This article aims to analyse Wittgenstein’s 1929–1932 notes concerning Frege’s critique of what is referred to as old formalism in the philosophy of mathematics. Wittgenstein disagreed with Frege’s critique and, in his notes, outlined his own assessment of formalism. First of all, he approvingly foregrounded its mathematics-game comparison and insistence that rules precede the meanings of expressions. In this article, I recount Frege’s critique of formalism and address Wittgenstein’s assessment of it to show that his remarks are (...) not so much a critique of Frege as rather a defence of the formalist anti-metaphysical investment. (shrink)

A milestone in Wittgenstein scholarship, this collection of essays ranges over a wide area of the philosopher's thought, presenting divergent interpretations of his fundamental ideas. Different chapters raise many of the central controversies that surround current understanding of the Tractatus, providing an interplay that will be particularly useful to students. Taken together, the essays present a broader and more comprehensive view of Wittgenstein's intellectual interests and his impact on philosophy than may be found elsewhere.The thirteen chapters treat topics (...) from both periods of Wittgenstein's work: More than half are devoted to his early thought, the Tractatus Logico-Philosophicus of 1921, reflecting a growing interest today among philosophers in reexamining this seminal book, while three chapters treat the Philosophical Investigations, published posthumously in 1953. The remaining chapters discuss such "nonstandard" topics as philosophy of religion, aesthetics, and anthropology.Contents: The Early Wittgenstein and the Middle Russell, Kenneth Blackwell; Frege and Wittgenstein, Michael Dummett; Wittgenstein and the Theory of Types, Hide Ishiguro; The So-called Realism of Wittgenstein's Tractatus, Brian McGuinness; The Logical Independence of Elementary Propositions, David Pears; The Rise and Fall of the Picture Theory, Peter Hacker; The Picture Theory and Wittgenstein's Later Attitude to It, Erik Stenius; Wittgenstein's Early Philosophy of Mind, Anthony Kenny; A Theory of Language?, G. E. M. Anscombe; Im Anfang war die Tat, Peter Winch; Wittgenstein's Full Stop, D. Z. Phillips; Quote: Judgments from Our Brain, Paul Ziff; Wittgenstein and the Fire Festivals, Frank Cioffi, Index.Irving Block is Associate Professor in the Philosophy Department at The University of Western Ontario. (shrink)

The paper identifies in Cartesian dualism a common target of the middle Wittgenstein and the early Merleau-Ponty. By relegating pain to mental awareness and location to bodily extension, Cartesian dualism renders common localizations of pain throughout the body as unintelligible ascriptions. Wittgenstein’s and Merleau-Ponty’s efforts to do justice to common localizations of pain illuminate one another. In their light, Cartesian dualism involves an objectification and a deappropriation of one’s body. Further, Wittgenstein’s acknowledgment of a heterogeneous multiplicity (...) of corporeal spaces (e.g. tactile space, feeling space) restores the view, reinforced by Merleau-Ponty, that corporeal pain is intimately related to corporeal localization, while corporeal space is not a continuation of the physical space of things. (shrink)

By 1929, after the full acknowledgment of the colour–exclusion problem, Wittgenstein had to admit that material incompatibilities presented in conceptual systems could not be reduced to formal tautologies and contradictions. Wittgenstein then, in his middle period, had to examine the kind of negation which, for instance, colour systems should render, which expose not just one but many or, in some cases, infinite inferentially articulated alternatives. Here, inspired by Brandom’s inferentialism, I explore the idea that Wittgenstein, in (...) his middle period, advocated a form of inferentialism based on the inferentially articulated content of propositions in Satzsysteme. At that time, Wittgenstein suggested that every sentence should be logically connected to many others. I call this feature inferential thickness. Therefore, I use Löf’s normative read of verificationism to explain Middle Wittgenstein’s holist solution to problems concerning the use of negation related to material incompatibilities and determination of propositional sense. I also investigate the distinction between contrariety and contradiction and some possible connections to a mandatory restriction of the principle of excluded middle in Satzsysteme. (shrink)

Spanning the period between Wittgenstein's return to Cambridge in 1929 and the first version of Philosophical Investigations in 1936, Piotr Dehnel explores the middle stage in Ludwig Wittgenstein's philosophical development and identifies the major issues which engrossed him, including phenomenology, philosophy of mathematics and philosophy of language. Contrary to the dominant perspective, Dehnel argues that this period was intrinsically different from the early and late stages and should not be viewed as a mere transitional phase. The distinctiveness (...) of Wittgenstein's middle work can be seen in his philosophical thinking as it unfolds in a non-linear trajectory: thoughts do not follow upon each other, ideas do not appear sequentially one by one, and insights do not form a straight chain. Dehnel portrays the diffused and multifarious quality of Wittgenstein's middle thinking, enabling readers to form a more comprehensive view of his entire philosophy and acquire a better grasp of his conceptual trajectory, complete with the intricacies and challenges that it poses. (shrink)

The paper discusses two aspects of Wittgenstein’s middle-period discussions of the self and the use of ‘I’. First, it considers the distinction Wittgenstein draws in his 1933 Cambridge lectures between two ‘utterly different’ uses of the word ‘I’. It is shown that Wittgenstein’s discussion describes a number of different and non-equivalent distinctions between uses of ‘I’. It is argued that his claims about some of these distinctions are defensible but that his reasoning in other cases is (...) unconvincing. Second, the paper considers the distinction drawn in the Blue Book between the use of ‘I’ as subject and the use of ‘I’ as object. A number of commentators have contended that this Blue Book distinction between uses of ‘I’ is erroneous, that Wittgenstein soon realized that, and that he dropped the idea of such a distinction from his later work. Against those claims, it is argued that Wittgenstein’s distinction between the use of ‘I’ as subject and its use as object is correct and illuminating. And it is shown that, though we do not find the ‘as-subject’/’as-object’ terminology in Wittgenstein’s subsequent work, the essential point of the Blue Book distinction is not abandoned but remains in place in Philosophical Investigations. (shrink)

In one of his meetings with members of the Vienna Circle, Wittgenstein discusses Hermann Weyl’s brief conversion to intuitionism and criticizes his arguments against applying the law of the excluded middle to generalizations over the natural numbers. Like Weyl, however, Wittgenstein rejects the classical model theoretic conception of generality when it comes to infinite domains. Nonetheless, he disagrees with him about the reasons for doing so. This paper provides an account of Wittgenstein’s criticism of Weyl that (...) is based on his differing understanding of what a general statement over infinite domains consists in. This difference in their conception of generality is argued to be central to the middle Wittgenstein’s overall stance on intuitionism as well. While Weyl (and other intuitionists) reject the law of the excluded middle on grounds of constructivity, Wittgenstein argues that general statements over infinite domains do not express propositions in the first place. The origin of this position as well as its consequences for contemporary debates on generality are further assessed. (shrink)

In her analysis the author comes to the conclusion, that Wittgenstein's conception of ethics in the end of 1920s was marked by: 1. an ambiguous and confusing explanation of the term "ethics"; 2. continuously putting stress on fact/value diffe_rence as well as on the ethical being beyond the expression; 3. introducing the difference between the relative and the absolute use of the words "good" and "right", "value" and differentiating between relative and absolute value judgments; 4. claiming the first person (...) discourse as the only possible ethical discourse, The shift in Wittgenstein's views of ethics consists in that 1. Wittgenstein started to use the word "ethics" in its traditional meaning; 2. in his discussions of ethics he deals with moral problems of everyday life; 3. he makes his views on the absolute judgments´ being beyond expression more accurate; 4. he takes ethics as an theoretical system; 5. he sees ethics not as one doctrine, but rather as a whole consisting of several theoretical systems; 6. the influence of language game on ethical system becomes visible. Nevertheless, considering ethics in its traditional meaning did not depress his understanding of ethics as something higher, transcendent and God related. (shrink)

Wittgenstein's 'middle period' is often seen as a transitional phase connecting his better-known early and later philosophies. The fifteen essays in this volume focus both on the distinctive character of his teaching and writing in the 1930s, and on its pivotal importance for an understanding of his philosophy as a whole. They offer wide-ranging perspectives on the central issue of how best to identify changes and continuities in his philosophy during those years, as well as on particular topics (...) in the philosophy of mind, religion, ethics, aesthetics, and the philosophy of mathematics. The volume will be valuable for all who are interested in this formative period of Wittgenstein's development. (shrink)

Rush Rhees, Elizabeth Anscombe and Georg Henrik von Wright were Wittgenstein’s literary heirs and edited many posthumous volumes from Wittgenstein’s writings. Their archived correspondence provides unique insights into this editorial work. The selection of letters written by Rhees which is presented here stems from an early phase of his editorial endeavour to shed light on Wittgenstein’s philosophical development between the _TLP_ and the _PI_. The letters were written between 1962 and 1964, in connection with the volume that (...) appeared as _Philosophische Bemerkungen_, and show how Rhees’ understanding of Wittgenstein’s texts developed during editing. They contain some of the central considerations that governed Rhees’ work as Wittgenstein’s literary executor. (shrink)

The edition of the Nachlass from the early thirties by Michael Nedo and the completion of the "Bergen Electronic Edition" (BEE) have provided Wittgenstein scholars with all the material required to investigate the author's philosophical development starting with his auto-criticism of the "Tractatus" and leading to his later views. Wittgenstein's strategy of dictating from his notebooks and cutting up the typescripts to rearrange paragraphs into sequences of remarks is well documented in Nedo's edition and the BEE provides convenient (...) facsimile access to every page Wittgenstein wrote or edited throughout the process. Some researchers have begun to revise received opinions that were based upon the "books" previously published by the trustees. (Hrachovec 2002, 2004, Kientzler 1997, Nyiri 2002, Pichler 2004, Stern 2002) Yet, the scientific community has barely begun to discover the richness and density of the philosophical endeavor manifesting itself in this material. There has, understandably, been an interest to trace the origin of remarks, well-known from the "Philosophical Investigations", providing some background to Wittgenstein's most popular ideas. Various doctrines of what is becoming known as the "middle Wittgenstein" have been noticed, but they have themselves been perceived as more or less consolidated theories. Wittgenstein's editorial activity has been recognized as a hypertextual undertaking avant la lettre, yet there has been insufficient attention to the philosophical impact of these hypertextual strategies themselves. It is all too easy to be caught by someprovisional result captured on a printed page and to overlook the fact that some of its philosophical significance can only be recognized by considering its genesis. (shrink)

Wittgenstein’s mention of the term “phenomenology” in his writings from the middle period has long been regarded as puzzling by interpreters. It is striking to see him concerned with that philosophical approach, generally regarded as foreign to the tradition of Russell and Frege, in which Wittgenstein’s thought is commonly taken to have primarily developed. On the basis of partially unpublished material from Wittgenstein’s Nachlass, the thesis provides a reconstruction of the rationale and fate of his conception (...) of phenomenology, which he advances after his return to Cambridge in 1929. On the one hand, that conception is tributary to his longstanding task to philosophically clarify the workings of language. On the other hand, Wittgenstein’s concern with phenomenology develops against the background of his reconsideration of the resources for clarification provided by his early philosophy. His 1929 paper “Some Remarks on Logical Form” is elucidatory in this respect. The paper expresses a dissatisfaction with the Tractarian account of logical grammar and pleas for a “logical investigation of the phenomena themselves”. That plea echoes Wittgenstein’s notion of a “phenomenological language” in the manuscripts from the same period. The thesis addresses the intricacies of that notion and the reasons for Wittgenstein’s coming to criticize it. By contrast to the prevalent view in the literature, it turns out that he did not fully endorse for a definite period, and then suddenly abandoned, the idea of phenomenological language. Wittgenstein rather attempts to develop a viable means of clarification and of philosophical expression through phenomenological language, while critically exploring the assumptions and implications of that attempt at the very same time. (shrink)

For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics grew from his Early and Middle philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.

Wittgenstein introduced his claim about colour incompatibility originally in the Tractatus Logico-Philosophicus , where he stated that there could be only one colour in one place and time. It is commonly believed that Wittgenstein abandoned his conception of logical atomism when he realized the consequences of this claim. The aim of this article is to provide an interpretation of the colour incompatibility claim in terms of Wittgenstein’s phenomenology. I will focus on two works of great significance for (...) the claim: Some Remarks on Logical Form and Philosophical Remarks . These two works were written between 1929 and 1930, which is the beginning of the “middle period” in Wittgenstein’s philosophy. I will focus not only on Wittgenstein’s formulation of the colour incompatibility claim, but also on how this claim was justified. The explanation of Wittgenstein’s justification of this claim will help to understand his phenomenology and theory of philosophical grammar. (shrink)

The idea of ‘committing oneself’ or ‘being committed’ by the use of language, or ‘linguistic commitment’, occurs in Wittgenstein’s notebooks and lectures from the end of 1930 together with remarks characteristic of this period, such as those on language as a system, and early reflections on other themes that would assume more importance in later years, such as rule-following and meaning as use. This paper examines the nature and contours of the concept of linguistic commitment (as well as some (...) cognate concepts),with a focus on the question why Wittgenstein temporarily insisted on the concept, but rapidly abandoned it. In doing so, I aim to shed light on some features of Wittgenstein’s middle period, both in their own right and in their relationship to later reflections. One aspect that will emerge is that, contrary to what is normally believed, pragmatic and even pragmatist themes began to play a role in his thought as early as 1930. (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)

The concept of intentionality — what Brentano called ‘the mind’s direction on its obj ects’ — has been a preoccupation of many of the most significant twentieth century philosophers. The purpose of this essay is to examine the place of the concept of intentionality in Wittgenstein’s later philosophy, and to criticize one aspect of his treatment of intentionality. Although the word ‘intentionality’ is not (to my knowledge) used in Wittgenstein’s philosophical writings, the idea it expresses was central at (...) all stages of his philosophical development. This should be obvious on a little reflection, not least because the philosophical notion of intentionality is closely related to the notion of meaning, and questions about meaning are, of course, central to both the T ractatus and Wittgenstein’s later work.‘ A full treatment of Wittgenstein’s views on meaning is not a task for a single essay. Instead, what I want to do here is to narrow the focus and discuss some specific claims in Wittgenstein’s middle and later work about the role of the notion of grammar in his attempts to solve (or dissolve) some quite specific problems of intentionality. In particular, I want to restrict myself to the discussion his later remarks about the relationship between expectation and fulfillment, and the.. (shrink)

This book collects 13 papers that explore Wittgenstein's philosophy throughout the different stages of his career. The author writes from the viewpoint of critical rationalism. The tone of his analysis is friendly and appreciative yet critical. Of these papers, seven are on the background to the philosophy of Wittgenstein. Five papers examine different aspects of it: one on the philosophy of young Wittgenstein, one on his transitional period, and the final three on the philosophy of mature (...) class='Hi'>Wittgenstein, chiefly his Philosophical Investigations. The last of these papers, which serves as the concluding chapter, concerns the analytical school of philosophy that grew chiefly under its influence. Wittgenstein’s posthumous Philosophical Investigations ignores formal languages while retaining the view of metaphysics as meaningless -- declaring that all languages are metaphysics-free. It was very popular in the middle of the twentieth century. Now it is passé. Wittgenstein had hoped to dissolve all philosophical disputes, yet he generated a new kind of dispute. His claim to have improved the philosophy of life is awkward just because he prevented philosophical discussion from the ability to achieve that: he cut the branch on which he was sitting. This, according to the author, is the most serious critique of Wittgenstein. (shrink)

This dissertation looks to make sense of the role 'grammar' plays in Wittgenstein's philosophy of mathematics during the middle period of his career. It constructs a formal model of Wittgenstein's notion of grammar as expressed in his writings of the early thirties, addresses the appropriateness of that model and then employs it to test Wittgenstein's claim that mathematical propositions are ultimately grammatical. ;In order to test Wittgenstein's claim that mathematical propositions are grammatical, the dissertation provides (...) a formalized theory of grammatical analysis and applies it to a portion of language big enough to contain numerical expressions. It attempts to prove that, if the object language contains the appropriate numerical expressions, the resulting grammar will include at least some rules with a natural mathematical interpretation. In particular, it tries to show that Wittgenstein's grammatical analysis of the ordinary use of numerical expressions yields familiar theorems of arithmetic. ;The dissertation also endeavors to extend these results to a coherent picture of Wittgenstein's peculiar view of mathematics as grammar. It fits the formal results into the larger picture of Wittgenstein's philosophy of mathematics during this period. A large portion of the dissertation explains how, by combining the notions of grammar and mathematics, Wittgenstein allowed himself to offer original answers to some central questions in the philosophy of mathematics. In this regard, the dissertation pays special attention to four main issues: Wittgenstein's use of the term 'grammar' in his philosophical writings of this period, in comparison with traditional understandings of 'grammar', mathematics as part of the syntax of language, his explanation of mathematical application, and Wittgenstein's account of mathematical necessity. Taking these points in consideration situates the dissertation's results in the larger philosophical discussion of these themes. (shrink)

According to Dummett's interpretation, one finds Wittgenstein denying the existence of a general linguistic action of “communicating something” at many places in the Investigations. In Wittgenstein's view, however, the author errs when (in philosophical contexts) he ignores the projective step and concludes from the meaningful applicability of the expression that he is speaking here of an “inner object of feeling” that should arouse the epistemological interest. The author proposes the middle passage of § 363, which is so (...) important for Dummett's interpretation: Wittgenstein certainly does not want to deny that linguistic actions do include speech acts of communicating something or informing. (shrink)

For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. (...) Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary. (shrink)

In this paper, I examine the transmission of some ideas of the pragmatist tradition to Wittgenstein, in his ‘middle period,’ through the intermediary of F. P. Ramsey, with whom he had numerous fruitful discussions at Cambridge in 1929. I argue more specifically that one must first come to terms with Ramsey’s own views in 1929, and explain how they differ from views expressed in earlier papers from 1925-27, so a large part of this paper is devoted to this (...) task. One is then in a better position to understand the impact of Ramsey’s astute critique of Wittgenstein’s Tractatus Logico-Philosophicus in conjunction with his pragmatism, and explain how it may have set into motion the ‘later’ Wittgenstein. I then argue that Ramsey introduced his notion of ‘variable hypothetical’ as a rule, not a proposition, on pragmatist grounds and that Wittgenstein picked this up in 1929, along with a more ‘dynamic’ view of meaning than the ‘static’ view of the Tractatus, and that this explains in part Wittgenstein’s turn to his ‘later philosophy.’. (shrink)

Wittgenstein frequently uses the word 'aspect' (Aspekt) in his writings from 1947 to 1949. There he uses the word along with aspect-seeing and aspect-change, so that readers are misled into thinking his primary concern in using the word is something like Gestalt psychology or philosophy of psychology per se. However, Wittgenstein's late treatment of aspect is only a special case of a more general problem, namely phenomenology. In the middle-period writings, the word 'aspect' refers to a phenomenological (...) object. Basically, Wittgenstein's aspect means the way an object appears to us. For him, an 'aspect' is a phenomenological object. (shrink)

Wittgenstein is accused by Dummett of radical conventionalism, the view that the necessity of any statement is a matter of express linguistic convention, i.e., a decision. This conventionalism is alleged to follow, in Wittgenstein's middle period, from his 'concept modification thesis', that a proof significantly changes the sense of the proposition it aims to prove. I argue for the assimilation of this thesis to Wittgenstein's 'no-conjecture thesis' concerning mathematical statements. Both flow from a strong verificationist view (...) of mathematics held by Wittgenstein in his middle period, and this also explains his views on the law of excluded middle and consistency. Strong verificationism is central to making sense of Wittgenstein's middle-period philosophy of mathematics. (shrink)

Wittgenstein's middle period work has been brought into the current debate on rule following and representation by Kripke and the Hintikkas. In my dissertation, I argue that approaches which aim at a consistent reconstruction of Wittgenstein's argument, while valuable in their own right, fail to do justice to his focus on the conflicting intuitions that lie behind philosophical theory building. For this hidden and ambiguous side to his thought is the turning point in his philosophical development. ;One (...) can summarise my findings as follows: In 1929, Wittgenstein recognised that the analysis of colour propositions forced him to give up the Tractarian doctrine that analysis must end in logically independent elementary propositions. From this point, his work branched out in two main directions. On the one hand, he worked on 'philosophical grammar': analyses of the rules we follow in talking about such matters as colour, visual experience, intention, time, memory and the philosophical subject. Here, the picture theory provided the basis for an account of how the mind represents the world. On the other hand, he also thought of language as a 'secondary' system, to be contrasted with direct apprehension of the 'primary' phenomena. This view, which is set out most fully in several chapters of an unpublished typescript , led to a seemingly inexpressible solipsism on which 'all is in flux.' The attempt to reconcile the two conceptions of the pictorial analogy--language as a system of representational conventions and experience as a direct presentation of the phenomena--ultimately led him to see the dangers in that analogy and thus to his later notion of a 'philosophical picture.'. (shrink)

I've been teaching Wittgenstein's On Certainty lately, and coming again to the question of Wittgenstein's relation to pragmatism.1 This is of course a question Wittgenstein raises himself when he writes in the middle of that work: 'So I am trying to say something that sounds like pragmatism'.2 He adds to this sentence the claim that 'Here I am being thwarted by a kind of Weltanschauung', but in the remarks to follow I want to focus not on (...) Wittgenstein's differences from or antipathy to pragmatism, nor on the world view that he felt thwarted him, but on those elements of his philosophy that sound like pragmatism-as he says. I will work primarily from On Certainty but also from the Philosophical Investigations, which intersects with that late, unfinished work at various places, and which also, at times, sounds like pragmatism. (shrink)

From 1929 through 1944, Wittgenstein endeavors to clarify mathematical meaningfulness by showing how (algorithmically decidable) mathematical propositions, which lack contingent "sense," have mathematical sense in contrast to all infinitistic "mathematical" expressions. In the middle period (1929-34), Wittgenstein adopts strong formalism and argues that mathematical calculi are formal inventions in which meaningfulness and "truth" are entirely intrasystemic and epistemological affairs. In his later period (1937-44), Wittgenstein resolves the conflict between his intermediate strong formalism and his criticism of (...) set theory by requiring that a mathematical calculus (vs. a "sign-game") must have an extrasystemic, real world application, thereby returning to the weak formalism of the Tractatus. (shrink)

It will be argued that Wittgenstein did not outright reject the law of excluded middle for mathematics or the proof-techniques that constructivists reject in connection with the law of excluded middle. Wittgenstein can be seen to be critical of the dogmatic claims of Brouwer and Weyl concerning how proofs should be constructed. Rather than himself laying down a requirement concerning what is and is not a proof, Wittgenstein can be read as exploring the differences between (...) constructive and non-constructive proofs. I will read Wittgenstein as arguing that Brouwer’s rejection of excluded middle is based upon an over-extension from examples that Wittgenstein reads as special cases. Wittgenstein is certainly interested in the difference between constructive and non-constructive proof but only for the purposes of exploring the easily-missed differences between the two, not in order to reject non-constructive approaches. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Wittgenstein, Tolstoy, and ShakespearePeter B. LewisNear the middle of the first of his 1938 Lectures on Aesthetics, Wittgenstein talks about what he calls "the tremendous things in art"(LC, I 23 8, italics in original).1 Apart from a brief indication of the way in which our response to the tremendous differs from the non-tremendous, he does not refer again in this way to the tremendous things in (...) art, though he does refer elsewhere to what he calls "supreme art." But he does provide a couple of examples of the tremendous in art, the symphonies of Beethoven and Gothic Cathedrals. Suppose, now, like the student in the Investigations §185, we are asked to continue the series. I take it that, even given the lack of information, we could safely propose, say, Homer—the Iliad and the Odyssey—and Michelangelo—the Sistine Chapel—as further examples of the tremendous things in art. The idea is that the tremendous things in art are not works that are just very good or very fine, but rather they are great, supremely great; works of stature; special cases; instances of the highest kind of artistic achievement, occupying a distinctive place in the history of (Western) civilization.Another obvious candidate for the list of the tremendous things in art would be Shakespeare, where the name is shorthand for the great plays, the tragedies in particular, Lear, Hamlet, Othello,and so on. So it comes as something of a surprise to discover on reading that miscellaneous compendium of remarks known as Culture and Value that Wittgenstein himself had serious doubts about including Shakespeare in the pantheon of the tremendous things in art. There are seven passages in Culture and Value in which Wittgenstein reflects on Shakespeare.2 The earliest is dated 1939–40, though this passage does not appear to be critical of Shakespeare. The next two passages are [End Page 241] dated August 1946, the remainder coming in 1949 and 1950. The remarks critical of Shakespeare are, then, all very much late Wittgenstein.It is well-known that lots of people dislike Shakespeare's plays. Generations of school children have developed indifference or boredom or hatred that persists throughout their lives. And yet that does not count against Shakespeare's greatness; for, to borrow Hume's remark on those who would prefer Ogilby to Milton, "no one pays attention to such a taste; and we pronounce without scruple the sentiment of these [people] to be absurd and ridiculous."3 That rhetoric is, however, not available, at least not immediately, when the "pretended critic" (Hume's phrase) has the intellectual clout and aesthetic sensibility of a Wittgenstein; nor, for that matter, the artistic achievement of a Tolstoy.I have particular grounds for bringing Tolstoy into this discussion. In the first place, there is the importance of Tolstoy in the development of Wittgenstein's thinking about religious, moral and aesthetic issues. Secondly, it is by contrast with Tolstoy's criticism of Shakespeare that we can gain further understanding of Wittgenstein's remarks on Shakespeare. These two points are related. For it seems to me that it is partly through his reflections on Tolstoy's theories about art that Wittgenstein is led into commenting upon Shakespeare.Tolstoy famously attacks Shakespeare in his pamphlet, "Shakespeare and the Drama,"4 published in 1903 when Tolstoy was seventy-five years of age. Some have taken this essay as evidence that Tolstoy was in his dotage, his mind warped by religious-moralistic fervor. Not only does this fail to do justice to Tolstoy's reasons for criticizing Shakespeare—reasons that Howard Mounce has recently argued are by no means ridiculous5 —it also neglects the fact that the essay is the culmination of Tolstoy's life-long antagonism to Shakespeare. Nevertheless, that very slur on Tolstoy's sanity attests to Shakespeare's status in our culture as something tremendous. His achievement is a standard against which others are measured. And this, I think, is at least partly what Wittgenstein is hinting at in his remarks about the contrast between the tremendous and the non-tremendous in art when he says of the tremendous that "it plays an entirely different role... (shrink)

In his early philosophy as well as in his middle period, Wittgenstein holds a purely syntactic view of logic and mathematics. However, his syntactic foundation of logic and mathematics is opposed to the axiomatic approach of modern mathematical logic. The object of Wittgenstein’s approach is not the representation of mathematical properties within a logical axiomatic system, but their representation by a symbolism that identifies the properties in question by its syntactic features. It rests on his distinction of (...) descriptions and operations; its aim is to reduce mathematics to operations. This paper illustrates Wittgenstein’s approach by examining his discussion of irrational numbers. (shrink)

David Bloor and Crispin Wright have argued, independently, that the proper lesson to draw from Wittgenstein's so-called rule-following considerations is the rejection of meaning Platonism. According to Platonism, the meaningfulness of a general term is constituted by its connection with an abstract entity, the (possibly) infinite extension of which is determined independently of our classificatory practices. Having rejected Platonism, both Bloor and Wright are driven to meaning finitism, the view that the question of whether a meaningful term correctly applies (...) to a given entity is not determined in advance of anyone's judgement about the matter. I argue that the two views do not form a dichotomy - there is room for a middle position which can account for the correct applications existing in advance of anyone's judgements without being committed to meaning Platonism. Furthermore, I will show how such a middle position arises quite naturally from the view that our competence with semantically basic terms is response-dependent. (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)

the ready availability of wittgenstein's previously unpublished writings from his so-called middle period of 1929 to 1936 has greatly enriched our understanding of the development of his thought. For obvious reasons, however, it has had little effect on the interpretation of Wittgenstein's contemporaries. At the time, few, even amongst those who had by then taken note of the Tractatus Logico-Philosophicus, were apprised of the new avenues Wittgenstein's thought had begun to take. One such rare exception was (...) Moritz Schlick, the nominal head of the Vienna Circle and an eminent philosopher of science. Even before Wittgenstein's return to... (shrink)

Resumo: o propósito desse artigo é circunscrever e discutir a autocrítica, feita por Wittgenstein no período de 1933-39, a uma das teses mais fundamentais do Tractatus (TLP): ”Há uma e apenas uma análise completa da proposição” (3.25). Chamaremos esse procedimento peculiar de a “Grande análise”. Os argumentos de Wittgenstein contra a sustentabilidade da sua antiga tese podem ser encontrados em algumas passagens do livro Investigações Filosóficas (IF), bem como em passagens do Grande Datiloscrito (BT). Conforme será argumentado nesse (...) artigo, essa autocrítica é uma consequência direta da preocupação de Wittgenstein, no período intermediário, com duas importantes propostas feitas por Frege nos §§18-24 do Os Fundamentos da Aritmética (FA) em relação o seu entendimento da noção de “atribuição numérica”. Nosso objetivo principal será mostrar de que maneira o movimento de autocrítica feito por Wittgenstein em relação a sua antiga concepção de “Grande Análise” teria sido influenciado por suas preocupações, no período intermediário de sua obra, com essas duas propostas feita por Frege no FA a respeito da noção de “atribuição numérica”. A fim de completar tal tarefa, será apresentada inicialmente de modo breve uma versão de como seria a “Grande análise” no TLP. Em seguida, selecionaremos e discutiremos algumas passagens do IF nas quais Wittgenstein recusa a completude e unicidade envolvida em sua prévia concepção tratariana de “análise”. Procuraremos destacar com clareza uma noção que estaria envolvida de um modo essencial na autocrítica de Wittgenstein: a noção de “ver como/ver aspectos”. Como será argumentado, essa noção, assim como a autocrítica feita por Wittgenstein, foram ambas diretamente influenciadas pela noção fregiana de “atribuição numérica”. Para completar essa segunda tarefa, teremos de revisitar e discutir algumas noções pertencentes ao período inicial da filosofia de Wittgenstein -- como a de “propriedades internas e externas” e a distinção entre “dizer e mostrar” -- ambas noções discutidas no TLP. No decorrer de nossa discussão, apresentaremos uma crítica feita por Wittgenstein a Russell, mas também a Frege, sobre a concepção de generalidade, ou mais especificamente, sobre o uso do quantificador existencial, proposta por ambos. Abstract: The purpose of this article is to discuss Wittgenstein 1933-39 self-criticism of one of the most fundamental tractarian theses: There is one and only one complete analysis of the proposition (3.25). Wittgenstein's arguments against his previous thesis can be found in some passages of the Philosophical Investigation (PI) as well as in the Big Typescript (BT). As we shall argue, Wittgenstein's self-critique is directly related to two important ideas proposed by Frege in §§18-24 of The Foundations Arithmetic (FA) with respect to his construal of “number attributions”. Our main goal in this paper will therefore be to show how Wittgenstein's self-criticism of his old conception of the tractarian “analysis” would have been influenced by his concerns in the middle period of his work with these two proposals made by Frege in FA regarding the notion of “numerical attribution”. Our first task will then be to connect Wittgenstein's self-criticisms to his former conception of “analysis” in the Tractatus Logico-Philosophicus (TLP). To accomplish this first goal, we will have to briefly present a version of how such analysis would look like in TLP. Our next task will be to pinpoint some passages of the PI in which Wittgenstein rejects the completeness and uniqueness involved in his previous construal of the analytical process. We will try to circumscribe clearly a crucial notion involved in Wittgenstein's self-critique: the idea of “seeing as/seeing aspects”. Our claim is that this notion, as well as Wittgenstein's self-criticism, were both directly influenced by Frege's construal of the “number attribution” presented in FA. To accomplish this second task, we will have to revisit and discuss some further concepts from an early period of Wittgenstein's philosophy, like “internal and internal properties” and the “saying/showing distinction” in TLP. On our way towards accomplishing this goal, we will present a curious complaint by Wittgenstein regarding Russell's, as well as Frege's conception of generality, or more specifically, on the usage of the existential quantifier suggested by both these authors. (shrink)

In his middle and later periods one of Wittgenstein’s concerns was perception. This is, of course, precisely what one would expect given his obvious interest then in the notion of experience and in the language we employ to describe and express our experiences. However, the passage which has attracted most attention is the discussion in sec. XI of part II of Philosophical Investigations which is concerned with “seeing as”, or “aspect seeing”. In this paper the examples that (...) class='Hi'>Wittgenstein uses are examined, and some puzzles about them raised. It is suggested that Wittgenstein’s aim is to discredit some supposedly mistaken accounts of what ‘seeing as’ is. These mistaken accounts are supposed to made by Gestalt psychologists such as Kohler, and traditional sense-datum theorists. It is further argued that Wittgenstein’s criticisms are not uniformly cogent. It is, though, conceded that this rich and original passage contains far more than the elements investigated here, so much more needs to be scrutinised. (shrink)

In his middle and later periods one of Wittgenstein’s concerns was perception. This is, of course, precisely what one would expect given his obvious interest then in the notion of experience and in the language we employ to describe and express our experiences. However, the passage which has attracted most attention is the discussion in sec. XI of part II of Philosophical Investigations which is concerned with “seeing as”, or “aspect seeing”. In this paper the examples that (...) class='Hi'>Wittgenstein uses are examined, and some puzzles about them raised. It is suggested that Wittgenstein’s aim is to discredit some supposedly mistaken accounts of what ‘seeing as’ is. These mistaken accounts are supposed to made by Gestalt psychologists such as Kohler, and traditional sense-datum theorists. It is further argued that Wittgenstein’s criticisms are not uniformly cogent. It is, though, conceded that this rich and original passage contains far more than the elements investigated here, so much more needs to be scrutinised. (shrink)

This chapter discusses some general features of Ludwig Wittgenstein's work, then gives an overview of his early writings, and finally surveys his philosophical activities after 1929. The evidence collected suggests that there is quite substantial continuity, but also one major turning point in Wittgenstein's way of handling philosophical questions. This turning point took place around 1931‐1932. Wittgenstein took great care of his manuscripts. To him philosophy was definitely not one of the sciences, but neither was it to (...) consist of “transcendental twaddle”. Coming from an engineering background, Wittgenstein entered philosophy through reading and meeting Frege and Russell around 1911. From a more philosophical perspective it is tempting to look for differences of doctrine. In this way one can distinguish, e.g., Wittgenstein's early logical atomism, his middle theoretical holism, and his late practical holism. His aim changed from deducing logical syntax to a description of the grammar of our language. (shrink)

I explore and outline Wittgenstein's original response to the Romantic discourse concerning musical depth, from his middle-period on. Schopenhauer and Spengler served as immediate sources for Wittgenstein's reliance on Romantic metaphors of depth concerning music. The onset for his philosophic intervention in the discourse was his critique of Schenker's view of music and his general shift toward the 'anthropological view', which occurred at the same time. In his post-PI period Wittgenstein was able to reimagine musical depth (...) in terms of vertically interrelated language-games which facilitate Menschenkenntnis. (shrink)

Much has been written on the relative merits of different readings of Wittgenstein's Tractatus Logico-Philosophicus. The recent renewal of the debate has almost exclusively been concerned with variants of the ineffabilist (metaphysical) reading of TL-P - notable such readings have been advanced by Elizabeth Anscombe, P. M. S. Hacker and H. O. Mounce - and the recently advanced variants of therapeutic (resolute) readings - notable advocates of which are James Conant, Cora Diamond, Juliet Floyd and Michael Kremer. During this (...) debate, there have been a number of writers who have tried to develop a third way, incorporating what they see as insights and avoiding what they see as flaws in both the ineffabilist and resolute readings. The most prominent advocates of these elucidatory readings of TL-P are Dan Hutto (2003) and Marie McGinn (1999). In this paper we subject Hutto's and McGinn's readings of TL-P to critical scrutiny. We find that in seeking to occupy the middle ground they ultimately find themselves committed to (and in the process commit Wittgenstein to) the very ineffabilism they (and Wittgenstein) are seeking to overcome. (shrink)

Wittgenstein composed five original musical fragments during his transitional middle period, in which he employs musical notation as a means by which to convey his philosophical thoughts. This is an overlooked aspect of the importance of aesthetics, and musical thinking in particular, in the development of Wittgenstein’s philosophy. We explain and evaluate the way the music interlinks with Wittgenstein’s philosophical thoughts. We show the direct relation of these musical examples as precursors to some of Wittgenstein’s (...) most celebrated ideas (the push beyond the inner/outer picture, the problem of rule-following, and aspect perception). We also show how important broad aesthetic notions such as style and composition concerning the very possibility of philosophizing were to Wittgenstein. (shrink)

The thesis according to which the meaning of a mathematical sentence is given by its proof was held by both Wittgenstein and the intuitionists, following Heyting and Dummett. In this paper, we clarify the meaning of this thesis for Wittgenstein, showing how his position differs from that of the intuitionists. We show how the thesis originates in his thoughts, from the middle period, about proofs by induction, and we sketch his answers to a number of objections, including (...) the idea that, given the particular meaning he gives to this thesis, he cannot account for mathematical conjectures. We conclude by showing how his views find a favourable echo today in the paradigm of “proposition-as-type” and extensions of the Curry-Howard isomorphism from which this paradigm originates. (shrink)

In this Element, the author set out to answer a twofold question concerning the importance of music to Wittgenstein's philosophical progression and the otherness of this sort of philosophical importance vis-à-vis philosophy of music as practiced today in the analytic tradition. The author starts with the idea of making music together and with Wittgenstein's master simile of language-as-music. The author traces these themes as they play out in Wittgenstein early, middle, and later periods. The author argues (...) that Wittgenstein's overarching reorientation of the concept of depth pertaining to music in the aftermath of his anthropological turn, and against the backdrop of the outlook of German Romanticism, culminates in his unique view of musical profundity 'knowledge of people'. This sets Wittgenstein's view in sharp contrast with certain convictions and debates that typify current analytically bent philosophy of music. (shrink)

In this paper, I present a summary of the philosophical relationship betweenWittgenstein and Brouwer, taking as my point of departure Brouwer's lecture onMarch 10, 1928 in Vienna. I argue that Wittgenstein having at that stage not doneserious philosophical work for years, if one is to understand the impact of thatlecture on him, it is better to compare its content with the remarks on logics andmathematics in the Tractactus. I thus show that Wittgenstein's position, in theTractactus, was already quite (...) close to Brouwer's and that the points of divergence are the basis to Wittgenstein's later criticisms of intuitionism. Among the topics of comparison are the role of intuition in mathematics, rule following, choice sequences, the Law of Excluded Middle, and the primacy of arithmetic over logic. (shrink)