The rationalist’s account, very roughly, has it that a statement is justified a priori if understanding what it means suffices for accepting what it says as necessarily true. Understanding, on the rationalist account, constitutes a precondition for an act of rational insight, that which is supposed to yield knowledge of the necessary truth of the statement. To maintain, as many empiricists have done, that upon understanding an analytic statement in the reductive class one can see that the statement is true may seem to be just an alternative way of saying the same thing. So, unless the kind of seeing involved is not specified in further details, or its apparent assimilation to the rationalist notion of insight is disambiguated, no clear difference between the empiricist and the rationalist account of the statements in the reducing class is forthcoming. On the other hand, the move of appealing to the undifferentiated seeing that a statement is true seems to be of dubious explanatory value, unless it is paired with a clear explanation of how language mastery is supposed to yield, or somehow to result, in knowledge of what the statement in the reducing class says (see Casullo 2003, p. 220). For all these reasons, any sound account of a priori knowledge cannot just invoke a reductive notion of analyticity. Room must be made for non-reductive accounts of analyticity: the a priori knowability of analytic statements in the reductive class must therefore be accounted for in an independent way.

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Implicit Definition, Logical Truth, and the Recalcitrant A Priori The contemporary debate about a priori knowledge has devoted considerable attention to the notion of implicit definition. Such a notion is a natural candidate for accounting for the a priori epistemological status of the statements in the reduction base. Implicit definitions are in fact normally invoked in order to account for our knowledge of logic, and there is no doubt that the truths of logic should be part of the reduction base. As we have already seen, Frege was of the mind that a statement is analytic either if it is a substitutional instance of a truth of logic, or if, by using definitions, it can be reduced to a substitutional instance of a truth of logic. Therefore, Frege’s notion of analyticity calls for an explanation as to how the truths of logic can be known a priori. As recently maintained by Morscher, Carnap’s notion of analyticity is also, strictly speaking, to be identified with the notion of logical truth. By taking Quine’s reconstruction thereof, Morscher argues that Carnap’s identifies analytic truths with the statements whose truth is due just to the logical form. More precisely, drawing an interesting comparison with Bolzano, Morscher suggests that a statement is analytic in Carnap’s sense if it is true and the uniform substitution of every expression of the statement belonging to the non-logical vocabulary yields a true substitutional instance of the original statement (Morscher 2006, p. 257). Clearly enough, for every statement p allegedly known a priori, appeal to p’s analyticity in Carnap’s sense helps to account for its a priori knowability only to the extent to which it is available an account of our knowledge of the truths of logic in the first place. How is the notion of an implicit definition to help? To put it in the terms of Boghossian’s recent, and influential proposal, It is by arbitrarily stipulating that certain sentences of logic are to be true, or that certain inferences are to be valid, that we attach a meaning to the logical constants. More specifically, a particular constant means that logical object, if any, which would make valid a specified set of sentences and/or inferences involving it (Boghossian 1997, p. 348).

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The main idea is that there is a specific connection between the way the meaning of certain primitive notions is established, and the knowledge we thereby acquire of certain basic contexts containing those very expressions. The suggestion is that certain contexts, containing an undefined expression, are stipulated to express a truth. Such a stipulation, so goes the theory, affects that the definiendum acquires the meaning, if any, which is necessary to make the context correct (either true, if the context at issue is a sentence, or valid, if the context at issue is a set of rules of inference). How can a stipulation of that sort bestow a meaning on the definiendum? As Horwich has put it, the widely accepted answer is that “the decision to regard ‘#f’ as true is, implicitly, a decision to give ‘f’ the meaning it would need to have in order that ‘#f’ be true” (Horwich 1998, pp. 132-133). Our decision, in other words, performs the role of constraining the definiendum to take up the meaning that accords to the way in which we have decided to use the context containing it: that is to say to take up the meaning that renders the entire context correct. Before devoting our attention to several criticisms put forward against the actual viability of this model, let’s just pause to stress two important points. If the meaning of certain primitive expressions is defined in the indicated way, there seems to be a direct route from our understanding certain contexts and the knowledge we have of what they say. For it is our understanding those context in the way we do that, according to the model, is constitutively involved in the explanation of why those contexts have the meaning they do, and, moreover, the meaning which makes those contexts express truths. So, the model of implicit definition seems to provide the desideratum of a sound theory of the a priori based on some non-reductive notion of analyticity. This model seems naturally to apply to the truth of logic. As Boghossian’s quote makes it apparent, a natural suggestion as to how the meaning of the logical constant is determined is that it is determined by our resolve to accept as valid certain basic rules for the introduction and the elimination of those constants; rules, respectively, which specify what contexts not involving the logical constant are sufficient to introduce contexts involving it, and rules specifying what contexts, not involving the constant, can be derived by the previous contexts involving it. It is by our resolve to accept these rules

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as truth-preserving that we bestow the meaning needed for those rules to be valid, and it is by our understanding these rules in the intended way that we effect that these rules do preserve truth. Since we do (know we do) understand the rules in the intended way, then we know that these rules are truth-preserving. Accordingly, we have a good explanation why such logical principles or rules are such that as soon as we understand them we are in a position to accept them as correct. Moreover, the explanation is clearly different than the account offered by the Rationalist. No direct insight into the nature of necessary logical facts is called into question. Just a fairly modest account of how the meaning of the logical constants is determined. Secondly, the account nicely promises to generalise to those statements normally regarded as problematic from within the reductive conceptions of analyticity. Such recalcitrant statement may be exemplified as follows: (H) if a thing is red all over it is not at the same time and under the same respects green all over or (H1) Every sound has a pitch. While both (H) and (H1) can be hardly regarded as substitutional instances of logical truths, hence not analytic in the reductive sense, they can be regarded as implicit definitions of the chromatic expressions they contain. The general argument for the former claim is that, contrary to “bachelor” and “unmarried adult male”, “red” is neither equivalent to “not green”, nor it is equivalent to the conjunction of all negative chromatic predicates other than “red”. The reason is simply that such predicates are potentially infinite, and it hardly constitutes a plausible condition on the understanding of the predicate “red” that one understands such not finitely conceivable (conjunctive) predicate (Delius 1963, p. 42-46). Such an argument does not apply to the suggestion that statements like (H) or (H1) are implicit definitions. Their status as implicit definitions does not require that the ingredient predicates be decomposa-

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ble in any appropriate way. It just requires that a speaker be disposed to accept every substitutional instance generated by the insertion of variable distinct chromatic predicates x and y into the schema (H2)

if a thing is x all over it is not at the same time and under the same respects y all over,

for her to understand the chromatic predicates. Moreover, it doesn’t require the meaning of a chromatic predicate to be exhausted by the disposition to accept every (relevant) substitutional instance of (H2). Ostensive definition can still play an important role in determining the predicate’s extension. Implicit definition then seems promising under two general respects: it yields a good non-reductive explanation of logical knowledge, and it yields a good explanation of our a priori knowledge of statements generally regarded as recalcitrant with respect to reductive notions of analyticity. As a consequence, it seems to offer the prospects of a sound epistemology of the a priori based on the notion of analyticity. Problems with Implicit Definition Though promising, the account of a priori knowledge based of implicit definition (hereafter, borrowing a label from Bob Hale and Crispin Wright, “traditional connection”) is not immune from criticism. Much to the contrary, the epistemological role of implicit definition has been widely disputed. L. BonJour, echoing a traditional rationalist objection, has maintained that implicit definition is not able to discharge the definitional role traditionally attributed to it. The problem is that in order to understand what meaning is bestowed upon a given expression “f” by the resolution to accept a given context “#f” as true, one has already to know, of an already understood expression “g”, that “#g” is true. Only in such a way can one understand what is expressed by “f” after having stipulated “#f” to express a truth. However, if this is the correct picture, implicit definition is a dispensable semantic device. For it can contribute to determine a meaning for a new expression only if this meaning is the same of some other, previously understood, expression available in the

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vocabulary. Secondly, and more importantly, the traditional connection is clearly undercut; for “#f” can play the definitional role only if it is already known, very presumably on a different and independent basis, that “#g”, which is equivalent to “#f”, is true. So whichever content “#f” comes to express whenever it serves as an implicit definition of “f”, the definition is successful only to the extent to which such content is already and independently known. Fodor and Lepore have advanced a second criticism. Its overt target is not the model of implicit definition. Rather it is conceptual role semantics (hence CRS), the theory that identifies the meaning of an expression with its conceptual role, the role it performs in inferences. As it is apparent, the difference between the CRS and the theory of implicit definition is not relevant in this context. The CRS is in fact the theory of implicit definition as applied just to inferences. The CRS just states that the meaning of an expression is specified by the contribution it gives to the inferential power of the statements it occurs in. Fodor and Lepore’s objection is that acceptance of the CRS commits to the rejection of the compositional nature of meaning. Compositionality is the property according to which the meaning of a complex expression (statement) is entirely a function of the meanings of its constituents. The requirement that meaning be compositional derives from the fact (among others) that, if it was not the case, language learning would be reconstructed as the (infinite) task of learning, one by one, the meanings of all the (atomic and molecular) expressions (contained or constructible) in a language. According to Fodor and Lepore, conceptual roles are not compositional: if the meanings of complex expressions are constituted by their conceptual roles, the correct inferences the complex expressions enter in should be a function of the correct inferences their constituents are separately part of. The complex expression “brown cow”, however, seemingly enters in the inference “brown cows → dangerous” – if just one happens to believe that brown cows are dangerous – which is not a function of the inferences “brown” and “cow” separately allow for. According to Fodor and Lepore, the objection at issue is inescapable, because the only available answer requires the identification of meaning with the conceptual role in analytic inferences, which, in turn, implies the acceptance of the analytic/synthetic distinction. Since, ac-

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cording to Fodor and Lepore, the distinction at issue has been definitively dismissed by Quine’s attacks, there is nothing (i.e. analytic inferences) to which the conceptual role semanticist could appeal to in defending its position. P. Horwich has put forward a third objection to the traditional connection. According to him, the theory according to which the decision to accept as true certain (partially) uninterpreted sentences bestows upon the uninterpreted constituents the meaning required for the sentence (once fully interpreted) to be true, is flawed by problems whose solutions deprive the proposed account of any explanatory power in relation to a priori knowledge. If effective, this objection doesn’t impede attributing implicit definition a primary semantic role. It would just undercut the explanatory relation between such a semantic notion and a priori knowledge. BonJour’s Objection BonJour’s critique of the traditional connection seemingly stems from the following line of reasoning. If a priori knowledge of p is genuinely to be explained in terms of the employment of a method M, then the employment of the method M clearly does not have to presuppose (a priori) knowledge that p. This condition is to prevent the alleged explanation either from bare circularity or from dispensability. In fact, if M presupposes knowledge of p, either knowledge that p will be circularly explained by making reference to M, or by making reference to some other method M*. In this case, explanation of a priori knowledge that p in terms of M is dispensable, for M* provides a more fundamental and direct way to explain it. In either case M does not provide an explanation at all. BonJour’s allegation is that the traditional connection doesn’t satisfy this condition, and that, as a consequence, it either provides a circular explanation of a priori knowledge or a dispensable one. Let us quote BonJour at length: Thus, for example, one might stipulate that the sentence ‘40 @ 8 = 5’ is to count as a (partial) implicit definition of the symbol ‘@’. This along with other stipulations of the same kind, might be a useful way of con-

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veying that ‘@’ is to stand for the operation of long division (assuming that the other symbols in the sentence are already understood). But if this is the right account of implicit definition, then the justification of the proposition that 40 divided 8 is equal to 5 (as opposed to that of the linguistic formula ’40 @ 8 = 5’) is not the result of the implicit definition, but is rather presupposed by it: if I were not justified in advance, presumably a priori, in believing that forty divided by eight is equal to five, I would have no reason for interpreting ‘@’ in the indicated way (BonJour 1998, p. 50).

The problem with BonJour’s suggestion is that, contrary to his assumption, it doesn’t seem to be concerned with the correct account of implicit definition. His suggestion is that an implicit definition works by making available to its addressees a recipe for translating the definiendum it contains into previously understood vocabulary. In BonJour’s example, the recipe is to take the expression in the language which, when substituted into “40 @ 8 = 5” in the place of “@”, gives rise to a true statement. If this is the right account of implicit definition, then the traditional connection turns out to be either circular or dispensable. In fact the recipe cannot be implemented unless one already knows, in the case at issue, that 8 divided 5 is equal to 4, which is the bit of knowledge the traditional connection was to explain in the first place. However, it should be clear that the implicit definition of an expression has not to take the form of a recipe for translating the definiendum into previously available vocabulary. First of all, implicit definitions would turn out to be very dispensable semantic devices. Why on earth, it might be asked, should a community bother to define implicitly the expression “@” in the indicated way – let alone introduce the sign in the first place –, when an explicit definition like “let ‘@’ mean ‘long division’” would provide in a much more direct and safer way the definiendum with a meaning? The answer is clearly: for no reason at all. The point of implicit definition is in fact to provide an account of the way the meaning of so-called primitives (or indefinables) is determined, not to account for alternative ways in which the meanings of expressions oth-

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erwise explicitly definable in terms of previously understood vocabulary could be determined2. BonJour’s objection actually assumes that acceptance of an implicit definition as true and understanding the meaning of its definiendum are logically (perhaps temporarily) distinct moments. As we have seen, BonJour regards the acceptance as true of “40 @ 8 = 5” as a necessary condition, whose fulfilment enables the addressee of it to find out which meaning, given the things she knows, “@” does need to take up. In light of the different roles performed by implicit definitions, however, the obvious alternative BonJour disregards is that understanding the definiendum of an implicit definition actually coincides with the disposition to use it in accordance with its truth. When an implicit definition is so understood, BonJour’s critique no longer stands. If acceptance of an implicit definition and understanding its definiendum are not two distinct processes, but one and the same, the traditional connection is immune from the charge of circularity or of dispensability. Being able to understand an expression implicitly defined by stipulating that a certain context containing it be true does not require anymore antecedent knowledge of the proposition that such context, once interpreted, comes to express. Sure, this is just to say that the problem specifically addressed by BonJour does not survive closer inspection of the way implicit definition is supposed to work. It is not also to say that implicit definition may be taken to work in that way without any problem, nor that, once built upon this model, the traditional connection can be vindicated with ease. In particular, a major difficulty seems to tell against the second suggestion. Horwich has suggested the first one: on the model I have outlined, understanding consists in the acceptance of the implicit definition as true, 2

Though directed against a different target, the following quote from Hale and Wright seems to be highly pertinent to BonJour’s reconstruction of the model of implicit definition: “that is tantamount to the demand that successful, implicit definition requires a recipient to have—or to have access to—independent resources sufficient for an explicit definition of the definiendum. Yet it was all along an absolutely crucial point about implicit definitions, as traditionally conceived, that they were to serve in cases—fundamental mathematical and logical concepts, and scientific-theoretical terms—where no resources for (non-circular) explicit definition were available”, Hale and Wright 2000, p. 293.

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and is not consequent upon the identification, by independent means, of the true proposition the implicit definition, once the definiendum has been interpreted in the intended way, comes to express. This picture is supposed to rescue the traditional connection from BonJour’s attack. However, if meaning consists in merely accepting the implicit definition as true, the traditional connection seems to be undercut for a different reason: on the model at issue, we simply have no guarantee that, besides our resolve to regard the implicit definition as true, it is actually true. Let us now consider Fodor and Lepore’s objection, which seems to raise very general doubts against the claim that understanding the meaning of an expression may coincide with accepting certain basic contexts containing it. Fodor and Lepore’s Objection As already seen, the target of Fodor and Lepore’s attack is not the theory of implicit definition, but the CRS. According to this view, roughly, the meaning of every expression is exhausted by its role in inferences. However, a closer specification of this doctrine requires more than this. Every expression enters many different inferences, and a principled distinction among those inferences that are relevant for determining its meaning and those that are not is called for. The problem with the CRS, so suggest Fodor and Lepore, is that it is not clear what answer could be given to such a request. On the one hand, the CRS theorist cannot simply grant that all the inferences an expression enters in are relevant for determining its meaning. The following argument is supposed to explain why. Take the complex expression “brown cow”. Brown cows are dangerous animals, so if every inference an expression enters in cooperates to determine its meaning, the meaning of “brown cow” is also determined by the fact that it enters the inference “brown cow / dangerous”. However, consider the expression “brown” and the expression “cow”. Not everything that is a cow is dangerous, neither everything that is brown is dangerous. So, the following inferences do not seem to hold: “x is a cow / x is dangerous”, and “x is brown / x is dangerous”. A fortiori, such inferences do not determine the meaning of “cow” and of “brown”. So, the meaning of

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the complex expression “brown cow” is at least not entirely a function of the meanings of its constituent expressions “brown” and “cow”. That much is equivalent to denying the Compositionality of Meaning, the very plausible thesis that the way we understand complex expressions is entirely a function of the way we understand its constituting expressions. As long as the Compositionality of Meaning is not a negotiable belief, then, it is simply not open to the CRS theorist to identify the meaning of an expression with all the inferences this expression enters in. A plausible reaction would be to restrict CRS to the role an expression has in analytic inferences. The following argument is in fact supposed to show that compositional inference and analytic inference are equivalent notions: if an inference is compositional (e.g. “brown cow / brown animal”), then it is warranted by the inferential roles of the constituent expressions (in the case at issue, “brown” and “cow”); inferential roles, within CRS, are nothing but meanings. Therefore, for an inference to be compositional is for it to be warranted by the meanings of its constituent expressions. But for an inference to be warranted by the meanings of its constituent expressions it is to be analytic. Conversely, if an inference is analytic, it is warranted by the meanings of its constituent expressions; but meanings are inferential roles; so for an inference to be analytic is for it to be warranted by the inferential roles of its constituent expressions. Which, again, is tantamount to saying that it is compositional (Fodor and Lepore 1991, p. 336). Also this second option, however, does prove to be unviable. For it rests on the endorsement of the analytic/synthetic distinction, a distinction, the authors claim, that almost no one is anymore inclined to accept. A first question that might be raised in trying to elaborate an answer concerns what a proponent of the CRS is actually being asked by such an objection. Intuitively, what Fodor and Lepore require (and what they claim to be hopeless) is a correct and satisfying specification of the notion of synonymy. For every couple of intensionally non-isomorphic expressions (in Carnap’s sense) “A” and “BCD”, in fact, all that is required by Fodor and Lepore’s Compositionality constraint is a criterion to evaluate whether they are synonymous and whether, as a consequence, all the following inferences: A / BCD, A / B, A / C, A / D etc. are more or less directly transformable into instances of identity statements (if

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“man” and “rational being” were synonymous, the implication “man → rational” would be equivalent, by substitution of synonymous for synonymous, to “rational man → rational”, which is an instance of the following tautology: AB → B). If, then, one could supply a satisfactory notion of synonymy, one could narrow the notion of meaning constituting inference to the inferences which are grounded on synonymy relations, plus the truth of identities of the form “a → a” (plus, maybe, the truth of other logical facts)3. As it is apparent, Fodor and Lepore seem to think that Quine’s criticism of the analytic/synthetic distinction basically involves the rejection of the idea that, given any two different expressions, it is possible to decompose them in a way that makes it perspicuous whether they are synonymous, and so whether the inference from the former to the latter is analytic, and so compositional. So, it seems, Fodor and Lepore’s objection just addresses the reductive notion of analyticity, rather than the non-reductive notion supposedly explained in terms of the notion of implicit definition. In particular, their objection seems to be silent as to whether, along with the main non-reductive proposal, the truths of logic can be identified with implicit definitions of the logical constants (in other words, as to whether accepting the introduction and eliminations rule for the logical constants determines their meanings)4. 3

Boghossian roughly makes the same point when he maintains that the notion of analyticity at stake in Fodor and Lepore’s objection is the notion of impure analyticity. A sentence is impurely analytic iff “facts about its meaning suffice for its truth all by themselves, without any contribution from any other facts”, and by “any contribution from any other fact” what is excluded is the relevance of facts other than the logical ones. Meaning, as they do, impure analyticity, Fodor and Lepore just want to maintain, by claiming analyticity to be uninstantiated, that relations of synonymy are. If they were instantiated, Fodor and Lepore – who do not call into question the analytic truth of logical claims – arguably would not object to the thesis that meaning constituting inferences actually are inferences warranted by meaning and logic alone. See Boghossian 1994, pp. 112-13. 4 In Two Dogmas Of Empiricism Quine writes quite explicitly: “Statements which are analytic […] fall into two classes. Those of the first class, which may be called logically true, are typified by: (1) No unmarried man is married. […] But there is also of analytic statements, typified by (2) No bachelor is married. […] The major difficulty lies not in the first class of analytic statements, the logical statements, but rather in the second class, which depends on the notion of synonymy” (Quine 1953, pp. 22-24). The account of logically analytic statements Quine has in mind is very

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Moreover, it seems that Fodor and Lepore’s assumption that no viable account of reductive analyticity is available can be resisted along the following lines. As already seen, Quine’s argument is supposed to address specifically the notion of synonymy. Boghossian has proposed two different reconstructions of such argument, and has convincingly shown that both can be resisted. The first argument starts by ascribing to Quine the intention to show that synonymy is a property that cannot be instantiated: so it construes Quine’s view as coming to a non-factualist conception of reductive analyticity. The argument works by showing that the very argument Fodor and Lepore raise against CRS is inconsistent with the positive account they offer of meaning. As such, it sounds like an ad personam argument. If sound, though, its real accomplishment is a reductio ad absurdum of Quine’s claim that synonymies are necessarily instantiated. The argument, roughly, runs as follows: meaning realism, which is common ground between the principal disputants in the debate over CRS, just states that questions of meaning are factual in nature, i.e. that there are bound to be facts of the matter as to what means what. If this is true, though, there are bound to be facts as to whether two expressions do or do not mean the same, i.e. as to whether they are or they are not synonymous5. If Quine is right in claiming that there are not facts of the matter as to whether to expressions are synonymous, then, meaning realism must be false. But meaning realism cannot be coherently denied.

likely not to involve the notion of implicit definition. However, what matters in this context is that Quine himself recognises that the main problem affects the notion of synonymy, not the notion of implicit definition. 5 The argument closely parallels Grice and Strawson’s point against Quine. According to them synonymy can intelligibly be accounted for in terms of sameness of meaning if only the concession is made that linguistic expressions are not just sequences of marks, but meaningful entities. Harman has replied that “such an argument assumes that thee are such things as meanings”. However, it should be admitted that what the argument assumes is just that linguistic expression are meaningful, not that “queer entities” like meanings exist. See Grice and Strawson 1956, and Harman 1967-68, p. 134.

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Boghossian (see Boghossian 1990) defends meaning realism by showing that semantic scepticism (the view according to which either there are no content properties or our content ascriptions should be interpreted along non-factualist lines) turns out to be an incoherent position. The argument, roughly runs as follows: for every area of discourse (e.g. moral discourse, mental discourse), the realism/antirealism controversy is normally centred on whether its central predicates denote existing properties or on whether the properties the predicates aim to denote really exist. In the latter case, the antirealist does not deny that the sentences under dispute are truth-conditional; she claims that, since there is nothing in the world which answers to the predicates in question, they are systematically false. In the former case, on the contrary, the antirealist straightforwardly denies that the sentences in question have genuine truth conditions. Non-factualist antirealism, according to Boghossian, presupposes a strong conception of truth. If truth is conceived as Deflationism recommends it should, i.e. either as “a compliment we pay to the sentences we are disposed to assert” or as a logical device for linguistic ascent, every significant assertive sentence is bound to be truthconditional, and no relevant cognitive distinction can be drawn between sentences which have truth-conditions and those which lack them. If the predicate “true” is conceived either way, in fact, it seems sensible that a sentence is truth-apt just in case it has a role in the language (its use is properly constrained) and it possesses certain syntactical properties (it is assertive). On the modest assumption that for something (a sentence, a mental state) to have content means to have truth conditions, antirealist positions about content must take the form either of an Error Theory about truth conditions, or of a Non-Factualism about the ascription of truthconditions. Non-Factualism about content commits one to the following claim: (NF) for every sentence (mental state) S and every truth condition p, “S has truth condition p” is non-factual

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According to NF, there is no fact of the matter as to whether any given sentence possesses, or fails to possess, genuine truth conditions. NF commits to (NR) the predicate “has truth conditions p” does not denote a property, for the lack of truth conditions amounts to the lack of reference. (NR), in turn, seems to imply (NR’) the predicate “is true” does not denote a property. The link between NR and NR’ is the following. Two factors are relevant for a sentence’s being true: its truth conditions, and the way the world is. If the world is the way required by the sentence’s truth conditions, then the sentence is true. If, though, having truth conditions is not a property, it follows that being true is not a property, for in order to be true a sentence must possess determinate truth conditions. Yet NR’ actually comes to a proper formulation of a deflationist conception of truth. As we have seen, Deflationism is the view that truth is not a property, and that the corresponding predicate either has to be construed along expressivist lines or as a logical device for semantic ascent. Yet, as we have seen, (NR’) entails the falsity of NF, for if truth is deflated, there is no coherent sense in denying of sentences of the form “S has truth conditions p” that they possess truth conditions. Conversely, NF entails the falsity of NR’: if truth-conditions-attributing sentences are not truthconditional, truth has to be a property which meaningful and assertive sentences may fail to possess. Non-factualism about content is then an incoherent position. An Error Theory, in turn, comes to the incoherent view according to which no sentence of the form “sentence S has truth conditions p” is true: where the incoherence stems from the fact that every sentence of the indicated form, by being false, necessarily has to be attributed truth conditions (truth conditions that, on the error theoretic account, never obtain).

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So, on either way it can be interpreted, meaning antirealism is shown to be an incoherent position. So, there have to be fact of the matter as to what any expression means. Then Quine must be wrong6. In Boghossian 1997 we found a different argument. Contrary to the first, it relies on the presupposition that Quine’s rejection of synonymy should be regarded as coming to a form of Error Theory about the notion7. The notion of synonymy is intelligible, according to this reading, but every statement to the effect that a pair of expressions are synonymous is nonetheless systematically bound to be false. On the one hand, Boghossian maintains that the error-theoretic claim should be weakened; in fact Quine’s notion of logical truth (a statement is logically true if it is true and remains true under all reinterpretations of its constituting expressions other than the logical constants), requires the admission that two distinct tokens of the same orthographic type may be synonymous8. More than this, Quine himself allows for the possibility that two tokens of different types may be synonymous, provided that they were explicitly stipulated to be so9. On the other hand, however, Boghossian questions the reasons as to why every statement to the effect that a pair of expressions are synonymous is bound to be false. The answer he returns 6

I think that Boghossian’s argument is at least improperly presented as an argument purporting to deny that “if Quine is right about the a/s distinction, then an inferential role semantics is false” (Boghossian 1994, p. 114). The argument, so presented, wouldn’t work. It is in fact sensible that one cannot prove the falsity of a conditional by denying its antecedent. What one has to show is that the consequent can be false even if the antecedent is true. I think it would fare much better to read Boghossian argument, as suggested above, as a direct reductio of Quine’s claim about the analytic/synthetic distinction. 7 An Error Theory – as it has been introduced by Mackie in meta-ethics – is an antirealistic conception about the statements of a given area of discourse, according to which all the statements in question, although syntactically and semantically well equipped for truly describing some facts, come out invariably false. See Mackie 1977. 8 Were it not possible that two distinct tokens of the orthographic type “man” are synonymous, the substitution instance of “either x is y or x is not y”, which is obtained by uniformly substituting “man” for “y” (“either the yeti is a man or the yeti is not a man”), could not be held to express a truth. 9 When talking of the stipulative introduction of a new term, Quine maintains that “[h]ere we have really a transparent case of synonymy created by definition; would that all species of synonymy were as intelligible”, Quine 1961, p. 26.

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basically hinges on Quine’s meaning holism: given the fact that the meaning of an expression is determined by the totality of the sentences and inferences it enters in – Boghossian suggests – it is extremely unlikely that two expressions, by entering exactly the same sentences and the same inferences, may coincide in meaning. However unlikely, though, we are not given any substantive reason to suppose that it is impossible. Even if it is conceded that “unlikelihood” may be held to entail impossibility, however, it could be argued that meaning holism (the thesis that the meaning of a word depends on all the inferential links to other words) is correct only provided that (a) the Duhem-Quine thesis (according to which the justification of any sentence depends on the justification of every other sentence) is correct and (b) Verificationism (the claim according to which the meaning of a sentence is determined by its verification conditions) is correct. Yet, it could be argued that, as many philosophers have done, Verificationism could be rejected and the link between epistemological to semantic holism could be interrupted. More than this, Boghossian proposes to regard the indicated link between Semantic Holism and Error-Theory about synonymy as a reduction ad absurdum, given the intuitive implausibility of the rejection of synonymy, of the latter conception. Things could be taken the other way around and an argument might be proposed to the effect that, since synonymy (and analyticity) (i) seem to be intelligible notions which (ii) we have good reasons to think as being instantiated, Semantic Holism must be rejected, for its admissions entails the denial of (i) and (ii). It is my opinion, however, that Semantic Holism should be rejected for a further reason: by denying analyticity, it could be argued, Quine eventually commits himself to regarding every change in belief (a sentence once regarded as true, at a certain point, comes to be denied) as a change in theory. Meaning Holism, however, entails, contrary to Quine’s commitments, that every change in belief determines a change in meaning. As a consequence, if the negation of a sentence – say “…M…” – which was previously regarded as true, effects a change in the meaning of “M”, “non-…M…” cannot be regarded as correcting the theory about whatever “M” may have happened to denote, but as supplying a true assertion of a new theory, which is about whatever, given its new meaning, “M” now happens to denote. As a consequence, it might be urged that,

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since the consequences of the rejection of analyticity are actually inconsistent with the consequences of Meaning Holism, which in turn constitutes a premise for the rejection of analyticity, Meaning Holism – by Quine’s own lights – should be denied. Even if such arguments pursue the goal of showing that the notion of meaning constitutive inference (or sentence) is specifiable by means of the notion of (impure) analyticity, Boghossian’s intentions are more ambitious, though leading to conclusions that, in my opinion, fall short of being convincing. What Boghossian tries to reject, in fact, is what he calls the Principle; the thesis, maintained by Fodor and Lepore, according to which the only plausible way to specify non-problematically the notion of meaning constitutiveness is to narrow it to the notion of analyticity (i.e. the thesis that if the conceptual role semantics is true and Quine is wrong, then, if there are meaning constituting inferences or sentences, then they are analyticities). The argument his rejection relies on is the following: if a sentence – let’s say “dogs bark” – or an inference – “x is a dog → x barks” – are to be constitutive of their meaning, then acceptance of what they say is necessary for their meaning what they do. If, then a sentence (or an inference) is meaning constitutive, then its meaning what it does suffices for holding true what it says. From this, the conclusion would follow that meaning constitutive sentences (or inferences) are analyticities only if a sentence’s being held true amounted to nothing else than its being true. Against this, Boghossian claims that “there is all the difference in the world between saying that a sentence must be held true, if it is to mean this, that or the other, and saying that it is true”10. While it is certainly true that there is all the difference in the world, for a sentence, between being true and merely being held to be so, I am not convinced that the asymmetry holds even with the qualification “if it is to mean what it does”. What seems impossible to make sense of, in fact, is the (implicit) claim that while being held to be true constitutes the meaning of a sentence (i.e. bestows on the sentence the meaning it needs in order to be true), the sentence, with the meaning it receives by 10

See Boghossian 1994, p. 119. His point is stated also in the following way: “To claim that a certain sentence is constitutive is just to say that it must be held true; it is not to say anything, in and of itself, whether the sentence is true”, ibid.

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being accepted, is still allowed to be false11. A sentence, in order to be truth-assessable, needs an interpretation. Since a (partially) uninterpreted sentence’s being accepted as true provides the interpretation (if any) that renders the sentence true, it does not seem to be possible that the sentence, with the same interpretation, can fall short of expressing a truth. It would seem arguable, in such case, that the sentence did not receive, or did change, the intended interpretation12. Boghossian’s position is closely related, at this point, to Horwich’s. Before commenting on it, though, it seems necessary to draw some conclusions as regards the standing of my position as long as Fodor and Lepore’s objection – and Boghossian’s answers – are concerned. Let’s sum up the situation: according to Fodor and Lepore the compositionality constraint requires the identification of meaning constitut11

One might be tempted to defend Boghossian’s claim by putting forward the following example: imagine a pre-scientific community for whom the concept [whale] has its content constituted (in part) by the inference “x is a whale → x is a fish”. As it has been recently concluded on a paper available on the Internet by R. Horsey, “this inference would be content-constitutive for members of this community, even though the inference is not in fact valid (and so not analytic)”, (Psychosemantic Analyticity, p. 6). Yet I cannot see how the fact that a zoologist has informed us that whales are not – widespread impression to the contrary – any kind of fish, can have any bearing on the truth of a sentence (“whales are fish”) of the pre-scientific community which, by hypothesis, does not intensionally coincide with the homophonic sentence one of us (informed) might utter regarding whales and fishes. 12 Peacocke’s notion of determination theory seemingly stands in the way of Boghossian’s argument. The determination theory associated to the possession conditions of a concept, in fact, fixes its semantic value in a way that renders the beliefforming practices mentioned by its possession conditions truth-conducive. The semantic value of the concept [red], for instance, is a binary function from objects to truth values which, for every object presented through a non-conceptual content red, if environmental conditions are standard and the perceptual organs work properly, maps it to the truth value “true”. According to Peacocke, then, the satisfaction of the possession conditions for one concept, together with the determination theory which is associated to them, secures the truth and the a priori knowability of the contents whose acceptance is constitutive of concept possession. There is no room, in Peacocke’s position, for a belief being constitutive of the possession of a concept (respectively, in Boghossian’s case, of the meaning of a term) and nonetheless being false. See Peacocke 1987, 1993a, 1993b, and 2000. It is fair to say, however, that Boghossian has actually changed his mind and that he has proposed (in Boghossian 1997) an account of logical knowledge which is based on the notion of implicit definition.

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ing inferences (and sentences) with reductive analyticities. In order to assess the question whether a given inference (or sentence) is reductively analytic, one should have to check whether it is reducible, through substitution of synonymous for synonymous, to a logically valid inference (sentence). If Quine is right, though, the relation of synonymy is not instantiated (either because it is unintelligible or because there are principled reasons why it is not). Therefore analytic inferences (and sentences) are, in turn, uninstantiated with disastrous consequences for the task of specifying which, among the inference any term does participate in, are constitutive of its meaning. Boghossian reply has been twofold: (i) he maintains that, in both interpretations of Quine’s position about analyticity, its conjunction with the Principle (meaning constitutiveness ↔ analyticity), does not imply that the meaning constituting (analytic) inferences (sentences) cannot be effectively specified; (ii) he directly attacks the Principle, by maintaining that while the meaning constituting function of an inference (sentence) requires that it is held true, it does not imply its truth (and, a fortiori, its analytic truth). While it is arguable that Boghossian is right in rejecting Fodor and Lepore’s conclusion – at least as long as meaning realism is correct –, I have been commenting, about (ii) that its conclusion should be rejected and that meaning constituting inferences (sentences) should be identified with analyticities of both sorts13. What should be emphasized, however, is seemingly something that should allow relaxing. If, in fact, Boghossian is right about (ii), then there is enough hope to specify whether any two expressions are synonymous, and then there is enough hope to specify whether a sentence or an inference – is indeed reducible to a logical truth. Since Fodor and Lepore do not question whether the proposed account succeeds in explaining how the meaning of logical constants is fixed, there seems to be, at least as long as their argument is concerned, enough hope to explain why certain analytic sentences or inferences (the one instantiating logical truths, or being thereto reducible) are known a priori by ascribing to them a meaning constituting function as regards logical words. 13

In fact Boghossian does not even mention the reason why, according to Fodor and Lepore, one should identify meaning constituting inferences (sentences) with analyticities, i.e. the respect of Compositionality of meaning.

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Horwich’s Objection Even if the preceding conclusion is sound, there is still to be considered Horwich’s objection. As anticipated, the objection at issue neither concerns the specification of which sentences and inferences are meaning constitutive nor the issue of analyticity. Granted that Boghossian is right about synonymy – and granted that we have been right in claiming that our position, in the light of Fodor and Lepore’s objection, is allowed to stand – there seems to be the problem regarding the genuine epistemological value traditionally associated with the notion of implicit definition. According to Horwich the traditional connection is false. To show why, he offers a reconstruction of how implicit definition has been traditionally taken to work; he maintains that the model is affected by four distinct problems which seemingly undermine its capability to genuinely define uninterpreted expressions; then he proposes a different construal of the notion of meaning which arguably allows for the solution of the problems – thereby re-establishing the definitional status of implicit definition –, but stands in the way of attributing to it any epistemological function in explaining a priori knowledge. The first two problems identified by Horwich concern the relation between meaning and reference. Let us start with the existence problem. The stipulation of the truth of an implicit definition constrains its definiendum to take up the meaning (if any) that is necessary for the entire context to express a truth. An implicit definition, then, may fail to bestow a meaning to it its definiendum if it constitutes a possibility that such a meaning does not exist. Take the following tentative implicit definition of the expression “f”: (ID1)

#f and 40 divided 8 is not equal to 5.

ID1 is a conjunction whose second conjunct is necessarily false. So, no matter what meaning can be bestowed upon “f”, ID1 is necessarily false. Accordingly, it is a priori that the meaning necessary for ID1 to express a truth simply does not exist. This is a rather trivial case, for it is apparent that the context at issue cannot be regarded as true from the

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very beginning. To keep implicit definitions safe from this kind of failure it seems sufficient to stipulate that an implicit definition has to respect the condition according to which, given its interpreted part, there is a possible interpretation of the uninterpreted part under which the entire context expresses a truth. ID1 clearly fails to meet this condition: given its second conjunct, there is no possible interpretation of the definiendum under which the conjunction possibly expresses a truth. A conjunction with a false conjunct cannot be true. Are there non-trivial instances of the existence problem? It is here that the connection between meaning and reference seems to be relevant. Meaning is commonly regarded as the way reference is presented. Accordingly, it might be suggested, the meaning necessary for the truth of an implicit definition might non-trivially fail to exist in the sense that there is no possible reference such meaning could present which makes the implicit definition true14. Suppose that the meaning of “The monster of Florence” is tentatively defined by the resolve to accept as true the following context containing the expression: (ID2)

The monster of Florence is responsible for the killings of eighteen persons perpetrated around Florence in-between 1968 and 1985.

It seems to constitute a possibility that these ghastly crimes have been perpetrated by a team of interconnected murderers, or that, superficial similarities notwithstanding, such crimes have been perpetrated by eighteen independent and unrelated murderers. Accordingly, it just con14

The existence problem is anticipated in Sellars 1956. Sellars’s version of the problem draws on the possible mismatch between linguistic meaning and real meaning: as far as we know, it constitutes a possibility that the stipulation of an implicit definition as unconditionally assertible bestows on the definiendum a linguistic meaning to which no real meaning corresponds, the implicit definition thereby coming to express a falsehood. Since the truth of a statement is said to depend on its real meaning, I take real meaning to be a variant of reference. “Even should there be a syntactical rule (implicit definition) authorizing us to assert ‘All A is B’ unconditionally (and therefore to derive ‘x is B’ from ‘x is A’) might there not be an object which conforms to the real meaning of ‘A’ without conforming to the real meaning of ‘B’?” (p. 144).

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stitutes a possibility that “the monster of Florence” fails to denote. If it is so, we have a non-trivial sense in which the meaning required for the truth of an implicit definition fails to exist. It is just sufficient that, given the way the world is, there is no actual reference that makes the statement true. The uniqueness problem is just a variant of the aforementioned problem. As ID1 may fail because it constitutes a possibility that nothing in reality meets the condition it specifies as to the identity of the referent of the definiendum, an implicit definition may fail also because it proposes too loose a condition. In such a case, more than one meaning (referent) is identified. Accordingly, in such case the implicit definition fails because the choice among more than one meaning is underdetermined with respect to the condition specified by the implicit definition (Horwich 1998, p. 134; Belnap 1966). Let us concentrate upon the existence problem. To take account of possible cases of failure like ID2, Horwich reviews two solutions. The first one undercuts the traditional connection from the very beginning. It reads as follows: whenever it constitutes a possibility that the definiendum fails to have a reference, reassurance that indeed it does flows naturally from every ground we might have to regard the implicit definition to express a truth. However, if our confidence that our implicit definition successfully bestows the intended meaning on the definiendum depends on additional information telling in favour of the truth of the implicit definition, then our knowledge of what it says cannot be explained by the definitional role it performs. Such knowledge will depend on the additional information we have and will be correspondingly explained in the light of the way we have gathered it (Horwich 1998, p. 134). The second one is equally devastating for the traditional connection. Horwich is of the opinion that a broadly Wittgensteinean interpretation of meaning – couched in terms of the slogan meaning is use – is sufficient to block the envisaged problem, though at the cost of undercutting the traditional connection. As to the use-theoretic interpretation favoured by Horwich, its main tenet has it that “the meaning of a word is engendered by there being a certain regularity governing its use” (ibidem, p. 138). From this point of view, the resolve to accept a given context, say our “#f”, as true constitutes, if successfully implemented, a new regularity

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governing the use of “f”, and then engenders a new meaning for the definiendum. The existence problem, then, can be dealt with by merely imposing the very loose condition that an implicit definition be such as to characterise a regularity of use that can be implemented. It is one thing to write down an alleged set of regularities, and another thing for it to be logically possible that they be satisfied; and an implicit definition can be successful only if it specifies a regularity that can be satisfied (ibidem) .

If it is just the resolve to accept as true an implicit definition that engenders a meaning for its definiendum, Horwich concludes echoing Boghossian’s contention, we cannot conclude that whenever “#f” plays an implicit definitional role, we thereby come to know what it comes to expresses. For the very good reason that knowledge that p requires the truth of p, and an implicit definition’s being regarded as true is consistent with its being, as a matter of fact, false. There is a certain ambiguity in Horwich’s account that must be clarified. According to Horwich meanings are not to be identified with (set of) regularities. Meanings are rather explicitly identified with concepts15. It is meaning-constituting properties that are identified with (set of) regularities of use. A meaning-constituting property, in turn, is identified with that property in virtue of which every meaningful expression has the meaning it has. So, Horwich contends, it is in virtue of the particular regularities that govern the word “dog” that this expression expresses the concept [dog]. As it is clear, this suggestion is rather vague as it stands. What we are not told is what kind of connection there is between a particular regularity and a particular concept, that is to say, what kind of relation explains what regularities of use of an expression determines which concept it expresses. If a regularity plays a meaning-constituting function, then there must be something specific of that particular regular15

See Horwich (ibid., 4): “I shall identify meanings with concepts (complex and simple), which I shall take to be abstract objects of belief, desire, etc., and components of such objects (i.e. propositions and their constituents). […] Moreover, I will suggest […] that properties should be identified with such concepts – e.g. that the property of doggyness (i.e. the property ‘being a dog’) is the same thing as the concept dog”.

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ity that makes it the case that the word regulated by it expresses a determinate concept, and not another concept. The most natural suggestion is that the regularity somehow constrains the identity of that concept, in a way, so to say, that whoever displays that practice cannot but mean the concept whose identity is so constrained. Naturally enough, the hard job seems to be that of specifying the kind of constraint at issue. Given the context of this discussion, we can disregard Horwich’s general theory of meaning, and concentrate on the particular case of implicit definition, as interpreted by Horwich. Here the regularity putting the constraint on the identity of the concept expressed by the expression it governs is the one specified by regarding a given sentence containing an occurrence of that expression as true. In this case, the constraining relation arguably is (or supervenes on) that of regarding as true the context in which the expression occurs. How is this constraint supposed to work? Horwich is explicit in denying that the kind of constraint it puts on the identity of the concept is that it be the concept required for the truth of the context. He explicitly countenances the possibility that the constraint can be fulfilled without its being the case that the implicit definition is true. Horwich himself suggests a promising solution when he distinguishes between direct implicit definitions and indirect implicit definitions. [A] sentence S is the direct implicit definition of a term, when our acceptance of S is necessary, as well as sufficient, for the term to mean what it does. And more broadly, I shall say that any stronger sentence will (indirectly) implicitly define the term, in so far as it entails the direct implicit definition. The acceptance of those stronger sentences will be sufficient, but not necessary, for the term to mean what it does. Thus if “∃x (#x) → #f” is the direct implicit definition of “f”, then “#f” will be an implicit definition of it (ibidem, p. 143).

Horwich says that the identity of the concept expressed by a given expression can be constrained by the resolution to regard a determinate context containing it as true. At the same time, he denies that the constraint put on the identity of this concept is that it be the one necessary for the truth of the context. Though it does not say it explicitly, the quotation seems to suggest that the compatibility of these contentions can be explained as follows. For every sentence providing an implicit definition

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of a term, there is a basic form, labelled “direct implicit definition”, that this implicit definition can take. Such form is conditional in nature, and features as antecedent an existential quantification asserting that there is an x that meets the condition specified by the initial sentence, and as consequent this very sentence. So, if ID2 is an implicit definition, the direct implicit definition that corresponds to it is (ID2C)

∃x (x is responsible of the killings of eighteen persons perpetrated around Florence in-between 1968 and 1985) → The monster of Florence is responsible of the killings of eighteen persons perpetrated around Florence in-between 1968 and 1985.

Now, Horwich says that acceptance of this form constitutes a necessary and sufficient condition for the definiendum – in this case “the monster of Florence” – to mean what it does. If it is necessary, then arguably the expression “the monster of Florence” wouldn’t mean what it does if the identity of the concept it expresses were not constrained by ID2C. Given its form, ID2C is not under the threat of the existence problem. Accordingly, the kind of constraint it puts on the identity of the concept “the monster of Florence” expresses can intelligibly be framed in terms of truth, rather than merely in terms of regarding as true. The stipulation of the truth of the conditional indeed entails that it is true, much independently of the true story concerning the author of the assassinations. For the conditional just says that, if just one single person has perpetrated these crimes, then this person is the monster of Florence (if you like, will be hereafter called “the monster of Florence”). It is at our liberty to stipulate, of a certain individual, that if this individual exists it will be referred to by means of a given expression. How are these considerations to help to understand Horwich’s claim that the outright stipulation of the truth of ID2 is sufficient, though not necessary, for the term to mean what it does? The implicit suggestion seems to be as follows: ID2 is logically stronger than ID2C, so that whoever believes the first context is committed to believe the second context. Believing the second context is necessary and sufficient for “the monster of Florence” to mean what it does. Since believing the first en-

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tails believing the second, believing the first guarantees the satisfaction of the necessary and sufficient conditions for “the monster of Florence” to mean what it does. So, believing the first guarantees that “the monster of Florence” means what it does. However, the first belief is open to defeat. It might be that no single murder perpetrated the assassinations. Accordingly, the first belief can be false. Yet, its meaning-constituting function is guaranteed by the fact that entertaining the belief involves entertaining the second belief. Which in turns constrains the identity of the concept expressed by “the monster of Florence” in terms of the concept necessary for ID2C to be true. Accordingly, believing ID2 does perform an (indirect) meaning-constituting function, and is possibly false. If this is the right interpretation of Horwich’s position, we can summarize the situation as follows: the traditional model of implicit definition has it that the meaning of certain expressions is implicitly constrained, by our resolve to accept certain contexts containing the expression, to be the one necessary for the truth of such contexts. Horwich has objected that such a stipulation is not guaranteed to succeed in bestowing a meaning on the definiendum, for the world may fall short of providing a suitable denotation for it. He then offers a different account of meaning, by maintaining that it is sufficient for an expression to receive a meaning that certain contexts containing it be regarded as true. If merely regarding a context to be true affects that the definiendum receives a meaning – that is to say expresses a particular concept – then it must be in virtue of the particular stipulation at issue that the definiendum expresses a particular concept instead of another. I have questioned in which way the resolve to accept a given context may determine which concept the definiendum expresses, and have answered that by accepting the context one is implicitly accepting its conditional, direct variant, whose role can be interpreted in the traditional manner, as constraining the identity of the concept to be the one which guarantees the implicit definition’s truth. The truth of such direct variant is not hostage of the referential success of the definiendum, and so it is something that is at our liberty to stipulate. So Horwich’s proposal, if correctly interpreted, seems to be that the epistemic deliverances of implicit definition cannot be identified with a priori knowledge of (indirect) implicit definitions,

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but rather with their epistemologically less interesting direct (conditional) variants. This seems to be confirmed by the following quote: An inclination to suppose that the content of an implicit definition must be known a priori can derive from the idea that implicit definitions involve nothing more than trivial linguistic convention. But this impression is quickly dispelled once we appreciate the difference between an indirect implicit definition and a conventional decision to convey a certain meaning in one way rather than another. As we have seen, an indirect implicit definition, in which we decide to assert a certain body of postulates, may be regarded (à la Carnap et al.) as the product of two intertwined commitments: first to believe a certain set of propositions (of logic, geometry, arithmetic, or whatever), and second, to express them in one way rather than another. Only the second of these could be plausibly regarded as an arbitrary linguistic convention16. The former – the decision about what to believe (which constitutes the decision about what concepts to deploy) – precedes any decision about how to label those concepts. This could be a priori if (a) there were some source of aprioricity other than linguistic convention, and (b) the web-of-belief model were incorrect (ibidem, p. 145).

Horwich’s position, if my interpretation is correct, is less revisionary with respect to the traditional model than it seems at a first glance. In accordance with the traditional model, Horwich thinks that the meaningconstituting relation that explains why a particular expression expresses a given concept is the constraint, put into action by the stipulation to regard a given context as true, to the effect that the definiendum must take up the meaning necessary for the very truth of the context. He just addresses the existence problem, and suggests that in order to avoid it, an implicit definition must take a direct form, that is to say the form of a conditional innocent of new referential commitments. Since any logically stronger commitment entails the weaker belief in the direct implicit definition, Horwich also maintains that the stronger commitment – in 16

In Horwich 2000 we find the more explicit proposal to characterise just direct implicit definitions, as contrasted with indirect ones, as “purely meaning constituting”. Distinguishing between a certain theory formulation (∃x(#x)) and its conditionalised version (∃x(#x) → #f) Horwich explicitly attributes just to the latter a meaning-constituting function (pp. 156-7).

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our example, outright belief in ID2 – is sufficient for an expression to receive the intended meaning. This stronger commitment, Horwich maintains, is not epistemically safe, for its meaning constituting function is derivative, and the propositional content it conveys might turn out to be false. Therefore it does not convey a priori knowledge, only the weaker commitment does. Hale and Wright’s Defence of the Traditional Connection In a recent article, Hale and Wright have questioned Horwich’s conclusion (Hale and Wright 2000). They have granted that a wittgensteinean picture of meaning is necessary to make good sense of the suggestion that the semantic role played by implicit definition is neither derivative nor dispensable. However, they have maintained that the traditional connection is not undercut by this theory of meaning. It is worth noticing that Hale and Wright’s reading of Horwich’s proposal is not in line with mine. In contrast with my interpretation, they maintain that his arguments are completely negative, in that they undercut every connection between implicit definition and a priori knowledge. If I am right, however, Horwich’s arguments have also a positive side, in that they conclude that a limited version of the traditional connection, as restricted to direct implicit definitions, can be vindicated. Indeed, if I am correct, the restricted variant of the traditional connection is a consequence of Horwich’s reconstruction of the way the identity of the concept expressed by the definiendum of an implicit definition is constrained. This observation is not immaterial when trying to assess Hale and Wright’s critical stance toward the claims put forward by Horwich. As we will see, Hale and Wright acknowledge that there is an existence problem the traditional connection has to cope with. However, they maintain that – pace Horwich – such problem has two good solutions consistent with vindicating the traditional connection. The first one is to restrict it to what they call Carnap conditionals, that is to say to restrict it to what Horwich calls direct implicit definitions. So, if my reading of Horwich is correct, the first solution is not a source of a real disagreement.

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The second one is to restrict the traditional connection to implicit definitions of a conditional kind. This solution differentiates from the first one, in that it doesn’t require the sentence containing the definiendum to be conditionalized, as in the case of “the monster of Florence”, on the actual referential success of it. As such, it can be regarded as a generalisation of the former solution. The existence problem motivates the condition that the stipulation of the truth of an implicit definition has not to be arrogant, that is to say its success has not to depend on the fulfilment of existential commitment whose satisfaction is matter of independent epistemic work. The first solution squares with the condition that the outright stipulation of a sentence’s truth has not to be arrogant. As we have seen, when analysing Horwich’s proposal, conditionals like ID2C do not involve new existential commitments. The general suggestion is now that every conditional context, specifying the conditions under which a sentence having the definiendum as constituent can be introduced, or any conditional context specifying what follows from the acceptance of such sentence, is safe from the charge of being arrogantly stipulated to be true. When commenting on direct implicit definitions like ID2C Hale and Wright write: Here the crucial point – what makes the stipulation acceptable [i.e. nonarrogant] – has to do not with any special relationship between sense and reference characteristic of expressions other than singular terms – for the example precisely concerns a singular term – but with the fact that the stipulation is conditional in such a way that no commitment to successful reference on the part of the definiendum is entrained. (Hale and Wright 2000, pp. 298-9)

They then explain the generalisation they propose as follows: One attractive general suggestion would be that all any definition – implicit or otherwise – can legitimately (non arrogantly) do is to fix necessary and sufficient conditions on the identity of the Bedeutung, if any, of its definiendum: to determine how it has to be of an entity of the appropriate kind if it is to be the Bedeutung of the appropriate kind. […] So since a non-arrogant stipulation of the condition of the identity of the reference of a singular term will likewise assume a conditional shape […] our working suggestion is going to be that, in order to avoid arro-

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gance in implicit definition, and irrespective of the syntactic type of the definiendum involved, it will in general be sufficient to restrict attention to sentences which are appropriately conditional. (Hale and Wright 2000, p. 299)

So, Hale and Wright think that framing every implicit definition in “appropriately conditional” terms can solve the existence problem. In what follows I will try to specify what “appropriate” in this context is supposed to mean17. For the time being, however, we need to consider a different problem potentially affecting the semantic deliverances of implicit definition. According to Hale and Wright, the non-arrogant stipulation of the truth of a context containing a non-interpreted expression may still fail to bestow an intelligible meaning on that expression. The reason is that such stipulation may fall short of providing adequate means by which the understanding of that expression may be imparted to someone who doesn’t know its meaning. If it is so, the traditional connection is again 17

One major concern is whether the conditionals schematising some canonical introduction and elimination rules for a logical connective are “appropriately conditional” in form. Horwich, for one, denies that they are. Very roughly, to take the example of the elimination rule for conjunction, Horwich suggests that (E) (p ∧ q) → q doesn’t perform a purely meaning-constituting function. Rather, it is accepting it on the condition that there is a concept expressed by “∧” which does. This, according to Horwich, explains why those who endorse rival logical systems – for instance the classical and intuitionist – may be represented as meaning the very same principles when they disagree as to whether they are valid. For an intuitionist to grasp the logical constants it is sufficient to endorse a “conditional commitment that one would be prepared so to deploy them [the classical rules of inference] if one were to accept classical reasoning” (ibidem, p. 158). As we will see, Hale and Wright have a more nuanced position. On the one hand, they seem to think that the conditional formulation of (E) is already appropriate to guarantee the non-arrogance of its stipulation. However, they do not think that being conditional is enough when it is the non-arrogance of the stipulation of a pair of introductory and eliminative conditionals that is in question. In this case, they also require the rules to be in harmony and to extend conservatively the language within which they introduce the logical constant. Clearly, much hinges on whether one regards (E) or its conditional (carnapian) formulation as an implicit definition of “∧”. If the latter, what the traditional connection establishes is just that we know a priori the carnapian formulation of (E), not (E) itself. So, no epistemological account of logical a priori knowledge is forthcoming if one accepts Horwich’s perspective (see Horwich 2000, p. 161).

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undercut. Even if the non-arrogant nature of the implicit definition’s stipulation guarantees its truth, its definitional failure results in the inability, on the part of its addressee, to understand what it says. So, even if an addressee acquainted with the model may know that a non-arrogant implicit definer – let’s say our “#f” – is true, she won’t be in a position to derive, from her knowledge that “#f” is true, (a priori) knowledge that #f; for she will simply fail to grasp this proposition. However, we might ask, can the non-arrogant stipulation of an implicit definition fail to bestow a meaning on its definiendum? The following line of thought seems to suggest that such a possibility cannot be countenanced. If the concept that is expressed by the definiendum is identified as the concept that is necessary, given the meaning of the interpreted part of an implicit definition, for it to express a true proposition, there seems to be no option, once the implicit definition is recognised (for it is guaranteed) to express a truth, to suppose that the expression received just that concept as its meaning. The problem is however that just knowing that there is a concept that the definiendum received as its meaning, and that such concept is the one necessary for the truth of the implicit definition, is consistent with failing to grasp which concept it is. An implicit definition then must put its addressee in the position to understand its definiendum. For reasons we already know, however, being able to grasp the concept it receives as a meaning should not involve bringing the referent of it under some other identifying concept. As we already saw when discussing BonJour’s objection, if understanding the concept expressed by the definiendum involved interpreting and translating it into some independently accessible vocabulary, then when “g” was such an interpretation of the definiendum, the proposition expressed by “#f” could be as well expressed by “#g”, and the recognition of the adequacy of the translation would presumably depend on antecedent knowledge of the truth of the latter. […] The traditional connection thus demands that a good implicit definition can invent a meaning – that it is at the service of a first-time construction of a meaning […] (ibidem, p. 300)

If the traditional connection is to stand, then, understanding the definiendum must coincide with complying with “a novel but intelligible

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pattern of use”, acquiring the means for deploying it in a successful communicative practice. Much will be said of the conditions whose satisfaction, according to Hale and Wright, ensures that an implicit definition characterises an intelligible and possibly successful pattern for the use of a new expression. For the time being, let’s pause to take stock a little. Two independent conditions are operative within Hale and Wright’s proposal. Given that a new expression receives (if any) the meaning that is necessary for the truth of the implicit definition that contains it, the first condition is that the stipulation of the truth of an implicit definition must be guaranteed a priori, by the very form of the implicit definer, not to fail. Given the relevance of the notion of reference within the context of this condition, I shall dub it the extensional condition. The second one is that the implicit definition must conform with certain conditions which ensure that it provides the means necessary to grasp a new meaning, so that one stipulating it to be true does not only affect that the definiendum receives a meaning, but also receives a meaning one can understand. For clearly understandable reasons, I shall dub it the intensional condition. If both conditions are satisfied “nothing will stand in the way of an intelligent disquotation: the knowledge that “#f” is true will extend to knowledge that #f” (ibidem, p. 296). One thing to notice concerns the relation between the extensional and the intensional conditions. The satisfaction of the first condition ensures that a unique reference is determined for the definiendum; the satisfaction of the second condition ensures that (i) the way this reference is presented is intelligible, (ii) independently of the mastery of previously understood vocabulary other than the one necessary to understand the matrix in the implicit definition. So stated, these conditions act independently one of another. It is one thing to ensure reference, and quite another to present this reference while respecting the condition that it be understandable. There is possible interaction in that the intensional condition may dictate which non-arrogant implicit definitions may be taken to sustain the traditional connection. As we have seen, unless the nonarrogant implicit definition respect certain intensional conditions, either it will be the case that an addressee of it won’t be in a position to understand the meaning bestowed on the definiendum, or it will be the case

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that such understanding will have to take the form of a translation of it into previously understood vocabulary. On either case the traditional connection is blocked: either because a thinker will just know of a sentence that it is true, but won’t be able to grasp what proposition this sentence expresses, or because her ability to grasp what proposition the sentence expresses will have to be explained in the light of previous knowledge that this proposition is true. However, what seems to be ruled out is that the intensional condition also plays a role in determining whether an implicit definition is such that its outright stipulation as true is not arrogant. That is the province of the extensional condition alone. Moreover, if the traditional connection is to deliver any important insight into the nature of a priori justification, there ought to be no such interaction between the extensional and the intensional condition. For it seems that, so long as the truth of a given implicit definition is concerned, just extensional concerns matter: in particular, it must be settled whether a suitable reference is attributed to the implicit definition so that, (a) the fully interpreted implicit definition is associated with conditions of truth, which (b) we have a priori ground to regard as fulfilled. No consideration concerning the way this reference is presented seems to have a say about whether (a) or (b) is met. However, Hale and Wright’s treatment seems to constitute a counterexample. Consider how they could establish that the stipulation of Prior’s (alleged) implicit definitions of tonk is arrogant. Prior proposed the following rules as specifying a meaning for the logical operator “tonk”:

(I-tonk)

p / p tonk q

and (E-tonk)

p tonk q / q.

The admission of tonk is clearly disastrous, for it allows the derivation of every proposition. However, the rules that allegedly specify a

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meaning for tonk apparently respect the extensional condition. For their sentential variants, (IS-tonk)

p → (p tonk q)

(ES-tonk)

(p tonk q) → q,

have what might be regarded as an appropriate conditional form. In fact, when Hale and Wright discuss the case of the material conjunction, they recognize that (IS-conjunction)

p → (q → (p ∧ q))

and (ES1-conjunction) (p ∧ q) → p

(ES2-conjunction) (p ∧ q) → q

have the required conditional form. So, it would seem, the extensional condition does not prevent by itself that the stipulation of an implicit definition is arrogant. One way to see what goes wrong with (IS-tonk) and (ES-tonk) is that it is their joint stipulation that is arrogant. To see this, it seems sufficient to check whether there is a unique semantic assignment to “tonk”, at the level of its reference, that is sufficient for both (IS-tonk) and (ES-tonk) to be true. A moment of reflection reveals that there is none. Let’s start with (IS-tonk). It just requires that when p is true, p tonk q is also true. So the truth of p tonk q is independent of the truth of q. Accordingly, a suitable truth table for “tonk” will associate the value true to p tonk q both when q is true and when q is false, provided that p is true. However, (EStonk) just requires that when p tonk q is true, q is true, much independently of the truth or the falsity of p. Accordingly, (ES-tonk) will dictate that p tonk q will be true both when p is true and p is false, provided that q is true. As it is apparent, there is no unique truth table dictated by both conditionals: the first one requires the truth-function thereby identified to assign true to p tonk q for the following assignments (p = true; q =

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true) and (p = true; q = false), and false otherwise; the second to assign true to p tonk q for the couples (p = true; q = true) and (p = false; q = true), and false otherwise. So, under the same assignments of truth value to p and q the first truth-table requires p tonk q to be true, when the second requires it to be false, and vice versa. So, there is no unique truthfunction which, when associated to “tonk” as its reference, makes both (IS-tonk) and (ES-tonk) true. The same story can be told with respect to (IS-conjunction), (ES1conjunction) and (ES2-conjunction). There is a unique truth-function that makes these conditionals true. However, this is not the kind of story that can be told if the traditional connection is to be vindicated. Indeed, according to this story, the stipulation of the truth of (IS-conjunction), (ES1conjunction) and (ES2-conjunction) is safe, but for the very good reason that we have independent means for establishing that there is a suitable reference which validates both the introduction and the elimination rules. In the same vain, we are ensured that the stipulation of the truth of (IStonk) and (ES-tonk) is not safe because we simply see that there is no reference assignment of a truth-function to “tonk” that is consistent with the truth of both conditionals. Adverting to such considerations in order to solve the extensional problem is simply to fall short of establishing the traditional connection. As a matter of fact, Hale and Wright propose a different diagnosis of what is wrong with “tonk”. The problem is that the adoption of (IS-tonk) and (ES-tonk) engenders a non-conservative extension of the language within which they are supposed to introduce the new expression “tonk”. Very roughly, a language L is non-conservatively extended when the linguistic apparatus necessary for the extension of it (for instance, necessary for the introduction of “tonk”) makes available the means for establishing statements of L that were simply unavailable before L was so extended. As a simple example take the statement “p ∧¬p”. This statement is logically false, so it can never be established given the logical part of the L we accept. However, consider L+ tonk, the extension of L engendered by the adoption of (IS-tonk) and (ES-tonk) as logical principles. In L+ tonk we can establish p ∧¬p by means of the following deduction:

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1. 2. 3. 4. 5.

p→p (p → p) → ((p → p) tonk p ∧¬p) (p → p) tonk p ∧¬p ((p → p) tonk (p ∧¬p)) → (p ∧¬p) p ∧¬p

Instance of (IS-tonk) MPP 1, 2 Instance of (ES-tonk) MPP 3, 4

Hale and Wright regard the satisfaction of the requirement that the introduction of a new expression conservatively extends the language within which it is introduced as sufficient for the satisfaction of the requirement that the introduction of this expression be not arrogant, i.e. not carried on by the arrogant stipulation of the truth of one (or more) contexts containing the expression. In particular, they seemingly contend that the requirement of conservative extension finds its most interesting application when a new expression is introduced within a language not just by stipulating the truth of a context containing the expression, but by stipulating the truth of two such contexts, one specifying the conditions under which a sentence containing the expression can be derived by sentences not containing it, and one specifying the conditions under which a sentence not containing the expression can be derived from a sentence containing it. When the definiendum is “f”, There will be, however, no arrogance in what we shall call the introductory stipulation that the truth of some other sentence or sentences […] S1, is to suffice for the truth of S(f). Further – provided that our stipulations taken as a whole are conservative […] – there will, likewise, be no arrogance in the eliminative stipulation that the truth of S(f) is to be itself sufficient for that of certain other sentence or sentences […], SE. Equivalently, we may – subject to the same proviso – non-arrogantly stipulate the truth of introductory and/or eliminative conditionals, S1 → S(f) and S(f) → SE (ibidem, p. 299).

The idea is that when two conditionals act in tandem to implicitly define an expression, if they conservatively extend the language within which the expression they define is introduced, then they can be non-arrogantly stipulated as true. In the light of the latter thesis, it would seem that Hale and Wright’s treatment of the “tonk” case is in line with the general suggestion that the primary condition an implicit definition has to fulfil in

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order to establish a meaning for its definiendum is to be an appropriate candidate for stipulative truth. If it is sufficient that an implicit definition conservatively extend a language for it to be something whose truth we can establish at will, then constraining a set of implicit definitions to conservatively extend a language is to constrain their stipulation not to be arrogant. However, problems for this solution seem to lie just one step further. If the stipulation of an implicit definition is to avoid arrogance, as we have already seen, there must be some feature of the implicit definer that explains why its stipulation as true cannot fail. If the implicit definition is a pair of introductory and eliminative conditionals the envisaged proposal is to identify this feature with that of conservatively extending a language. So, the proposal is arguably that if a pair of introductory and eliminative conditionals possesses this feature then their truth is guaranteed a priori. That the stipulation of such a set of conditionals is nonarrogant, in fact, just means that they cannot be false. A way to substantiate this proposal could be to argue for the contrapositive claim that a non-conservative extension is necessarily engendered by means of the arrogant stipulation of a pair of introductory and eliminative conditionals. To stick with the “tonk” example, what we need to be shown is that both the (IS-tonk) and (ES-tonk) do not conservatively extend L, and that their stipulation is arrogant. We have already seen that the introduction of “tonk” non-conservatively extends (our) L. A natural proposal to show that the stipulation of (IS-tonk) and (ES-tonk) is also arrogant could take the form of the following reductio ad absurdum: 1. 2. 3. 4. 5. 6. 7. 8.

¬(p ∧¬p) (p → p) → ((p → p) tonk p ∧¬p) (p → p) (p → p) tonk p ∧¬p ((p → p) tonk (p ∧¬p)) → (p ∧¬p) p ∧¬p (p ∧¬p) ∧ ¬(p ∧¬p) ¬ (p → p) → ((p → p) tonk p ∧¬p)

Axiom Instance of (IS-tonk) Axiom MPP 2, 3 Instance of (ES-tonk) MPP 4, 5 CONG. INTR. 1, 6 RAA

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The same argument can be run to show that (ES-tonk) is false. So either (IS-tonk) or (ES-tonk) has to go, since each principle is necessary for deducing the contradiction at line 7. As it is apparent, we must again resort to deduction in order to show that (IS-tonk) and (ES-tonk) are not possibly true at the same time, and so that the stipulation that they are both true is not possibly successful (so that, a fortiori, it is arrogant). So, the condition that the introduction of an expression into a language has conservatively to extend it for the linguistic apparatus by means of which the introduction is carried out to be safe from arrogance depends on the crucial assumption that the logical principles embedded into the un-extended fragment of the language are true. Conversely, it seems that the condition of conservative extension is equivalent to the non-arrogance condition only to the extent that we have reasons to regard the logical principles that are actually part of our language as true. This is not a minor shortcoming, for on pain of circularity one cannot maintain that logical knowledge is always to be explained by resorting to the model of implicit definition. Some different account must be envisaged to explain at least basic cases of logical knowledge. The only available alternative, it seems, is to detach the condition of conservative extension from the condition of non-arrogant stipulation. In particular, it could be argued that the first condition does not need to be defended in the light of the second condition. Rather, it could be argued, it stands for independent reasons. The suggestion would roughly involve the thought that logic as a system must pull in the same direction, and that a non-conservative extension doesn’t subserve this purpose because it potentially engenders conflicts between old and new rules of inference (or between their axiomatic variants). A rationale for this view is that a non-conservative extension runs the risk of altering the deducibility relation in a language. Let’s go back to the tonk example. Suppose that we have established that “all ravens are black” (the induction problem should not matter in this context; what matters here is just the deducibility relation). So, we can propose the following deduction crucially involving (IS-tonk) and (ES-tonk):

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1. All ravens are black 2. All ravens are black → (all ravens are black tonk no whale is white) 3. All ravens are black tonk no whale is white 4. (All ravens are black tonk no whale is white) → no whale is white 5. No whale is white The acceptance of (IS-tonk) and (ES-tonk) alters the deducibility relation in that it engenders a change in its extension: in the extended language the statement “no whale is white” is deducible (it can be validly inferred from) the statement that “all ravens are black”, while it was not deducible from the same statement within the un-extended language. So, it might be argued, the potential problem of an implicit definition is not that the stipulation of its truth may fail; rather it is that its acceptance may engender a change in the deducibility relation. So, the main suggestion would be that the stipulative acceptance of a new principle is succesfull provided that it is conservative in the aforementioned respect. This rationale has however a different, though not insignificant shortcoming with respect to the traditional connection. According to the proposal, an implicit definition can be accepted only if the expression it introduces within the language does not engender a non-conservative extension of it. In this way it becomes understandable that the pattern of use proposed for the newly introduced expression is something that can be followed and deployed in a succesfull communicative practice. However, its acceptability does not have anything to do with the conditions under which we can know that what the implicit definition expresses, when its definiendum is interpreted, is true. It just has to do with the conditions under which, along with the intensional condition, it is something that can be understood along with the Wittgensteinean conception of meaning sub-serving the purpose of establishing the traditional connection. The satisfaction of the intensional condition is clearly insufficient to guarantee the truth of the implicit definition. For it just ensures that the insertion of the new expression is consistent with the logical part of the un-extended part of the language. Also if we focus on the second subcondition mentioned in the intensional condition, we can reach the same

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conclusion. Hale and Wright suggest that “a further requirement which it seems should be imposed […] is, to put it very loosely, that various ingredient definitions pull in the same direction so that we do not have a situation where some members of the network of implicit definitions make a mystery of the others” (ibidem, p. 305). When brought down to our linguistic practice, the suggestion is that our conditional implicit definitions should respect a constraint of harmony. Take, as before, the example of a pair of introductory and eliminative conditionals. As we have seen these conditionals specify, respectively, the truth of what sentences not containing the definiendum is to suffice for the one of what sentences containing the definiendum, and the truth of what sentences containing the definiendum is to suffice for that of what sentences not containing it. One operational shortcoming – so Hale and Wright qualify it – is that there is a mismatch between the kind of sentences which, in accordance with the second conditional, can be derived by a sentence containing the definiendum and the kind of sentences that, in accordance with the first conditional, are sufficient for deriving that very sentence. Whenever it is so, the conditionals are not in harmony. In one case, lack of harmony may boil down to a non-conservative extension of the language. This is the case when the eliminative conditional allows the derivation of conclusions from a sentence containing the definiendum that are not independently derivable from the sentences that, in accordance with the introductory conditional, are sufficient to derive that sentence. However, the mismatch may take the inverse direction. It might be that the eliminative conditional allows less than is independently derivable from the sentences that are sufficient for introducing the definiendum. In this case, we have the paradoxical situation in which from certain sentences S1 we can directly derive certain sentences SE that we cannot derive with the aid of MMP and the introductory and eliminative conditionals. Again, we can ask which kind of justification can be envisaged for imposing the Harmony constraint. As it is clear for reasons already specified, the following line of thought is not going to help to vindicate the traditional connection. Let us focus on the latter case, when the stipulation of the two conditionals does not engender a non-conservative ex-

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tension of the language. Imagine that “∧” were introduced by means of the following conditionals: (IC-∧) p → (q → (p ∧ q)) (EC-∧) (p ∧ q) → p Now, it is obvious that we have a recognisable case in which “the strongest conclusion permissibly inferable by an application of the elimination rule(s) is weaker than can independently be inferred from the type of premise stipulated as sufficient by the introduction rule(s)” (ibidem., p. 305) only to the extent to which we know that when we have grounds Γ for p and grounds ∆ for q, then we have, separately, grounds for p and for q. Having this knowledge, however, is already to deploy the standard elimination conditional for conjunction. So, the harmony condition plausibly constrains pairs of introductory and elimination conditionals only against the backdrop of our independent knowledge of the truth-preservingness of other transitions. Naturally enough, this kind of knowledge cannot be explained, amongst other things, by noticing that the standard introductory and elimination conditionals for the conjunction are in harmony. Accordingly, the justification for accepting the harmony constraint cannot derive from our willingness to avoid conflicts between our rules of inference, if this constraint is to play any interesting role in explaining how it is that we know a priori the contents conveyed by harmonious introductory and eliminative conditionals. So far, my arguments have exposed a certain threat of circularity in the attempt, envisaged by Hale and Wright, to vindicate the traditional connection. As we have seen, they suggest that harmonious implicit definitions conservatively extending a language may guarantee at the same time that what these implicit definitions come to express is true, and something we are given the resources to understand for the first time. I have suggested that the conservativeness and harmony constraints can be motivated against the backdrop of supposedly antecedent logical knowledge. However, I have suggested, if these constraints are to play

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any role whatsoever in explaining logical knowledge, then their adoption must be motivated independently of the extensional condition. The problem is that, in this way, we loose any clear connection between the thought that our implicit definitions meet the requirements issued by those constraints and the thought that the contents they express are true. A natural response seems to relax the requirement on the kind of justification at issue, by maintaining that logic is, roughly speaking, a matter of our choice, and that it is natural to suppose that the needs its adoption subserves are best satisfied by avoiding certain “operational drawbacks”. This line of though involves the thesis that logic is conventional, and that the best we can do is to justify its adoption or its alteration, is to make sure that it respects certain pragmatic constraints. This view, then, is at odds with the realist thesis that our knowledge of logic is knowledge of independently constituted and very general logical facts; therefore constitutes a serious limitation of the traditional connection. The second option is to suggest that the best way to regard the arguments I have proposed is not to say that they expose a vicious circularity in the attempt to vindicate our logical knowledge; rather, such arguments should be regarded as suggesting that there is nothing better than, for there is no viable alternative to, offering what Dummett has called a pragmatic justification of deduction. The main suggestion is that we should not find the conclusion that any justification of logic has to take the form of a circular argument dramatically outrageous. At least, not if we realise that the kind of reassurance we need for accepting a given logical law is not the one that just a suasive argument, one purporting to persuade “someone who genuinely doubts whether the law is valid” (Dummett 1991, p. 202) could give us. In opposition with this sceptic, we are prone to endorse such laws; so all that we need is an explanation of how it is that such laws are valid. And, so long as this purpose is concerned, a pragmatic, rule-circular argument will work. In the final section of this chapter I shall take into consideration the first conventionalist option, for it seems to fit better Hale and Wright’s suggestions. I shall leave the second option for the third chapter. The second chapter will be devoted to illustrating why a theorist of a priori knowledge should not remain content with the suggestion that our basic a priori knowledge of logic is conventional in nature, and to defend from

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recent attacks the suggestion that logical truth can indeed be conceived, in contrast with the conventionalist treatment, as objective. I shall conclude with a reconsideration of Boghossian’s most recent suggestion that our objective logical knowledge, much in the spirit of Dummett’s suggestion, can be circularly justified. Logic and Convention To begin with, let us summarize the result of the preceding sections. I have presented Horwich’s claim that the traditional connection is undermined. Due mainly to the existence problem, the outright stipulation of the truth of an implicit definition may fail, as we have no assurance that the meaning necessary for the truth of the implicit definition exists. Horwich downplays the problem by proposing a wittgensteinean conception of meaning, according to which a meaning for the definiendum of an implicit definition exists just provided that the acceptance of the implicit definition as true discloses a pattern for the use of the definiendum that is possibly implemented in successful linguistic practice. One major consequence, once this picture is put into effect, is that a meaning is constituted just by the acceptation as true of the implicit definition: so, that a context serves to define implicitly an expression does not ensure that the content thereby constituted is true. I have proposed a less revisionary reading of Horwich’s position by suggesting that a meaning is constituted by the resolve to accept a given context only to the extent to which the commitment one thereby endorses implicitly involves a commitment to the truth of the direct version of this context, whose conditional form pre-empts the existence problem and so ensures the context’s truth. I have then introduced Hale and Wright’s position. Despite their critical stance toward Horwich’s (programmatic) conclusion that the traditional connection cannot be vindicated, I have maintained that Hale and Wright’s defence of it might be regarded as a generalisation of Horwich’s (real) position. The authors in fact require that if the resolve to accept as true an implicit definition has to secure a priori knowledge, then it must not be arrogant – that is to say, it does not have to presuppose existential commitments that are matter of additional epistemic obligations – and so propose that every implicit definition must take an ap-

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propriately conditional form. That is enough for ensuring that our stipulation of the truth of an implicit definition results in the implicit definition actually coming to express a truth. However, the authors also advert to a different problem, related to BonJour’s objection. The problem is that knowledge that an implicit definition expresses a truth is not enough to secure knowledge of this truth unless a subject is also in a position to grasp it. However, the ability to grasp this proposition does not have to rely on the ability to translate the definiendum into previously understood vocabulary. For such ability must rely on previous knowledge of the proposition, thereby empting the implicit definition of every epistemological significance. So, along with the wittgensteinean proposal also advocated by Horwich, the ability to grasp this proposition must be constituted by the very acceptance of the implicit definition, which, subject to the satisfaction of certain constraints of conservativeness and harmony, must disclose a meaning-constituting pattern for the use of the definiendum. Accordingly, I have proposed to distinguish an extensional condition, and an intensional condition within Hale and Wright’s proposal. Satisfaction of the extensional condition supposedly ensures that the implicit definition comes to express a truth, and satisfaction of the intensional condition supposedly ensures that the proposition thereby expressed be understood without trivialising the epistemological role of implicit definition. I have focused my attention to logical knowledge. According to the authors, in fact, introductory and eliminative conditionals for the logical constants meet both conditions and therefore perform a meaning constituting function in the light of which our a priori knowledge of the principles they convey can be explained in a satisfactory way. I have denied that it is so. To begin with, Hale and Wright contend that the stipulation of introductory and eliminative conditionals for a connective meets the extensional condition if it engenders a conservative extension of the language within which they contribute to introduce a new expression. However, I have shown that the latter thesis can be vindicated only provided that we have independent means for accepting the truth of the logical part of the un-extended language, with which newly introduced non-conservative conditionals may engender a conflict. Accordingly, I have concluded that the requirement of conservative extension, together with the harmony constraint, must be moti-

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vated independently of their relation to the satisfaction of the extensional condition, if both have to play a role in explaining fundamental cases of logical knowledge. The problem with this suggestion is, however, that unless this relation is established, there seems to be no prospect of vindicating the traditional connection. For if the satisfaction of conservativeness does not ensure the truth of the introductory and eliminative conditionals, there seem to be no way to establish the thesis that the stipulative truth of a conservative and harmonious pair of such conditionals explains a priori knowledge. As already hinted at, a completely different picture of logical truth could explain why, in the face of what has been so far objected, the traditional connection should be retained. The picture at issue is that, in a sense to be explained shortly, logical truths are merely conventional, stipulative truths. Let us start by briefly reviewing a classical problem affecting the conventionalist account of logical truth, and by sketching a plausible solution to it as proposed by N. Tennant. As I it will become apparent, Tennant’s account of logical truth seems to provide the theoretical framework needed to make sense of Hale and Wright’s suggestion that, subject to the abovementioned provisos of harmony and conservative extension, implicit definition provides an intelligible model of our epistemic grasp of logical truth. Since Quine’s Truth by Convention, it is a widely accepted result in the philosophical literature that conventionalism is an inadequate picture of logical truth. The main argument, roughly, is that if a statement is conventionally true in the sense that its truth has been individually stipulated, then the infinite number of logical truths results in a problem for the conventionalist. For if logical statements are infinite, it is impossible that they have been stipulated to be true one by one. The only available alternative is that our conventions as to the truth of certain classes of statements have taken a very general form, and that the truth of each logical statement is regarded as conventional in that it follows from the general convention. However, here’s Quine’s worry, each logical statement will follow from the general convention only by means of some other logical truths, necessary for its derivation, whose truth will not have been accounted for in the same way. So, according to Quine, the

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conventionalist picture involves us in an infinite regress, and must be rejected (see Quine 1976). Quine’s argument, again very roughly, involves the presupposition that the sense in which the (conventional) truth of each statement follows from the statement of a general convention is that it can be inferred from such convention, taken as a premise. However, as N. Tennant has proposed, this assumption can be resisted. The link between convention and logical truth might be conceived in a different way: in a plausible alternative, the conventions might be taken not to provide the premises from which all the logical truths are derived, but can instead be thought of as rules of inference, by means of which all the logical truths may be generated without thereby making any use of additional premises whose truth would still have to be accounted for. If conventions are identified with rules of inference, rather than with statements (axioms), it is clear that the sense in which the truth of individual logical truths ‘follows from’ conventions is not the same as that in which the consequent of a logically true conditional follows from the antecedent. It would be better to speak of logical truth […] as arising from or flowing from the conventions in question (Tennant 1987, p. 88).

If this is a permissible form of conventionalism, not any more open to the Quinean regress problem, then the crucial question hinges on how one determines, either implicitly or explicitly, which rules of inference must be adopted. The preliminary answer returned by Tennant is that the adoption of certain rules as conventional is not to be traced back to an explicit choice on the part of a linguistic community; rather, in line with D. Lewis’ account (Lewis 1969), it has to be identified as “a behavioural regularity in a group by virtue of being a salient solution to a recurring coordination problem” (Tennant 1987, p. 82). If it is so, the implicit adoption – the convention “without convention” – of a set of such rules is justified if it respects the condition that it effectively serves the purpose of providing a salient solution to recurring coordination problems.

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Hale and Wright’s condition of conservative extension and harmony seem pretty well to fit this purpose. As Tennant writes, On this account, logical truths and logical consequence, and the necessity of both, arise as by-products of the harmony principle constraining both the evolutionary adoption of logical operators, and speakers’ acquisition of grasp of their meanings (ibidem, p. 89).

The harmony principle referred to in this quote is the principle according to which the adoption of a new logical operator should not extend the class of assertible statements not involving that operator; it also involves the requirement, already presented in relation to Hale and Wright’s proposal, that introduction and elimination rules do not have to clash, in the sense that they must mutually determine each other. The respect of such a principle guarantees that the logical operators that are introduced in a language fit the purpose of facilitating the exchange of information for which that language is designed: Our idea of necessity arises because we enter fixed points in our practice, in order not to overstretch our communicative net. But the sense in which we enter these fixed points (our rules of inference) is not that explicit, deliberative sense which Quine seemed to believe was required of any convention worth of the label. Rather, that the logical operators of an evolved and graspable language do obey rules displaying this sort of harmony is the sort of fact that one would expect, on naturalistic or evolutionary grounds, when confronted with the very fact that the language serves the function of facilitating information exchange among its speakers. Just as the heart must expand and contract in order to pump blood around, so must we be able to infer conclusions, and reason away from premises, in order to circulate information (ibidem).

The idea, to put it bluntly, is that logic is a by-product of certain linguistic devices which, as a matter of natural selection, have been selected for their adaptive value in the blind strive of humans to enhance their performances in the symbolic exchange of information. Once such instruments – the rules of inference – become part of a language, they then spontaneously generate all the logical truths, but only in the sense that these truths can be derived by an application of these rules from

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premises that are discharged, and in this sense they owe their truth only to these rules. A crucial aspect of Tennant’s proposal is that the logical rules of inference – derivatively, the logical truths – are only to be regarded as devices selected for their instrumental value. Accordingly, there is no question, concerning a given set of rules of inference, about their being correct. The only available possibility of appraisal, concerning any given set of rules, is its capacity to discharge the role for which it has been selected. Once this role is identified with enhancing the circulation of information within a linguistic community, then, there seems to be no further question, besides the specific advantage made available to the speakers through the introduction of a specific set of rules, than the epistemic neutrality of the device with respect to the goods it helps deliver. Reflect on the following metaphor to see the point. The introduction of checks has arguably been motivated by the need of reducing the disadvantage of distance in monetary exchanges. Oversimplifying more than a little, Florence merchants might have found it advantageous to sell their goods to Dutch customers, but might have found it very difficult physically to transport all the money involved in these exchanges. In such a situation, having at one’s disposal checks proves advantageous, provided that the rules which govern their introduction and elimination in economic transactions are conservative with respect to monetary value. If a given merchant in Amsterdam must receive an amount of money which I am at pains to transport all around Europe, then every solution other than carrying a coffer is of some interest just provided that, by implementing it, I can achieve in an easier way the same result: that is to say deliver in time the same amount of money. Accordingly, checks must be conservative entities: the (physical) money I have to give to an employee in a bank in Florence, if I am to receive the check I will transport with ease, must correspond to the physical money the Dutch merchant will receive when, my check in hand, she will knock at the branch office in Amsterdam. In the same way, information delivery is really enhanced provided that the means introduced to speed up its exchange do not alter the very content of this exchange. When such devices are identified with rules of inference, requirements of harmony and conservative extension seem to guarantee the desired result; for their respect guarantees that no more (or no less) information

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was available to a speaker when she let circulate the inferential check than the information I found in my hands when I cash it in accordance with conventionally agreed rules. Given the function they perform, this brand of conventionalism regards the (implicit) introduction of rules of inference within a language as epistemically innocuous. No new information is introduced in the linguistic market once the range of possible actions within it is enhanced – to stick to Tennant’s metaphor – through the addition of the new fixed points. It is just the ease with which the information independently available to the players in this market can be transmitted that is enhanced through the introduction of inferential liaisons which put every possible assertion in a context of inferential premises and consequences. In the light of the foregoing account, there is a clear sense in which the respect of consistency, conservativeness, and harmony is sufficient to provide a given set of logical principles with justification. Logical principles, on this view, just provide the means for enhancing our language, by making available the means to exchange information in an effective way. So they are justified so long as they effectively discharge their role. In this way, our worries seem to dissolve. There is no problem if, contrary to Hale and Wright’s suggestion, the conservativeness and harmony constraint cannot be motivated against the backdrop of the aforementioned extensional condition, that is to by noticing that their respect is sufficient to bar arrogant stipulations. Truth, in the case of logical principles, is just a (more or less trivial) by-product of the introduction of certain linguistic devices, and such devices are just liable to a rather pragmatic kind of normative assessment. Coda As it is apparent, the cost of this move is that the traditional connection is vindicated only in the limited sense that the logical truths we know by implicit definition, once the aforementioned constraints are respected, are truths of our own creation to which no more objectivity can be attributed than the bit of objectivity encapsulated by the logical procedures by means of which logical truths are derived by application of the rules

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of inference from premises that are discharged. On the picture outlined, there is no substantive question concerning the objective correctness of a given class of inferences, only a pragmatic question concerning their utility, provisionally dealt with by laying down certain general principles of harmony and conservativeness. Is this a result that an a priori theorist can live with? The motivation behind a common negative answer to this question is that, in this way, the door is open to unpleasant forms of relativism and scepticism. More will be said about this at the beginning of the second Chapter. For the time being, I shall conclude by outlining an argument against the particular version of conventionalism advocated by Tennant. The general structure of the argument is the following: suppose that we grant to the kind of conventionalist described by Tennant that logical truths are generated by the rules of inference that, as a matter of fact, have been selected for their adaptive value. Adaptive value is arguably at variance with the nature of the agents involved, the nature of their needs, the conditions under which their activity takes place. All these conditions are contingent. In the same way certain inferential rules prove adaptively advantageous only contingently upon the nature of human agents, their needs, the conditions under which their activity takes place. This means that, had human agents, their needs, and the conditions under which they operate been different, they would have adopted, as a matter of contingency, different rules of inference. Given the envisaged relation between rules of inference and logical truths, according to which the latter flow from the former, this means that had human agents, their needs, and the conditions under which they operate been different, the logical truths would have been different. This conclusion, however, seems unacceptable in itself: that Modus Ponens, to take just one example, is a valid rule of inference (the corresponding conditional, a true logical statement) doesn’t seem a matter of contingency. It seems necessary that if, for any given p and q, it is the case that p and it is the case that p → q, then it is also the case that q. There is something intuitively outrageous in the suggestion that, had we or the conditions in which we operate been different than we or they actually are, then Modus Ponens might have failed to be valid (true). Moreover, Modus Ponens seems something that would have been true much independently of the existence of

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a linguistic community that has implicitly adopted certain conventions as to the use of “→”. However, both intuitions are frustrated by the kind of conventionalism that, if I am right, is necessary to make sense of Hale and Wright’s proposal. Logical truths supervene – flow from – conventions that we have (implicitly) found convenient to adopt to enhance, given the beings we are, the needs we have and the conditions under which we operate, the flow of information. So, they are at variance with those conditions, and no objective point of view is left from which we could as much as normatively appraise their status. If this is true, logic becomes, in an important sense, non-objective. This has major consequences in epistemology, in particular concerning the notion of justification (derivatively of knowledge). By an epistemic rule, I mean any rule with the following form: if conditions are such-and-so, then believe that p. The rule is meant to specify under what the conditions – in response to what kind of evidence – one’s beliefs should be modified so as to incorporate the belief that p. Epistemology is in the business of certifying certain rules as worth endorsing, and rejecting certain other rules as dispensable. However, a rule, as such, is neither true nor false. Given its link to belief-formation, the question whether a thinker should follow a determinate epistemic rule seems then to reduce to the question whether a corresponding epistemic principle is, in turn, true. Whether, so to say, it is true that when the conditions are as specified by the such-and-so clause, one is justified in coming to believe that p. Whether it is so, again seems to depend on the kind of relation there is between the conditions specified by the such-and so clause and p. Take the following rule, stated generally with propositional variables: if p, and p → q, believe that q. Is this a rule we should adopt? The answer, according to the recipe described above, must depend on what we answer to the question whether knowledge that p and knowledge that p → q, justifies one in believing that q. Now, suppose we know that the following logical relation holds: (p → (p → q)) → q. This seems to be what is required to answer affirmatively the second question. If we know that the truth of p and the truth of p → q jointly entail the truth of q, then

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one is certainly justified, if she knows that p and she knows that p → q, if she forms the belief that q. Accordingly, the corresponding rule is one we should adopt. The problem is that the advertised route from certain truths to epistemic principles, is that epistemic principles are not objective unless the truths they depend on are, in turn, objective. Unless it is an objective fact that (p → (p → q)) → q, it is not objectively true that knowledge that p and knowledge that p → q, justifies one in believing that q. This is an unwelcome result, in the light of epistemic relativism, the view according to which what counts as justified (or known) within a determinate (cultural, social, specific) setting does not count as justified (or known) within a different (cultural, social, specific) setting. If one, with the conventionalist, argues that logic is not objective, then one is left with the view that the corresponding epistemic principles are also not objective. So one is left with the view that what one is justified in believing when one believes certain premises is in an important sense relative to those facts which determine the logic one accepts as true. In the next chapter I shall again take up the issue of relativism, and its connection with the notion of logical truth. Against the anti-objectivist, I shall try to show that there is no principled objection to the idea that logic is objective.

Realism about Logic Introduction In the preceding chapter I have taken into consideration the empiricist’s suggestion that our logical knowledge can be explained in the light of the semantic role performed by logical rules of inference and logical axioms. According to this general view, the implicit definitional status of a logical principle (or rule of inference) ensures a priori its truth (or validity), for the quite simple reason that the meaning which the definition, if successful, bestows on the uninterpreted logical constant is constrained to be the one which makes the principle (or inference), true (or valid). Hale and Wright’s analysis of this epistemological model has revealed a problem in its standard formulation. On the one hand, the model has it that the resolve to regard a context containing a new expression as true determines that it comes to express a true proposition; so, acquaintance with the semantic function of such context constitutes good reason to believe that the proposition thereby expressed is true, and then ensures (a priori) knowledge of it. On the other hand, knowledge of this proposition requires the conceptual ability to grasp it. Unless a thinker is in a position to know which proposition an implicit definition expresses, once it is fully interpreted, no “intelligent disquotation” is forthcoming from one’s knowledge that it expresses a truth to one’s knowledge of this particular truth. BonJour’s criticism has however revealed that the way an implicit definition makes available to a thinker the conceptual resources to grasp the proposition it expresses cannot be that it encodes instructions as to how its definiendum should be interpreted or translated. Not at least if the model of implicit definition is to explain fundamental cases of a priori knowledge; in fact, given the meaning of a matrix “#_”, a thinker will be in a position to identify the correct translation of “f” – when constrained to be the one that is necessary for the truth of “#f” – only to the extent to which she will know, for some “g” she already understands, that #g is true. In this case, knowledge that #f will be ensured by (acquaintance with) the implicit definitional role performed by “#f”, yet against the backdrop of previously (and independently) acquired knowledge that #g. Accordingly, Hale and Wright have proposed to identify the kind of understanding made available by an implicit defi-

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nition with the disposition to use its definiendum along the pattern of use disclosed by the stipulation of its truth. However, according to Hale and Wright, not every such stipulation discloses a viable pattern of use for an expression. An implicit definition must respect the condition that the stipulation of its truth must not be arrogant, and must conservatively extend the language within which its definiendum is introduced; moreover, if the implicit definition is constituted by introductory and eliminative conditionals (rules of inference) acting in tandem, such conditionals (rules) must be in harmony. A substantial issue concerns how such conditions can be justified in the context of the traditional connection; that is to say how one can defend the view that if an implicit definition respects these conditions it is bound to express a truth we can understand and consequently come to know. I have contended that, on pain of circularity, the respect of such conditions cannot be taken to guarantee the truth of the proposition(s) thereby expressed. That conservative and harmonius implicit definitions are bound to be true can in fact be shown just against the backdrop of previously (and independently) acquired a priori knowledge. So, for instance, the claim that a pair of introductory and eliminative conditionals for a logical constant is in harmony and conservatively extends a language helps explain our knowledge that they cannot fail to be true only if we presuppose independent logical knowledge whose acquisition we cannot explain in the same way. However, I have also suggested that the difficulty can be avoided if logical truth is interpreted along conventionalist lines. Tennant’s conventionalism, in fact, is the view that logical truths simply flow from conventionally agreed rules of inference, where such rules, subject to the satisfaction of conservativeness and harmony constraints, are just given the role of facilitating the exchange of information within a linguistic community. Logic, on the conventionalist reading, does not convey any ontological commitment: it is just the by-product of the conventional adoption of rules that have the function of letting circulate, rather than conveying, information. The conventionalist interpretation of logic, I have suggested, entails the claim that logic is not objective. As Boghossian puts it Logical Conventionalism is the view that, although the sentences of logic are factual – although they can express truths – their values are not ob-

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jective, but are, rather, determined by our conventions (Boghossian 1997, p. 349)1.

Strictu sensu, if logical truth is just a by-product of conventional stipulations, there is nothing objective to know about it. If we characterise the position that logical rules of inference (or logical claims) are valid (true) in an objective sense as realism about logic2, conventional1

Boghossian maintains that implicit definition does not entail Conventionalism. However, the argument he presents is wanting under two important respects. The argument rests on a counterexample to the thesis that the proposition every implicit definition expresses has its truth-value conventionally determined. According to Boghossian, “Stick S is a meter long at t” can be regarded as an implicit definition of “meter”; however, he plausibly suggests, the proposition it expresses is clearly objective, for it is the very length S possesses at t that makes the statement true once “meter” has been conventionally stipulated to refer to that length. However, it might be argued that the counterexample is spurious under two distinct respects. First of all, it might be argued that Boghossian’s example isn’t an example of a priori knowledge. It could be suggested that the full statement of the implicit definition of “meter” has to take the following conditional (direct, in Horwich’s sense) form: “if stick S has a length at t, then Stick S is a meter long at t”. In this case, knowledge of the proposition that stick S is a meter long at t is not fully a priori, for knowledge of the antecedent of the conditional, that stick S has a length at t, must depend on a posteriori ingredients, like the ones necessary to know that there is a stick S, that at a given time it has a determinate length etc. Secondly, even granted that the justification is fully a priori, it could be argued that in this case implicit definition does not explain a fundamental case of a priori knowledge. In fact, we know how to interpret the word “meter” because we already know, of the length identified by some demonstrative concept we already understand, that stick S has that length at t. Even granted that this piece of knowledge is a priori, this knowledge cannot be accounted in terms of the model of implicit definition. In sum, Boghossian’s counterexample does not show that fundamental cases of a priori knowledge, meeting in a satisfactory way the understanding problem denounced by Hale and Wright, are not to be interpreted along conventionalist lines (see Boghossian 1997, pp. 350-352). 2 In his paper Inventing Logical Necessity, Crispin Wright has challenged the view that logic is objective. It is nonetheless helpful to borrow the way he characterizes the position he eventually comes to argue against. Wright general characterisation is the following: “proof in logic ought […] to be viewed as a medium of discovery of a special category of facts, and […] logical relations […] do stand independent of our cognition of them in the manner of, say, spatial relations among material objects”, Wright 1986, p. 187. In particular, Wright summarizes the view by constraining it to the acceptance of the following three claims. (1) There is a special category of truths which a language is not able to express unless it contains a defined sentential operator equivalent to “it is logically necessary that”; (2) what constitutes a correct implementation of a logical procedure is conceptually predeter-

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ism is to be characterised as a form of anti-realism or irrealism. In what follows I shall not embark into a general characterisation of the kind of realism at issue, nor into a plausible specification of the kind of facts that, according to the realist, are responsible for the objective truth of logical claims. I shall only outline some unpalatable ramifications of the claim that logic is not objective into general epistemology, and try to defend the view that, contrary to the conventionalist thesis, logical truth could and should be regarded as objective. The result will be that the traditional connection, given its dependence on the conventionalist thesis, should be abandoned in favour of some other account of logical knowledge. As a consequence, in the third chapter I will consider the rule-circular alternative mentioned at the end of the fist chapter, recently rehearsed by Boghossian to vindicate the objective status of our logical knowledge. Logical Principles, Justification, and Epistemic Relativity Why should a realistic construal of the content of logical claims be preferred to the conventionalist one (implicitly) advocated by Hale & Wright? The reason has to do with the general issues of relativism and skepticism. In particular, as it has been recently emphasized3, it seems that any anti-realist or anti-objectivist conception of logic commits to some forms of epistemic relativism and skepticism. As Creath has emphasized there is a close link between logic and the epistemic notion of justification. Given a body of beliefs, the relations of logical inference which are recognized as holding between them determine part of the relations of justification also holding between them. With the sole exclusion of perceptual beliefs (arguably together with first-person beliefs), which are commonly held to be susceptible of a non-inferential kind of observational justification, it seems that inference is needed in order to transmit, to the major part of the things we ordinarily take ourselves to know, the kind of justification which suffices for knowledge. What seems required if a belief has to be inferentially justified is that (i) the reason for believing it relies in some other – independently – justified mined by the character of the procedure and the identity of the tested formula; (3) the logician’s task is to chart the (objective) extension of the following notions: logical necessity, logical consequence and cogent argument. See Wright (ibidem, p. 188). 3 See Boghossian 2001b, and Wright 2001.

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belief and that (ii) the first and the second belief stand to each other in an appropriate relation. According to Creath it is the special province of logic to specify what relations among our beliefs (and most importantly among the sentences that give voice to their content) are to be counted as appropriate for justification. The same point is stressed by BonJour: he mentions, among the most compelling reasons why we need a concept of a priori justification, the fact that without being able to justify (a priori) the rules of inference needed to go beyond the domain of the beliefs justified by observation, we would be probably left with a very damaging scepticism of the first person4. Last but not least, Boghossian observes that the question whether we are justified in deducing a conclusion from a determinate set of premises reduces to the question about whether the epistemic principle we (implicitly) rely upon when forming the belief in the conclusions on the basis of the premises is true. The epistemic principle is true, though, only provided that a corresponding logical claim is. So for instance the epistemic principle according to which “if S is justified in believing p and is justified in believing ‘if p then q’, and S infers q from those premises, then S is prima facie justified in believing q, […] will in turn be true provided that a certain logical fact obtain, namely: (MMP) p, p → q imply q”5. So, it would seem that in light of the close link between the notion of logical consequence and the notion of epistemic justification, two requirements are needed in order to avoid relativism and scepticism: (O) Logical principles, like MMP, are objectively true; (K) Logical principles, like MMP, can be known to be objectively true. About the first condition, it could be said that the entire enterprise of knowledge – of attaining justified true beliefs – is impossible unless we may confidently assume that the epistemic principles which are in place in our justificational practice are true. Those principles tell us which be4

See BonJour 1998, pp. 4-6. BonJour’s claim derives from the preliminary acceptance of Internalism about justification. Internalism does not limit itself to claim that a belief, in order to be justified, must be attained at by the deployment of a principle which is truth-conducive or reliable. It further requires the principle to be justifiably known to possess such properties. As a consequence, the request that logical (and generally epistemic) principles be objectively true constitutes a necessary but not a sufficient condition for justification. 5 See Boghossian 2001b, p. 5.

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liefs are justified, to which extent and by what other beliefs. So, no belief we may form following these principle can be justified unless the principles themselves are true; since however any such principle is true provided that the truth of the premises ensures the truth (or at least enhances the likelihood) of the conclusions, it seems reasonable to require certain alethic principles, appropriately corresponding to the epistemic principles, to be true. For instance, to resort to another example proposed by Boghossian, the principle (EP) If S is in good lighting conditions etc, then if it visually appears to S that there is an x in front of him, then S would be prima facie justified in believing that there is an x in front of him is true provided that the following principle holds true: (aEP) If lighting conditions are good enough etc., then the visual appearance of an x in front of a subject entails (highly enhances the probability) that it is true that there is an x in front of the subject. More than this, the logical principles are to be objectively true. Were they true in a non-objective way, their truth would have to be conceived as relative to something else. Conventionalism, as we have seen, is the thesis that the truth of logical principles is relative – in that it depends on – the conventions we as cognitive agents have (maybe implicitly) adopted as a matter of utility. The view, as we have tried to show, has the consequence that if our constitution had been otherwise, or if the conditions under which we operate had been different, the logical truths would have come out much differently. Accordingly, under a conventionalist interpretation of the status of logic, the answer to the question whether a given set of premises justifies a belief someone actually entertains, depends, in the sense that is relative to, the conventions that have been adopted. Such a notion of justification would fall short of being a credible reconstruction of the concept involved by the ordinary notion of knowledge: it should be admitted that what counts as knowledge for someone legitimately does not count, or could have not counted, as knowledge for someone else. A premise from which one could even jump to the sceptical conclusion that every claim to possess knowledge must rejected as illegitimate.

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A general argument from epistemic relativity to scepticism could be given in the following terms. Logic is relative (let us not put any constraints about what logic may taken to be relative to: we can think of logic as being relative to the psychological constitution of a subject, his preferences in matters of logical inference, conventions, or whatever). Which beliefs are justified by which other beliefs depends on the logical relations holding between them. What logical relations hold between them depends on what logic one adopts. What logic one adopts depends on what her psychological constitution, attitudes towards inference, conventions (or whatever) are. So, what relations of justification one recognizes depends on such facts as well. So, what counts as justified belief for a subject (relative to his psychological constitution, her attitudes, her conventions, or whatever) can legitimately count as unjustified for another. So, what counts as knowledge for a subject (relative to her psychological constitution, her attitudes, her conventions or whatever) can legitimately count as error for another. Since, by hypothesis, there is no way of deciding what logic is the correct one, there is no way of deciding what claims to knowledge are correct. Hence there is nothing as the correct attribution of knowledge6. If the argument is sound, then, it is clear why its main premise should be resisted. However, the mere fact that relativism about logic, together with epistemic relativity, entails scepticism about knowledge, is not still an argument to the effect that relativism abut logic should be denied. As such it would beg the sceptic’s question. The main question is rather whether relativism about logic is a well-supported view. The most common strategy in favour of a relativistic interpretation of logic adopted in the literature is to argue that the very supposition that logic is objective entails counterintuitive consequences, or that it entails some form of conceptual incoherence. So, evaluating the stability of logical relativism 6

The argument parallels a corresponding argument from perceptual relativity to irrealism about perceptual properties. From the premise that different subjects may perceive, depending on their respective sensory structures, the world much differently, and from the second premise that they can live equally well adapted lives, it draws the conclusion that there is no correct distribution of perceptual properties and that perceptual properties are better thought as entirely mind-dependent. The main difference between both arguments is that the latter needs a further premise. It is in fact necessary that entities differing in their perceptual systems may be attributed equally adapted lives, to jump to the conclusion that there is no correct distribution of perceptual properties. In the case of the former argument, the very premise that logic is relative ensures the availability of a direct link to the conclusion.

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must involve assessing the various arguments put forward against the objectivity (of our knowledge of) logic. The problem can be seen from a metaphysical and an epistemological point of view. On the one hand, in fact, it has been questioned whether the notion of objective logical truth does make sense, or whether there is some notion of objectivity logical truths can be defensibly seen to satisfy. On the other hand, though, we shall not forget the requirement that any notion of objective logical truth must prove to be compatible with the possibility of giving some credible picture of the way we come to know it. At least in principle, there should be a satisfactory account of our justifiably coming to know that the certain logical principles are objectively true. In the absence of such an account, whatever reason we could try to elaborate to defend the notion of objective logical truth, we should have to meet the further challenge of explaining how, in the face of its independence from our conventions, we are able to know it. Accordingly, my strategy will be the following. First, I will consider an argument put forward by Shapiro in defence of logical realism and elaborate on it in order to meet a broadly Wittgensteinean response that could be mounted in defence of a full-blooded form of conventionalism about logical truth; then I will try to show that, under the modified constraints that, according to Wright, an objective discourse should be able to satisfy, logic should be regarded as objective. In the following chapter, I will elaborate on a recent debate over the epistemology of logic, whose result, I contend, can be seen as introductory to (or in need of the integration of) the third, phenomenological part of the present essay. Objective Truth Objective truth is truth which is independent, in its metaphysical status, from the fact that it can, even in principle, always be detected. As it is customary to say, someone who defends objective truth – for a certain area of discourse – endorses a non-epistemic conception of truth. She argues that the extension of the predicate is fixed independently of what humans actually know, will know and would know, were their epistemic powers and/or the epistemic conditions an idealization of some sort of ours. The antirealist holds that truth is an epistemically constrained property; so she argues that the extension of “true” coincides with that of a (complex) epistemic predicate, like “warrantedly assertible”, “warrant-

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edly assertible under idealized epistemic conditions”, “incontrovertibly warrantedly assertible”, etc. However, the notion of objectivity has recently received a different (more general) treatment. According to a very influential proposal, it is not necessary that the sentences of a given area of discourse be conceived as evidence-transcendent if they are to be counted, when true, as objectively true. The satisfaction of further requirements can be sufficient for objectivity7. The principal lines of attack to an objective notion of logical truth have been directed towards both notions of objectivity: it has been argued by M. Resnik that, in the light of the underdetermination of logical theories by data, the very notion of objective logical truth – together with its objectivist pendant of evidence-transcendence – should be rejected, in favour of a non-cognitivist, broadly projectivist construal of the semantics of logic. Resnik’s argument echoes Benacerraf’s dilemma against mathematical Platonism in that it argues against the claim that logic is objective from the epistemological claim that the best procedures that yield knowledge of logic might ratify different, rival logics. On the other hand, Wright has argued for a non-objectivist construal of the truth predicate which is applied to the logical principles, by denying that they pass the test of Cognitive Command (roughly requiring from an objective discourse that it is a priori true that every disagreement about the truth value of anyone of its constituting statements can be traced back either to error or to ignorance on the part of at least one of those who disagree). In an interesting reply, Shapiro has recently maintained that, in the light of both criticisms, there is no reason to deny objective truth to logic. Let us see in further detail the contents of those attacks and Shapiro’s argument against them. Resnik’s Attack In his Mathematics as a Science of Patterns, Resnik defines logical realism as the doctrine that statements attributing logical properties or relationships, such as ‘ “0 = 0” is logically true’ or ‘ “0 = 0” does not imply “0 = 1’, are true or false independently of our holding them to be true, our psychol7

Wright indicates Cognitive Command, Wide Epistemological Role and Eutyphro Contrast.

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ogy, our linguistic and inferential conventions, or other facts about human beings (Resnik 1997, p. 162).

Resnik opposes to realism the projectivist conception according to which logical claims do not state anything: utterances of logical principles serve purposes related to the expression of attitudes toward certain schemes of inference. Their function is accordingly taken to be quite distinct from that characteristic of fact-stating sentences. Resnik mounts an argument from epistemic indeterminacy against realism. The argument roughly runs as follows. Logical theories are achieved through the employment of Goodman’s method of reflective equilibrium. According to this method, logicians should start with their pre-theoretic intuitions about matters of logical consequence, construct a theory to systematize matters, and then correct the theory, or reject some of the initial intuitions, until the theory perfectly fits with the ‘data’ they accept, i.e. until the theory rejects no example they are determined to preserve and accepts none they are determined to reject. However, it is not a priori certain that two logicians, by deploying the method, will come to the same result; accordingly, there are cases where exactly the same method warrants conflicting theories; in the light of such cases, the correctness of a logical theory cannot consist in its ‘representing’ something objective; would it be so, it should be admitted that being in wide reflective equilibrium is compatible with error and mistake8. The argument, as Shapiro has emphasized, parallels the famous argument against Platonism presented by Benacerraf in his Mathematical Truth9. The main thought underlying both arguments is that a semantic theory about a given area of discourse, such as Platonism – according to which mathematical sentences are true of a mind independent realm of objective abstract entities (the numbers) – must be rejected if it entails, contrary to widespread intuition, that we cannot know the truth values of its constituting sentences. Platonism, according to Benacerraf, places the facts whose occurrence allegedly makes mathematical statements true beyond the reach of human cognition. So it renders inexplicable how we can, as we think we do, know anything about them. In the same fashion Resnik asks more or less the following question: if there are logical facts which renders true the logical claims, how can we ever be justified in believing that we have attained logical knowledge, “especially in the 8 9

The argument is presented in Resnik 1997. See Benacerraf 1973.

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light of the consideration that the methodology of reflective equilibrium may not yield a unique logic?” (Shapiro 2000, p. 352) 10. Shapiro’s strategy is to show that the argument is not compelling. The main reason is that there is no immediate relation between the observation that realism about logic entails that the best methodologies we rely upon are fallible and the conclusion that realism must be rejected. Clearly enough, if realism about logic is correct, the methodology of reflective equilibrium must be characterised as a fallible method of belief acquisition. If there is just one correct logic, the disagreement between two logicians in wide reflective equilibrium entails that (at least) one of them must be wrong. So, if the classical logician and the intuitionist both achieve their logical beliefs by employing that method, at least one of them must have been led to mistake. However, a different question is whether the advertised fallibilist consequence concerning wide reflective equilibrium really warrants the repudiation of the objectivity of logic. Resnik’s affirmative answer arguably depends on the implicit endorsement of the following principle: (R) If a given area of enquiry A is objective, then no method M of belief formation concerning A is epistemically acceptable if employment of M does not ensure convergence as to the facts in A.

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Resnik’s argument also differs from Benacerraf’s under one important respect. Benacerraf argues that Platonism provides mathematics with the wrong semantics, for if mathematical statements were about abstract objects we could not know about them. Since we think that we know mathematics, it cannot be true that mathematics is about abstract objects. As it is clear, the main presupposition in Benacerraf’s argument is that we actually know mathematics: in the light of this assumption, every condition inconsistent with it – like the semantic postulated by the Platonist – must be rejected. Nothing plays the same function in Resnik’s argument. The problem is not that we have a fixed body of logical statements we regard as known, and we have a metaphysical claim that implies that such statements cannot be known. Resnik’s worry rather stems from the principle that the way we adjudicate the metaphysical status of a given domain does not have to imply that the procedures that are employed within it are not epistemically best. Clearly, if logic is objective, the methodology of reflective equilibrium cannot be regarded as best: if there is just one correct logic a method that yields different, rival logics can not be epistemically best. Once Resnik’s argument is so reconstructed, acceptance of the principle it relies upon leaves to the objectivist about logic the possibility of vindicating her position simply by denying that wide reflective equilibrium is the methodology (that should be) adopted by logicians.

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With R in place, Resnik’s argument can be put as follows. The classical logician and the intuitionist’s employment of wide reflective equilibrium does not prevent their divergence in opinion. So, via (R), the supposition that logic is objective entails that wide reflective equilibrium is not an acceptable method of belief formation. However, (we know that) wide reflective equilibrium is such a method. So, logic must not be objective. A quite natural reaction to this argument would be to deny the premise that (we know that) wide reflective equilibrium is an acceptable method. However, that wide reflective equilibrium is and should be accepted as a legitimate method of enquiry is a supposition that most logical realists, arguing both for the role of intuition in the process of logical discovery and defending a weakened (fallibilist) conception thereof, would concede11. A better line of response seems to doubt the very principle R. As a matter of fact R seems to engender unpalatable and quite counterintuitive consequences. R, in fact, entails that every area of discourse where agreed methods of enquiry do not guarantee a priori that those who inquire in accordance with them will converge in opinion (at least in the long run) should be regarded as deserving an anti-objectivist interpretation. The problem is that most of the methods employed within science do not seem to guarantee the needed convergence. Rival scientific theories, justified in the light of the same method (assessment of its empirical adequacy), may in fact be epistemically indiscernible when they are underdetermined by empirical data. Empirical underdetermination is the property enjoyed by conflicting scientific theories when they are exactly on a par as long as their empirical adequacy is concerned: every empirical consequence derivable from one theory is also derivable from its rival, and vice versa. It seems that the same reasoning employed by Resnik can be generalised to every area of scientific inquiry where empirical underdetermination by data threatens. Suppose that A is any such area, and M is a standard method of determining the correctness of every theory of A by assessing its empirical adequacy. If underdetermination constitutes a possibility, employment of the very same M may lead to conflicting theories. Is it enough for concluding any form of scientific irrealism? Moreover, if one accepts R one is bound to reject realism across the 11

BonJour 1999 and Peacocke 2000 are suitable examples of logical realists who endorse both views. Broadly phenomenological considerations about the structure of cognitional acts arguably sustains a similar conclusion.

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board, since “the underdetermination of theory by data is ubiquitous, holding for a vast area of inquiry”12. Is it a legitimate conclusion? The clear answer seems to be that it is not. First of all, it is a fact that many theorists – Resnik included, who is inclined to accept realism in mathematics and in ordinary scientific discourse – are not prepared to accept any such form of global antirealism. So, Resnik’s argument against objectivity in logic is open to the ad hominem reply13 that its combination with realistic inclinations in other fields is, to say the least, an instable one. Either one is prepared to generalize her antirealism, for the grounds it is based upon in the case of logic apply across the board; or, if she is not, she must recognize the insufficiency of her reasons in the case of logic. Furthermore, acceptance of R seems to betray what could be properly regarded as a misunderstanding of the position advocated by the (logical) realist. It seems constitutive of a realist position in every area of discourse that it incorporates, as C. Wright puts it, an attitude of deference. The idea is that if an area of discourse A is interpreted in a realist, objectivist sense, then the facts constitutive of this area are conceived of as independent of the concepts in terms of which we think of them, independent of the beliefs we actually form and we would form under the most favourable conditions about them, etc. This deferential component entails that our conceptions of the facts in A can at best be regarded as a map of the terrain in question, but “nothing about the terrain will depend for its existence on […] the conventions and techniques employed therein” (Wright 1993, p. 3). In accordance with the deferential attitude, the realist is committed to the possibility of a systematic mismatch between A and our representation of it. It is constitutive of the realist understanding of the metaphysical status of the facts in A that her cognitive grasp of them, given the envisaged independence of these facts from human cognition, may be systematically frustrated. Since the facts in A do not conceptually depend on our beliefs, methods, and conventions it constitutes a possibility that the latter are all mistaken. Realism about A then is consistent with scepticism about our capacity to track facts in A. However, it does not constitute a vindication of scepticism. For one reason or another, it can be that our cognitive efforts suffice for establishing, at least in local cases, a good measure of fit between the facts in A 12

Shapiro 2000, ibidem. An argument, to be sure, that can be generalized against all anti-realists about logic who are not prepared to defend global anti-realism.

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and our thoughts about them. It is the province of epistemology to establish whether we can reasonably take our cognitive efforts to guarantee this result and, in the affirmative case, in what measure they do. In the positive cases, realism about A so incorporates, again in Wright’s terms, a self-assured component. Realism is so to be regarded as the result of a balance of both components. Benacerraf’s dilemma is intuitively compelling because the deferent component – the identification of numbers with abstract objects – rules out the self-assured component – if number are abstract objects, we cannot know anything about them. So, its general significance is that realism, the thesis that certain entities exist, is not to be accepted if it makes a mystery of the cognitive capacities in the light of which we are supposed to know about such entities. However, its significance is not that whenever we think of a domain as objective, then the self-assured component must be such as to rule out the possibility of local and contingent cases of mismatch between the facts in the domain and our thinking of it. The problem with R, however, seems to be that acceptance of it betrays an overreaction to the first component, for it seems to entail that realism is an advisable conception of a given area of discourse only if we are in a position to rule out that the methods we regard as best are such as to guarantee that no case of mismatch, or informed disagreement, will ever be possible. However, the case of ordinary scientific discourse should have made clear that there is nothing in itself wrong in thinking, about an area of discourse we deferently regard as independent from our cognitive efforts, that the conditions under which we cognitively operate are not always good enough for systematically tracking all the facts in it, and for being always in a position to discriminate the only correct theory from the rest. The point is that there is nothing conceptually amiss in the thought that a given area of discourse deserves a realist interpretation and the idea that our cognitive practice are not always the best to track the truths in it. So long as the deference component is a constitutive trait of realism, it constitutes a conceptual possibility that such unfortunate cases may plague our efforts to attain knowledge. Consider again the asymmetry between Resnik’s objection and Benacerraf’s dilemma: the latter argument concludes by rejecting Platonism in the philosophy of mathematics from the premise that we, at least locally, know mathematical statements, and the conditional premises that if mathematical objects are abstract objects, then it is not possible that we know anything about them. Nothing similar is available in Resnik’s

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argument. The supposition that logic is objective does not put logical facts beyond the reach of human cognition for principled reasons, nor does it make a mystery of our coming to know, at least locally, that certain logical facts obtain. Another consideration seems to go against Resnik’s argument. Even if it is conceded that realism in the case of logic cannot be correct, for its truth entails the unavailability of a sound epistemology, the conclusion that logic has to be interpreted along non-cognitivist lines does not seem immediately to follow. Quite to the contrary, the main reason the argument puts forward for rejecting realism comes from the implicit claim that we need a sound epistemology for logic; i.e. the implicit claim seems to be that we are (somehow) aware of the fact that we possess logical knowledge, our intellectual perplexities stemming from our need to understand how we could rationally reconstruct the way we have achieved it. In the end, by using the argument to establish noncognitivism about logic, Resnik is open to the charge of begging the question of the realist, whose main concern is to explain logical truth and our knowledge of it. Shapiro acknowledges, for charity’s sake, that it could be stressed that antirealism about logic is relevantly asymmetric to other forms of antirealisms. In fact the ‘data’, in the case of logic, are intuitions to which it is not obvious that a cognitive content should be ascribed; while, in the case of empirical sciences, they normally are observational reports whose proper function is to track some objective kind of facts. This line of response would undercut Shapiro’s reply. For the advertised asymmetry would block the generalisation from antirealism about logic to global antirealism modulo the observation that underdetermination by data is an ubiquitous epistemic phenomenon. Even if all this is conceded14, and the antirealist “wins the preliminary skirmish”, there is a second argument, which purportedly shows that the realist is bound to win the war. Shapiro achieves this conclusion by establishing the following link between the notion of logical consequence and the notion of objective truth. A common slogan is that logical consequence is truth-preserving. The relevant feature here is that consequence must preserve objective truth, since logic is applicable in 14

Shapiro, in fact, does not think it should. He thinks, quite to the contrary, that the aforementioned rejoinder would beg the question of the logical realist, whose position is best described by maintaining that logical intuitions track objectively correct inferential patterns. See Shapiro 2000, p. 354.

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areas which are up for realist construal, such as science. Logical truth must answer to, and preserve, objective truth. That’s the point of logic (Shapiro 2000, p. 354). The argument has it that, were it not the case that it is an objective matter whether a proposition logically follows from a certain set of premises, or from some other proposition, it would be inexplicable why, where the truth predicate is given an objective construal, a proposition cannot fail to be objectively true when the premises from which it is derived are objectively true. The rationale is arguably this: let us assume, for the sake of argument, that logic is not objective and that the inferential liaisons it recognizes are valid just as long as they are agreed upon by human conventions. According to this view, for instance, there is nothing objective in the claim that Modus Ponens preserves truth. It is just a matter of the way we have conventionally agreed to use certain symbols that, for any given p and q, if p is true, and p → q is true, then q is true. Shapiro’s worry is that where the truth of p and q is an objective matter, independent of the inferential liaisons they might happen to stand in, it is hard to understand why truth is only preserved if the consequence-relation they stand in is not, in turn, conceived in objective terms. The thought, somehow spelled out in a less technical manner, is the following: if the sentences of a determinate area of discourse are recognized to correspond to a reality independent of us – and so, when true, to be objectively true – the correctness of a rule of inference must be responsible to what an independent world, when it makes true the premises of an inference, puts in front of our eyes as regards the truth of the inference’s conclusion. An inference cannot be held to be valid – truth preserving – if, as a matter of what goes on in a mind-independent world, its conclusion is false when the premises are true15. For instance, if the world is such as to make true the following sentences: 15

This is not to say that in order to acquire a warrant for the belief that a rule of inference is valid one should check whether, its premises being true, its conclusion is also true. Rather, it is to say that the rules for tonk cannot be valid since it is permissible to derive objectively false propositions from true premises. If “it rains” is objectively true, according to the introduction rule, “it rains tonk it does not rain” is also true, from which, according to the elimination rule, it is true that it does not rain, which is objectively false. The argument seems to pose a challenge to the antirealist about logic: to explain how, in the light of her account of logical truth, logical relations do preserve objective truth. If the observation of the truth of a proposition, which is the conclusion of an (MPP) argument whose premises are true, constituted evidence for the validity of (MPP), it would follow, from the simple princi-

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It rains at 3 o’clock on Tuesday, the 17th, and if it rains, then the number of open umbrellas increases,

it is, at least as long as the assumption is conceded that meteorological and statistical reports are objective, because it is a fact that it rains at 3 o’clock on Tuesday, the 17th and it is a fact that, when it rains, the number of open umbrellas increases. Now, since the modus ponens relation between (1) and (2) requires the truth of (3)

the number of open umbrellas increases,

and it is a fact that, when there are facts that make (1) and (2) true, there is also a fact that makes (3) true, a natural realistic complaint to an antirealistic conception of MMP’s validity would stress her inability to explain why, in the light of their conventional construal of MMP, (3) is bound to come out objectively true, whenever (1) and (2) are objectively true. The only explanation why, Shapiro contends, is that logic “is objective if anything is”16. Conventionalism, at this point, could be prima facie credited with a Wittgensteinean response17. It is certainly true, a wittgensteinean conple that if x is an evidence for P, non-x is an evidence against P, that (MPP) would not be empirically indefeasible, and therefore not a priori. Field (2000, p. 118) distinguishes between empirical justification and empirical evidence, and says that, even though the observation that the conclusion of an argument is true justifies the belief that the rules by means of which it has been deduced are valid, it does not constitutes evidence for it. Therefore, he concludes, a proposition can be indefeasible and a priori even if some observation can count as an empirical justification of it. It is sufficient that it does not count as an evidence for it. 16 Shapiro 2000, p. 355. 17 That Wittgenstein’s position should be equated to some form of conventionalism is not widely accepted. B. Stroud, for instance, maintains, against Dummett, that Wittgenstein’s rule following considerations (according to which there should not be any logical contradiction in the thought of someone fully understanding a proof and rejecting its conclusion) need not be interpreted as expressing a “full-blooded conventionalism”. The idea is that such a thinker could not be said, according to Stroud, to have at her disposal different choices as to the correct application of the rules of inference involved in the proof. It is just a matter of contingency that such an entity does not exist and that our “form of life” makes it more natural, to us, to understand logical rules the way we do. “[…] it is ‘a fact of our natural history’ in Wittgenstein’s sense that we agree in finding certain steps in following a rule ‘doing the same’”. See Dummett 1959 and Stroud 1965, p. 15.

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ventionalist could reply, that the logic we adopt commits us to the truth of certain sentences, featuring as conclusions in suitable proofs, given the truth of certain other sentences, i.e. the premises of the proofs. And it is also true that, were it the case that the conclusion came out false when the premises are true, we would be bound to reject the inference as incorrect. It is simply that, by adopting certain rules of inference, we are a priori certain that the conclusion will never come out false if the premises are true. Logic, a conventionalist might urge us, is, in this sense, antecedent to truth. Let us spell out the thought some more. In his Remarks on the Foundation of Mathematics, Wittgenstein says about logical inference: Die Schritte, welche man nicht in Frage zieht, sind logische Schlüsse. Aber man zieht sie nicht in Frage, weil sie ‚sicher der Wahrheit entsprechen’ – oder dergl. – sondern, dies ist eben, was man ‚Denken’, ‚Sprechen’, ‚Schließen’, ‚Argumentieren’, nennt. Es handelt sich hier gar nicht um irgendeine Entsprechung des Gesagten mit der Realität; vielmehr ist die Logik vor einer solchen Entsprechung; nämlich in dem Sinne, in welchem die Festlegung der Maßmethode vor der Richtigkeit oder Falschheit einer Längenangabe18.

As Wright puts it, logical inferences are not something about which it is meaningful to say that they are ‘correct’. Quite to the contrary, they constitute a precondition “of giving certain sorts of description of the world”19. The thought underlying Wittgenstein’s consideration is here best recognized if we follow the indicated analogy with measurement and correct descriptions of length. Wittgenstein on the Necessity of “1 inch = 2.54 cm” and Logical Inference According to Wittgenstein’s reconstruction of necessary truth, its origins must be traced back to the explicit adoption of conventional rules. As 18

Wittgenstein 1984, p. 96. “[…] the reason why logical inferences are not brought into question is not that they ‘certainly correspond to the truth’ or something of the sort. Rather it is just that this is called ‘thinking’, ‘speaking’, ‘inferring’, ‘arguing’. There is not any question at all here of some correspondence between what is said and reality. Logic is antecedent to any such correspondence; in the same sense, that is, as that in which an establishment of a method of measurement is antecedent to the correctness o incorrectness of a statement of length”. 19 Wright 1980, p. 61.

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Dummett has put it, the source of the special status we attribute to any necessary statement is, according to Wittgenstein, “our having expressly decided to treat that very statement as unassailable”20. Let us see, by way of exemplification, how Wittgenstein’s account applies to the necessity of the conversion rule according to which 1 inch, in the imperial system, corresponds exactly to 2.54 cm, in the metrical system. As we will see, it bears interesting similarities to the case of necessary logical statements which are worth stressing in full detail. According to Wittgenstein, it is a matter of discovery whether 1 inch corresponds exactly to 2.54 cm in the metrical system. But this does not exhaust the whole story about the statement. Were it so, the conclusion would be unavoidable that it expresses a contingent truth; at best a contingent truth whose inductive corroboration is very strong. Wittgenstein, to the contrary, takes the statement to express a necessary truth. Wittgenstein’s reconstruction has it that people, motivated by practical interests, have developed methods to describe the dimensions of things. Measurement with rulers is one – indeed the most natural – of them. It is possible to suppose that different groups of people, while sharing the same interests in determining the dimensions of things, have developed different systems of measurement: they may have chosen rulers of different lengths and have divided them into bigger equal segments, performing the role of the units of measurement. This is arguably the case of the actual communities of French and English. The former have chosen a metrical system, the latter the imperial system. A practical interest, arising from commercial exchanges between both communities (or something of that sort), must have, sometimes, motivated an inquiry as to the respective sizes of English and French units of length. English (or French) merchants wanted to know how many square inches of silk (how many square meters of wool) they were buying. At this point in the western history Wittgenstein locates the discovery of the proposition describing the proportion between inches and centimetres. By careful application of the standard of correct measurement – do not allow rulers to slip, etc. – a French inquirer has measured one inch with a metric ruler, and has found out, as a matter of discovery, that 1 inch measures, more or less, 2.54 centimetres. The notion of correct measurement, though, carries with it a conceptual connection with the notion of change in the object and the notion of 20

Dummett 1959, p. 170. Page numbers correspond to the paper’s reprinting in Dummett 1978.

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sameness of results. Every statement to the effect that an object has been correctly measured at t as possessing a length of n, entails something like the above commitment: if the object remains unchanged between t and t1, and in t1 the object is correctly measured, then the result of the measurement at t1 must be equal to the result of the measurement in t, i.e. n. By the same token, it is built into the concept of correct measurement that if an object is measured a t with an imperial ruler, the result being a quantity m, and the object does not change between t and t1 and the object is correctly measured in t1 with a metric ruler, there must be a quantity, say n, such that n centimetres = m inches, and the result of the measurement at t1 is n. Under the pressure of both factors (the empirical discovery of the proportion between inches and centimetres, and the conceptual constraints imposed by the notion of correct measurements), the contingent claim “1 inch = 2.54” is dignified of the status of a rule; both communities “give a specific value to the rigid correspondence which our concept of correct measurement leads us to suppose that there must be”21. Hence the necessity of the claim and the notion of its unassailability. According to Wittgenstein, though, more than the mere “filling” of a still unoccupied conceptual role is effected, when the conventional decision is taken to regard “1 inch = 2.54” as necessary. In fact, what is effected is, in his opinion, a change in the very concept of correct measurement. New criteria are available, once the convention is introduced, to assess whether a measurement has been carried out properly; hence, new criteria are available to determine the extension of the concept. Before the decision about the rule, English and French had at their disposal operational criteria, like the mentioned absence of the rulers’ movement during the process, to emanate verdicts of correctness. By the conceptual link between correctness of measurement, sameness of results, and lack of change on the part of the object, then, they had operational criteria to decide whether, between two distinct measurements of an object, it had changed its dimension or not. For instance, if by operational criteria the measurements have been carried out properly on two temporally distinct moments, and their results are different, the object must have changed its dimensions. Correspondingly, if by operational criteria the object did not change its dimensions, and the results of two distinct measurements diverge, there must have occurred a mistake either in the first or in the second measurement. After the decision as to the ‘rule’ status of the 21

Wright 1980, p. 75.

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proposition describing the proportion, a new criterion is available. Clearly, before the equivalence was introduced, a three-step measurement of an object, giving as first and third inch-result x, and as second centimetres-result 2.58x, would not have forced a claim to the effect that the object changed or to the effect that some mismeasurement took place (it would have at least suggested the possibility of both factors simultaneously operating, to the effect that the result was compatible with the object remaining unchanged and its measurement taking place correctly). If, though, the convention is adopted, every pair of results which does not respect the proportion entails either that a change in the object occurred or that an error in measurement has been made. More than this, if we recast the example by supposing that a pair of divergent results are obtained after two contemporary measurements – in a way that a priori rules out the possibility of a change in the object – the conclusion necessarily follows that a mismeasurement has taken place, even if by our ordinary criteria, there was no error in either of the two measurements. Notably, if the convention had not been adopted, any pair of results which did not respect the proportion – as it is now commended by the rule – would not have entailed that a mismeasurement occurred, unless by ordinary, operational criteria it could have been possible to detect that it did. The foregoing account offers the key for understanding what it was meant, before, when the suggestion was given that Shapiro’s argument could be resisted by endorsing something like Wittgenstein’s conception of logical truth. In particular, it should clarify the notion of our conventional decisions about logical inference contributing to rule out the possibility that the conclusion of a logically valid argument turns out to be false, when its premises are true. Compare the situation where our ordinary criteria for correct measurement tell us that an error was made and the new criterion, introduced by our adoption of the rule of conversion, tells us that it did not, with the situation where the methods by means of which we ordinarily assess the truth values of empirical statements tell us that the statement p is false and p features as the conclusion of a logically true argument whose premises are true. Shapiro’s argument rests on the assumption that, where the described conflict emerges, the logical rule of inference must be rejected; by doing so, he implicitly endorses a principle to the effect that what logically follows from what cannot be established at will, but must cohere with what is objectively the case. It cannot be the case that

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it is a logical consequence of a true statement that a certain statement, which is in fact false, must be true. As Wright puts it If one statement is a logical consequence of others, its truth is guaranteed by theirs. So, we should want to say, the possibility of a ‘conflict with truth’, were we to use quite different principles of inference, resides in our generally possessing other criteria for the truth of a statement than that it is a consequence of other statements about whose truth we are independently satisfied22.

So, according to Wright, a natural suggestion about whether logic, contrary to the standard conventionalist proposal, must answer to something in reality, should be that […] the reality to which rules of inference in general are answerable is that of the truth values of the propositions which they allow us to link as premises and conclusions23.

Quite to the contrary, Wittgenstein thinks that both cases parallels each other exactly. As in the case of measurement, where there is no genuine conflict between distinct criteria of correctness of measurement, but, in fact, two distinct concepts of correctness of measurement, in the case of logic there seems to be a genuine conflict between distinct criteria of truth assessment, where in fact there are two distinct concepts of truth assessment. The status of necessary truth which is attributed both to the conversion rules and to the logical rules of inference effects a genuine conceptual change, in the concept of correct measurement and in the concept of truth assessment respectively. As in the former case, if by ordinary criteria a statement must be recognized as false, which is a logical consequence of true statements, either the criteria must be rejected or an incorrect application of them must be assumed to have undetectably occurred, and the statement must be recognized as true. In this sense logic is said to be antecedent to truth: since the adoption of determinate rules of inference effects a change in our concept of truth assessment, which sentences are to be recognized as true is consequent upon which rules of inference we are disposed to regard as necessarily valid. In this very sense, then, the adoption of a logical convention stands in the way of its

22 23

Ibidem, p. 58. Ibidem, p. 64.

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being a possibility that the rules of inference a community might agree upon somewhere conflict with truth. Let us pause a little, and try to summarize the situation. Resnik’s attack against logical realism has been resisted by the argument according to which a rule of inference must answer to reality: an inference must be rejected as incorrect if it allows for the derivation of a sentence, which by ordinary, non-inferential criteria of truth-assessment, must be denied. The wittgensteinean response has been that by regarding a determinate rule of inference as necessarily valid, we effect a modification in our concept of truth assessment: by adopting the convention, we determine that nothing is to count as an accurate truth assessment if it does not produce results compatible with the rules of inference which we have chosen. Now, there seem to be two distinct ways to resist the wittgensteinean repudiation of logical realism. The first has been expounded by Dummett, who has proposed his objection in the form of a dilemma24. The second way is arguably needed if the wittgensteinean is credited to have at her disposal an answer to Dummett’s objection which essentially makes reference to the spirit of the rule following considerations. Dummett’s Objection Dummett imagines a tribe that, while lacking any notion of addition, acknowledges criteria for correct counting which are identical with ours. A tribesman, for instance, has perfectly defined criteria of correct counting to assess the question whether the members in some group – say a class of pupils – have been properly counted. According to Wittgenstein’s suggestion, the introduction to the tribesman of the concept of addition effects a change in the concept of correct counting. If the tribesman is given the rule that 7 + 5 = 12, something changes in the situation where, having separately counted the girls and the boys in the classroom as being, 5 and 7 respectively, the tribesman answers the question of how many pupils are there, by saying, after a count, that they are 13. Without the rule, the tribesman did not have any means, besides his ordinary criteria of correct counting, to assess whether the count, giving as a result 13, was correct or not. In particular, it is a conceivable case that, according to those very criteria, there are 5 girls, 7 boys and 13 pupils. When the rule is accepted, though, the conclusion follows that a mistake must 24

See Dummett, ibid.

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have occurred, either in the separate countings of the girls and the boys, or in the counting of all the pupils in the classroom. Dummett’s reply yields the following dilemma. If the adoption of the rule entails that a mistake must have occurred, then either a mistake actually occurred such that, had the tribesman noticed it, he would have recognized it as a mistake (some pupil has been counted more than once, etc.) or it did not. If the former, then in any clear sense of the term, the rule just gives the tribesman the capability of recognising symptoms to the effect that some mistake has occurred that, by his ordinary criteria, the tribesman would have been in the position to recognize, had he noticed it. If the latter, though, it seems that the rule entails that a disjunction – to the effect that either this material mistake occurred, or this material mistake occurred, etc. – must be true, without there being any true disjunct to make the disjunction true. “But this – Dummett urges – is absurd: one cannot make some mistake without there having been some particular mistake which one has made”25. Dummett’s objection has it that, while the rule gives a new criterion for the correctness of application of the old criteria, it by no means overlaps or contrasts with the old criteria. If, according to the new criterion, a mistake must have occurred, then it must have been detectable by our ordinary criteria; if it did not, it must have been in virtue of the fact that the old criteria have been somehow misapplied. To Dummett’s objection it might be replied that it misconstrues Wittgenstein’s position: given the fact that the story about the tribesman deals with a rule which is already incorporated in our concept of correct counting, we find it natural to think that the rule and our ordinary criteria of correct counting cannot but be in harmony. In fact, since the rule is there, the conceptual change which is thereby effected is already operative: our incapability of conceiving of a rule which is not in harmony with the ordinary criteria of correct counting entirely derives from the fact that those very criteria have been re-shaped after the rule has been accepted. So, a Wittgensteinean should urge us, Dummett’s case invites us to think that the concept of a whale cannot but respect the criteria we ordinary employ to assess whether any determinate entity does, or does not belong to the species of fish, where in fact such criteria have been radically re-shaped when it was agreed that whales are best described as mammals rather than as fishes. The foregoing objection, however, seems in turn to induce a misconstrual of Wittgenstein’s position. It is represented as coming to the view 25

Ibidem, p. 175.

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according to which it is always open to a community to revise some set of criteria in the light of further information which, before, was simply unavailable. Our concept of fish is modified in light of scientific discoveries about whales, and, as a consequence, our previous criteria are recognized as insufficient, and so in need of a reformulation. Quite to the contrary, Wittgenstein’s considerations stem from his opposition to the general thesis that the way we understand the meanings of the words we use, commit us to – and definitely predetermines, once and for all – which applications of those words will have to be recognized as correct or incorrect. According to Wittgenstein, for instance, there is nothing in the way we understand the notion of a proof, and the way we conceive of the sense of a proposition as determining which constructions have to be counted as proofs of it, that mechanically predetermines – logically entails – that someone confronted with a determinate construction will have to recognize it as a proof of a determinate proposition. Even if a proposition is a logical consequence of some other propositions, there is nothing in our understanding of the premises, nor in our understanding of the logical principles which guide the inference, that necessitate the acceptance of the conclusion. If the necessity of the conclusion is accepted, it is because a specific and explicit decision as to its necessity has been taken. A decision that, as we have seen, effects a change in our concepts, somehow ratifying, and fixing, a new way to understand them. To take the example of measurement (or the one of logical inference), Wittgenstein’s opposition to the thesis – as we will see, liable to be endorsed both by realists and antirealists – that there is the correct rule of conversion between inches and centimetres (or that there are correct and incorrect rules of inference) does not derive from the conviction that it is always possible to revise the way we understand the concept of correct measurement and the concept of correct truth assessment in a way that makes the conversion rule (respectively, some rule of inference) come out correct under that reformulation. The conviction such an opposition relies upon is that there is not anything like ‘the way we understand the concept of correct measurement’ and ‘the concept of correct truth assessment’. There is no any definite pattern of use for such expressions that may clash with our conventional decisions to regard conversion rules or inferential liaisons as necessary and, as a consequence, that may supply the touchstone for the correctness of such decisions. If these considerations correctly describe the sense of Wittgenstein’s proposal, though, they might be put at the service of a much more sub-

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stantial reply to Dummett’s objection. Dummett puts the matter in the following form: suppose that, as a conversion rule between inches and centimetres, it is chosen ‘1 inch = 3.54 cm’. The adoption of such a rule entails that the measurements which our ordinary criteria ratify as correct must have been mistakenly applied, for they corroborate the conclusion that the correct ratio should be located elsewhere. So, according to the rule, there must have been a mistake that we made in applying such criteria. Such mistake, in turn, either occurred or not. If it occurred, the conclusion follows that our ordinary criteria actually succeed in constraining the adoption of a rule of conversion, and that there is a reality to which our adoption of such rule must answer26. If no single mistake occurred, though, the bewildering conclusion must be allowed that (a) at least one mistake was made such that, had we noticed it, we would have recognized as such, and (b) no such single mistake has been made. The flaw in Dummett’s argumentation, though, is precisely located at the level of its premise. It is not true, in the first place, that the rule ‘1 inch = 3.54 cm’ entails that the measurements which our ordinary criteria ratify as correct must have been mistakenly applied. The premise presupposes that there is a determinate pattern, sustained by our ordinary criteria, as to how the notion of correct measurement should be applied. But that such a determinate pattern exists, is precisely what Wittgenstein is in the business to deny. The realist and the antirealist accommodate the notion of a rule’s being incorrect by recognizing the generalization according to which, roughly, an incorrect rule introduces a conflict between different criteria regulating the application of the concept of mismeasurement. The modification entailed by the adoption of 1 inch = 3.54 cm., for instance, ensures an ‘internal connection’ between two distinct patterns of use for the notion of mismeasurement, according to which, necessarily, when according to the former the concept (mismeasurement) applies, 26

In such a case, the rule can be seen as supplying a criterion equivalent to the previous ones, but, as a matter of its constitution, easier to apply. Wright puts forward the example of a new rule for determining whether any given number is prime, alternative to Eratosthene’s Sieve. Such a rule is thought as much easier to apply. As a consequence it can be used to test whether Eratosthene’s Sieve has been misapplied, but, by no means does it supply an alternative criterion. Every number which is prime according to new criterion is prime according to Eratosthene’s Sieve, and vice versa. It is just that, due to its complexity, some (undetected) incorrect applications of the Eratosthene’s Sieve might induce the conviction that a number is not prime which, under the alternative criterion (and a correct application of the first criterion), is easily recognized as prime.

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according to the latter the opposite concept (correct measurement) does as well. Yet, according to Wittgenstein, there is nothing objective answering to the notion of pattern of use, nor, a fortiori, something like an internal relation – like the preceding – between objective patterns of use. It is not that the case that our understanding of our words commits us, though implicitly, to making a determinate use of them. As Wright recognizes, “[t]he concepts of correct counting, and of the various ways in which the size of a group can alter, are always capable of further determination just because our understanding of them in no way settles in advance what we ought in future cases to count as their correct application. Dummett’s objection poses a difficulty for Wittgenstein’s brand of conventionalism only if we think of our understanding of notions like ‘correct counting’ as frozen by procedural rules, as predetermining which situations may and may not be rightly regarded as involving counting errors etc. But Wittgenstein’s conventionalism, as so far interpreted, emanates precisely from a repudiation of such a conception of understanding”27. Wittgenstein thinks that we have only inductive grounds for the conclusion that the correct application of the notion of correct measurement, as ‘defined’ by our ordinary criteria of correct measurement, will always involve the ratification of measurements which clash with the one which, according to the rule, we should regard as incorrect. To be precise, favouring the sceptical readings of the rule following considerations, we only have inductive grounds to suppose that, whenever we are disposed to acknowledge that contemporary readings are carried out properly, we are disposed to accept results that will be nearly identical or, if carried out on different units, results which will come close to a certain fixed ratio. We could turn out to apply the concept of proper measurement differently. We have just witnessed, so far, that only those readings which satisfy the condition of near identity or fixed ratio of the results are to be considered proper readings. The adoption of a convention is the acceptance as a necessity of these inductive considerations. What we should think as frozen, then, are not procedural rules – which, according to Wittgenstein, do not predetermine anything – but their further determination, effected by means of the conventional stipulation of the rule’s necessity. In the same way, there is nothing in the non-inferential procedures we ordinarily employ to assess the truth values of empirical statements 27

Wright (ibid., p. 93), emphasis mine.

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that constitutes a pattern against which the introduction of some rules of inference could speak: there is nothing objectively implicit in the ordinary criteria by means of which we assess questions about the truths of statements, correctness of measurement etc. So, there is nothing to which our conventional choices could answer. Rule Following Considerations and the Adoption of a Convention The foregoing reply was entirely based on the moral of the rule following considerations. According to them, the idea that the way we understand the meaning of a word determines, once and for all, how the word ought to be used on every conceivable circumstance, should be rejected. The reason why can be located elsewhere, depending on which interpretation of the rule following considerations one happens to favour. A plausible first interpretation is sceptical: it is just that, due to the problem of induction, we are never in a position to decide whether the speakers of a language share a rule; for, in order to share the rule, the members of the community should have reached the same inductive conclusions as regards future uses of a rule from (arguably) shared past applications of it. But infinitely many different inductive conclusion about future uses are consistent with the shared evidence. So, on the first construal, Wittgenstein’s point is that there are facts as to which interpretation people has adopted, but we are simply never in a position to say what those interpretations are. Therefore, it is always an epistemic possibility that there is not one single way people understand a rule, that there are indefinitely many rules associated to a proper formulation of what we intuitively regard as a determinate rule. The second interpretation is non-factualist. If, as it seems correct, Wittgenstein is attributed an anti-realistic conception of the truth predicate regarding the descriptions of the way people understand rules, it seems to follow that there are no facts as to what interpretation is the one endorsed by any member of a language community. In order for there to be such facts, it should be possible to determine when two people share the same understanding, but that would require some means to verify “some open set of statements about their behaviour in actual and hypothetical circumstances”28. The general idea is that understanding is manifested in actual and potential linguistic behaviour, so that it is true that S understands in way x the term M, only if it is true that in actual and po28

Wright (ibid., p. 29).

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tential circumstances S uses M in way y. But, from an anti-realistic point of view, something is true when it is an ideal possibility that it is decided to be so. And it is plainly not possible that we can verify an open set of sentences describing actual and potential uses. So, there are no facts as to the way people understand M. Both readings are related. The sceptical doubt supplies, if an epistemic conception of truth is adopted, a ground for non-factualism. If one endorses antirealism, sentences like ‘S means M in a way x’ are, for the reason stressed by the sceptic, neither true nor false. Wright suggests a third interpretation. Both the latter and the former interpretations, in fact, allow for an asymmetry between the notion of third-person understanding and first-person understanding, which Wittgenstein would not have accepted. Both the sceptic and the nonfactualist interpretations, in fact, seemingly allow for there being a sense in which the way I understand a word determines the way I will have to apply it on every conceivable circumstance. Even if I have no means to convince a sceptic, in the light of the way a pupil has so far proceeded in applying the rule ‘add 2’, that some particular hypothesis about the way he understands the rule is warranted, I can be sure of the fact that, given the way I myself understand the rule, I will continue the series in a determinate way (after 1000, I won’t continue the series by saying 1004, 1008 etc.). In fact, if room is made for its having a sense to assert that the way I understand a word transparently determines the use I ought to make of the word, it could be said that whenever someone’s use of an expression diverges from mine, there is still a true description of his understanding that explains that use; if that conclusion is allowed for, however, no clear content can be attributed to the general claim that understanding does not determine use. My understanding determines the use I make of a word, and in general people’s (divergent or convergent) understanding of the same word explains their (divergent or convergent) use of it. Starting from self-ascriptions of the content associated to an expression, arguably incorporated in the acceptance of a rule governing the use of the expression, there seems to be room at least for the thought that, whenever someone’s use differs from ours, her use complies with her – reflectively transparent – interpretation of the rule; and that, as a consequence, there is room for the notion of one’s understanding an expression determinately governing its future use on her part. In the light of the foregoing asymmetry, then, the following third interpretation should be admitted. Wittgenstein should be taken to give

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something like the following argument, to support the general claim that the way everyone understands a meaning does not predetermine the use she ought to make of it. The assumption is that first-person knowledge (contrasted with third-person hypothetical ascriptions of knowledge) of the meaning of an expression – say predicate F – consist in the knowledge of a rule, say R, to the effect that F is to be applied only to things satisfying property φ. Knowledge of that rule consists (is revealed) in the capacity to acknowledge as such a correct description thereof. However, if two speakers do agree about the rule’s formulation rendering their understanding of the meaning of F, but do not agree in the way they eventually end up using F, it is no more possible to credit either of them with the capacity to acknowledge as such a correct description of the rule. In fact, on both sides, the same characterization which has been initially agreed upon, has turned out to apply to what in fact are different rules, and since there is no way to say which one is mistaken, no one is in a position to be credited with the capacity. The idea is that I cannot be credited with knowing something if I am disposed to accept as a correct description of it one which, in point of fact, also applies to things that I take to be different than the one I take my self to know. The preceding considerations about Wittgenstein’s reply to Dummett’s dilemma actually favours a sceptical reading of the rule following considerations. A fortiori, though, they might be proposed under the third reading. If there is not any clear sense in which someone’s understanding of a meaning determines which uses of a word she ought to regard as correct, then there does no exist any pre-determined pattern of use of a concept against which the conventionally stipulated necessity of a rule might be regarded as correct or incorrect. On the generalized moral of the rule following considerations, there is nothing in the way the concept of correct measurement is normally applied, by ordinary operational criteria, that constraints any particular rule about the exact ratio between inches and centimetres. At bottom, there is nothing like ‘the way people understand the concept of correct measurement by ordinary criteria’. As a consequence, we are at liberty to fix any particular way of characterising our understanding of a concept, by stipulatively regarding certain rules as necessary. Yet, it might be objected that if the rule following considerations hold, then they should bear also to the rules which, according to Wittgenstein, we stipulatively agree as necessary. The final question, then, seems to be what, according to Wittgenstein, the adoption of a conven-

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tion consists in, and whether it is not supposed to entail precisely the kind of understanding of a concept from whose repudiation Wittgenstein’s position – according to Wright – emanates from. For, at a first glance, the adoption of a convention, say ‘1 inch = 2.54 cm’, seems to entail the commitment of always applying the concept of mismeasurement and correct measurement in the same way; in a way, that is, which is compatible with the correctness of the rule. There should not be any room, on this reading, for the application of the concept of incorrect or correct measurement in cases where, respectively, contemporary measurements of an object by different units of length yield, or do not yield, readings of the form ‘the object is x inches and is 2.54 cm’. On a broadly intuitive level, what the rule following considerations are supposedly meant to refute is nothing but the notion of something being true just in virtue of what we mean by certain concepts; i.e. they are meant to be a refutation of a theory whose aim is to explain the origin of the necessary truth of our mathematical, and logical statements. It is then arguable that such a position cannot be built around a notion like the one of necessary, though conventional truth. So, if the preceding considerations are sound, the result of Wittgenstein’s considerations is actually incompatible with the aim of securing, in one way or another, a special status to the claims of logic. There seems to be no room for something being antecedent to language. Everything should be seen as hanging on the nonpredetermined moves that the players of the language game of inferring, measuring, etc., as a matter of fact, make. The idea is that, if there are no facts as to how a concept objectively applies, then there are bound not be facts to that matter, independently of whether our commitments are implicit, as in the case of our adoption of methods for assessing the truth values of sentences, or are explicit, as in the ‘ratification’ of certain rules of inference. Summarising Remarks A Wittgensteinean reply to Shapiro’s argument in defence of logical realism has been considered. According to the wittgensteinean response, there is no reality to which the rule of inference we adopt should answer. Contrary to Shapiro’s suggestion, according to which such a reality should be identified with the truth values which we ascribe to sentences by deploying non-inferential criteria of truth assessment, we have been describing the opposite view that the adoption of a rule of inference

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might be taken to consist in our deciding that nothing is to count as accurate truth assessment which does not produce results compatible with the rules of inference which we have chosen. Against this we have examined Dummett’s dilemma: if a rule of inference we have agreed upon requires that some mistake has occurred when non-inferentially assessing the truth of a statement, then either it occurred or not. If it occurred, then the rule of inference still complies with our non-inferential criteria of truthassessment (which, by chance, have been misapplied), and can be taken to answer to them. If it did not occur, then we must absurdly admit that some particular mistake occurred even if there was nothing such that, had we noticed it, we could have recognised it as a mistake. We have considered how Dummett’s dilemma could be resisted in the light of the rule following considerations. In fact, as the rule following considerations show, there is nothing objectively implicit in the ordinary criteria by means of which we assess questions about the truths of statements. Nor, as a consequence, is there some application – under those criteria – that might be regarded as objectively correct or incorrect. In fact there is nothing – no pattern of correct applications – to which our conventional choices could answer. If this is so, though, it seems that it should be admitted that there is nothing even in the idea that a convention supplies a modified criterion of truth. In order to be so, it should be conceded that, contrary to our usual understanding of concepts like correct truth assessment, correct measurement etc., our regarding as necessary any particular rule of inference commits us to a determinate pattern of use. If it is a rule, in fact, then it trivially falls under the rule following considerations: it should be conceded that whether a determinate statement should be recognised as true would be as indeterminate under the criterion of truth assessment supplied by the adoption of a rule of inference, as it is, according to the rule following considerations, under the non-inferential criteria. So the conclusion seems to follow that no solution is envisaged by employing the aforementioned reply to Dummett. It just seems to entail an extreme form of relativism, according to which every application of a concept can always be regarded as appropriate. So, unless one is prepared to allow for such relativistic consequences, the conclusion seems to follow that realism about logic should be endorsed. We still have to see, though, whether on Wright’s modified notion of objective truth, logic can be said to be objective. After a brief exposition of Wright’s general reformulation of the question of objectivity, I will present his specific attack against the objectivity of logic. I

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will try to show that Wright’s argument allows for a twofold response: on the one side, I shall try to exploit Shapiro’s reply, according to which either logic is trivially objective or logic is not under the general constraints which, according to Wright, an objective truth predicate must satisfy; on the other side, by stressing some weakness in Shapiro’s positive account of the objectivity of logic, I will reformulate his argument in a way that avoids certain shortcomings I will concentrate on. Eventually, I will propose a weakened version of my reformulation and endorse a more general strategy, trying to support the conclusion that if logic is not objective, in Wright’s sense, the objectivity of every discourse, even the one of paradigmatically objective discourses, is bound to disappear. Wright’s Attack In Truth and Objectivity Wright has proposed to reform the realist/antirealist debate, by articulating a minimal notion of truth which, independently on any commitment to either realism or antirealism, should be attributed to all the sentences which satisfy minimal constraints of syntactical and semantic regimentation29. Contrary to non-factualist and error theoretic versions of antirealism, then, Wright has proposed to regard what is at issue in a debate about the objectivity of a given area of discourse not in terms, respectively, of the truth-aptness or of the widespread truth of its central sentences, but in terms of the properties which can be attributed to the truth predicate finding application within it. He has argued that a position concerning a determinate area of discourse is to be counted as realist, provided that the truth predicate that finds application within the area is defensibly an objective truth predicate. Contrary to Dummett’s proposal, according to which the objective truth predicate the realist should argue for is straightforwardly an evident-transcendent

29

According to Wright every predicate which satisfies the following conditions is a legitimate truth predicate: (a) it coincides in normative force with the predicate of warranted assertibility (i.e. it constitutes a norm of assertoric discourse), and (b) it does not extensionally coincide with the property of warranted assertibility. The epistemic notion of Superassertibility meets these conditions and, according to Wright, constitutes the minimal truth predicate which every area of discourse, if satisfying the constraints on semantic and syntactical regimentation, should be attributed by default.

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notion, Wright claims that even an epistemically constrained30 truth predicate can be regarded as an objective truth predicate. For a truth predicate to be so regarded, it is sufficient that one or all of the following conditions be satisfied. (a) The facts allegedly reported by the sentences of an area of discourse figure in explanations which are beyond the ones related to the discourse in question. The ‘fact’ that Benigni’s performance was amusing does explain the fact that I laugh, or facts ‘internal’ to the comical context, but does not figure in explanations of other sorts; on the contrary, the fact that the walls of my house are made of bricks explains several facts: their perceptual appearances to me, my evaluation of them as contributing to make my house a safe shelter against a wolf, the fact that I have an headache after I bump my head against them, and so on. If the facts reported by the disputed sentences of an area of discourse are of the second kind, they possess a Wide Cosmological Role, and are to be attributed an objective truth predicate. (b) If it can be said that the best judgments in a given area of discourse – made in circumstances which are known to be normal, under optimal evidential conditions, etc. – are true because they track, and correctly report, certain facts, then the truth predicate finding application is objective. If, on the contrary, it is because it is reported by one of our best judgments that something is the case, then the truth predicate is not to be construed as objective. Wright’s proposal here derives from what he calls the Euthyphro Contrast, i.e. the contrast between Socrates – holding that what pleases the gods is good because the gods are capable of discerning the good from the evil – and Euthyphro, who maintains that what is good is good because it pleases to the gods. If one is allowed, about the statements of a given area of discourse, to side with Socrates, then the discourse is said to pass the Euthyphro test and the truth predicate finding application within it is said to be objective31. 30

A truth predicate finding application in a given area of discourse is epistemically unconstrained if it is possible for there to be unknowable truths essentially involving the central predicates of the area. 31 A method for adjudicating the Euthyphro contrast in a given area is to ask whether it is a priori certain that the best judgments in the area are bound to be true. If it is a priori, then Euthyphro wins. If it is true, but contingently so, then wins Socrates. The ascriptions of colors to objects, for instance, are a priori guaranteed to be true when evidential conditions are optimal etc., for on a dispositional account of

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(c) If it is a priori certain that a disagreement between two thinkers about the truth value of a sentence in a given area of discourse is to be explained by a cognitive shortcoming on the part of at least one of them, then the discourse, and the truth predicate within it, are objective. For if a discourse is meant to represent some objective features of reality, it is sensible to expect that, if two subjects correctly represent a state of affairs (i.e. if neither is guilty of not taking into account some available evidence or neither makes some error in forming a belief on the basis of the available evidence), they cannot but agree in the way they represent reality to be. Conversely, if they disagree, it is sensible to draw the conclusion that at least one of them is guilty of either ignorance or error32. It should be noted that the requirement posed by the Cognitive Command does not entail that the truths of a given area of discourse should be known by all ideal inquirers, after having performed a sufficiently careful investigation. It just entails that all ideal inquirers, in any particular state of information, will not disagree about the degree to which a statement, if it is objective, is assertible.33 According to Wright’s proposal then, in order to show that logic is objective, what has to be shown is that logical claims satisfy one or all of the conditions (a) – (c). In Inventing Logical Necessity, though, Wright has argued that, since logical claims fail to satisfy Cognitive Command, a broadly anti-realistic approach to logic should be acknowledged as the correct interpretation of its metaphysical status. As a consequence, it might be thought that, according to Wright, Cognitive Command is relevantly asymmetric in respect to condition (a) and (b), in that it constitutes a necessary condition for the factuality and objectivity of a discourse. Wright’s argument could be represented as a challenge against a realist’s account of logical necessity. The realist is required to explain why, if X acknowledges, while Y rejects, the logical necessity of a given colour predicates the definition of the chromatic word “x” is roughly the following: “a thing is coloured of x iff a subject under ideal conditions etc., when perceptually presented with the thing is disposed to judge that it is x”. See Johnston 1993. 32 Wright countenances also the possibility that, in case of disagreement, (at least) one of the thinkers is subjected to prejudice (she correctly represents the available evidence, but either underestimates or overestimates the warrant it confers to a determinate belief she respectively does, or does not, want to entertain) or the statement disagreed upon is vague. 33 See Wright 1987, p. 198.

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proof, their disagreement is not always to be interpreted as humean34. In other terms, the realist has to provide grounds to sustain the claim that either X or Y (or both) have committed some material mistake, or are guilty of error or of prejudicial assessment of the available data. According to Wright, the last possibility should be excluded from the outset. Prejudicial assessment of data requires both X and Y to agree about the evidential basis, i.e. about some objective feature of the proof that X, but not Y, regards as sufficient to establish its logical necessity. If this is the case, the realist owes an explanation why the objective features Y keeps track of (arguably the truth of the conclusion and the psychological trait of being unable to think how the premises could be true and the conclusion false) should be held to be sufficient for the conclusion that the argument establishes a necessary truth. And, according to Wright, it is unclear how the realist could answer such a question. Error can be excluded, since there is no need to attribute to the non-factualist any misperception of the structure of the proof nor any technical error in evaluating its inferential steps. There remains ignorance. But the only thing Y could be held to be ignorant of is the necessity itself of the proof, which, in turn, either entails that Y’s perception of the proof, together with her alleged incapability to conceive of its falsity, actually constitutes her grasping its necessity without her being able to recognize it, or that Y lacks a special faculty – which could be appropriately described as proof-sensitivity – which, together with the other features of Y’s epistemic situation, would enable her to recognize the proof’s necessity. Yet, both possibilities seem problematic. The former is problematic, for the realist again is required to explain what in the epistemic situation Y recognizes should convince her to arrive at the conclusion that the proof is necessary (it is precisely Y’s point that her incapability to imagine counterexamples is not a sufficient ground to dignify the proof with the special status of being logically necessary). And the latter is problematic, for it rests on an assumption that threatens to destroy the distinction between objectivity and non-objectivity. If the move is conceded that, in order to explain the logical disagreement, it is possible to attribute to Y a special cognitive shortcoming (for instance, her inability intellectually to perceive that a proof is necessary), then there seems to be no ground to denying it in any given case. Discourse about what is comic 34

“Let us say that a dispute is Humean provided there is no material misunderstanding of any concept involved in the formulation of the object statement, and the source of the dispute is not error, nor ignorance nor prejudice”, (ibidem, p. 201).

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should be regarded, as long as Cognitive Command is concerned, as objective. If a special faculty of comic-sensitivity is allowed for, every disagreement about whether a given situation is comic can in principle be traced back to its malfunctioning or its incorrect employment on the part of some of the disputants. Hence, unless the logical realist is prepared to allow for an objectivist interpretation of such paradigmatically nonfactual areas of discourse, she cannot defend her position in the indicated way. Shapiro’s response is multi-faceted. He tries to argue for the thesis that logic’s objectivity is in good standing as long as the Euthyphro Contrast, The Wide Cosmological Role, and the Cognitive Command are concerned. As we have seen, however, Wright’s attack centres on logic’s inability to satisfy the Cognitive Command. Therefore, I will concentrate on Shapiro’s argument against such a contention. For those who might not be satisfied with it, though, I’ll start by briefly dwelling upon Wide Cosmological Role and the Euthyphro Contrast. My intention, here, is to indicate some alternative strategy to secure logic’s objectivity in the face of an alleged failure, on its part, to pass the Cognitive Command. In the end I will propose an argument to the effect that, unless logic is allowed non-problematically to pass the test of Cognitive Command, every area of discourse should be regarded as possibly failing to meet the requirement. As we have seen at the beginning of this section, Wright suggests that, if some facts in a disputed area are able to feature “in at least some kinds of explanations of contingencies which are not of that sort – explanations whose possibility is not guaranteed merely by the minimal truth aptitude of the associated discourse”35, then a realist interpretation of their status should be seen to be the most natural. Shapiro acknowledges a certain vagueness in the concept of an explanation. However, he thinks that the following general structure could be generally acknowledged as supplying a necessary condition for something contributing to the explanation of a given phenomenon. An explanation normally takes the form of a deduction, from an established theory, of consequences which are identical with the phenomena we are trying to explain. The tides and the orbit of the moon are explained when they are deduced from gravitational theory and a sufficiently definite description of the initial status of the system. In general, a phenomenon φ is explained by a theory Γ, when, being I the initial conditions, (Γ & I) → φ. In a sense, 35

Wright 1992, p. 197.

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then, logic plays the widest cosmological role, for it constitutes a necessary condition for giving any explanation whatsoever. It might be replied that logic does not feature in an explanation in the same way as, say, the gravitational theory features in an explanation of the tides and the orbit of the moon. Quite in an anti-quinean way – in deep opposition to Resnik’s philosophical beliefs, for instance – it might be said that logic never constitutes an explanans, but just supplies the general framework for giving any explanation whatsoever. That distinction might be conceded. Does it follow from this admission, that logic should not be regarded as objective? Suppose that, since it does not perform a proper explanatory role, logic should not be held to be objective. As a consequence, there could not be, in any objective sense, any genuine question as to which explanatory framework is the correct one. Two mutually incompatible rules of inference should be seen as on a par, as long as their capability of constituting the framework of genuine explanations is concerned. But such an admission would seem to destroy the very notion of explanation; for, by appropriately choosing a particular framework, one would seem always capable of putting at the service of some still unexplained phenomenon some dubiously objective theory, however remotely located from the explanandum it might be. Suppose, for instance, that a deduction were allowed to take the following form: 1. Monty Payton is amusing 2. Monty Payton is amusing tonk there is a ghost in my bedroom 3. There is a ghost in my bedroom

tonk I, 1 tonk E, 2

On its general description, the foregoing should be regarded as a genuine explanation of the fact that there is a ghost in my bedroom; at least, as long as no substantial issue as to the correctness of the implicated rules of inference can be raised. Since it would seem that it is not, the premise should be denied that, because logic does not feature as a proper premise in any explanation, it should not be attributed any kind of objectivity. So, even if, in the indicated sense, logic does not perform a wide cosmological role, the conclusion does not seem to follow that, for that reason, logic should not be regarded as objective. In fact, if it is not, the very criterion of wide cosmological role seems to loose its strength, allowing for the acceptance, as genuine explanations, of structures whose unavailability, in Wright’s intentions, represents a constituting trait of some discourses’ lack of objectivity.

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Whenever the statements in a given area of discourse are subject to the Euthyphro Contrast, one party (Socrates) contends that their truth is recognised under ideal epistemic conditions because, under such conditions, every truth is bound to be tracked; the other party (Euthyphro), contends that truth in the discourse is conceptually constituted by acceptation under ideal epistemic conditions. This, as applied to the case of logic, suggests the following test for adjudicating its objectivity: are logical statements true because they are recognized to be so or are they recognized to be so because they are true? If, for the sake of argument, we accept the premise that logic is epistemically constrained (and, therefore, we accept that there are no unknowable logical truths), we have to accept the following biconditional: An argument is valid if and only if an ideal agent, acting under optimal conditions, judges it to be valid.

If an argument is valid, then it is true that (under idealized epistemic conditions) it will be recognized to be so; and, if it is true that (under idealized epistemic conditions) an argument will be recognized to be valid, then it is valid. The question, suggested by the Euthyphro Contrast, is which direction has to be seen as explanatorily primary. The argument we have been defending before would seem to be of some help here. Since an inference must preserve objective truth, its validity can be tested against the truth values of the premises and conclusions which are adjudicated by non-inferential criteria of truth assessment. Since “no fiat and no non-cognitive stance can make an inference truth preserving”36, the conclusion seems to follow that Socrates, who defends the left-toright order of explanation, will win the contrast. More than this, since logic is explicitly deployed in articulating the Euthyphro Contrast, either logic comes out automatically objective, for it constitutes a background assumption of a procedure by means of which verdicts of objectivity are alleged to emanate, or, if it is not, logic seems to be exempted from the contrast. In the latter case, though, there seems to be no sense in questioning whether logic is objective. A discourse, in Wright’s sense, exhibits Cognitive Command iff it is a priori certain that every disagreement about some of its central sentences can be traced back to cognitive shortcomings on the part of at least one of the disputants. Naturally enough, the question whether logic 36

Shapiro (ibid., p. 363)

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does exhibit Cognitive Command can be answered – almost analytically – in the affirmative, only if inferential mistakes are listed among the possible cognitive shortcomings that can be employed to explain some disagreement over an objective statement. Wright, as we have seen, denies that inferential mistake can be so regarded. The move of postulating a special proof-sensitivity – whose malfunctioning could supply the required sort of cognitive shortcoming – destroys the distinction between objective and non-objective. The objectivity of every area of discourse could be secured, as long as Cognitive Command is concerned, just by postulating a special cognitive faculty, expressible as a form of sensibility to the (allegedly) objective properties dealt with in the area of discourse. For instance, it could be said that the discourse about what is funny is objective because those who fail to find Benigni’s performances amusing must have committed a cognitive mistake, i.e. must have failed adequately to keep track of how the property of amusingness is distributed in reality. Elsewhere, though, Wright includes logic in the list: he says that a discourse exhibits Cognitive Command if it is a priori certain that differences in opinion about some of its central sentences can be satisfactorily explained only in terms of “’divergent input’, that is, the disputants working on the basis of different information (and hence guilty of ignorance or error), of ‘unsuitable conditions’ (resulting in inattention or distraction and so on inferential error, or oversight of data, and so on) or ‘malfunction’”37. A natural proposal to harmonize the apparently diverging opinions, would stress the fact that inferential blindness is not listed as an explicit cognitive shortcoming; in fact, it involves neither error nor ignorance. An error is indeed involved, but one of distraction. Therefore it would seem that logic should be construed just as supplying a general framework against which the criterion of Cognitive Command might be applied. Errors in logic are just misapplication of the logical rules of inference two disputants must agree upon if the notion of their alleged disagreement must make sense in the first place. Beside the disputants’ agreement about some definite framework, nothing substantial hinges on the acceptance of some definite set of rules instead of another. To this, as we have anticipated, Shapiro replies, echoing the strategy pursued by Boghossian in his The Status of Content, that Wright empties of any significance the question whether logic is objective or not. In fact, either one accepts logic’s objectivity, by recognizing its status of background assumption, or, if one “removes logic” – for that very reason – 37

Wright (ibid., p. 93), emphasis mine.

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“from the Arena in which Cognitive Command operates”, falls short of giving a fully negative answer to the very question the application of the criterion should help in deciding. By resorting to another criterion proposed by Wright, however, Shapiro mounts an argument directly to support the claim that logic is objective. The argument involves Wright’s notion of disputational supervenience. According to Wright, a discourse A disputationally supervenes upon a discourse B, when every disagreement about the truth value of some sentences in A depends on some disagreement about the truth value of some sentences in B. According to the definition, a discourse’s disputational supervenience upon another does not entail, in and of itself, that the latter must, or must not, be regarded as objective. In fact, the notion of disputational supervenience allows for the following widened reformulation of the Cognitive Command: (Cog)

A discourse exhibits Cognitive Command iff (a) every disagreement arising within it can be satisfactorily explained only in terms of “divergent inputs”, “unsuitable conditions” or “malfunction” or (b) it disputationally supervenes upon a discourse which meets condition (a).

According to the enlarged criterion Cog, whether or not a discourse exhibits Cognitive Command can be made apparent by inspecting its argumentative ramifications, and the cognitive status of the discourses it ramifies in. If a discourse A ramifies into, i.e. disputationally supervenes upon, an objective discourse B exhibiting Cognitive Command, every disagreement within the A can be traced back to a disagreement within B; since every disagreement within B involves, by definition, a cognitive shortcoming, a cognitive shortcoming must be responsible of every disagreement within the former. All this seems correct. Yet Shapiro tries to mount an argument from logic’s disputational supervenience which, as it were, get things the other way around. Shapiro calls the reader’s attention to the fact that, given its pervasive role, disagreements about logic will likely result in disagreements elsewhere. He rightly emphasizes, for instance, that the classical and the intuitionistic logicians, who disagree about the logical status of the principle of excluded middle, are likely to disagree about the intermediate-value theorem, which states that if f is a continuous function to real numbers to real numbers such that for some a