The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific (...) consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic. (shrink)

This article offers an overview of inferential role semantics. We aim to provide a map of the terrain as well as challenging some of the inferentialist’s standard commitments. We begin by introducing inferentialism and placing it into the wider context of contemporary philosophy of language. §2 focuses on what is standardly considered both the most important test case for and the most natural application of inferential role semantics: the case of the logical constants. We discuss some of the (alleged) benefits (...) of logical inferentialism, chiefly with regards to the epistemology of logic, and consider a number of objections. §3 introduces and critically examines the most influential and most fully developed form of global inferentialism: Robert Brandom’s inferentialism about linguistic and conceptual content in general. Finally, in §4 we consider a number of general objections to IRS and consider possible responses on the inferentialist’s behalf. (shrink)

ABSTRACT I argue against both neuropsychological and cognitive accounts of our grasp of numbers. I show that despite the points of divergence between these two accounts, they face analogous problems. Both presuppose too much about what they purport to explain to be informative, and also characterize our grasp of numbers in a way that is absurd in the light of what we already know from the point of view of mathematical practice. Then I offer a positive methodological proposal about the (...) role that cognitive science should play in the philosophy of mathematics. (shrink)

This paper offers an account of the a priori. According to this account, the fundamental notion is not that of a priori knowledge, or even of a priori justified belief, but a notion of an a priori justified inferential disposition. The rationality or justification of such a priori justified inferential dispositions is explained purely by some of the basic cognitive capacities that the thinker possesses, independently of any further experiences or other conscious mental states that the thinker happens to have (...) had. It is then shown how a priori justified inferences and beliefs can be explained on the basis of such a priori justified inferential dispositions. (shrink)

This paper defends the thesis that counterfactuals are strict conditionals. Its purpose is to show that there is a coherent view according to which counterfactuals are strict conditionals whose antecedent is stated elliptically. Section 1 introduces the view. Section 2 outlines a response to the main argument against the thesis that counterfactuals are strict conditionals. Section 3 compares the view with a proposal due to Aqvist, which may be regarded as its direct predecessor. Sections 4 and 5 explain how the (...) view di ers from the theories of counterfactuals advocated by Stalnaker and Lewis, and from some contextualist strict conditional accounts of counterfactuals that have emerged recently. Finally, section 6 addresses the thorny issue of disjunctive antecedents. (shrink)

We are reliable about logic in the sense that we by-and-large believe logical truths and disbelieve logical falsehoods. Given that logic is an objective subject matter, it is difficult to provide a satisfying explanation of our reliability. This generates a significant epistemological challenge, analogous to the well-known Benacerraf-Field problem for mathematical Platonism. One initially plausible way to answer the challenge is to appeal to evolution by natural selection. The central idea is that being able to correctly deductively reason conferred a (...) heritable survival advantage upon our ancestors. However, there are several arguments that purport to show that evolutionary accounts cannot even in principle explain how it is that we are reliable about logic. In this paper, I address these arguments. I show that there is no general reason to think that evolutionary accounts are incapable of explaining our reliability about logic. (shrink)

The notion of harmony has played a pivotal role in a number of debates in the philosophy of logic. Yet there is little agreement as to how the requirement of harmony should be spelled out in detail or even what purpose it is to serve. Most, if not all, conceptions of harmony can already be found in Michael Dummett's seminal discussion of the matter in The Logical Basis of Metaphysics. Hence, if we wish to gain a better understanding of the (...) notion of harmony, we do well to start here. Unfortunately, however, Dummett's discussion is not always easy to follow. The following is an attempt to disentangle the main strands of Dummett's treatment of harmony. The different variants of harmony as well as their interrelations are clarified and their individual shortcomings qua interpretations of harmony are demonstrated. Though no attempt is made to give a detailed alternative account of harmony here, it is hoped that our discussion will lay the ground for an adequate rigorous treatment of this central notion. (shrink)

We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...) both in general and for the particular case of logic. I also argue that two seemingly attractive responses – appealing to a faculty of rational insight or to the nature of concept possession – are incapable of answering the challenge. (shrink)

According to Rosenthal’s Higher-Order Thought (HOT) theory of consciousness, first-order mental states become conscious only when they are targeted by HOTs that necessarily represent the states as belonging to self. On this view a state represented as belonging to someone distinct from self could not be a conscious state. Rosenthal develops this view in terms of what he calls the ‘thin immunity principle’ (TIP). According to TIP, when I experience a conscious state, I cannot be wrong about whether it is (...) I who I think is in that state. We first suggest that TIP is a direct consequence of the HOT theory. Next we argue that somatoparaphrenia—a pathology in which sensations are sometimes represented as belonging to other people—shows that TIP can be violated. This violation of TIP in turn shows that the HOT theory’s claim that conscious states are necessarily represented as belonging to self is in error. Rosenthal’s attempt to account for pathological cases is found to be inadequate when applied to somatoparaphrenia, and other possible defenses are also shown to be incapable of preserving TIP. We further conclude by suggesting that the HOT theory’s failing in this regard is not a failing that is peculiar to this theory of consciousness. (shrink)

Semantic justifications of the classical rules of logical inference typically make use of a notion of bivalent truth, understood as a property guaranteed to attach to a sentence or its negation regardless of the prospects for speakers to determine it as so doing. For want of a convincing alternative account of classical logic, some philosophers suspicious of such recognition-transcending bivalence have seen no choice but to declare classical deduction unwarranted and settle for a weaker system; intuitionistic logic in particular, buttressed (...) by assertion-conditional semantics, is often considered to enjoy a degree of meaning-theoretical respectability unattainable by classical logic.The decision to forgo the classical inference rules is not always made lightly. Thus, Dummett: " In the resolution of the conflict between [the view that generally accepted classical modes of inference ought to be theoretically accommodated, and the demand that any such accommodation be achieved without recourse to bivalence] lies, as I see it, one of the most fundamental and intractable problems in the theory of meaning; indeed, in all philosophy. "The present article ventures to suggest that the conflict need not be irresoluble. Helping ourselves only to such conceptual resources as are standardly invoked by proponents of intuitionistic logic, we shall formulate a rudimentary meaning theory for a selection of logical constants, define a relation of valid inferability, and prove that the latter includes all of classical first-order logic. The result is essentially that reported in Sandqvist as Theorem 2.20.2. TheoryWe will be considering a standard-syntax first-order language with ⊃, ⊥ and ∀ as its only primitive logical constants. We assume countable supplies of individual constants, individual functors , and predicates , as well as a denumerably infinite set of individual variables. By a basic 1 formula we will mean one that …[Full Text of this Article]. (shrink)

This thesis aims to develop a psychologically plausible account of concepts by integrating key insights from philosophy (on the metaphysical basis for concept possession) and psychology (on the mechanisms underlying concept acquisition). I adopt an approach known as informational atomism, developed by Jerry Fodor. Informational atomism is the conjunction of two theses: (i) informational semantics, according to which conceptual content is constituted exhaustively by nomological mind–world relations; and (ii) conceptual atomism, according to which (lexical) concepts have no internal structure. I (...) argue that informational semantics needs to be supplemented by allowing content-constitutive rules of inference (“meaning postulates”). This is because the content of one important class of concepts, the logical terms, is not plausibly informational. And since, it is argued, no principled distinction can be drawn between logical concepts and the rest, the problem that this raises is a general one. An immediate difficulty is that Quine’s classic arguments against the analytic/synthetic distinction suggest that there can be no principled basis for distinguishing content-constitutive rules from the rest. I show that this concern can be overcome by taking a psychological approach: there is a fact of the matter as to whether or not a particular inference is governed by a mentally-represented inference rule, albeit one that analytic philosophy does not have the resources to determine. I then consider the implications of this approach for concept acquisition. One mechanism underlying concept acquisition is the development of perceptual detectors for the objects that we encounter. I investigate how this might work, by drawing on recent ideas in ethology on ‘learning instincts’, and recent insights into the neurological basis for perceptual learning. What emerges is a view of concept acquisition as involving a complex interplay between innate constraints and environmental input. This supports Fodor’s recent move away from radical concept nativism: concept acquisition requires innate mechanisms, but does not require that concepts themselves be innate. (shrink)

According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...) The issues discussed include reductionism, rejectionism, the Julius Caesar problem, the Bad Company objections, and the charge that second-order logic is set theory in disguise. (shrink)

In virtue of what are we justified in employing the rule of inference Modus Ponens? One tempting approach to answering this question is to claim that we are justified in employing Modus Ponens purely in virtue of facts concerning meaning or concept-possession. In this paper, we argue that such meaning-based accounts cannot be accepted as the fundamental account of our justification.

When Bishop published Foundations of Constructive Analysis he showed that it was possible to do ordinary analysis within a constructive framework. Bishop's reasons for doing his mathematics constructively are explicitly philosophical. In this paper, I will expound, examine, and amplify his philosophical arguments for constructivism in mathematics. In the end, however, I argue that Bishop's philosophical comments cannot be rounded out into an adequate philosophy of constructive mathematics.

In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well-defined form of language or linguistic framework we please. A linguistic framework defines framework-internal standards of correct reasoning that guide us in our first-order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not (...) itself constrained by these standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance. (shrink)

Je suis trés reconnaissant à Michel Seymour d'avoir soumis mon livre à un examen détaillé, pénétrant, et charitable et d'avoir, par ses objections, mis le doigt sur un certain nombre de présupposés des thèses défendues dans ce livre, qu'il a souvent articulés bien mieux que je n'ai été capable de le faire. Le principal de ces présupposés est mon rejet implicite de la thése quinienne de l'indétermination de la traduction, qui m'engage, selon Seymour, à défendre une conception conservatrice de la (...) logique et à insister sur une détermination de son domaine qui lui paraît injustifiée. Seymour soutient au contraire qu'il faut admettre cette thése, qui «commande une tout autre perspective» que la mienne. Je voudrais à la fois résister à la prémisse et à la conclusion de cette inférence. (shrink)

The Taming of the True continues the project Neil Tennant began in Anti-realism and Logic of investigating and defending anti-realism. Tennant’s earlier book anticipated a second volume, in which issues related to empirical discourse would be addressed in greater detail. The Taming of the True provides this sequel. It also attempts a ground-clearing project, by addressing challenges to some of the presuppositions and implications of Tennant’s anti-realist position. Finally, it takes an opportunity to revisit some of the issues examined in (...) the earlier book, in light of the evolving debate over realism and anti-realism. (shrink)

Various possibilities, that one is dreaming, that one is being deceived by a deceitful demon, that one is a brain in the vat being stimulated to think one has a body and is in a regular world, have been invoked to show that all one's experience-based beliefs might be false. Descartes in Meditation I advises that in order not to lapse into his careless everyday view of things he, or at least his meditator, should pretend that all his experience-based beliefs, (...) indeed all his …. (shrink)

This article offers a critical review of various ontological-relativist arguments, mostly deriving from the work of W. V. Quine and Thomas K hn. I maintain that these arguments are (1) internally contradictory, (2) incapable of accounting for our knowledge of the growth of scientific knowledge, and (3) shown up as fallacious from the standpoint of a causal-realist approach to issues of truth, meaning, and interpretation. Moreover, they have often been viewed as lending support to such programmes as the 'strong' sociology (...) of knowledge and the turn towards wholesale cultural-relativist doctrines, whether of the Wittgensteinian ('language-games') or Heideggerian (depth-hermeneutic) varieties. Thus Richard Rorty recommends that we should henceforth drop all that old-fashioned talk of 'truth', 'knowledge', or 'reality', since whatever warrants those descriptions from time to time is just the product of some currently favoured language-game or range of elective metaphors. Such ideas have little in common with Quine's general outlook of robust physicalism, nor again - though the case is less clear - with Kuhn's reconsidered approach to these issues as set forth in his 1969 Postscript to The Structure of Scientific Revolutions . However, both thinkers have left themselves open to misconstrual by adopting a sceptical-relativist fallback position in response to the well-known problems with logical empiricism. This essay therefore reviews those problems with reference to alternative, more adequate accounts of what is involved in the process of scientific discovery and theory-change. (shrink)

Brandom's book Making It Explicit defends Davidson's claim that conceptual thought can arise only on the background of a practice of mutual interpretation, without endorsing the further view that one can be a thinker only if one has the concept of a concept. This involves giving an account of conceptual content in terms of what Brandom calls practical deontic attitudes. In this paper, I make a plea for the conclusion that these practical attitudes are best seen as intentional, but non-conceptually (...) contentful. In particular, I argue that the hypothesis that Brandom's practical deontic attitudes are non-conceptually contentful wouldn't conflict with his view that non-conceptual intentionality is merely derivative. I then explore some of the implications which this hypothesis might have with respect to various forms of «intentional ascent». (shrink)

In the first chapter, we discuss Dummett’s idea that the notion of truth arises from the one of the correctness of an assertion. We argue that, in a first-order language, the need of defining truth in terms of the notion of satisfaction, which is yielded by the presence of quantifiers, is structurally analogous to the need of a notion of truth as distinct from the one of correctness of an assertion. In the light of the analogy between predicates in Frege (...) and open formulas in Tarksi, we concentrate on the semantic status of predicates. We register a dual attitude of Dummett towards Frege’s ascription of reference to predicates. On the one it is needed to endow quantifiers with their appropriate meaning. On the other hand, the introduction of concepts, as semantic correlate of predicates, smuggles a realist flavor in the overall semantic picture. In concluding the excursus (and with it the chapter), we stress Dummett’s will of developing a semantic picture free from this realist trait. In the second chapter, we present the idea of a proof-theoretic semantics. As for Frege true sentences denotes the truth-value True, so here closed' (i.e. categorical) valid argumentations denotes proofs. If a language contains implication-like operators, in order to characterize the condition of validity of a closed argumentation one has to introduce a notion of validity applying to ‘open’ (i.e. hypothetical) argumentations. We argue that this problem is analogous to the one posed by quantifiers in Frege-Tarksi’s style semantics. That is, implication forces one to introduce notion of validity for argumentations, which is more substantial than the correctness of the assertion of their conclusions. As we saw, the corresponding claim in the truth-based approach—that quantifiers require one to introduce a notion of truth, which is more substantial than the one of an assertion being correct—was the source of realism. Hence, Dummett proposes to reduce the semantic contribution of open argumentations to the one of their ‘closed instances’. In the truth-based perspective, this would correspond to the denial of the need of introducing concepts as the semantic correlates of predicates. We argue that Dummett’s fear, that an irreducible notion of function (represented by the need of ascribing validity to open argumentations) would lead to realism, turns out to be ill-founded. In the third chapter, we discuss the role played by the notion of truth in the anti-realist account. The notion of truth is what the anti-realist needs to cope with the so-called paradox of deduction. The analysis of the paradox yields to distinguishing between the truth of a sentence and the truth of a sentence being recognized. In terms of these conceptual couple, we reconsider the relationship between truth and assertion in an anti-realist perspective. Grounds are provided for a thesis (which was already advanced in chapter two), according to which the notion of the assertion of a sentence being correct is primarily connected only with the canonical means of establishing a sentence. The possibility of establishing a sentence by indirect means is conceptually dependent on the practice of establishing logical relationship of dependence among sentences. That is, the notion of a closed valid non-canonical argumentation is of any theoretical relevance only in presence of a notion of validity applying to open argumentations. In the fourth chapter, we discuss the possibility of characterizing in the proof-theoretic-semantics a notion of refutation. We develop an original characterization of refutations starting from an informal inductive specification of the condition of refutations of logically complex sentences. A sub-structural logic, called dual-intuitionistic logic, stands to this notion in the same relationship in which intuitionistic logic stands to the notion of proof so far consdered. All notions developed in chapter 2 have their corresponding (dual) ones in the framework developed. In particular, the distinctions canonical/non-canonical and closed/open argumentations. In the refutation based perspective, elimination rules have priority over introductions and the (only) assumption over the (many) conclusions. In the conclusions, we indicate the ingredients that an anti-realist approach to meaning should incorporate, in order to avoid the difficulties we registered. The core of an alternative view is a different conception of the relationship between categorical and hypothetical notions, in which the validity of open argumentations is not reduced to that of their instances, but rather it is directly defined. As a limit case, one would get a notion of validity applying to closed argumentations. (shrink)

According to Michael Dummett, we may think of the meaning of an expression as given by the principles governing the use we make of it. The principles regulating our linguistic practices can then be grouped into two broad categories (Dummett 1973: 396, 1991: 211). We might state them as follows: I-principles: state the circumstances under which an assertion of a sentence containing the expression in question is warranted. E-principles: state the consequences of asserting a sentence containing the expression. In the (...) case of the logical constants, we may associate a constant's I-principles with the set of its introduction rules and its E-principles with the set of its elimination rules (Dummett 1973: 454).1. (shrink)

Neil Tennant and Joseph Salerno have recently attempted to rigorously formalize Michael Dummett's argument for logical revision. Surprisingly, both conclude that Dummett commits elementary logical errors, and hence fails to offer an argument that is even prima facie valid. After explicating the arguments Salerno and Tennant attribute to Dummett, I show how broader attention to Dummett's writings on the theory of meaning allows one to discern, and formalize, a valid argument for logical revision. Then, after correctly providing a rigorous statement (...) of the argument, I am able to delineate four possible anti-Dummettian responses. Following recent work by Stewart Shapiro and Crispin Wright, I conclude that progress in the anti-realist's dialectic requires greater clarity about the key modal notions used in Dummett's proof. (shrink)

According to logical inferentialists, the meanings of logical expressions are fully determined by the rules for their correct use. Two key proof-theoretic requirements on admissible logical rules, harmony and separability, directly stem from this thesis—requirements, however, that standard single-conclusion and assertion-based formalizations of classical logic provably fail to satisfy :1035–1051, 2011). On the plausible assumption that our logical practice is both single-conclusion and assertion-based, it seemingly follows that classical logic, unlike intuitionistic logic, can’t be accounted for in inferentialist terms. In (...) this paper, I challenge orthodoxy and introduce an assertion-based and single-conclusion formalization of classical propositional logic that is both harmonious and separable. In the framework I propose, classicality emerges as a structural feature of the logic. (shrink)

The standard approach to what I call “proof-theoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of proof-theoretic semantics, this paper investigates in detail various notions of proof-theoretic validity and offers certain improvements of the definitions given by Prawitz. Particular emphasis is placed on the relationship between semantic validity concepts and validity concepts used in normalization theory. It (...) is argued that these two sorts of concepts must be kept strictly apart. (shrink)

This article concerns the ongoing neo-logicist program in the philosophy of mathematics. The enterprise began life, in something close to its present form, with Crispin Wright’s seminal [1983]. It was bolstered when Bob Hale [1987] joined the fray on Wright’s behalf and it continues through many extensions, objections, and replies to objections . The overall plan is to develop branches of established mathematics using abstraction principles in the form: Formula where a and b are variables of a given type , (...) Σ is a higher-order operator denoting a function from items of the given type to objects in the range of the first-order variables, and E is an equivalence relation over items of the given type. In what follows, I will sometimes omit the initial quantifiers.Frege [1884, 1893] himself employed three abstraction principles. One of them, used for illustration, comes from geometry: "The direction of l1 is identical to the direction of l2 if and only if l1 is parallel to l2."Call this the direction principle. The second was dubbed N= in [Wright, 1983] and is now called Hume’s principle: Formula where F≈G is an abbreviation of the second-order statement that there is a one-to-one relation mapping the F’s onto the G’s. In words, states that the number of F is identical to the number of G if and only if F is equinumerous with G. Unlike the direction-principle, the relevant variables, F, G here are second-order. Georg Cantor …. (shrink)

The paper is a defense of a strict form of anti-realism, competing the "in principle" form defended by Michael Dummett. It proposes to ground anti-realism on the basis of two principles ("immanence" and "implicitness") and to develop the consequences of these principles in the light of sub-structural logics.

Michael Dummett's argument for intuitionism can be criticized for the implicit reliance on the existence of what might be called absolutely undecidable statements. Neil Tennant attacks epistemic optimism, the view that there are no such statements. I expose what seem serious flaws in his attack, and I suggest a way of defending the use of classical logic in arithmetic that circumvents the issue of optimism. I would like to thank an anonymous referee for helpful comments. CiteULike Connotea Del.icio.us What's this?

I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed (...) by human activity in a manner similar to the constitutive construction of the US Supreme Court by certain legal and political activities. Finally, I outline some of the philosophical merits of metaphysical interpretations of mathematical theories of this type. (shrink)

§1. Overview. Philosophers and mathematicians have drawn lots of conclusions from Gödel's incompleteness theorems, and related results from mathematical logic. Languages, minds, and machines figure prominently in the discussion. Gödel's theorems surely tell us something about these important matters. But what?A descriptive title for this paper would be “Gödel, Lucas, Penrose, Turing, Feferman, Dummett, mechanism, optimism, reflection, and indefinite extensibility”. Adding “God and the Devil” would probably be redundant. Despite the breath-taking, whirlwind tour, I have the modest aim of forging (...) connections between different parts of this literature and clearing up some confusions, together with the less modest aim of not introducing any more confusions.I propose to focus on three spheres within the literature on incompleteness. The first, and primary, one concerns arguments that Gödel's theorem refutes the mechanistic thesis that the human mind is, or can be accurately modeled as, a digital computer or a Turing machine. The most famous instance is the much reprinted J. R. Lucas [18]. To summarize, suppose that a mechanist provides plans for a machine,M, and claims that the output ofMconsists of all and only the arithmetic truths that a human, or the totality of human mathematicians, will ever or can ever know. We assume that the output ofMis consistent. (shrink)

If correct, Christopher Peacocke’s [20] “manifestationism without verificationism,” would explode the dichotomy between realism and inferentialism in the contemporary philosophy of language. I first explicate Peacocke’s theory, defending it from a criticism of Neil Tennant’s. This involves devising a recursive definition for grasp of logical contents along the lines Peacocke suggests. Unfortunately though, the generalized account reveals the Achilles’ heel of the whole theory. By inventing a new logical operator with the introduction rule for the existential quantifier and the elimination (...) rule for the universal quantifier, I am able to show that Peacocke’s theory only avoids verificationism to the extent that it does not satisfy manifestationism. (shrink)

The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.

Throughout his philosophical career, Michael Dummett held firmly two theses: the theory of meaning has a central position in philosophy and all other forms of philosophical inquiry rest upon semantic analysis, in particular semantic issues replace traditional metaphysical issues; the theory of meaning is a theory of understanding. I will defend neither of them. However, I will argue that there is an important lesson we can learn by reflecting on the link between linguistic competence and semantics, which I take to (...) be an important part of Dummett’s legacy in philosophy of language. I discuss this point in relation to Cappelen and Lepore’s criticism of Incompleteness Arguments. (shrink)

We show that, by choosing definitions carefully, a version of Frege's theorem can be proved in intuitionistic logic.

This paper can be read as an attempt at providing philosophical foundations to linear logic. The only plausible form of philosophical antirealism deals with practical feasibility rather than with effectivity in principle. The very notion of recognizability is ambiguous, audit has to be considered from a stricter perspective than currently done. The intuitionistic assertability conditions are to be reinforced. This change requires a move towards a frame in which the circumstances of the application of a logical rule can be specified. (...) Gentzen's sequential calculi provide such a frame, when some structural rules have been removed or limited. (shrink)