Fabrice Pataut

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

Realism is the claim that truth may transcend all possible verification. The familiar Dummettian argument against that modal claim is that there is no way to manifest an understanding of it in actual linguistic practice. The Dummettian anti-realist's provisional conclusion is that the modal claim must be false. ;The attack on truth-conditional semantics and on the principle of bivalence are familiar ingredients of the anti-realist negative programme. I agree that, whether mathematical formulae or ordinary sentences in the past tense are concerned, we cannot manifest a knowledge of the truth-conditions of particular instances of 'It is possible that ' by deciding their truth. There is nevertheless a way to argue in favour of specific instances of the modal claim when s is a sentence in the past tense. The proposed argument does not appeal to the recognitional abilities which, in the standard anti-realist perspective, constitute grasp of meaning. It does not commit one to the endorsement of the principle of bivalence, although the principle implies the modal claim. ;Our understanding of the workings of nature, whether grounded on scientific theories or on common sense, implies the modal claim. Since we are only contingently connected to the evidence pro or con past events and since the existence of evidence is itself a contingent matter, sentences which say that those events occurred could be true whether or not we can, at any point in time, detect that they are true. The possibility that truths about past facts transcend all possible verification is a purely natural possibility, grounded on what we know of the workings of nature. ;This implies that decidable statements in the past tense are not immune to the realism vs. anti-realism debate. Although they do not transcend verifiability, they could transcend whatever our recognitional abilities, no matter how extended, would allow us to establish at any point in time, either in the past, right now, or in an indefinitely extensible future

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.)

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

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

Many philosophers hold that physical laws have a unique modal status known as nomic necessity which is weaker than metaphysical necessity. This orthodox view has come into question in the past few decades. In particular, the metaphysical view known as essentialism has provided an argument that the laws of nature are necessary in the strongest possible sense. It seems obvious to many that at least some essentialist arguments in favor of the necessity of scientific claims are going to be sound. For example, the view that claims like "water is H2O" are necessary has itself 2 become an orthodox view. However, the question of whether laws, like the law of conservation of energy, or the law of gravity, are necessary is far more contentious. Philosophers divide roughly into two camps, law necessitarians1 who hold that the laws are necessary in the strongest sense and contingency theorists who hold that they are at least in some sense contingent. One argument for the necessitarian position is via an essentialist theory of the transworld identity of properties. In this paper I defend such a theory of the identity of properties and its necessitarian consequences from one major criticism. To focus the paper, I center the discussion on a single critic, E. J. Lowe. In his book, The Four Category Ontology, he offers a criticism of the essentialist argument for necessitarianism via an analogy with other forms of transworld identity and intuitions about the contingency of the physical constants2. I undermine the usefulness of Lowe's analogy by examining the purposes of attributions of properties. I also show that the essentialist's position can allow it to accommodate the intuitions of contingency in a way that fits best with the purpose behind property attributions

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)

Modernism, in the book under review, is characterized as the belief that "there can be no philosophical language; that the kind of truth sub specie aeterni that was sought by philosophers is either meaningless or more appropriately expressed by the arts -- especially by literature and poetry" (p. xiii). The author wishes to show that this thesis rests upon unquestioned dogmas, presuppositions or presumptions "regarding the distinction between representation and presentation," which should be rejected (p. 9). She proposes to criticize the distinction, along with the other unwarranted distinctions thereby embedded in the central tenet of modernism, and to overcome the "modernist overcoming of metaphysics" by drawing on the works of Jacques Derrida and Michael Dummett.

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

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

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