In this chapter a new problem about rule-following is outlined, one that is distinct both from Kripke’s and Wright’s versions of the problem. This new problem cannot be correctly responsed to, as Kripke’s can, by invoking Wright’s Intentional Account of rule-following. The upshot might be called, following Kant, an antinomy of pure reason: we both must — and cannot — make sense of someone’s following a rule. The chapter explores various ways out of this antinomy without here endorsing any of (...) them. (shrink)

This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.

Explores the stable core of Wittgenstein's philosophy as developed from the Tractatus to the Philosophical Investigations.

forthcoming in R. Cameron, B. Hale and A. Hoffmann (ed.s), The Logic, Epistemology and Metaphysics of Modality, Oxford University Press. Presents a concept-grounding account of modal knowledge.

This paper presents a new argument to defend the normativity of meaning, specifically the thesis that there are no meanings without norms. The argument starts from the observation inferentialists have emphasized that incompatibility relations between sentences are a necessary part of meaning as it is understood. We motivate this approach by showing that the standard normativist strategy in the literature, which is developed in terms of veridical reference that may swing free from the speaker’s understanding, violates the ought-implies-can principle, but (...) ours does not. In addition, our approach is superior because, unlike the representationalist approach, it can be extended from declarative sentences to non-representational uses of language. In this paper, however, we only formulate the argument for the base case that involves incompatibility relations between declarative sentences. The goal is not to derive norms from something that is not normative, but to explicate the distinctive type of normativity that is built into meaning as it is understood by language-users. The explication proceeds in two steps. (1) For any sentence s a speaker understands, there is an incompatible sentence s’ the speaker understands to be incompatible with s. (2) In virtue of understanding this incompatibility of meanings, she ought not to be committed to both s and s’. This prohibition is not derived from instrumental practical reason, nor is it based on representational correctness, but its source is the incompatibility of meanings. (shrink)

Ludwig Wittgenstein in his later works often implies commitment to a doctrine of the autonomy or arbitrariness of grammar. This chapter discusses the conception of grammar that is presupposed in this doctrine and then explains the doctrine itself. The chapter also explains a sense in which grammar is not autonomous or arbitrary for Wittgenstein and discusses some possible criticisms of the doctrine. It should be noted at the outset that this whole area of exegetical concern is one in which the (...) fairly widespread conception in the secondary literature that the later Wittgenstein is a complete “quietist” in philosophy ‐ i.e., someone who advances no positive doctrines of his own, although encouraged by some of his own statements, seems impossible to sustain. Wittgenstein's doctrine of the autonomy or arbitrariness of grammar presupposes a highly distinctive conception of grammar, one which at least prima facie has little to do with our everyday conception of grammar. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

The paper develops an account of semantic notions which occupies a middle ground between antirealism and traditional forms of realism, using some ideas from the work of John McDowell. The position is based on a contrast between two points of view from which we might attempt to characterize our linguistic practices from the cosmic exile s point of view and from the midst of language as a going concern. The contrast is drawn in terms of whether our characterization of our (...) linguistic practices is taken to result from engagement in the very same practices that we are trying to characterize. The position takes realism to be correct when understood as an account from the internal perspective, but incorrect when taken as an account from the external perspective. However, the intelligibility of the question as to what our practices would look like from the cosmic exile s point of view is presented as problematic. (shrink)

I argue that a target of the rule - following considerations is the thought that there are mental episodes in which a consciously accessible item guides me in my decision to respond in a certain way when I follow a rule. I contend that Wittgenstein’s position on this issue invokes a distinction between a literal and a symbolic reading of the claim that these processes of guidance take place. In the literal sense he rejects the claim, but in the symbolic (...) sense he sees nothing wrong with it. I consider some arguments that Wittgenstein deploys against the literal sense of the claim. (shrink)

This is a short, and therefore necessarily very incomplete discussion of one of the great questions of modern philosophy. I return to a station at which an interpretative train of thought of mine came to a halt in a paper written almost 20 years ago, about Wittgenstein and Chomsky,[1] hoping to advance a little bit further down the track. The rule-following passages in the Investigations and Remarks on the Foundations of Mathematics in fact raise a number of distinct issues about (...) rules, meaning, objectivity, and reasons, whose conflation is encouraged by the standard caption, "the Rule-following Considerations".[2] So, let me begin by explaining my focus here. (shrink)

In this paper I argue that there can be genuine (as opposed to merely verbal) disputes about whether a sentence form is logically true or an argument form is valid. I call such disputes ?cases of deviance?, of which I distinguish a weak and a strong form. Weak deviance holds if one disputant is right and the other wrong, but the available evidence is insufficient to determine which is which. Strong deviance holds if there is no fact of the matter. (...) In section 2 I argue that weak deviance need not be trivial and may even be interesting. Section 3 considers what it could mean to say that logic is determined by a theory, especially a theory of meaning, an idea that arises in section 2. In section 4 I discuss the dispute between classical and relevance logicians over entailment and argue that it is a case of strong deviance. Finally, in section 5 I show that the result of the previous section is not absolute but relative to the background logic used in reaching it. (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)

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)

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two— the super-task argument and the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily (...) idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic. (shrink)

En este trabajo examino el argumento de McFetridge a favor de la necesidad de la creencia en la necesidad. El argumento pretende establecer un dilema fatal para el “nihilista” modal, aquel que no cree que al menos alguna proposición es necesaria. Mi objetivo principal es mostrar que el dilema que presenta el argumento de McFetridge no es sólido, pues tiene una limitación muy importante con respecto al segundo de sus cuernos, el cual es el más interesante. El segundo cuerno del (...) dilema plantea una especie de argumento trascendental: es necesario creer en la necesidad si es que vamos a ser capaces de razonar confiablemente bajo suposiciones contrafácticas. Sin embargo, este argumento asume que la suposición contrafáctica es una actividad esencial en nuestras vidas, lo cual señala, sostengo, un punto central alrededor del cual el nihilista modal intentaría reafirmar su posición. Así, pretendo mostrar que el segundo cuerno del dilema de McFetridge revela que el quid de la discusión entre creyentes y nihilistas modales debe moverse propiamente de la cuestión del rol de la creencia en la necesidad a la cuestión del rol de la suposición contrafáctica. (shrink)

In this paper Section 1 distinguishes between two modes of interpreting legal rules: rehearsal and discourse, arguing that the former takes priority over the latter in law, as in many other contexts. Section 2 offers two arguments that following a legal rule in the rehearsing mode presents a riddle. The first argument develops from law, and submits that legal rules do not tell us anything, because they are tautological. The second one develops from philosophy (Wittgenstein's later works), confronting us with (...) the paradox that incompatible courses of action may be derived from any rule. My solution presents a theory of rules as icons (Section 3). I use “icon” rather than “picture,” partly to avoid confusion with what is known among philosophers as “the picture theory of meaning.” Interpretation in the rehearsing mode hinges on imagination: imagining oneself in the space of reasons for action rather than reasoning oneself. In this act of imagination, we project ourselves into the rule in ways that are similar to the way we grasp the sense of paintings, music, stories, or poems. Finally (Section 4) I will defend the position that my view solves the puzzles in the second section, by arguing (a) that it is a better account of what Wittgenstein wrote than two competing theories (intuitionism and conventionalism), and (b) that it provides a more satisfactory account of how lawyers deal with legal rules in actual practice. (shrink)

ABSTRACT In ‘The philosophical basis of intuitionistic logic’, Michael Dummett discusses two routes towards accepting intuitionistic rather than classical logic in number theory, one meaning-theoretical and the other ontological. He concludes that the former route is open, but the latter is closed. I reconstruct Dummett's argument against the ontological route and argue that it fails. Call a procedure ‘investigative’ if that in virtue of which a true proposition stating its outcome is true exists prior to the execution of that procedure; (...) and ‘generative’ if the existence of that in virtue of which a true proposition stating its outcome is true is brought about by the execution of that procedure. The problem with Dummett's argument then is that a particular step in it, while correct for investigative procedures, is not correct for generative ones. But it is the latter that the ontological route is concerned with. (shrink)

Despite the otherwise-dominant trends towards physicalism and naturalism in philosophy, it has become increasingly common for metaphysicians to accept the existence either of modal facts and properties, or of Lewisian possible worlds. This paper raises the historical question: why did these heavyweight realist views come into prominence? The answer is that they have arisen in response to the demand to find truthmakers for our modal statements. But this demand presupposes that modal statements are descriptive claims in need of truthmakers. This (...) presupposition was, however, rejected by many earlier analytic philosophers, including the logical positivists, Wittgenstein, Ryle and Sellars, all of whom denied that modal statement were descriptive at all. Yet the non-descriptivist approach has largely fallen out of discussion and out of philosophical consciousness. In this paper I examine why non-descriptivist views first came into and then fell out of favor, and consider what the prospects are for reviving this more deflationary approach to modality. (shrink)

Modality presents notorious philosophical problems, including the epistemic problem of how we could come to know modal facts and metaphysical problems about how to place modal facts in the natural world. These problems arise from thinking of modal claims as attempts to describe modal features of this world that explain what makes them true. Here I propose a different view of modal discourse in which talk about what is “metaphysically necessary” does not aim to describe modal features of the world, (...) but, rather, provides a particularly useful way of expressing constitutive semantic and conceptual rules in the object language. The result is a “modal normativist” view that enables us to avoid the epistemic problems of modality and mitigate the metaphysical worries, while also leaving open the possibility of a unified account of the function of modal language. Finally, I address a serious challenge: we have the norms we do in order to track the modal facts of the world, so that the order of explanation must go in the opposite direction. I close by showing how the normativist may answer that challenge. (shrink)

Those who aim to give an account of modal knowledge face two challenges: the integration challenge of reconciling an account of what is involved in knowing modal truths with a plausible story about how we can come to know them, and the reliability challenge of giving a plausible account of how we could have evolved a reliable capacity to acquire modal knowledge. I argue that recent counterfactual and dispositional accounts of modal knowledge cannot solve these problems regarding specifically metaphysical modal (...) truths—leaving us with the threat of skepticism about large portions of metaphysics, and certain other areas of philosophy. I argue, however, that both of these problems look insuperable only if we assume that metaphysical modal discourse serves a describing or tracking function. If we adopt instead a normativist approach to metaphysical modal discourse, which sees the basic function of modal discourse as giving us perspicuous ways of conveying, reasoning with, and renegotiating semantic rules, the problems show up very differently. The modal normativist can give a plausible response to both of the classic problems of how we can come to know metaphysical modal truths. (shrink)

According to Wittgenstein, mathematics is embedded in, and partly constituting, a form of life. Hence, to imagine different, alternative forms of elementary mathematics, we should have to imagine different practices, different forms of life in which they could play a role. If we tried to imagine a radically different arithmetic we should think either of a strange world or of people acting and responding in very peculiar ways. If such was their practice, a calculus expressing the norms of representation they (...) applied could not be called false. Rather, our criticism could only be to dismiss such a practice as foolish and to dismiss their norms as too different from ours to be called ‘mathematics’. (shrink)

To explain an intentional action one must exhibit the agent’s reasons. Donald Davidson famously argued that the only clear way to understand action explanation is to hold that reasons are causes. Davidson’s discussion conflated two issues: whether reasons are causes and whether reasons causally explain intentional action. Contemporary work on explanation and normativity help disentangle these issues and ground an argument that intentional action explanations cannot be a species of causal explanation. Interestingly, this conclusion is consistent with Davidson’s conclusion that (...) reasons are causes. In other words, reasons are causes, but rationalizing explanations are not causal explanations. Key Words: action theory • explanation • causal explanation • rationality • Donald Davidson. (shrink)

The main question of metasemantics, or foundational semantics, is why an expression token has the meaning (semantic value) that it in fact has. In his reading of Ludwig Wittgenstein’s later work, Saul Kripke presented a skeptical challenge that threatened to make the foundational question unanswerable. My first contention in this paper is that the skeptical challenge indeed poses an insoluble paradox, but only for a certain kind of metasemantic theory, against which the challenge effectively works as a reductio ad absurdum (...) argument. My second contention is that as a result of rejecting the theory which entails a paradoxical outcome, we will see that the foundational question essentially involves a temporal dimension. After arguing that the skeptical challenge gives us a strong reason to adopt a historical view of meaning, I shall further argue against certain authors who claim that meanings not only have histories but futures as well, or that the meaning of a word may change retroactively in time as a consequence of counterfactual change in its future use. The major aim of the paper is thus to bring together the arguably interrelated debates about the skeptical challenge and temporal externalism in philosophy of language. (shrink)

The two main challenges of the theory of conceptual content presented by Robert Brandom in Making It Explicit are to account for a referential dimension of conceptual content and to account for the objectivity of conceptual norms. Brandom tries to meet both these challenges in chapter 8 of his book. I argue that the accounts presented there can only be understood if seen against the background of Brandom's theory of communication developed in chapter 7. This theory is motivated by the (...) well-known problem that semantic holism threatens the possibility of communication because it has the consequence that words mean different things in different mouths. Brandom offers a solution to this problem in terms of what he calls recurrence commitments. I show that chapter 8 of Making It Explicit should be understood as arguing that a practice that includes acknowledging interpersonal recurrence commitments institutes both conceptual contents with a referential dimension and objective conceptual norms. I close by raising the objection that Brandom's argument can only show that conceptual norms are communally shared and not that they are objective. I propose an emendation of this argument, having recourse to a practice Brandom refers to as rational rectification in his new book Between Saying and Doing. (shrink)

This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.

In its most general form, the issue of intentionality takes the following shape: How can something be about something else? In basic cases, this relation is one between a subjective occurrence and a state of affairs, allowing the problem of intentionality to be articulated in this manner: What makes it the case that a subjective occurrence has the capacity to be about something external to it? The views of John McDowell on intentionality form the focus of this article. They are (...) examined through the notion of content and via the later Wittgenstein's standpoint on content and intentionality. The main objective is to reach a conspicuous perspective of McDowell's stance on intentionality in order to uncover its presuppositions. This leads to the identification of a pivotal point of tension in McDowell's philosophical commitments, in particular the extent to which he can legitimately claim to be a quietist. (shrink)

In the scholarship on Wittgenstein’s later philosophy of mathematics, the dominant interpretation is a theoretical one that ascribes to Wittgenstein some type of ‘ism’ such as radical verificationism or anti-realism. Essentially, he is supposed to provide a positive account of our mathematical practice based on some basic assertions. However, I claim that he should not be read in terms of any ‘ism’ but instead should be read as examining philosophical pictures in the sense of unclear conceptions. The contrast here is (...) that basic assertions that frame philosophical ‘isms’ are propositional such that they are subject to normal argumentative evaluation, while pictures in Wittgenstein’s sense are non-propositional—they lack a clear truth condition. They, therefore, need clarification rather than argumentation. In this paper, I provide a detailed analysis of Wittgenstein’s treatment of philosophical pictures with special focus on his argument on contradiction. I begin by explaining the problem with this trend of theoretical interpretation, taking Steve Gerrard’s otherwise excellent interpretation as a representative example and pointing out why it is problematic. Next, I will argue that those problems do not arise if we take Wittgenstein’s task as the clarification of philosophical pictures. I do this, first, by explaining Wittgenstein’s method using his argument concerning the Augustinian Picture in Philosophical Investigations and then pointing out that the same method can be identified in the crucial arguments in his philosophy of mathematics. Finally, in order to connect my interpretation with the current scholarship, I will explain the relation of my interpretation with those of New Wittgensteinian scholars. (shrink)

This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following, Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a (...) variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others. (shrink)

Abstract This paper discusses the semantic theory presented in Robert Brandom’s Making It Explicit . I argue that it is best understood as a special version of dynamic semantics, so that these semantics by themselves offer an interesting theoretical alternative to more standard truth-conditional theories. This reorientation also has implications for more foundational issues. I argue that it gives us the resources for a renewed argument for the normativity of meaning. The paper ends by critically assessing the view in both (...) its development and motivations. Content Type Journal Article Pages 1-22 DOI 10.1007/s11098-011-9768-4 Authors Bernhard Nickel, Harvard University, Cambridge, MA, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (shrink)

Explaining intuitions in terms of "facts of our natural history" is compatible with rationally trusting them. This compatibilist view is defended in the present paper, focusing upon nomic and essentialist modal intuitions. The opposite, incompatibilist view alleges the following: If basic modal intuitions are due to our cognitive make-up or "imaginative habits" then the epistemologists are left with a mere non-rational feeling of compulsion on the side of the thinker. Intuitions then cannot inform us about modal reality. In contrast, the (...) paper argues that there are several independent sources of justification which make the feeling of compulsion rational: the prima-facie and a priori ones come from the obviousness of our basic modal intuitions and our not being able to imagine things otherwise, others, a posteriori, from the epistemic success of these intuitions. Further, the general scheme of evolutionary learning is reliable, reliability is preserved in the resulting individual's cognitive make-up, and we can come to know this a posteriori. The a posteriori appeal to evolution thus plays a subsidiary role in justification, filling the remaining gap and removing the residual doubt. Explaining modal intuitions is compatible with moderate realism about modality itself. (shrink)

The paper defends causal explanationism concerning our modal intuitions and judgments, and, in particular, the following claims. If a causally explainable mirroring or “pre-established harmony” between our mind and modal reality obtains, we are justified in believing it does. We do not hold our modal beliefs compulsively and blindly but with full subjective and objective justification. Therefore, causal explanation of our modal beliefs does not undermine rational trust in them. Explanation and trust support each other. In contrast, anti-explanationists, claim that (...) causal explanation of intuitions and judgments undermines rational trust in them. They especially target causal explanation in terms of pre-established harmony between our mind, shaped by causal processes, and the underlying modal structure of reality. The paper argues against them. The argument builds upon the claim that the appeal to modal facts is indispensable for systematization and explanation of non-modal ones. Therefore, we should assume that modal facts exist and are not disjoint and isolated from actual facts. The modal structure of the universe intervenes in the non-modal reality. Causal processes indirectly carry information about deep modal structure. Any causal explanation of our intuitional modal beliefs should start from this indirect contact with and information about modal facts. Therefore, if our intuitional modal beliefs are true and causally explainable, they are true in virtue of the deep underlying modal structure. They are sensitive to modal reality and track it. We can come to know this fact, and thus strengthen our spontaneous trust in our modal intuitions. (shrink)

Phenomena such as our “understanding in a flash” and our immediate knowledge of the meaning of our own utterances seem to point to problems that call for philosophical explanation. Even though the meaning of an utterance appears to depend on where and when we use it, on what we use it for and on what we expect in response, we do not examine such circumstances when asked what we mean. Instead we simply say what we mean. Similarly, our having grasped (...) a rule is something shown by how we perform certain tasks and respond to certain requests. But we frequently declare that we have indeed grasped a rule without paying any attention to those overt performances and, despite this, we are normally correct. These facts seem puzzling and impel us towards a certain philosophical picture of meaning and understanding. This picture identifies the meaning of a subject’s utterances, and his understanding of the rules that he follows, with some kind of structure of which he has immediate knowledge. By virtue of their connection with these private, meaning-constituting phenomena, the public manifestations of meaning and understanding are invaluable as clues to the meaning of an utterance or a subject’s understanding of a rule. But the latter are, nevertheless, ultimately fixed by the inner structures to which only the subject in question has immediate access and upon which he or she therefore has authority. This picture prompts a host of perplexing questions. “What are these immediately-knowable structures?” “What does it mean to say that we have immediate acquaintance with them?” “How are these private structures connected with those public performances?” These questions are notoriously difficult to answer. (shrink)

In classical logic, a contradiction allows one to derive every other sentence of the underlying language; paraconsistent logics came relatively recently to subvert this explosive principle, by allowing for the subsistence of contradictory yet non-trivial theories. Therefore our surprise to find Wittgenstein, already at the 1930s, in comments and lectures delivered on the foundations of mathematics, as well as in other writings, counseling a certain tolerance on what concerns the presence of contradictions in a mathematical system. ‘Contradiction. Why just this (...) spectre? This is really very suspicious.’ ( Philosophical Remarks III–56) In the last decades, several authors (e.g. Arrington, Hintikka, Van Heijenoort, Wright, Wrigley) have been digging into Wittgenstein’s rather non-standard standpoint on what concerns the interpretation and import of contradiction in logic and mathematics, and many other authors (e.g. da Costa, Goldstein, Granger, Marconi) have been investigating the possibility of taking Wittgenstein seriously as one of the early forerunners of paraconsistency. While many advances have been made on the first front, the second set of investigations has led almost exclusively to negative results: no, no operational proposal about the construction of a logic in which (some) contradictions are made inoffensive can be read from Wittgenstein’s philosophical work; in fact, it appears that the most one can find there is the exhortation for mathematicians to alter their attitude with respect to contradictions and to consistency proofs. The play is done, and one looks for a resume of the opera. This paper fills that blank, as a thorough investigation of the possible relations between Wittgenstein and paraconsistency. DOI:10.5007/1808-1711.2010v14n1p135. (shrink)

In this paper, elementary but hitherto overlooked connections are established between Wittgenstein's remarks on mathematics, written during his transitional period, and free-variable finitism. After giving a brief description of theTractatus Logico-Philosophicus on quantifiers and generality, I present in the first section Wittgenstein's rejection of quantification theory and his account of general arithmetical propositions, to use modern jargon, as claims (as opposed to statements). As in Skolem's primitive recursive arithmetic and Goodstein's equational calculus, Wittgenstein represented generality by the use of free (...) variables. This has the effect that negation of unbounded universal and existential propositions cannot be expressed. This is claimed in the second section to be the basis for Wittgenstein's criticism of the universal validity of the law of excluded middle. In the last section, there is a brief discussion of Wittgenstein's remarks on real numbers. These show a preference, in line with finitism, for a recursive version of the continuum. (shrink)

In recent years, several systematic theories of linguistic meaning have been offered that give pride of place to linguistic practice, or the process of linguistic communication. Often these theories are referred to as neo-pragmatist or new pragmatist; I call them 'practice-based'. According to practice-based theories of meaning, the process of linguistic communication is somehow constitutive of, or otherwise essential for the existence of, propositional linguistic meaning. Moreover, these theories disavow, or downplay, the semantic importance of inflationary notions of representation. I (...) introduce the basic ideas and motives behind some practice-based theories of meaning, and offer some reasons why an eliminativist, non-quietist, epistemic practice-based approach to meaning that 1) disavows any explanatory role for the linguistic community as such, 2) prioritizes sentence meaning over word meaning, and 3) may , in the end, be naturalistic, should be favored over its practice-based competitors. (shrink)

Traditional conventionalism about modality claims that a proposition is necessarily true iff it is true by convention. In the wake of the widespread repudiation of truth-byconvention, traditional conventionalism has fallen out of favour. However, a family of theories of modality have arisen that, whilst abandoning truth-by-convention, retain the spirit of traditional conventionalism. These ‘neo-conventionalist’ theories surpass their forebears and don’t fall victim to the criticisms inherited through truth-by-convention. However, not all criticisms levelled at traditional conventionalism target truth-by-convention. Any conventional theory (...) of modality must face the contingency problem. This claims that the contingency of our linguistic conventions jeopardises the necessity of the necessities they determine. I present the contingency problem as relevant to both the traditional conventionalist and the neo-conventionalist. I examine a response from Einheuser that builds upon a response from Wright. I show that the Einheuser response does more to accommodate the conventionalist’s modal beliefs, but that it does not fully satisfy some further conditions that ought to be laid upon such a response. I then suggest how the response can be revised so as to satisfy these conditions. The resulting model of conventionalism is compatible with the validity of S4, and suitably in the spirit of conventionalism. (shrink)

This article tackles the problem of normativity in naturalism and considers it in the context of the philosophy of historiography. I argue that strong naturalism is inconsistent with genuine normat...

The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory of which the green-hypothesis (...) is a part has an unintended model in which the grue-hypothesis is equally confirmed; and there are no meaning-facts that determine reference, because the objects referred to by the referring terms of any language or set of intentional mental states are permutable in a way that is consistent with the truth-values of all other sentences in that language or beliefs in that set. The upshot is that the three paradoxes need to be solved in a unified way. (shrink)

The German physicist Heinrich Hertz played a decisive role for Wittgenstein's use of a unique philosophical method. Wittgenstein applied this method successfully to critical problems in logic and mathematics throughout his life. Logical paradoxes and foundational problems including those of mathematics were seen as pseudo-problems requiring clarity instead of solution. In effect, Wittgenstein's controversial response to David Hilbert and Kurt Gödel was deeply influenced by Hertz and can only be fully understood when seen in this context. To comprehend the arguments (...) against the metamathematical programme, and to appreciate how profoundly the philosophical method employed actually shaped the content of Wittgenstein's philosophy, it is necessary to make an intellectual biographical reconstruction of their philosophical framework, tracing the Hertzian elements in the early as well as in the later writings. In order to write Wittgenstein's biography, we have to take seriously the coherence of his thought throughout his life, and not let convenient philosophical ideologies be our guidance in drawing up a “Wittgensteinian philosophy”. To do so, we have to take a second look upon what he actually wrote, not only in the already published material, but in the entire Nachlass. Clearly, this is not easily done, but it is a necessary task in the historical reconstruction of Wittgenstein's life and work. (shrink)

In my previous paper "Has the later Wittgenstein accounted for necessity?" I argued against the conventionalist account of necessity proposed by Wittgenstein and his followers. Glock has addressed some of my objections in his paper "Necessity and Language: In Defence of Conventionalism". This brief rejoinder considers Glock's replies to three of those objections. In the course of doing so, I revisit Wittgenstein's explanation of the special status of necessary propositions, the supposedly arbitrary nature of colour-grammatical propositions, and the relation between (...) rules and modality. (shrink)

It is argued that the finitist interpretation of wittgenstein fails to take seriously his claim that philosophy is a descriptive activity. Wittgenstein's concentration on relatively simple mathematical examples is not to be explained in terms of finitism, But rather in terms of the fact that with them the central philosophical task of a clear 'ubersicht' of its subject matter is more tractable than with more complex mathematics. Other aspects of wittgenstein's philosophy of mathematics are touched on: his view that mathematical (...) propositions are 'grammatical propositions' (and so, Strictly speaking, Not genuine propositions at all) and his view that in mathematics 'everything is algorithm, Nothing meaning'. His views on consistency and his anti-Foundationalism are linked with this central thesis. (shrink)

Dummett's case against platonism rests on arguments concerning the acquisition and manifestation of knowledge of meaning. Dummett's arguments are here criticized from a viewpoint less Davidsonian than Chomskian. Dummett's case against formalism is obscure because in its prescriptive considerations are not clearly separated from descriptive. Dummett's implicit value judgments are here made explicit and questioned. ?Combat Revisionism!? Chairman Mao.