Throughout its history philosophy has been thought to be a member of a community of intellectual disciplines united by their common pursuit of knowledge. It has sometimes been thought to be the queen of the sciences, at other times merely their under-labourer. But irrespective of its social status, it was held to be a participant in the quest for knowledge – a cognitive discipline.

The purpose of this paper is to apply Crispin Wright’s criteria and various axes of objectivity to mathematics. I test the criteria and the objectivity of mathematics against each other. Along the way, various issues concerning general logic and epistemology are encountered.

Does Wittgenstein have a method? There are two challenges to an affirmative answer. One is put forth by Schulte, who claims that Wittgenstein’s method is little more than a skill, and thus not a method in any ambitious sense of that word. Another is Conant’s view that the philosophy of the later Wittgenstein entertains not one method, but a variety of methods. I tackle these challenges by questioning what I take to be their presupposed conceptions of ‘method’ and conclude that (...) we can indeed speak of Wittgenstein’s method in an interesting sense. Thereby, the concept of method will be elucidated and the sense in which Wittgenstein’s philosophy has a method clarified. (shrink)

A comparison is given between two conditions used to define logical constants: Belnap's uniqueness and Hacking's deducibility of identicals. It is shown that, in spite of some surface similarities, there is a deep difference between them. On the one hand, deducibility of identicals turns out to be a weaker and less demanding condition than uniqueness. On the other hand, deducibility of identicals is shown to be more faithful to the inferentialist perspective, permitting definition of genuinely proof-theoretical concepts. This kind of (...) analysis is driven by exploiting the Curry–Howard correspondence. In particular, deducibility of identicals is shown to correspond to the computational property of eta expansion, which is essential in the characterization of propositional identity. (shrink)

SummaryMany contemporary philosophers of language believe that realist metaphysics and a beha‐viouristic approach to language are incompatible, debate centring on which is to be given up. In this paper I argue that no incompatibility has been shown to exist. In the first section I attempt to give both a characterization of, and an argument for, behaviourism. Then I attempt to characterize realism more generally than is often done, evaluating the work of Dummett, Quine, Putnam and Wittgenstein, as recently interpreted, in (...) that light. Finally I attempt to sketch a behaviouristic justification of classical predicate logic and offer some programmatic remarks on behaviouristic accounts of mathematics and natural science.RésuméBien des philosophes contemporains du langage, estimant qu'une métaphysique réaliste et une approche behavioriste sont incompatibles, centrent le débat sur la question «lequel des deux doit‐il être sacrifité?» Je montre dans ce papier qu'on n'a jamais pu prouver l'existence d'une incompatibilité. Dans la première partie, je tente de caractériser et de défendre le behaviorisme. Puis j'essaie de caractériser le réalisme plus généralement que cela n'a été souvent fait et évalue dans cette perspective les oeuvres de Dummett, de Quine, de Putnam et de Wittgenstein à la lumière de leurs interprétations récentes. Finalement, je propose une justification behavioriste de la classique logique des prédicats et quelques remarques programmatiques quant à une approche behavioriste des mathématiques et des sciences naturelles.ZusammenfassungManche zeitgenössische Philosophen glauben, dass eine realistische Metaphysik nicht mit einer behavioristischen Betrachtungsweise der Sprache vereinbar sei, wobei sich der Streit um die Frage dreht, welche der beiden Haltungen aufgegeben werden müsse. Ich argurnentiere, dass die Unvereinbarkeit nicht wirklich nachgewiesen wurde. Im ersten Abschnitt versuche ich, den Beha‐viorismus genauer zu charakterisieren und zu seinen Gunsten zu argumentieren. Ich versuche dann, eine allgemeinere Charakterisierung des Realismus zu geben, als das üblich ist, indem ich die Werke von Dummett, Quine, Putnam und Wittgenstein, wie sie neuerdings unter diesen Gesichts‐punkt interpretiert werden, beurteile. lch versuche schliesslich, eine behavioristische Rechtferti‐gung der klassischen Prädikatenlogik zu skizzieren, und lege auch einige programmatische Bemerkungen zur behavioristischen Behandlung von Mathematik und Naturwissenschaft vor. (shrink)

This paper is concerned with vagueness in language, its relation to logico-philosophical questions on the one hand, and to so-called syncategorematic terms and their linguistic use on the other hand. It attempts to show that it is not language itself which is vague but rather the way we use it.

Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at two ways (...) to obtain a quantitative conception of information added. One, the most direct, mirrors Bernard Koopman’s construction of conditional probability: by making a strong structural assumption, it leads to a measure that is, transparently, some function of a function P which is, formally, an assignment of conditional probability (in fact, a Popper function). P reverses the information added order and mislocates the natural zero of the scale so some transformation of this scale is needed but the derivation of P falls out so readily that no particular transformation suggests itself. The Cox–Good–Aczél method assumes the existence of a quantitative measure matching the qualitative relation, and builds on the structural constraints to obtain a measure of information that can be rescaled as, formally, an assignment of conditional probability. A classical result of Cantor’s, subsequently strengthened by Debreu, goes some way towards justifying the assumption of the existence of a quantitative scale. What the two approaches give us is a pointer towards a novel interpretation of probability as a rescaling of a measure of information added. (shrink)

The first half of Mark Quentin Gardiner’s recent book, Semantic Challenges to Realism: Dummett and Putnam, is a sustained, systematic, and, for the most part, novel attempt to demolish the case against semantic realism instigated by Michael Dummett. In this article I reply on the anti-realist’s be-half. I aim to demonstrate that none of Gardiner’s main anti-Dummettian arguments are successful, and moreover that his errors are, in the main, consequences of serious misconstruals of vital aspects of the semantic realist and (...) anti-realist positions. (shrink)

Dummettian anti-realism–the refusal to endorse bivalence–is generally thought to be associated with idealism This paper argues that this is only true of the position developed by early Dummett. In a later manifestation Dummettian anti-realism is better thought of as providing the logic for anti-realisms of an error theoretic kind. Early on Dummett distinguished deep from shallow arguments for giving up bivalence: deep arguments followed a strong ‘sufficiency’ reading of Frege’s context principle, and made the sentence the primary vehicle of meaning. (...) Enriched by an account of truth in terms of verifiability, deep arguments implied a form of linguistic idealism. From within a perspective that had already made ontology relative to theory, it was natural for the difference between realism and idealism to hinge on the notion of truth for sentences. Having given up the distinction between deep and shallow arguments against bivalence, Dummett, post 1990, asserts that every rejection of bivalence leads to a form of anti-realism. In the intervening years, he has also come to cast doubt on the sufficiency reading of the context principle, particularly as developed by Crispin Wright. These doubts open the space for some more simple-minded criticisms of this strong version of the context principle, developed in the paper. Once the sufficiency reading of the context principle is given up, arguments for failing to assert bivalence come to hinge on beliefs about ‘genuine’ existence. These forms of anti-realism cannot be taken to imply idealism. Rather, in many cases they will be the expression of views of an error-theoretic kind, that are quite compatible with a thorough-going rejection of idealism. (shrink)

: Radical sceptical possibilities challenge the anti-realist view that truth consists in ideal rational acceptability. Putnam, as part of his defence of an anti-realist view, subjected the case of the brain in a vat to a semantic externalist treatment, which aimed to maintain the desired connection between truth and ideal rational acceptability. It is argued here that self-consciousness poses special problems for this externalist strategy. It is shown how, on a standard model of first-person reference, Putnam's brain in a vat (...) will be mistaken in its rational self-ascription of externalist predicates. The natural response, which employs an alternative model of first-person reference, is shown to have the equally realist consequence that there are enquiry-transcendent truths about the self. (shrink)

The relation between Wittgenstein's philosophy of mathematics and mathematical Intuitionism has raised a considerable debate. My attempt is to analyse if there is a commitment in Wittgenstein to themes characteristic of the intuitionist movement in Mathematics and if that commitment is one important strain that runs through his Remarks on the foundations of mathematics. The intuitionistic themes to analyse in his philosophy of mathematics are: firstly, his attacks on the unrestricted use of the Law of Excluded Middle; secondly, his distrust (...) of non-constructive proofs; and thirdly, his impatience with the idea that mathematics stands in need of a foundation. These elements are Fogelin's starting point for the systematic reconstruction of Wittgenstein's conception of mathematics. (shrink)

I develop a solution to the Sorites Paradox, according to which a concatenation of valid arguments need not itself be valid. I specify which chains of valid arguments are those that do not preserve validity: those that pass the vague boundary between cases where the relevant concept applies and cases where that concept does not apply. I also develop various criticisms of this solution and show why they fail; basically, they all involve a petitio at some stage. I criticise the (...) conviction that if every short argument in a long concatenated argument is valid, so is the long argument: it is, I argue, the result of an unjustified generalisation from the case of arguments that do not employ vague concepts (as in mathematics) to arguments that do employ them. My approach is Wittgensteinian in its “leaving everything as it is,” in its claiming that the “beginning” has been searched too far back (see paper's epigraph) and in its claim that the paradox was generated by a misapplication of a partial picture of the behaviour of arguments. I conclude my paper by comparing and contrasting my approach to the few precedents found in the vagueness literature and by answering a few additional objections that were raised there. (shrink)

This paper deals with the possibility of faultless disagreement in law. It does this by looking to other spheres in which faultless disagreement appears to be possible, mainly in matters of taste and ethics. Three possible accounts are explored: the realist account, the relativist account, and the expressivist account. The paper tries to show that in the case of legal disagreements, there is a place for an approach that can take into account our intuitions in the sense that legal disagreements (...) are genuine and at times faultless. (shrink)

Abstract The paper is concerned with the status of vague predicates. It is argued that they are for the most part ?classifiers?, which are covertly comparatives and name not monadic properties but relations. The Sorites Paradox, it is claimed, is thus defused and a verdict theory of vague predicates is presented. Our practice in using vague words is described and it is contended that in our use of these predicates we always have a permanent possibility of independent demarcation. Wittgenstein's picture (...) of the wall and the swamp is deployed to avoid the Transition Problem and it is argued against Fregeans that we need vague language for the advancement of knowledge and understanding. (shrink)

Abstract This paper compares Heidegger's conception of time with more prevalent physical and broadly psychological analyses of time. The ?vulgar? notion of time, as Heidegger understands it, is based on the assumption that time, regardless of whether it is identified with tense or not, is something that is essentially measurable by clocks. Heidegger maintains that the vulgar notion of time is a distortion of his own preferred conception of temporality. I show how temporality may be understood as the non?sequential tensed (...) structure underlying tensed discourse. I argue against any straightforward reduction of this tensed structure and the direction of time to physical occurrences. Nevertheless I argue that temporality can be distinguished from purely psychological analyses of temporal experience and from traditional conceptions of time as tensed experience. The selectiveness of demonstrative discourse provides the basis for Heidegger's critique and reconstruction of time understood as tensed discourse about things. Heidegger's scepticism about the interpretation of time as a sequence of nows that underlies the dominant interpretation of tense is due to his appropriation of the relativity of simultaneity from special relativity. But his interpretation of physical theory leads him to the thesis that time is pre?supposed but not completely analysed in physical theory. The meta?language of physical theory makes covert use of temporal notions, for entities can themselves only be understood in covertly temporal ways. I show how this claim may be understood and defended in the light of current physical theory. Heidegger's analysis gives us some basis for thinking that his own notion of temporality is built into an understanding of temporal experience. But I argue that Heidegger fails to make the case that physical time is ontologically dependent on human existence. (shrink)

Philosophers are very fond of making non-factualist claims—claims to the effect that there is no fact of the matter as to whether something is the case. But can these claims be coherently stated in the context of classical logic? Some care is needed here, we argue, otherwise one ends up denying a tautology or embracing a contradiction. In the end, we think there are only two strategies available to someone who wants to be a non-factualist about something, and remain within (...) the province of classical logic. But one of these strategies is rather controversial, and the other requires substantially more work than is often supposed. Being a non-factualist is no easy business, and it may not be the most philosophically perspicuous way to go. (shrink)

A new account of the semantic function (character) of ‘real’ and ‘really’ is defended. ‘Really’ as a sentential operator typically indicates that a report of what has been represented elsewhere ends and subsequent discourse is to be taken as making claims about the world. ‘Real’ and ‘really’ as applied to nouns or predicate phrases indicate that something is not being called an F merely because it represents an F. A way of drawing the distinction between realism and anti-realism based on (...) this new account is also defended. (shrink)

Realism is multiply ambiguous. The central concern of Part 1 of this paper is to distinguish several of its many senses — four (Theoretical Realism, Cumulative Realism, Progressive Realism and Optimistic Realism) in which it refers to theses about the status of scientific theories, and five (Minimal Realism, Ambitious Absolutism, Transcendentalism, Nidealism, Scholastic Realism) in which it refers to theses about the nature of truth or truth-bearers. Because Realism has these several, largely independent, senses, the conventional wisdom that Tarski's theory (...) of truth supports realism, and that the Meaning-Variance thesis undermines it, needs re-evaluation. The concern of the rest of the paper is to sort out in which senses the conventional wisdom, with respect to Tarski's theory (Part 2) and the Meaning-Variance thesis (Part 3), is correct. (shrink)

Amidst the progress being made in the various (sub-)disciplines of the behavioural and brain sciences a somewhat neglected subject is the problem of how everything fits into one world and, derivatively, how the relation between different levels of discourse should be understood and to what extent different levels, domains, approaches, or disciplines are autonomous or dependent. In this paper I critically review the most recent proposals to specify the nature of interdiscourse relations, focusing on the concept of supervenience. Ideally supervenience (...) is a relation between different discourses which has all the advantages of reduction, but without its disadvantages. I apply the more abstract considerations to two concrete cases: schizophrenia and colour. Usually an interlevel or interdiscourse relation is seen as asymmetrical: the overlaying discourse depends on the underlying discourse (and not vice versa), where the out- or un-spoken assumption is that the ultimate underlying discourse is physical. Instead I argue that scientific categories referred to in interdiscourse relations are, ultimately, dependent on common sense categories and common sense normative criteria. It is the manifest categories and common sense ideas about what is reasonable and what is right that determine the relevant categorisations at the deeper, underlying levels. I suggest that the implications of this are not merely methodological or epistemological. (shrink)

Dummettian anti-realism repudiates the realist's notion of verification-transcendent truth. Perhaps the most crucial element in the Dummettian attack on realist truth is the critique of so-called realist semantics, which assigns verification-transcendent truth-conditions as the meanings of (some) sentences. The Dummettian critique charges that realist semantics cannot serve as an adequate theory of meaning for a natural language, and that, consequently, the realist conception of truth must be rejected as well. In arguing for this, Dummett and his followers have appealed to (...) a certain conception of linguistic knowledge. This paper examines closely the appeal to speakers' knowledge of linguistic meaning, its force and limitations. (shrink)

Since its disc overy by Fitch, the paradox of knowability has been a thorn in the anti-realist's side. Recently both Dummett and Tennant have sought to relieve the anti-realist by restricting the applicability of the knowability principle -- the principle that all truths are knowable -- which has been viewed as both a cardinal doctrine of anti-realism and the assumption for reductio of Fitch's argument. In this paper it is argued that the paradox of knowability is a peculiarly acute manifestation (...) of a syndrome affecting anti-realism, against which Dummett's and Tennant's manoeuvres are not finally efficacious. The anti-realist can only cope with the syndrome by being much clearer about her notion of knowability. In fact, she'll have to offer an account which relativises the notion of knowability both to the world at which knowability is assessed and to the content of the proposition to which it is applied. This is not, however, merely an ad hoc manoeuvre to counter the problematic syndrome; rather it is just what we should expect from the anti-realist's intuitive use of the notion. A preliminary investigation indicates that there is no way of providing a general, systematic explanation of such a notion of knowability and thus an inherent restriction on the principle of knowability -- but one differing from those offered by either Dummett or Tennant -- is developed. (shrink)

I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.

I aim to show that standard theories of counterfactuals are mistaken, not in detail, but in principle, and I aim to say what form a tenable theory must take. Standard theories entail a categorical interpretation of counterfactuals, on which to state that, if it were that A, it would be that C is to state something, not relative to any supposition or hypothesis, but categorically. On the rival suppositional interpretation, to state that, if it were that A, it would be (...) that C is to state that it would be that C relative to the supposition that it were that A. The two interpretations make incompatible predictions concerning the correct evaluation of counterfactuals. I argue that the suppositional interpretation makes the correct prediction. (shrink)

This article selectively surveys recent work touching consciousness. It discusses some recent arguments and positions with a view to throwing light on a working principle of much influential philosophical psychology, namely that the first?person point of view is theoretically redundant. The discussion is divided under a number of headings corresponding to specific functions that have been attributed to the first?person viewpoint, from the experience of something it is like to undergo physical processes, to the presence of selfhood, mental substance, meaning, (...) understanding, and value. Arguments indicating limitations of the working principle are adduced, as well as arguments indicating possible exploitations of those limitations by first?personalist positions. Although some of the latter also have limitations, the direction in which the examination tends is that of a progressive widening of the concept of consciousness. (shrink)

Parsimony considerations are ubiquitous in the literature concerning the nature of mental states. Other things being equal, physicalist views are preferred over dualist accounts on the grounds of the fact that they do not posit new fundamental properties in addition to the physical ones. This paper calls into question the widespread assumption that parsimony can provide reasons for believing that physicalism is a better candidate than dualism for solving the mind–body problem. After presenting the theoretical core of physicalism and dualism, (...) I make explicit the meta-metaphysical assumptions the physicalist relies on when leveraging parsimony to support her view. In particular, the physicalist takes for granted that parsimony has an epistemic value in metaphysics. This point, however, is rather controversial. I argue that the most promising way to account for the epistemic value of parsimony is to ground it in the epistemic value of modesty, a higher-level theoretical virtue that has to do with the epistemic risk of a theory. Unfortunately for the physicalist, the modesty rationale does not ultimately favour physicalism over dualism. (shrink)

Several recent epistemologists have used understanding-assent links in theories of a priori knowledge and justification, but Williamson influentially argued against the existence of such links. Here I (1) clarify the nature of understanding-assent links and their role in epistemology; (2) clarify and clearly formulate Williamson’s arguments against their existence; (3) argue that Williamson has failed to successfully establish his conclusion; and (4) rebut Williamson’s claim that accepting understanding-assent links amounts to a form of dogmatism.

It is difficult to imagine that a Royal Institute of Physics would organize an annual lecture series on the theme ‘conceptions of physics’. Similarly, it is quite improbable that a Royal Institute of Astronomy would even contemplate inviting speakers for a lecture series called ‘conceptions of astronomy’. What, then, is so special about philosophy that the theme of this lecture series does not appear to be altogether outlandish? Is it, perhaps, that philosophy is the reflective discipline par excellence, so that (...) the very nature of philosophy is a topic that belongs to its domain of investigations? Or is there something more serious at issue? Let me first tell you how the question concerning the nature of philosophy arose for me as a young student, and how I tried to answer it, quite naively, by endorsing Edmund Husserl's programme of turning philosophy into a rigorous science. In a second section, I shall offer three diagnoses of the fact that all such attempts seem to have failed. Finally, I'd like to say a few words on my own research agenda in philosophy and on a public function of philosophers. (shrink)

The macaque washes a potato in a stream. It does this because it has seen the dirt come off as another macaque washed its potato, and it knows that clean potato.

Classical logic rests on the assumption that there are two mutually exclusive and jointly exhaustive truth values. This assumption has always been surrounded by philosophical controversy. Doubts have been raised about its legitimacy, and hence about the legitimacy of classical logic. Usually, the assumption is stated in the form of a general principle, namely the principle that every proposition is either true or false. Then, the philosophical controversy is often framed in terms of the question whether every proposition is either (...) true or false. The main purpose of the paper is to show that there is something wrong in this way of putting things. The point is that the common way of understanding the controversial assumption is misconceived, as it rests on a wrong picture of propositions. In the first part of the paper I outline this picture and I argue against it. In the second part I sketch a different picture of propositions and I suggest how this leads to conceive the issue of classical logic in different terms. (shrink)

This paper is an investigation in the use of truthmaker theory for exploring the relation of logic to world, and as a tool for metaphysics. A variant of truthmaker theory, which we call the simple theory, is defined and defended against objections. It is characterized formally, and its central features are derived. As part of this project, we give a formal metaphysics based on nondeterministic necessitation relations among possible entities. In what is called the fundamental theorem of truthmaking, it is (...) shown that, as long as a logic is sound and complete, its inferential structure will be isomorphic to the necessitation structure of our metaphysics. We thus arrive at a purely structural logic–world relationship which can be used for metaphysical investigations. Other products of our investigation are a sound and complete semantics for first-order logic with identity and a solution to a result of Restall which has threatened to make truthmaker theory trivial. (shrink)

Can philosophy still be fruitful, and what kind of philosophy can be such? In particular, what kind of philosophy can be legitimized in the face of sciences? The aim of this paper is to answer these questions, listing the characteristics philosophy should have to be fruitful and legitimized in the face of sciences. Since the characteristics in question demand that philosophy search for new knowledge and new rules of discovery, a philosophy with such characteristics may be called the ‘heuristic view’. (...) According to the heuristic view, philosophy is an inquiry into the world which is continuous with the sciences. It differs from them only because it deals with questions which are beyond the present sciences, and in order to deal with them must try unexplored routes. By so doing, when successful, it may even give birth to new sciences. In listing the characteristics that philosophy should have, the paper systematically compares them with classical analytic philosophy, because the latter has been the dominant philosophical tradition in the last century. (shrink)

We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined classically, (...) and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic. (shrink)

'Realism' is multiply ambiguous. The central concern of Part 1 of this paper is to distinguish several of its many senses -- four in which it refers to theses about the status of scientific theories, and five in which it refers to theses about the nature of truth or truth-bearers. Because 'Realism' has these several, largely independent, senses, the conventional wisdom that Tarski's theory of truth supports realism, and that the Meaning-Variance thesis undermines it, needs re-evaluation. The concern of the (...) rest of the paper is to sort out in which senses the conventional wisdom, with respect to Tarski's theory and the Meaning-Variance thesis , is correct. (shrink)

The ArgumentL. E. J. Brouwer and David Hubert, two titans of twentieth-century mathematics, clashed dramatically in the 1920s. Though they were both Kantian constructivists, their notoriousGrundlagenstreitcentered on sharp differences about the foundations of mathematics: Brouwer was prepared to revise the content and methods of mathematics (his “Intuitionism” did just that radically), while Hilbert's Program was designed to preserve and constructively secure all of classical mathematics.Hilbert's interests and polemics at the time led to at least three misconstruals of intuitionism, misconstruals which (...) last to our own time: Current literature often portrays popular views of intuitionism as the product of Brouwer's idiosyncratic subjectivism; modern logicians view intuitionism as simply applying a non-standard formal logic to mathematics; and contemporary philosophers see that logic as based upon a pure assertabilist theory of meaning. These pictures stem from the way Hilbert structured the controversy.Even though Brouwer's own work and behavior occasionally reinforce these pictures, they are nevertheless inaccurate accounts of his approach to mathematics. However, the framework provided by the Brouwer-Hilbert debate itself does not supply an adequate correction of these inaccuracies. For, even if we eliminate these mistakes within that framework, Brouwer's position would still appear fragmented and internally inconsistent. I propose a Kantian framework — not from Kant's philosophy of mathematics but from his general metaphysics — which does show the coherence and consistency of Brouwer's views. I also suggest that expanding the context of the controversy in this way will illuminate Hilbert's views as well and will even shed light upon Kant's philosophy. (shrink)

Although there has been a recent swell of interest in theories of truth that attempt solutions to the liar paradox and the other paradoxes affecting our concept of truth, many of these theories have been criticized for generating new paradoxes, called revenge paradoxes. The criticism is that the theories of truth in question are inadequate because they only work for languages lacking in the resources to generate revenge paradoxes. Theorists facing these objections offer a range of replies, and the matter (...) seems now to be at a standoff. I aim, first, to bolster the revenge objections by considering a relation, internalizability, between languages and theories of truth. A theory of truth is internalizable for a language iff there is an extension of that language in which the theory is expressible and for which the theory provides an accurate and complete assignment of semantic values. There are good reasons to think that acceptable theories of truth are internalizable for any language. With this internalizability requirement in hand, I argue that properly formulated revenge objections are decisive and that the replies to them are inadequate. Second, I show that the internalizability requirement can be met by a certain theory of truth. The central claim of this theory is that truth is an inconsistent concept and should be replaced with a pair of consistent concepts that can then be used to provide a semantics for our truth predicates. This theory is compatible with classical logic, does not give rise to revenge paradoxes of any kind, and satisfies the internalizability requirement. (shrink)

SummaryEllis, Jardine and Putnam have argued that the would‐be scientific realist can only avoid being a metaphysical realist by becoming an “internal realist” . While metaphysical realism is unattractive, the approaches to truth offered by Ellis, Jardine and Putnam are quite unacceptable. However, the is no reason to think that one who wishes to be a scientific realist is limited to these two options.

Starting from John MacFarlane's recent survey of answers to the question ‘What is assertion?’, I defend an account of assertion that draws on elements of MacFarlane's and Robert Brandom's commitment accounts, Timothy Williamson's knowledge norm account, and my own previous work on the normative status of logic. I defend the knowledge norm from recent attacks. Indicative conditionals, however, pose a problem when read along the lines of Ernest Adams' account, an account supported by much work in the psychology of reasoning. (...) Furthermore, there seems to be no place for degrees of belief in the accounts of belief and assertion given here. Degrees of belief do have a role in decision‐making, but, again, there is much evidence that the orthodox theory of subjective utility maximization is not a good description of what we do in decision‐making and, arguably, neither is it a good normative guide to how we ought to make decisions. (shrink)

Amongst those views sometimes attributed to the later Wittgenstein are included both a deflationary theory of truth, as well as a non-factualism about certain regions of discourse. Evidence in favor of the former attribution, it is thought, can be found in Wittgenstein’s apparent affirmation of the basic definitional equivalence of ‘p’ is true and p in §136 of his Philosophical Investigations. Evidence in favor of the latter attribution, it might then be presumed, can be found in the context of the (...) so-called ‘private language argument’, wherein Wittgenstein provides an expressivist treatment of first-person present tense sensation utterances. In this paper, by contrast, I will argue that Wittgenstein’s later philosophy is best understood as endorsing neither a non-factualism about sensation utterances, nor a deflationism about truth. Wittgenstein should instead be understood as offering a ‘mixed’ view of sensation utterances according to which some while not others are apt for expressivist treatment. Moreover, he should be thought of as identifying truth-conditions with semantic ‘correctness-conditions’, and thus truth with semantic ‘assertibility’. (shrink)

I carry out in this paper a philosophical analysis of the principle of excluded middle (or, as it is often called in the version I favor here, principle of bivalence: any meaningful assertion is either true or false). This principle has been criticized, and sometimes rejected, on the charge that its validity depends on presuppositions that are not, some believe, universally obtainable; in particular, that any well-posed problem is solvable. My goal here is to show that, although excluded middle does (...) indeed rest on certain presuppositions, they do not have the character of hypotheses that may or may not be true, or matters of fact that may or may not be the case. These presuppositions have, I claim, a transcendental character. Hence, the acceptance of excluded middle does not necessarily require, as some have claimed, an allegiance to ontological realism or some sort of cognitive optimism, construed as factual theses concerning the ontological status of domains of objects and our capability of accessing them cognitively. DOI:10.5007/1808-1711.2011v15n2p333. (shrink)

I shall characterize normative functionalism and contrast it with its causal counterpart. After tracing both stripes of functionalism to the work of the classical American pragmatists, I then argue that they are not exclusive alternatives. Instead, both might be required for an appropriately illuminating account of human rational activity.

This study is in two parts. In the first part, various important principles of classical extensional mereology are derived on the basis of a nice axiomatization involving ‘part of’ and fusion. All results are proved here with full Fregean rigor. They are chosen because they are needed for the second part. In the second part, this natural-deduction framework is used in order to regiment David Lewis’s justification of his Division Thesis, which features prominently in his combination of mereology with class (...) theory. The Division Thesis plays a crucial role in Lewis’s informal argument for his Second Thesis in his book Parts of Classes. In order to present Lewis’s argument in rigorous detail, an elegant new principle is offered for the theory that combines class theory and mereology. The new principle is called the Canonical Decomposition Thesis. It secures Lewis’s Division Thesis on the strong construal required in order for his argument to go through. The exercise illustrates how careful one has to be when setting up the details of an adequate foundational theory of parts and classes. The main aim behind this investigation is to determine whether an anti-realist, inferentialist theorist of meaning has the resources to exhibit Lewis’s argument for his Second Thesis—which is central to his marriage of class theory with mereology—as a purely conceptual one. The formal analysis shows that Lewis’s argument, despite its striking appearance to the contrary, can be given in the constructive, relevant logic IR. This is the logic that the author has argued, elsewhere, to be the correct logic from an anti-realist point of view. The anti-realist is therefore in a position to regard Lewis’s argument as purely conceptual. (shrink)