Taking its orientation from Peter Winch, this article critiques from a Wittgensteinian point of view some “theoreticist” tendencies within constructivism. At the heart of constructivism is the deeply Wittgensteinian idea that the world as we know and understand it is the product of human intelligence and interests. The usefulness of this idea can be vitiated by a failure to distinguish conceptual from empirical questions. I argue that such a failure characterises two influential constructivist theories, those of Ernst von Glasersfeld and (...) David Bloor. These are considered in turn. Both theories seek to give a general, causal account of knowledge: von Glasersfeld's in term of cognitive subjectivity, Bloor's in terms of social agreement. Ironically, given that both writers cite Wittgenstein as a source of theoretical inspiration, assumptions of both theories run counter to key Wittgensteinian arguments. To show that Wittgenstein's views offer no solace to the realist, the article closes with a brief consideration of John Searle's theory of knowledge. (shrink)

Near the end of the last century, some legal philosophers adapted the so called causal theories of reference to solve internal problems in legal theory. Among those philosophers, Nicos Stavropoulos adjusted Hilary Putnam’s semantic externalism claiming it as a better philosophical view than legal positivism defended by Herbert Hart. According to him, what determines the correct application of a legal rule must be determined by the objects themselves. In that case, what determines the reference of legal terms is an issue (...) to be solved by the best theory developed. However, this is not the case necessarily: Hart’s model can reach to the same conclusions as an externalist adjustment of law. Furthermore, the epistemic criteria required by Putnam to deal with value judgements are also acceptable in a positivist model. This paper presents the central thesis of Putnam’s semantic externalism, with Stavropoulos adaptations to law, and defends that Hart’s approach to deal with legal rules and Putnam’s approach to deal with language rules can converge. (shrink)

This essay accounts for the notion of _Lebensform_ by assigning it a _logical _role in Wittgenstein’s later philosophy. Wittgenstein’s additions of the notion to his manuscripts of the _PI_ occurred during the initial drafting of the book 1936-7, after he abandoned his effort to revise _The Brown Book_. It is argued that this constituted a substantive step forward in his attitude toward the notion of simplicity as it figures within the notion of logical analysis. Next, a reconstruction of his later (...) remarks on _Lebensformen_ is offered which factors in his reading of Alan Turing’s “On computable numbers, with an application to the _Entscheidungsproblem_“, as well as his discussions with Turing 1937-1939. An interpretation of the five occurrences of _Lebensform_ in the PI is then given in terms of a logical “regression” to _Lebensform_ as a fundamental notion. This regression characterizes Wittgenstein’s mature answer to the question, “What is the nature of the logical?”. (shrink)

Drawing heavily on Wittgenstein, Winch’s The Idea of a Social Science advanced a forceful and still valuable critique of positivist/empiricist conceptions of social science. In its more self-confident assertions concerning the nature of philosophy and society, however, Winch failed to recognize Wittgenstein’s acknowledgement of and appreciation for the indeterminacy and unsettled character of social and moral life.

The author deals with the operational core oflogic, i.e. its diverse procedures ofinference, in order to show that logicallyfalse inferences may in fact be right because –in contrast to logical rationality – theyactually enlarge our knowledge of the world.This does not only mean that logically trueinferences say nothing about the world, butalso that all our inferences are inventedhypotheses the adequacy of which cannot beproved within logic but only pragmatically. Inconclusion the author demonstrates, through therelationship between rule-following andrationality, that it is (...) most irrational to wantto exclude the irrational: it may, at times, bemost rational to think and infer irrationally.Focussing on the operational aspects of knowingas inferring does away with the hiatus betweenlogic and life, cognition and the world(reality) – or whatever other dualism one wantsto invoke –: knowing means inferring, inferringmeans rule-governed interpreting, interpretingis a constructive, synthetic act, and aconstruction that proves adequate (viable) inthe ``world of experience'', in life, in thepraxis of living, is, to the constructivistmind, knowledge. It is the practice of livingwhich provides the orienting standards forconstructivist thinking and its judgments ofviability. The question of truth is replaced bythe question of viability, and viabilitydepends on the (right) kind of experiential fit. (shrink)

This paper discusses the meta-ethical implications of Wittgenstein’s later moral philosophy. According to Lovibond and Brandhorst, Wittgenstein provided a novel conception of moral facts, properties and objects by adopting deflationism. Lovibond argues that Wittgenstein’s seamless conception of language together with his non-foundational epistemology and non-transcendent understanding of rationality involves a change of perspective towards a plausible and non-mystificatory moral realism. Meanwhile, Brandhorst argues that Wittgenstein’s provides a deflationist conception of moral truths from which we obtain a deflationist conception of moral (...) facts. This paper argues, on the contrary, that the attribution of deflationism does not do justice to Wittgenstein’s later work. It is concluded, therefore, that the appeal to deflationism does not afford or substantiate the exegetical claims made by Lovibond and Brandhorst. (shrink)

Mathematicians and physical scientists depend heavily on the formal symbolism of mathematics in order to express and develop their theories. For this and other reasons the last hundred years has seen a growing interest in the nature of formal language and the way it expresses meaning; particularly the objective, shared aspect of meaning as opposed to subjective, personal aspects. This dichotomy suggests the question: do the objective philosophical theories of meaning offer concepts which can be applied in psychological theories of (...) meaning? In recent years cognitive scientists such as Chomsky [1980], Fodor [1981] and MacNamara [1982] have used philosophical approaches to the meaning of formal language expressions as the basis for their psychological theories. Following this lead it seems appropriate to review some of the main treatments of meaning with a view to their transferability. (shrink)

The theme of change is one of the most prominent traits of Wittgenstein’s later work, and his writings have inspired many contemporary thinkers’ discussions of changes in e.g. concepts, ‘aspect-seeing’, practices, worldviews, and forms of life. However, Wittgenstein’s conception of the dynamics of change has not been investigated in its own right. The aim of this paper is to investigate which understanding of the dynamics of changes can be found in the later Wittgenstein’s work. I will argue that what emerges (...) is a rich and complex picture that has the potential to aid our thinking in politics and elsewhere when developing strategies for creating changes. It can do so both as source of inspiration and by countering tempting, yet ultimately problematic ways of conceptualizing change like the hope for transforming harmful traditions and social practices with the help of a general explanatory theory of the fundamental dynamics of changes. (shrink)

In recent analytic philosophy, there is a growing interest in the project of conceptual engineering. This paper examines two ways this project might be applied to scientific research, specifically anthropological research. It argues that both of them are harmful to this research. Specifically, it argues that a reliance on the axiological standards of analytic philosophy conflicts with the goal of empirical adequacy. Section one proffers two forms that the engineering project might take when applied to the science. Section two proffers (...) a case study drawn from anthropology. Specifically, it lays out Evans-Pritchard’s Witchcraft, Oracles, and Magic Among the Azande, paying particular attention to the inconsistency he discovered in Azande witchcraft. Sections three and four argue that attempting to remove this inconsistency via the two forms of engineering disable critical features of emic research and discard empirical findings. Finally, I close by noting how the conflict between axiological standards and empirical adequacy might generalize beyond anthropology. (shrink)

The modal antirealist, as presented here, aims to secure at least some of the benefits associated with talking in genuine modal realist terms while avoiding commitment to a plurality of Lewisian (or ersatz) worlds. The antirealist stance of agnosticism about other worlds combines acceptance of Lewis's account of what world-talk means with refusal to assert, or believe in, the existence of other worlds. Agnosticism about other worlds does not entail a comprehensive agnosticism about modality, but where such agnosticism about modality (...) is enforced, the aim of the agnostic programme is to show that it is not detrimental to our modal practices. The agnostic programme consists in an attempt to demonstrate the rational dispensability of that disputed class of modal beliefs which the agnostic eschews, but which are held by the realist and the folk. Here I attempt to motivate, describe, and illustrate such an agnostic antirealist programme in modal philosophy. (shrink)

The modal antirealist, as presented here, aims to secure at least some of the benefits associated with talking in genuine modal realist terms while avoiding commitment to a plurality of Lewisian (or ersatz) worlds. The antirealist stance of agnosticism about other worlds combines acceptance of Lewis's account of what world‐talk means with refusal to assert, or believe in, the existence of other worlds. Agnosticism about other worlds does not entail a comprehensive agnosticism about modality, but where such agnosticism about modality (...) is enforced, the aim of the agnostic programme is to show that it is not detrimental to our modal practices. The agnostic programme consists in an attempt to demonstrate the rational dispensability of that disputed class of modal beliefs which the agnostic eschews, but which are held by the realist and the folk. Here I attempt to motivate, describe, and illustrate such an agnostic antirealist programme in modal philosophy. (shrink)

Extended Rationality: A Hinge Epistemology provides a novel account of the structure of epistemic justification. Its central claim builds upon Wittgenstein's idea in On Certainty that epistemic justifications hinge on some basic assumptions and that epistemic rationality extends to these very hinges. It exploits these ideas to address major problems in epistemology, such as the nature of perceptual justifications, external world skepticism, epistemic relativism, the epistemic status of basic logical laws, of the Principle of the Uniformity of Nature, of our (...) belief in the existence of the past and of other minds, and the nature of testimonial justification. Along the way, further technical issues, such as the scope of the Principle of Closure of epistemic operators under known entailment, the notion of transmission failure, and the existence of entitlements are addressed in new and illuminating ways. (shrink)

How does Quine fare in the first decades of the twenty-first century? In this paper I examine a cluster of Quinean theses that, I believe, are especially fruitful in meeting some of the current challenges of epistemology and ontology. These theses offer an alternative to the traditional bifurcations of truth and knowledge into factual and conceptual-pragmatic-conventional, the traditional conception of a foundation for knowledge, and traditional realism. To make the most of Quine’s ideas, however, we have to take an active (...) stance: accept some of his ideas and reject others, sort different versions of the relevant ideas, sharpen or revise some of the ideas, connect them with new, non-Quinean ideas, and so on. As a result the paper pits Quine against Quine, in an attempt to identify those Quinean ideas that have a lasting value and sketch potential developments. (shrink)

Modality and Anti-Metaphysics critically examines the most prominent approaches to modality among analytic philosophers in the twentieth century, including essentialism. Defending both the project of metaphysics and the essentialist position that metaphysical modality is conceptually and ontologically primitive, Stephen McLeod argues that the logical positivists did not succeed in banishing metaphysical modality from their own theoretical apparatus and he offers an original defence of metaphysics against their advocacy of its elimination. -/- Seeking to assuage the sceptical worries which underlie modal (...) anti-realism, McLeod provides an original contribution to essentialist epistemology, engaging with current debates about modality and suggesting that standard essentialist approaches to some issues in the philosophies of logic and language require revision. -/- This book offers valuable insights to professional philosophers, postgraduates and advanced undergraduates interested in metaphysics, philosophy of logic or the history of twentieth-century analytic philosophy. (shrink)

Peter Ludlow presents the first book on the philosophy of generative linguistics, including both Chomsky's government and binding theory and his minimalist ...

This volume consists of the invited papers presented at the 23rd International Wittgenstein Conference held in Kirchberg, Austria in August 2000. Among the topics treated are: truth, psychologism, science, the nature of rational discourse, practical reason, contextualism, vagueness, types of rationality, the rationality of religious belief, and Wittgenstein. Questions addressed include: Is rationality tied to special sorts of contexts? ls rationality tied to language? Is scientific rationality the only kind of rationality? Is there something like a Western rationality? and: Could (...) we genetically engineer human beings to be less wicked? (shrink)

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...) be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective. -/- We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways. -/- We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N. -/- We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences. -/- . (shrink)

What motivates the benevolent or charitable agent is regard for another’s good or well-being, but talk about regard for others’ good or well- being is simply talk about benevolence or charity in different terms. Yet Hume clearly holds that the regard for another’s good is a motive to produce benevolent acts that is distinct from a sense of their benevolence. So what is the difference? ‘Well’, one might say, ‘intuitively, rights are very different from wellbeing.’ Yes indeed. And that, I (...) shall contend, is Hume’s point. My general contention is that Hume’s discussion of justice is in fact an attack on that concept of rights we think of as having motivated the American and French revolutions, a concept that is still (deplorably in my view) prevalent. I think the very fact that it is so prevalent and so sanctified by its position in the American Constitution has blinded most readers to the power and plausibility of Hume’s attack, which I shall try to defend. (shrink)

This is a thesis in three parts. It concerns the normative capacity of attributive goodness. Specifically, it critically evaluates Attributivism, the theory that attributive goodness is fundamentally normative, or that the distribution of that property determines when, whether, and in what way agents ought to act. The first third develops, refines and defends Attributivism. Doing so is, in part, a ground-clearing exercise. I distil that theory from the arguments of many other philosophers. In doing so I isolate and precisify its (...) core commitments. I defend it from a number of objections. The second third analyses fundamental normativity. I stipulate that a standard or property is fundamentally normative if its distribution alone can ground normativity. I argue that for anything to be so fundamentally normative, it must minimally meet two criteria. It must be both authoritative and regulatory. The final third evaluates whether or not attributive goodness satisfies the established criteria, and so whether or not Attributivism is correct. I argue that in its canonical form it isn’t. I then develop a revised view of Attributivism that can satisfy the criteria. I argue, however, that the revised view is unsatisfying in almost every respect. Attributivism, revised or otherwise, should be rejected. (shrink)

This paper investigates a particular philosophical puzzle via an examination of its status in the writings of Wittgenstein. The puzzle concerns negation and can take on three interrelated guises. The first puzzle is how not-p can so much as negate p at all – for if p is not the case, then nothing corresponds to p. The second puzzle is how not-p can so much as negate p at all when not-p rejects p not as false but as unintelligible – (...) for if p is unintelligible, then p is nothing but scratches and sounds and does not seem apt for negation. And the third puzzle is how “not” could be anything but hopelessly equivocal if it sometimes (per the first puzzle) requires, and sometimes (per the second puzzle) precludes the intelligibility of p. The paper investigates these three puzzles, their respective structures, and their relations to each other. The second puzzle is expounded as the centre of gravity, and in countering two objections to the threefold puzzle, a special predicament is expounded with regard to the second puzzle’s concern with unipolar propositions – propositions that do not admit of an intelligible negation. The text concludes by indicating the first steps that could potentially lead us out of the threefold puzzle. (shrink)

Michael Beaney ha sugerido recientemente que la distinción fregeana entre sentido y referencia fue propuesta para resolver la famosa paradoja del análisis. Casi diez años antes, Michael Dummett ya insistia en que Frege fue uno de los prirneros en buscar una soluci6n satisfactoria de esta paradoja. En esre articulo, discuto algunas sugerencias de Beaney y Dummett de cómo resolver la paradoja al estilo fregeano y tarnbién sus propias contribuciones no fregeanas al debate en torno de la corrección y de la (...) informatividad del análisis. Mi intención en esta discusión es mostrar que ninguna de ellas funciona. Concluyo con una propuesta de inspiración witttgensteiniana --el enfoque de los conceptos abiertos- para apoyar la idea de que la apelación a contertidos abiertos es la rnejor rnanera de disolver la paradoja.Michael Beaney has recently suggested that the Fregean distinction between sense and reference was proposed to solve the famous paradox of analysis. Not as recently, Michael Dummett has insisted that Frege was one of the first to look for a satisfactory solution to this paradox. In this paper, I discuss Beanry’s and Dummett’s various suggestions for solving the paradox in a Fregean style as well as their own non Fregean contributions to the debate around analysis’s correction and informativeness. My intention in this discussion is to show that none of them works. I conclude with a proposal inspired by Wittgenstein’s later work -the open concepts’ proposal- designed to support the idea that the appeal to open contents is the best way to dissolve the paradox. (shrink)

Compulsion and Surprise Two phenomena conspire to convince people that the physical world exists independently of them. One is its recalcitrance, or insusceptibility to control. It resists and constrains our actions. Much as we might wish to do so, we cannot lift heavy boulders, walk through walls, jump rivers, breathe under water, or fly (unaided) over mountains. The other feature, which is connected to the first, is the world’s propensity to surprise us. The sights and sound, pressures and pains of (...) the world force themselves upon us in perception whether we want them to or not, and are often unexpected and surprising. An unusual bird appears in the garden, a stranger calls at the door and reveals he is a long-lost cousin, the post brings an invitation out of the blue, the car won’t start (surprises may be unpleasant as well as pleasant). These two phenomena, recalcitrance and surprise, form a large part of the platonist’s case for the existence of an independent mathematical reality. The recalcitrance of mathematical reality indeed appears to be stronger than that of the physical: the necessity with which mathematical results follow from assumptions is stricter than the physical necessity by which a wall resists attempts to walk through it. This has rarely been put more eloquently than by Jan Łukasiewicz. Speaking in particular of mathematical logic, he wrote.. (shrink)

Friedrich Hayek was a fervent advocate of the methodological specificity of the social sciences. However, given his contact with Karl Popper, several historians and philosophers have characterized his final position as Popperian, that is, a position that would have accepted the unity of scientific method. A closer look at Hayek's philosophy and Popper's own intellectual course shows that such a thesis is based on misconceptions that can be overcome by taking the Hayekian concept of 'spontaneous order' as the foundation of (...) a methodology immune to any kind of methodological monism. (shrink)

The following inquiry pursues two interlinked aims. The first is to understand Wittgenstein's idea of non-foundational certainty in the context of a reading of On Certainty that emphasizes its Pyrrhonian elements. The second is to read Wittgenstein's remarks on idealism/radical skepticism in On Certainty in parallel with the discussion of rule-following in Philosophical Investigations in order to demonstrate an underlying similarity of philosophical concerns and methods. I argue that for the later Wittgenstein, what is held certain in a given context (...) of inquiry or action is a locally transcendental condition of the inquiry or action in question. In On Certainty, Wittgenstein's analysis of the difference between knowledge and certainty forms the basis of his critique of both Moore's "Proof" and radical skepticism. This critique takes the shape of rejection of a presupposition shared by both parties, and utilizes what I identify as a Pyrrhonian-style argument against opposed dogmatic views. Wittgenstein's method in this text involves describing epistemic language-games. I demonstrate that this is consistent with the rejection of epistemological theorizing, arguing that a Wittgensteinian "picture" is not a theory, but an impressionistic description that accomplishes two things: (i) throwing into relief problems with dogmatic theories and their presuppositions, and (ii) describing the provenance of linguistic and epistemic practices in terms of norms grounded in convention. Convention, in turn, is not arbitrary, but grounded in the biological and social natures of human beings--in what Wittgenstein calls forms of life. Thus there is a kind of naturalism in the work of the later Wittgenstein. It is a naturalism that comes neatly dovetailed with Pyrrhonism--a combination of strategies traceable to Hume's work in the Treatise. I read Hume as someone who develops the Pyrrhonian method to include philosophy done "in a careless manner," and argue that Wittgenstein adopts a similar method in his later works. Finally, I explain the deference to convention in the work of both Hume and Wittgenstein by reference to a passage in Sextus' Outlines, on which I provide a gloss in the final chapter of this work. (shrink)

The contextual mind is found attested in various usages of the term complement, in the background of Kant. The difficulties of Kant's intuitionism are taken up through Quine, but referential opacity is resolved as semantic presence in lived context. A further critique of rationalist linguistics is developed from Jakobson, showing generic functions in thought supporting abstraction, binding and thereby semantic categories. Thus Bolzano's influential philosophy of mathematics and science gives way to a critical view of the ancient heritage acknowledged by (...) Plato. (shrink)

The paper focuses on the relationship between nature and eth- ics, particularly by considering nature as a convention, the result of a so- cial agreement, which is based on the criterion of social utility. In order to analyse this relationship, my assumption takes into consideration three pathways: evolutionary ethics, with reference to Paul Rée; error theo- ry, with reference to John Mackie; and the concept of commodification, with reference to Ralph W. Emerson. I try to connect these perspectives in order (...) to re-define the concepts of judgment and objectivity, showing that both can be viewed as standard or criteria of evaluation according to specific context and needs. My final aim is to show that Emerson’s concept of commodification corroborates the interpretation of nature in relation with the concept of social utility. (shrink)

How the interpretation of architecture differs from that of other artworks.

The aim of this paper is to provide a dynamic interpretation of Kant’s logical hylomorphism. Firstly, various types of the logical hylomorphism will be illustrated. Secondly, I propose to reevaluate Kant’s constitutivity thesis about logic. Finally, I focus on the design of logical norms as specific kinds of artefacts.

In his Wittgenstein on Rules and Private Language , Saul Kripke presents his influential reading of Wittgenstein’s later writings on language. One of the largely unexplored features of that reading is that Kripke makes a small number of suggestive remarks concerning the possible threat that Wittgenstein’s arguments pose for Chomsky’s linguistic project. In this paper, we attempt to characterise the relevance of Wittgenstein’s later work on meaning and rule-following for transformational linguistics, and in particular to identify the potentially negative impact (...) it has on that project. Although we use Kripke’s remarks to articulate some of the pertinent issues, we return to Wittgenstein’s later writings to address them. We argue that Wittgenstein’s main target in the relevant sections of the Philosophical Investigations is the notion of ‘logical compulsion’, which involves assuming that there is more to applying a word or rule than how we are naturally or “psychologically” compelled to apply. We characterise two of the main lines of argument in the Investigations in terms of the rejection of logical compulsion. We thus propose to address the relevance of Wittgenstein’s writings for Chomsky by considering whether Chomsky’s linguistics presupposes the targeted notion of logical compulsion. We argue that Chomsky’s conception of linguistic competence in terms of successive states of the “language faculty” (containing the principles of universal grammar) does presuppose this problematic notion. Chomsky responded to Kripke by devoting a chapter of his Knowledge of Language to defending this conception of linguistic competence against the Wittgensteinian arguments. We evaluate his response and argue that he has misidentified the threat to his linguistic project as consisting in the attack on its ‘individual psychology’ standpoint, rather than its commitment to logical compulsion. We conclude by arguing that Chomsky’s attempts at defending his individualist or non-communitarian standpoint are undermined by his inability to give a decisive response to Wittgenstein’s attack on logical compulsion. (shrink)

The concept of übersichtliche Darstellung is of fundamental significance for Wittgenstein . Hacker translates übersichtliche Darstellung as ‘surveyable representation’ and equates it with the tabulation of grammar. He asks what surveyability means, whether examples can be found in Wittgenstein’s work, and why this method characterizes the form of account he gives. Ultimately, however, Hacker is unable to answer these questions and he attributes this failure to Wittgenstein. This paper argues that it is Hacker’s interpretation that fails, and presents an alternate (...) understanding of übersichtliche Darstellung ; one that enables us to answer Hacker’s questions in a manner consistent with Wittgenstein’s philosophical practices. Normal 0 false false false EN-US X-NONE X-NONE. (shrink)

Russell’s initial project in philosophy (1898) was to make mathematics rigorous reducing it to logic. Before August 1900, however, Russell’s logic was nothing but mereology. First, his acquaintance with Peano’s ideas in August 1900 led him to discard the part-whole logic and accept a kind of intensional predicate logic instead. Among other things, the predicate logic helped Russell embrace a technique of treating the paradox of infinite numbers with the help of a singular concept, which he called ‘denoting phrase’. Unfortunately, (...) a new paradox emerged soon: that of classes. The main contention of this paper is that Russell’s new conception only transferred the paradox of infinity from the realm of infinite numbers to that of class-inclusion. Russell’s long-elaborated solution to his paradox developed between 1905 and 1908 was nothing but to set aside of some of the ideas he adopted with his turn of August 1900: (i) With the Theory of Descriptions, he reintroduced the complexes we are acquainted with in logic. In this way, he partly restored the pre-August 1900 mereology of complexes and simples. (ii) The elimination of classes, with the help of the ‘substitutional theory’, and of propositions, by means of the Multiple Relation Theory of Judgment, completed this process. (shrink)

The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. (...) In sections 5 and 6 I discuss some problems arising with regard to Prawitz’s views. (shrink)

The collection Virtual Mathematics: the logic of difference brings together a range of new philosophical engagements with mathematics, using the work of French philosopher Gilles Deleuze as its focus. Deleuze’s engagements with mathematics rely upon the construction of alternative lineages in the history of mathematics in order to reconfigure particular philosophical problems and to develop new concepts. These alternative conceptual histories also challenge some of the self-imposed limits of the discipline of mathematics, and suggest the possibility of forging new connections (...) between philosophy and more recent developments in mathematics. This component of Deleuze’s work has, to date, been rather neglected by commentators working in the field of Deleuze studies. One of the aims of this collection is to address this critical deficit by providing a philosophical presentation of Deleuze’s relation to mathematics; one that is adequate to his project of constructing a philosophy of difference and to the exploration of some of its applications. This project developed as a result of encounters with an increasing number of researchers who have been working on the mathematical aspects of Deleuze’s work and the key role that these play in his philosophy. By bringing this work together for the first time, this collection makes an important contribution to the emerging body of work that endeavours to explore the broad range of Deleuze’s philosophy. (shrink)

By a seemingly strange twist of fate, the formalist approach to language became popular after Hilbert’s project of providing a formalist foundation for mathematics foundered on G¨odel’s famous incompleteness theorems. Even in September 1930, during the congress in K¨onigsberg, where G¨odel presented his results for the first time, Carnap still defended logicism against the intuitionist and formalist views on the foundations of mathematics. Furthermore in linguistics, the formalist approach to syntactic issues had only become disseminated in the 1930s, due to (...) the distributionists of Bloomfield’s school, and found its paramount expression in Hjelmslev’s Prolegomena to a Theory of Language : according to Hjelmslev, both the linguistic theory and the grammar of a given language are nothing more than a calculus. (shrink)