Zettel, an en face bilingual edition, collects fragments from Wittgenstein's work between 1929 and 1948 on issues of the mind, mathematics, and language.

Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

Logical Atomism is a philosophy that sought to account for the world in all its various aspects by relating it to the structure of the language in which we articulate information. In _The Philosophy of Logical Atomism,_ Bertrand Russell, with input from his young student Ludwig Wittgenstein, developed the concept and argues for a reformed language based on pure logic. Despite Russell’s own future doubts surrounding the concept, this founding and definitive work in analytical philosophy by one of the world’s (...) most significant philosophers is a remarkable attempt to establish a novel way of thinking. (shrink)

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), (...) the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy. (shrink)

Wittgenstein on philosophical problems : from one fundamental problem to particular problems -- The Tractatus on philosophical problems -- Wittgenstein's later conception of philosophical problems -- Examples of philosophical problems as based on misunderstandings -- Tendencies and inclinations of thinking : philosophy as therapy -- Wittgenstein's notion of peace in philosophy : the contrast with the Tractatus -- Two conceptions of clarification -- The Tractatus's conception of philosophy as logical analysis -- Wittgenstein's later critique of the Tractatus's notion of logical (...) analysis -- Clarification in Wittgenstein's later philosophy -- From metaphysics and philosophical theses to grammar : Wittgenstein's turn -- Philosophical theses, metaphysical philosophy, and the Tractatus -- Metaphysics and conceptual investigation : the problem with metaphysics -- Conceptual investigation and the problem of dogmatism -- Wittgenstein's turn -- The turn and the role of rules -- Rules as objects of comparison -- Rules, metaphysical projection, and the logic of language -- Grammar, meaning, and language -- Grammar, use, and meaning : the problem of the status of Wittgenstein's remarks -- Wittgenstein's formulation of his conception of meaning -- The concept of language : comparisons with instruments and games -- Wittgenstein's development and the advantages of his mature view -- Examples as centers of variation and the conception of language as a family -- Avoiding dogmatism about meaning -- Wittgenstein's methodological shift and analyses in terms of necessary conditions -- The concepts of essence and necessity -- Constructivist readings and the arbitrariness/nonarbitrariness of grammar -- Problems with constructivism -- The methodological dimension of Wittgenstein's conception of essence -- The nontemporality of grammatical statements -- Explanations of necessity in terms of factual regularities -- Wittgenstein's account of essence and necessity -- Beyond theses about the source of necessity -- Philosophical hierarchies and the status of clarificatory statements -- Philosophical hierarchies and Wittgenstein's "leading principle" -- The concept of perspicuous presentation -- The (alleged) necessity of accepting philosophical statements -- The concept of agreement and the problem of injustice -- The criteria of the correctness of grammatical remarks -- Multidimensional descriptions and the new use of old dogmatic claims -- Wittgenstein's conception of philosophy, everyday language, and ethics -- Metaphysics disguised as methodology -- The historicity of philosophy -- Philosophy and the everyday. (shrink)

This pioneering book demonstrates the crucial importance of Wittgenstein's philosophy of mathematics to his philosophy as a whole. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations.

Intuitive judgments elicited by verbal case-descriptions play key roles in philosophical problem-setting and argument. Experimental philosophy's ‘sources project’ seeks to develop psychological explanations of philosophically relevant intuitions which help us assess our warrant for accepting them. This article develops a psycholinguistic explanation of intuitions prompted by philosophical case-descriptions. For proof of concept, we target intuitions underlying a classic paradox about perception, trace them to stereotype-driven inferences automatically executed in verb comprehension, and employ a forced-choice plausibility-ranking task to elicit the relevant (...) stereotypical associations of perception- and appearance-verbs. We obtain a debunking explanation that resolves the philosophical paradox. (shrink)

Notes taken by these last four are the basis for the thirty-one lectures in this book.

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

A survey of current evidence available concerning Wittgenstein's attitude toward, and knowledge of, Gödel's first incompleteness theorem, including his discussions with Turing, Watson and others in 1937–1939, and later testimony of Goodstein and Kreisel; 2) Discussion of the philosophical and historical importance of Wittgenstein's attitude toward Gödel's and other theorems in mathematical logic, contrasting this attitude with that of, e.g., Penrose; 3) Replies to an instructive criticism of my 1995 paper by Mark Steiner which assesses the importance of Tarski's semantical (...) work, both for our understanding of Wittgenstein's remarks on Gödel, and our understanding of Gödel's theorem itself. (shrink)

Six experiments explored the hypothesis that the members of categories which are considered most prototypical are those with most attributes in common with other members of the category and least attributes in common with other categories. In probabilistic terms, the hypothesis is that prototypicality is a function of the total cue validity of the attributes of items. In Experiments 1 and 3, subjects listed attributes for members of semantic categories which had been previously rated for degree of prototypicality. High positive (...) correlations were obtained between those ratings and the extent of distribution of an item's attributes among the other items of the category. In Experiments 2 and 4, subjects listed superordinates of category members and listed attributes of members of contrasting categories. Negative correlations were obtained between prototypicality and superordinates other than the category in question and between prototypicality and an item's possession of attributes possessed by members of contrasting categories. Experiments 5 and 6 used artificial categories and showed that family resemblance within categories and lack of overlap of elements with contrasting categories were correlated with ease of learning, reaction time in identifying an item after learning, and rating of prototypicality of an item. It is argued that family resemblance offers an alternative to criterial features in defining categories. (shrink)

There is a natural view of nonsense, which owes what attraction it has to the apparent absence of alternatives. In Frege and Wittgenstein there is a view which goes against the natural one, and the purpose of this paper is to establish that it is a possible view of nonsense.

Thought's Footing is an enquiry into the relationship between the ways things are and the way we think and talk about them. It is also a study of Wittgenstein's Philosophical Investigations: Charles Travis develops his account of certain key themes into a unified view of the work as a whole. The central question is: how does thought get its footing? How can the thought that things are a certain way be connected to things being that way?

In his Philosophical Investigations Wittgenstein describes, and represents himself as pursuing, a way of doing philosophy without putting forward philosophical theses. I exemplify his approach with a sketch of his treatment of rule following. I focus in particular on the simple case of following a signpost, conceived as an expression of a rule for getting to a destination. Wittgenstein uncovers a threat that we will find it mysterious how one could learn from a signpost which way to go, and he (...) dissolves the threat, not by putting forward philosophical theses, but by reminding us of things we already knew about signposts. Insofar as the point of Wittgenstein's procedure is to give philosophy peace, the label “quietism” fits. I take issue with readings of Wittgenstein's quietism that represent him as uncovering a need for positive philosophical work, but using quietism as a pretext for declining to do the work himself. Wittgensteinian quietism is not a stance of complacency or idleness. The kind of thing Wittgenstein does is difficult and laborious. It requires accurate and sympathetic engagement with frames of mind in which positive philosophy seems to be necessary. (shrink)

It is sometimes argued that Wittgenstein's conception of grammar and the role he allocated to grammar (in his sense of the term) in philosophy changed between the Big Typescript and the Philosophical Investigations. It is also held that some of the grammatical propositions Wittgenstein asserted prior to his writing of the Philosophical Investigations are theses, doctrines, opinions or dogmatism, which he abandoned by 1936/37. The purpose of this paper is to show these claims to be misunderstandings and misinterpretations. On all (...) important matters, his conception of grammar and of grammatical investigations, of grammatical statements or propositions and of grammatical clarification did not change between the Big Typescript and the Investigations. Grammatical propositions (e.g. the meaning of a word is its use; a sample in an ostensive definition belongs to the means of representation; belief is not a mental state) are no more theses, doctrines or opinions than is “a bachelor is an unmarried man.” Nor are they in any way dogmatic. (shrink)

In Part III of his Remarks on the Foundations of Mathematics Wittgenstein deals with what he calls the surveyability of proofs. By this he means that mathematical proofs can be reproduced with certainty and in the manner in which we reproduce pictures. There are remarkable similarities between Wittgenstein's view of proofs and Hilbert's, but Wittgenstein, unlike Hilbert, uses his view mainly in critical intent. He tries to undermine foundational systems in mathematics, like logicist or set theoretic ones, by stressing the (...) unsurveyability of the proof-patterns occurring in them. Wittgenstein presents two main arguments against foundational endeavours of this sort. First, he shows that there are problems with the criteria of identity for the unsurveyable proof-patterns, and second, he points out that by making these patterns surveyable, we rely on concepts and procedures which go beyond the foundational frameworks. When we take these concepts and procedures seriously, mathematics does not appear as a uniform system, but as a mixture of different techniques. (shrink)

This paper pioneers the use of methods and findings from psycholinguistics in experimental philosophy’s ‘sources project’. On this basis, it clarifies the epistemological relevance of empirical findings about intuitions – a key methodological challenge to experimental philosophy. The sources project (aka ‘cognitive epistemology of intuitions’) seeks to develop psychological explanations of philosophically relevant intuitions, which help us assess their evidentiary value. One approach seeks explanations which trace relevant intuitions back to automatic cognitive processes that are generally reliable but predictably generate (...) cognitive illusions under specific vitiating circumstances. The paper develops and experimentally tests such an explanation for intuitions at the root of a historically influential paradox about perception (‘argument from illusion’). The explanation traces these intuitions to stereotype-driven amplification, an automatic process routinely involved in language comprehension (e.g., understanding philosophical case-descriptions). Distributional semantics analysis and a forced-choice plausibility ranking task are employed to establish the relevant verb-associated stereotypes. The paper argues that the inferences facilitated by these stereotypes are generally reliable, but shows that vitiating circumstances obtain in the formulation of the targeted paradox. On this basis, the paper explores two complementary strategies for assessing the evidentiary value of intuitive judgments. (shrink)

The word “picture” occurs pervasively in Wittgenstein's later philosophy. Not only does Wittgenstein often use literal pictures or the notion of mental pictures in his investigations, but he also frequently uses “picture” to speak about a way of conceiving of a matter (e.g. “A picture held us captive” at Philosophical Investigations§115). I argue that “picture” used in this conceptual sense is not a shorthand for an assumption or a set of propositions but is rather an expression of conceptual bedrock on (...) the model of an organising myth. This reading builds primarily on work by Gordon Baker and Stanley Cavell. (shrink)

Wittgenstein famously remarks that ‘the meaning of a word is its use’ (PI §43). Whether or not one views this as gesturing at a ‘theory’ of meaning, or instead as aiming primarily at dissuading us from certain misconceptions of language that are a source of puzzlement, it is clear that Wittgenstein held that for certain purposes the meaning of an expression could profitably be characterised as its use. Throughout his later writings, however, Wittgenstein’s appeal to the notion of use pulls (...) in two directions. In several places, Wittgenstein seems to connect the notion of an expression’s meaning with that of use in the sense of usage or practice. More specifically, he suggests that for an expression to possess meaning is for there to be a practice of employing it according to certain rules. ‘That’, he tells us, ‘is why there exists a correspondence between the concepts “rule” and “meaning”’ (OC §62; cf. PG 68; PO 51; RFM VI §28; VW 103). Indeed, Wittgenstein goes so far as to say, ‘The rule-governed nature of our languages permeates our life’ (RC §303). Call the view that the meaning of an expression is determined by a general principle governing its use, rulism. (shrink)

In this article I examine three ways in which one might interpret Wittgenstein's Philosophical Investigations (PI). In a partial response to Hans‐Johann Glock's article in this journal, I suggest that since publication PI has, broadly speaking, been interpreted in three ways: doctrinal; elucidatory; or therapeutic. The doctrinal interpretation is shown to be, at best, difficult to sustain textually. The elucidatory (standard) interpretation, though seemingly closer to the text, is shown both to implicate Wittgenstein in some unfortunate philosophical commitments and to (...) face a problem of “motivation.” I argue that, correctly understood, any attempt to elucidate in PI is undertaken only in pursuit of the therapeutic goal. I conclude by arguing that the therapeutic interpretation is the only interpretation that can adequately make sense of Wittgenstein's text as a whole and the metaphilosophical remarks in particular. Furthermore, it is the only interpretation that can demonstrate Wittgenstein's continued importance and relevance as a philosopher. (shrink)

Wittgenstein's philosophy of mathematics has long been notorious. Part of the problem is that it has not been recognized that Wittgenstein, in fact, had two chief post-Tractatus conceptions of mathematics. I have labelled these the calculus conception and the language-game conception. The calculus conception forms a distinct middle period. The goal of my article is to provide a new framework for examining Wittgenstein's philosophies of mathematics and the evolution of his career as a whole. I posit the Hardyian Picture, modelled (...) on the Augustinian Picture, to provide a structure for Wittgenstein's work on the philosophy of mathematics. Wittgenstein's calculus period has not been properly recognized, so I give a detailed account of the tenets of that stage in Wittgenstein's career. Wittgenstein's notorious remarks on contradiction are the test case for my theory of his transition. I show that the bizarreness of those remarks is largely due to the calculus conception, but that Wittgenstein's later language-game account of mathematics keeps the rejection of the Hardyian Picture while correcting the calculus conception's mistakes. (shrink)

Abstract: “Resolute readings” initially started life as a radical new approach to Wittgenstein's early philosophy, but are now starting to take root as a way of interpreting the later writings as well—a trend exemplified by Stephen Mulhall's Wittgenstein's Private Language (2007) as well as by Phil Hutchinson's “What's the Point of Elucidation?” (2007) and Rom Harré's “Grammatical Therapy and the Third Wittgenstein” (2008). The present article shows that there are neither good philosophical nor compelling exegetical grounds for accepting a resolute (...) reading of the later Wittgenstein's work. It is possible to make sense of Wittgenstein's philosophical method without either ascribing to him an incoherent conception of “substantial nonsense” or espousing the resolute readers' preferred option of nonsense austerity. If the interpretation here is correct, it allows us to recognize Wittgenstein's radical break with the philosophical tradition without having to characterize his achievements in purely therapeutic fashion. (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)

A survey of Wittgenstein's writings on logic and mathematics; an analytical bibliography of contemporary articles on rule-following, social constructivism, Wittgenstein, Godel, and constructivism is appended. Various historical accounts of the nature of mathematical knowledge glossed over the effects of linguistic expression on our understanding of its status and content. Initially Wittgenstein rejected Frege's and Russell's logicism, aiming to operationalize the notions of logical consequence, necessity and sense. Vienna positivists took this to place analysis of meaning at the heart of philosophy, (...) while Ramey took extensionalism to result. Wittgenstein's interest in rule-following emerged through his reactions to these attempted appropriations. (shrink)

In this paper, I will investigate Wittgenstein’s idea about the context-sensitivity of utterance. It is the idea that there is a big gap between understanding a sentence in the sense of knowing the idioms and discerning the grammar in it, and what is said by using it in a particular context. Although context-sensitivity in this moderate sense is a familiar idea in Wittgensteinian scholarship, it has mainly been studied as an idea in “Wittgenstein’s philosophy of language.” However, Wittgenstein’s interest in (...) language is always connected with his interest in the treatment of philosophical problems. Therefore, what is lacking in those preceding studies is the study of the relation between Wittgenstein’s engagement with the idea of context-sensitivity and his philosophical therapy. Therefore, I shall investigate that relation and show that Wittgenstein’s philosophical method cannot be intelligible without taking context-sensitivity into consideration and Wittgenstein’s focus on context is deeply connected with his method for treating philosophers’ “pictures.” Below, I will examine recent debates on grammar, and argue that the standard interpretation is untenable once proper consideration is given to context-sensitivity. Next, I will argue that context-sensitivity is important because it gives us a good grasp of the process of a philosopher’s being caught in a picture by citing the discussion about mental process and about the Augustinian picture and rule-following in Philosophical Investigations. Finally, I will talk about the significance of my interpretation for contemporary arguments about philosophical methods. (shrink)

The paper develops a novel account of the nature and genesis of some philosophical problems, which motivates an unfamiliar form of philosophical criticism that was pioneered by the later Wittgenstein. To develop the account, the paper analyses two thematically linked sets of problems, namely problems about linguistic understanding: a set of problems Wittgenstein discusses in a core part of his Philosophical Investigations, and the ‘problem of linguistic creativity’ that is central to current philosophy of language. The paper argues that these (...) problems are generated by tacit and unwarranted presuppositions at odds with warranted beliefs the philosophers raising the problems reflectively hold at the same time. For a rigorous conceptualisation of this phenomenon, the paper develops the notion of a ‘philosophical picture’ first proposed by Wittgenstein, and specifies the particular class of philosophical problems that may be raised due to adherence to such pictures. The results motivate a new form of philosophical criticism: the systematic exposure of relevant philosophical pictures, and efforts to overcome their tacit influence on philosophical reflection. (shrink)

Peter Hacker defends an interpretation of the later Wittgenstein's notion of grammar, according to which the inherently general grammatical rules are sufficient for sense-determination. My aim is to show that this interpretation fails to account for an important contextualist shift in Wittgenstein's views on sense-determination. I argue that Hacker attributes to the later Wittgenstein a rule-based, combinatorial account of sense, which Wittgenstein puts forward in the Tractatus. I propose that this is not how we should interpret the later Wittgenstein because (...) he insists that particular circumstances of use play a necessary role in determining the boundary between sense and nonsense. (shrink)

Hilary Putnam, James Conant; On Wittgenstein's Philosophy of Mathematics, Proceedings of the Aristotelian Society, Volume 97, Issue 1, 1 June 1997, Pages 195–22.