The later Wittgenstein’s perspective on mathematical sentences as norms is motivated for sentences belonging to Hilbertian axiomatic systems where the axioms are treated as implicit definitions. It is shown that in this approach the axioms are employed as norms in that they function as standards of what counts as using the concepts involved. This normative dimension of their mode of use, it is argued, is inherited by the theorems derived from them. Having been motivated along these lines, Wittgenstein’s perspective on (...) mathematical language may appeal also to those who are not friends of or experts on Wittgenstein’s later philosophy of mathematics. (shrink)

In this article, I endeavor to analyze Wittgenstein’s remarks on certain aspects of Freud’s theory in the hope to show that his criticism can be epistemologically fruitful to pinpoint some insurmountable theoretical difficulties in the metapsychological aspect of psychoanalysis, especially with regard to Freud’s insistent remarks that his deep psychology must be viewed as a scientific approach of psychic phenomena.

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 Author [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] author makes clear that he does not see this book as a contribution to the philosophy of mathematics as traditionally understood. He takes it instead to be an essay about the philosophy of mathematics, one whose purpose is to explain its existence and to make clear the limited extent to which its current and past forms are properly regarded as philosophies of mathematics per (...) se.A little more exactly, the aim is to explain the seemingly ‘perennial’ interest1 western philosophers have had in mathematics 2 and how this became significant enough to give rise to and sustain an identified sub-discipline of philosophy....Hacking identifies two principal reasons for this, both of which he sees as having originated in what might broadly be termed our experience of mathematics. The first of... (shrink)

A fundamental question in responsibility theory concerns the relation between being responsible and our practices of holding responsible. ‘Strawsonians’ often claim that being responsible is somehow a function of our practices of holding responsible, while others think that holding responsible depends on being responsible, and still others think of being and holding responsible as interdependent. Based on a Wittgensteinian reading of Strawson, I develop an account of the relation between being and holding responsible which respects major concerns of all parties (...) in this debate. I characterize the way in which being responsible depends on holding responsible as genealogical, and the way in which holding responsible depends on being responsible as justificatory. I show how my account cuts across received ways of carving up the debate, and how it allows for all the kinds of fallibility about moral responsibility that are worth wanting. (shrink)

The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which are employed (...) in the original derivation of the Paradox. Instead we propose that the central tenet of verificationism is most accurately formulated as follows: if φ is true, then there exists a proof of φ Building on the work of Artemov (Bull Symb Log 7(1): 1-36, 2001), a system of explicit modal logic with proof quantifiers is introduced to reason about such statements. When the original reasoning of the Paradox is developed in this setting, we reach not a contradiction, but rather the conclusion that there must exist non-constructed proofs. This outcome is evaluated relative to the controversy between Dummett and Prawitz about proof existence and bivalence. (shrink)

Some interpreters have ascribed to Wittgenstein the view that mathematical statements must have an application to extra-mathematical reality in order to have use and so any statements lacking extra-mathematical applicability are not meaningful (and hence not bona fide mathematical statements). Pure mathematics is then a mere signgame of questionable objectivity, undeserving of the name mathematics. These readings bring to light that, on Wittgenstein’s offered picture of mathematical statements as rules of description, it can be difficult to see the role of (...) mathematical statements which relate to concepts that are not employed in empirical propositions e.g. set-theoretic concepts. I will argue that Wittgenstein’s picture is more flexible than might at first be thought and that Wittgenstein sees such statements as serving purposes not directly related to empirical description. Whilst this might make such systems fringe cases of mathematics, it does not bring their legitimacy as mathematical systems into question. (shrink)

Wittgenstein's conception of infinity can be seen as continuing the tradition of the potential infinite that begins with Aristotle. Transfinite cardinals in set theory might seem to render the potential infinite defunct with the actual infinite now given mathematical legitimacy. But Wittgenstein's remarks on set theory argue that the philosophical notion of the actual infinite remains philosophical and is not given a mathematical status as a result of set theory. The philosophical notion of the actual infinite is not to be (...) found in the mathematics of set theory, only in a certain associated philosophy – what Wittgenstein calls a certain kind of “prose”. (shrink)

Cognitive psychology and cognitive science are concerned with a domain of cognition that is much broader than the realm of judgement, belief, and inference. The idea of states with semantic content is extended far beyond the space of reasons and justification. Within this broad class of states we should, however, differentiate between the states distinctive of thinking persons — centrally, beliefs, desires, and intentions — and other states. The idea of consciousness does not furnish a principle of demarcation. But the (...) distinction between states whose content is conceptualized by the person whose states they are and states for which this is not so is more promising. This principle of demarcation contains the seeds of a problem for distributed connectionism. The article ends with some more general reflections about cognitive science. (shrink)

Alan Turing anticipated many areas of current research incomputer and cognitive science. This article outlines his contributionsto Artificial Intelligence, connectionism, hypercomputation, andArtificial Life, and also describes Turing's pioneering role in thedevelopment of electronic stored-program digital computers. It locatesthe origins of Artificial Intelligence in postwar Britain. It examinesthe intellectual connections between the work of Turing and ofWittgenstein in respect of their views on cognition, on machineintelligence, and on the relation between provability and truth. Wecriticise widespread and influential misunderstandings of theChurch–Turing thesis (...) and of the halting theorem. We also explore theidea of hypercomputation, outlining a number of notional machines thatcompute the uncomputable. (shrink)

The paper reviews the grounds for relativist interpretations of Wittgenstein's later thought, especially in On Certainty . It distinguishes between factual and virtual forms of epistemic relativism and argues that, on closer inspection, Wittgenstein's notes don't support any form of relativism – let it be factual or virtual. In passing, it considers also so-called "naturalist" readings of On Certainty , which may lend support to a relativist interpretation of Wittgenstein's ideas, finds them wanting, and recommends to interpret his positive proposal (...) in On Certainty as a form of "internal rationalism.". (shrink)

One consequence of the later Wittgenstein's influential critique of epistemological foundationalism has been to convince many contemporary philosophers that the ideal of universal and necessary cognitive grounds for moral or political norms is illusory. Recent neo-Wittgensteinian accounts of practical reason attempt to formulate a conception of a post-foundational politics in which a political ethos can be legitimate, rational or just even if its informing practices and cognitive standards lack foundational justification. Against these appropriations of Wittgenstein, I argue that his account (...) challenges foundationalism only by generating epistemological relativism at both the first-order level of belief systems and at the second-order level of the comparative evaluation of first-order belief systems and their non-comparable forms of justification. The result is a polytheism of forms of reason which imperils the methodological ideal of a non-relativistic practice of moral-political criticism. (shrink)

Joining a vast Wittgensteinian anti-theoretical movement, John Canfield has argued that it is possible to read the claims that (1) “language is essentially communal” and (2) “it is conceptually possible that a Crusoe isolated from birth should speak or follow rules” in such a way that they are perfectly compatible, and, indeed, that Wittgenstein held them both at once. The key to doing this is to drain them of any theoretical content or implications that would put each claim at odds (...) with the other. I argue here, first of all, that it is not possible to detheorize both (1) and (2) and still hope to say anything illuminating about the nature of language. In fact, Canfield himself does not succeed in detheorizing both (1) and (2) but ends up trivializing (1) and leaving (2) with quite a bit of theoretical content. I further argue, however, that this is getting the matter the wrong way around. Contra Canfield et al., it is only when we recognize this that we can appreciate how radical and innovative Wittgenstein's claims about language really are. (shrink)