The interview took place in Oxford on 10 September 1992. While working from the tape on the text of the interview, I decided to gather references to books and articles in footnotes so that the reader may have a sense of the flow of the conversation. I then divided the text into sections, according to the topics which were discussed. Some material has been edited from the original transcript.

This chapter contains sections titled: Realism vs. Anti‐realism in the Semantics of Mathematical Language Anti‐realism about the Empirical Realm and, in Particular, about the Past Historical Significance and Historical Insignificance Generality and Holistic Explanations The Objectivity of Historiography Conclusion Bibliography Further Reading.

Selon le holisme sémantique, les propriétés sémantiques sont par nature anatomiques, c’est-à-dire intrinsèquement collectives. Selon le holisme de l’interprétation, la signification ou le contenu sont attribués collectivement. La thèse de constitution holistique de la signification peut être raisonnablement défendue à l’aide d’une contrainte de molécularité, qui introduit une hiérarchie dans la complexité logique des phrases, et un ordre ou une articulation dans le langage, en faisant droit à une condition finitaire d’anatomicité.According to semantic holism, semantic properties are anatomic by nature, (...) i.e. intrinsically collective. According to interpretation holism, meaning, or content, is collectively attributed. The thesis that meaning is holistically constituted may be defended provided we take into account a molecularity requirement. The requirement’s rôle is to introduce order or articulation in the langage, via a hierarchy of logical complexity, and by paying due attention to a finitary condition of anatomicity. (shrink)

Although G¨odel proved the first incompleteness theorem by intuitionistically respectable means, G¨odel’s formula, true although undecidable,seems to offer a counter-example to the general constructivist or anti-realistclaim that truth may not transcend recognizability in principle. It is arguedhere that our understanding of the formula consists in a knowledge of itstruth-conditions, that it is true in a minimal sense and, finally, that it is recognized as such given the consistencyand ω-consistency of P. The philosophical lesson to be drawn from G¨odel’sproof is that (...) our capacities for justification in favour of minimal truth exceedwhat is strictly speaking formally provable in P by means of an algorithm. (shrink)

I offer several reasons for rejecting naturalism as a philosophical viewpoint or program envisaged for two paradigm cases: the case of mathematics and the case of ethics. Semantical, epistemological and metaphysical similarities between the two are investigated and assessed. I then offer a sketch of a different way of understanding the nature of mathematical difficulties and that of ethical puzzles.

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) (151 E-152C); as opposed to what he may have taught secretly to his pupils (152C-160D). Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken. (shrink)

This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a worskhop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical (...) conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of “Mathematical Truth” due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status of numbers: Frege’s logicism, fictionalism, structuralism, and Bourbaki’s theory of structures are called up for an appraisal of Benacerraf’s negative conclusions of “What Numbers Could Not Be.” The third is devoted to supertasks and bears witness to the unique standing of Benacerraf’s first publication: “Tasks, Super-Tasks, and Modern Eleatics” in debates on Zeno’s paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics. Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the mid 1970’s. A complete chronological bibliography of Benacerraf’s work to 2016 is provided.Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio Leòn-Sànchez and Ana Leòn-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro. (shrink)

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) ; as opposed to what he may have taught secretly to his pupils. Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken.In that part of the dialogue where the question is under examination whether or not knowledge and perception are the same, Socrates uses an idealized concept of knowledge. That is, he restricts the use of the word by setting down what he will consider to be the essential characteristics of knowledge, the sufficient and necessary conditions of its being instantiated. An excellent piece of philosophical procedure. (shrink)

[An Anti-Realist Perspective on Language, Thought, Logic and the History of Analytic Philosophy. .].

Because anticipated and retrospective regret play important roles in practical deliberation and motivation, better understanding them can illuminate the contours of human agency. However, the possibility of self-ignorance and the fact that we change over time can make regret—especially anticipatory regret—not only a poor predictor of where the agent will be in the future but also an unreliable indicator of where the agent stands. Granting these, this paper examines the way in which prospective and, particularly, retrospective regret can nevertheless yield (...) important insight into the sorts of creatures we are, both generally and individually. The experience of retrospective regret can show a person she values something in a way she did not know or that she is (or was) a different person than she had thought, insights which can factor into forward-looking, or prospective, deliberation. Such instances of revelatory regret reveal something to the agent about herself as agent. I examine two cases of agential self-ignorance. In the first, the experience of regret reveals what the agent values, not only to others but even to the agent himself. In the second, the agent anticipates experiencing regret for an action but does not experience the regret, suggesting that the agent did not value the rejected alternative in the way she thought. Anticipatory regret is forward-looking and can play an important role in practical deliberation. But insofar as anticipatory regret flows from one’s imperfect judgment and prospection about oneself, retrospective regret can be an important corrective in helping the agent understand her own standpoint. (shrink)

The author of “Parsimony and inference to the best mathematical explanation” argues for platonism by way of an enhanced indispensability argument based on an inference to yet better mathematical optimization explanations in the natural sciences. Since such explanations yield beneficial trade-offs between stronger mathematical existential claims and fewer concrete ontological commitments than those involved in merely good mathematical explanations, one must countenance the mathematical objects that play a theoretical role in them via an application of the relevant mathematical results. The (...) nominalist’s challenge is thus to undermine the platonistic force of such explanations by way of alternative nominalistic ones. The author’s contention is that such nominalistic explanations should provide a paraphrase of the proofs of the mathematical results being applied. There are reasons to doubt that proofs, construed here as formal derivations, actually contribute to the platonistc force to be undermined and, by parity, that nominalized proofs should bear responsability for the corresponding undermining. A discussion of two examples and of associated arguments by Lange, Pincock, Steiner and Tallant, point to a a wealth of worries concerning the construal of this explanatory role. Among those figure the distinction between the weak and strong role of proofs, the distinction between causal or “ordinary” explanations and genuine mathematical ones, and the unifying role of optimization explanations. More generally, the very idea that the explanatory advantages yielded by applied mathematical claims may be construed as gradual or progressive and the associated notion that the feasibility of their nominalistic paraphrases decreases as the generality and force of these claim increases, deserves a closer attention. (shrink)

My discussion addresses the differences between analytic and continental philosophy concerning the use of logic and exact reasoning in philosophical practice. These differences are mainly examined in the light of the controversial dominance of Hegel's concept of logic (and theory of concept) in twentieth-century continental philosophy. The inquiry is developed in two parts. In the first (Sections 1-2), I indicate some aspects of the analytic-continental divide, pointing to the role that the topic 'logic and philosophy' plays in it. In the (...) second part (Sections 3-6), I give a short account of the views of logic which are typical of the three main trends of continental philosophy (see Table 1). I also suggest how, with the aid of some typical analytical devices, some continental 'anti-logical' attitudes may be corrected, on their own terms. (shrink)

We investigate whether ordinary quantification over objects is an extensional phenomenon, or rather creates non-extensional contexts; each claim having been propounded by prominent philosophers. It turns out that the question only makes sense relative to a background theory of syntax and semantics (here called a grammar) that goes well beyond the inductive definition of formulas and the recursive definition of satisfaction. Two schemas for building quantificational grammars are developed, one that invariably constructs extensional grammars (in which quantification, in particular, thus (...) behaves extensionally) and another that only generates non-extensional grammars (and in which quantification is responsible for the failure of extensionality). We then ask whether there are reasons to favor one of these grammar schemas over the other, and examine an argument according to which the proper formalization of deictic utterances requires adoption of non-extensional grammars. (shrink)

I contrast two construals of the thesis that truth is independent of verifiability in principle: a modal one and a non modal one. I argue in favor of the modal construal and then, on that basis, that independence holds across the board, i.e., even for statements that are verifiable by us relative to familiar, customary, non-skeptical standards.

Philosophia (ISSN: 1105-2120) (Abstract), tome 30, 2000, p. 203-205.

In a nutshell, semantic antirealism is the doctrine that if a statement is true, then it must be possible, at least in principle, to determine that it is true. Consider the particular case of self-ascriptions of attitudes such as beliefs, desires and intentions, i.e. statements of the form "I φ [that] p", where φ ranges over propositional attitude verbs and p provides the content of whatever is φd by the self-ascriber. Should we be semantic antirealists about these when the putative (...) bearer of the attitude is the only individual who may retrieve a warrant in favour of his φing that p? We can't provide an answer to the question unless we're clear about (i) whether or not the "at least in principle" clause is too weak, and (ii) what the right construal of positive introspection should look like. 2 Thus two issues: strict finitism on the one hand and the phenomenological nature of introspective warrants on the other. I shall argue that recent views defended by Peacocke and Pryor are found wanting with respect to both. (shrink)

According to the antirealist view of history, history is something historians construct in the present. Although the warrants they may gather in favour of past events do not form a coherent class, such warrants constitute the assertibility conditions of our statements about the past. They are by nature partial, gradual and defeasible. The antirealist is then faced with two problems. One is to account for a notion of historical significance, either in terms of causal links, broad patterns, or justified historiographic (...) generalizations. A second one is to secure a bound to the holistic construal of historical cognitive content. A coherent antirealist about history must explain why historical claims are in the market for truth, without taking the position of an ideal observer looking at the past from an a-historical fixed point outside time. (shrink)

According to semantic antirealism, intuitionistic logic satisfies the requirement that truth should be constrained by provability in principle. Some philosophers have argued that semantic antirealism must be committed to effective provability and that the commitment leads to a stronger kind of logical revisionism exemplified by substructural logics. I shall take into account two different kinds of reply. The first is concerned with meaning per se and grasp or fixing of meaning. It rests on the idea that if we have a (...) method which may be used over some surveyable range, we have determined a way of applying the method everywhere in principle, and that this is enough as far as fixing or grasping meaning is concerned. The second concerns two radical antirealist principles disqualifying structural rules: Token Preservation and Preservation of Local Feasibility. Against criticisms, I shall argue that conceptual support may be provided for both. The main point in this debate is that there is a decisive difference between the rejection of classical logic via the curbing of the epistemic idealizations embedded in structural rules and the rejection of classical logic via the intuitionistic criticism of invalid introduction and elimination rules. It will be explained why the second rejection is stronger than the former. (shrink)

Professor Prawitz has made four claims in his talk. The first claim is that one should be able to generalize the intuitionistic theory of meaning already available for mathematical discourse to empirical discourse. Since each claim constitutes a step in an argument of a general form in favour of some new kind of antirealistically inclined theory of meaning (with a final pessimistic overtone), I shall go over each claim one by one, check whether the argument which links them in the (...) way described is sound, and assess on that basis the appropriateness of the project (and of the pessimism). (shrink)

There are several ways of conceiving objectivity -- scientific objectivity in particular -- and, accordingly, several ways of defending or attacking particular construals of it. According to one conception sometimes labelled "realism", objectivity in science is a semantic, modal and metaphysical notion: a scientific theory is objective insofar as it tells the truth about the way the world is independently of its epistemic accessibility to us. So, for instance, the Newtonian theory of gravition is objective insofar as it tells the (...) truth about the motion of particles submitted to gravitational forces. What it tells us, the realist contends, holds or is the case whether or not the physical world is accessible to us. The conception is semantic insofar as the notion of truth is involved, modal insofar as the conception of the possibility of a mind-independent natural world is involved and metaphysical insofar as a conception of a certain way the world is is involved. Philosophers as diverse as Berkeley, Kant and Dummett's antirealist will then ask: if this were the case, how could we know anything about it? How could we even form a bona fide conception of its possibility? (shrink)

May the theory of radical interpretation developed by Donald Davidson on the basis of Quine's arguments for the indeterminacy of translation help fix the meaning of the logical constants? In particular, may the theory exclude ways of conferring meaning on the constants which, although developed within the Davidsonian framework, would lead to unexpected results? Could an interpreter fix the meaning of the constants in a non classical way, although still in accordance with the guiding principles of the interpretative strategy? Or, (...) on the contrary, does the theory incorporate constraints on interpretation which are stronger than those imposed by the possibility of non classical, or deviant logics? I examine the particular case of negation within the framework of the natural deduction system developed by Gentzen and Prawitz, and conclude that Davidson's theory, understood as an empirical theory of truth, leaves the problem of knowing which meaning should be assigned to the constant for negation without a satisfactory solution. Although interpetation has to be carried out according to the principle of charity, disagreements may come up regarding which meaning should be assigned to "not" in a properly regimented natural language. (shrink)

Emotions are part of our culture ; particular emotions like resentment andguilt are part of specific cultural heritages. On the other hand, moral judgementsand imperatives have the appearance of objectivity. There lies - or so it seems -a conflict, even a contradiction. Statements like "Slavery is unjust" may beasserted, agreements may be reached concerning what they claim or express,and they may occur as antecedents in conditionals such as "If slavery is unjust,then it must be abolished". When it is claimed that (...) slavery is unjust or that it iswrong to harm others, it is thereby claimed that it is so objectively. We mean bythis (among other things) that it is so independently of the moral emotionsanyone may feel with respect to slavery or the infliction of pain.It will be argued here that there are grounds to believe that emotions must beevaluated cognitively and that they do have cognitive significance, value andcontent. In this cognitive or quasi-cognitive perspective, the appropriatecharacter of an emotion is akin to the truth of a proposition : just as the truth of aproposition may be evaluated in terms of the justifications we are able toprovide in its favour, the correctness of emotions may be evaluated relatively tocognitive bases and classes of available warrants. Some emotions may be ruledout as incorrect or inapproriate, just as some propositions may be rejected asunjustified or in need of a warrant. The parallel relies on the controversial notionof non-propositional forms of moral justification. The notion may be construedin a variety of ways, the most promising construals being, I believe, thoseprovided by the perceptual model.I shall focus on the following point. Moral judgements and imperatives areexpressed with the usual resources of natural languages. These typically includepredicates like "unjust" and "wrong", and deontic sentential operators like"must" and "should". Moral emotions, on the other hand, may be expressed bybodily movements and facial expressions. Although it may be argued thatemotions do not bear the cognitive marks of objectivity when expressed in thisway, there is no reason to think that a reformed language of ethics, i.e. a purelanguage of emotions, free of all the linguistic or symbolic marks of truth,assertability and objectivity, would thereby be free of normative input, or evenbe inadequate to express normative claims. I shall argue that once nonpropositionalforms of justifications are taken into account, the reformingstrategy of emotivists and neo-emotivists is indeed ineffective. (shrink)

As far as logic is concerned, the conclusion of Michael Dummett's manifestability argument is that intuitionistic logic, as first developed by Heyting, satisfies the semantic requirements of antirealism. The argument may be roughly sketched as follows: since we cannot manifest a grasp of possibly justification-transcendent truth conditions, we must countenance conditions which are such that, at least in principle and by the very nature of the case, we are able to recognize that they are satisfied whenever they are. Intuitionistic logic (...) satisfies the semantic requirement that we should either eschew the notion of truth altogether and replace it by provability in principle, or constrain it by provability in principle (Dummett [1973] 1978). (Handout: 1-5). Some philosophers have argued that the traditional antirealist desideratum of decidability in principle is too weak, so that semantic antirealism properly construed must be committed to effective decidability. As such, it either leads to strict finitism (Wright [1982] 1993) [Handout: 6] or to a much stronger kind of logical revisionism than the one considered by intuitionists (whether or not they accept the manifestability argument): substructural logics, and in particular linear logics, rather than intuitionistic logic, satisfy the semantic requirements of strict antirealism (Dubucs and Marion 2004) [Handout: 8-9]. I shall develop two different kinds of replies. The first is concerned with the notion of meaning per se and looks to strict finitism directly, although not on the ground that it would provide a correct way of dealing with Soritic-type paradoxes (the original and primary focus of discussion in Wright [1982] 1993). The second is concerned with the justification of structural and logical rules in a natural deduction system à la Gentzen. It will deal in particular with the criticism of the structural rules of Weakening and Contraction [Handout: 10 and 11]. The first kind of reply, which Dummett has partially taken into consideration, is that if we jettison the effectively vs. in principle distinction, as applied to manifestability-type arguments, we end up with an unsatisfactory explanation of how the meaning of statements covering the practically unsurveyable or pro tempora undecided cases is fixed. The idea is that if we have a method which may be used over some small range, we have determined a way of applying the method everywhere in principle and that this is enough as far as fixing meaning is concerned. Decidability in principle is just what we need with respect to manifestation of grasp of meaning. In this perspective, antirealism shouldn't be strict and manifestability-type arguments need not be applied as far as the strict finitist would want to [Handout: 7]. It follows that there is no reason to think that practical feasibility should be built in assertibility conditions and proofs be construed dynamically as acts in the strict antirealist's acception of that term [Handout: 8]. I shall then look at one radical antirealist principle disqualifying structural rules, namely Token Preservation, arguing against Bonnay and Cozic's criticisms of Dubucs and Marion (Bonnay and Cozic 3 2007) that some conceptual support may be provided for Token Preservation, which doesn't rely on a causal misreading of the turnstile [Handout: 13, 14]. I shall then assess the merits and limits of radical antirealism and the logic of feasible proofs with respect to the original Dummettian argument in favour of semantic antirealism (provided it has indeed revisionist implications for logic), whether the radical antirealist merely stipulates what human feasibility amounts to, or dispenses with structural rules in order to argue in favour of a curb on the epistemic idealizations they unwarrantedly embed. It will be noted here that there is a great difference, conceptually speaking, between the rejection of classical logic via the curbing of the epistemic idealizations embedded in structural rules, and the rejection of classical logic via the criticism of the introduction and elimination rules which fix the meaning of the classical constants. The kind of logical revisionism envisaged by intuitionists from Heyting on is in many respects stronger than the one envisaged by advocates of linear logic, should they ground their arguments on an endorsement of strict antirealism. The crucial case of excluded middle is telling. Because of the splitting of the constants in linear logic (Handout: 12], two distinct laws of excluded middle may be formulated (Handout: 15), but the traditional arguments of Brouwer and Heyting against the classical law yield a stronger revision than the substructural revision with its admission of these two (very) weak versions of the law. (Project: a clearer conception is needed of how the introduction and elimination rules for the logical connectives in the intuitionistic calculus depend on the structural rules which the radical antirealist wishes to reject.). (shrink)

Danielle Macbeth's purpose in Macbeth 2005 is threefold. Her monograph proposes "to provide a logical justification for all aspects of Frege's peculiar notation, to motivate and explain the developments in Frege's views over the course of his intellectual life, and to explicate his most developed, critically reflective conception of his Begriffschrift, his formula language of pure thought". I shall focus here on a few selected aspects of the first and third points and leave on the side the discussion of the (...) historical development of Frege's views on logic, semantics and mathematics. The book's underlying claim is that although Frege's logical language, "can of course be read as a language of quantificational logic, [it] can also be read very differently", so much so, as a matter of fact, that although Frege's logic is usually thought of as a "notational variant of standard quantificational logic", it is nevertheless "unknown to us". This naturally prompts three questions : "What is Frege's logic?", "What is quantificational logic?", and given the way we understand formal languages for first and higher order predicate logic, most notably the notions of argument 2 place, of scope and of binding : "How come Frege's logic says nothing about such notions, or something so different from what we say?". (shrink)

Ontological parsimony requires that if we can dispense with A when best explaining B, or when deducing a nominalistically statable conclusion B from nominalistically statable premises, we must indeed dispense with A. When A is a mathematical theory and it has been established that its conservativeness undermines the platonistic force of mathematical derivations (Field), or that a nonnumerical formulation of some explanans may be obtained so that the platonistic force of the best numerical-based account of the explanandum is also undermined (...) (Rizza), the parsimony principle has been respected.Since both derivations resorting to conservative mathematics and nonnumerical best explanations also require abstract objects, concepts and principles, ontological parsimony must also be required of nominalistic accounts. One then might of course complain that such accounts turn out to be as metaphysically loaded as their platonistic counterparts. However, it might prove more fruitful to leave this particular worry to one side, to free oneself, as it were, from parsimony thus construed and to look at other important aspects of the defeating or undermining strategies that have been lavished on the disposal of platonism.Two aspects are worthy of our attention: epistemic cost and debunking arguments. Our knowledge that good mathematics is conservative is established at a cost, and so is our knowledge that nominalistic proofs play a theoretical role in best explanations. I will suggest that the knowledge one must acquire to show that nominalistic deductions and explanations do play their respective theoretical role involves some question-begging assumptions regarding the nature of proofs. As for debunking, even if the face value content of either conservative or platonistic mathematical claims didn’t figure in our explanation of why we hold the mathematical beliefs that we do, we could still be justified in holding them so that the distinction between nominalistic deductions and explanations and platonistic ones turns out to be invidious with respect to the relevant propositional attitude, i.e., with respect to belief. (shrink)