ABSTRACT I argue that some of the central doctrines of Wittgenstein's Tractatus Logico-Philosophicus can be seen as addressing the twin problems of semantic unity and...

Volume 2, Issue 3, September 2018, Page 343-354.

The main question addressed by this article is this: How should one understand the role of the sentences of the Tractatus, given Wittgenstein’s statement that they are nonsensical? I begin with a presentation of three general principles of interpretation in order to avoid answering the question in an inappropriate way. I then move on to a short presentation and commentary on a selection of readings – namely, the ineffabilist, resolute and elucidatory ones – and elaborate the answers given by advocates (...) of these to the question explored here. I agree on many points with resolute and elucidatory readings: the Tractatus presents an austere conception of nonsense, and is not a book that seeks to present ontological or semantic theories. I point out, however, that these readings cannot fully explain the nature of Tractarian elucidations. Then I discuss those parts of the Tractatus which refer to the sentences of the book itself. The main proposal of my own approach is this: Tractarian elucidations should be construed as rules of translation, in that they show how to substitute certain expressions for others. They enable us to construct a notation in which everything that is expressible in ordinary language can be said perspicuously. (shrink)

I propose to sketch my views on several aspects of the philosophy of mathematics that I take to be especially relevant to philosophy as a whole. The relevance of my discussion would, I think, become more evident, if the reader keeps in mind the function of (the philosophy of) mathematics in philosophy in providing us with more transparent aspects of general issues. I shall consider: (1) three familiar examples; (2) logic and our conceptual frame; (3) communal agreement and objective certainty; (...) (4) the transcommunal universality of mathematics; (5) the big jump to the potential infinite; (6) the reconciliation of local creation with the hypothesis of discovery; (7) Platonism as realism plus conceptualism; (8) foundational studies and mathematical practice; and (9) the decomposition of philosophical disagreements. The views of Gödel and Wittgenstein are emphasized in order to add specificity to the discussions. (shrink)

Physical and biological measurements might display range values extending towards infinite. The occurrence of infinity in equations, such as the black hole singularities, is a troublesome issue that causes many theories to break down when assessing extreme events. Different methods, such as re-normalization, have been proposed to avoid detrimental infinity. Here a novel technique is proposed, based on geometrical considerations and the Alexander Horned sphere, that permits to undermine infinity in physical and biophysical equations. In this unconventional approach, a continuous (...) monodimensional line becomes an assembly of countless bidimensional lines that superimpose in quantifiable knots and bifurcations. In other words, we may state that Achilles leaves the straight line and overtakes the turtle. (shrink)

Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem (...) and its proof. An attempt is made to meet directly some of Wittgenstein’s critical comments on the mathematical treatment of infinity and irrational numbers. (shrink)

Here, the logical behaviour of negation in Wittgenstein's Tractatus is compared with Demos' account of denial. Even if we hold negation as a pure syntactical device, at least in some context, it brings a handful of complex semantic information – potentially an infinite amount. We advocate then the existence of at least two negations due to the existence of two different and non-reducible types of exclusion. The first negation is a Tractarian and classical one, based on the notion of contradiction, (...) whereas the second is a non-classical negation, based on the notion of contrariety. (shrink)

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

Cet article poursuit un double but : d’une part, situer dans le parcours philosophique de Wittgenstein une partie de l’histoire du « problème du champ visuel », thème clé de sa période intermédiaire ; d’autre part, mettre en lumière sa critique de l’idée d’un champ visuel (et celle de l’idée d’un objet interne). Nous croyons que ses arguments sont nouveaux, pénétrants, et ainsi leur intérêt dépasse les limites d’un exposé purement exégétique.

This paper portrays the later Wittgenstein’s conception of contradictions and his therapeutic approach to them. I will focus on and give relevance to the Lectures on the Foundations of Mathematics, plus the Remarks on the Foundations of Mathematics. First, I will explain why Wittgenstein’s attitude towards contradictions is rooted in: a rejection of the debate about realism and anti-realism in mathematics; and Wittgenstein’s endorsement of logical pluralism. Then, I will explain Wittgenstein’s therapeutic approach towards contradictions, and why it means that (...) a contradiction is not a problem for logic and mathematics. Rather, contradictions are problematic when we do not know what to infer from them. Once a meaning is established through a new rule of inference, the contradiction becomes a usable expression like many others in our inferential apparatus. Thus, the apparent problem is dissolved. Finally, I will take three examples of dissolved contradictions from Wittgenstein to clarify further his notion. I will conclude considering why his position on contradictions led him to clash with Alan Turing, and whether the latter was convinced by the Wittgensteinian proposal. (shrink)

Cora Diamond has recently criticised as mere legend the interpretation of a quip of Ramsey's, contained in the epigraph below, which takes him to be objecting to or rejecting Wittgenstein's Tractarian distinction between saying and showing. Whilst I agree with Diamond's discussion of the legend, I argue that her interpretation of the quip has little evidential support, and runs foul of a criticism sometimes made against intuitionism. Rather than seeing Ramsey as making a claim about the nature of propositions, as (...) Diamond does, we should understand him as making a claim about the grammar of the logical connectives. Such a view coheres with the extant evidence of the nature of Wittgenstein's and Ramsey's 1929 philosophical encounters. It is also compatible with attributing to Ramsey a recognition of Wittgenstein's distinction and with denying that criticising it is the lesson of the quip. (shrink)

In 2003 I published a survey of Wittgenstein’s lectures in Public and Private Occasions. Much has been learned about his lectures since then. This paper revisits the earlier survey and provides additional material and corrections, which amount to over 25%. In case it is useful, I have provided interlinear pagination from the original publication.

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

Les Remarques philosophiques sont la première tentative de mettre en oeuvre le programme qui découle de l’échec du projet du Tractatus Logico-Philosophicus. Le noyau de ce programme est donné par l’abandon de l’analyse des nombres avancée dans le Tractatus. Wittgenstein se rend compte que les nombres doivent se trouver à la base même du langage, dans la structure des propositions élémentaires. En même temps, il se rend compte qu’il est impossible de fournir la logique sousjacente au langage avant d’avoir procédé (...) à l’analyse. Le projet d’une investigation logique des phénomènes s’imposait, donc, même après l’abandon de l’idée d’un langage phénoménologique. The Philosophical Remarks is a first attempt at pursuing the philosophical agenda determined by the failure of the Tractarian project. The central point of this agenda is the abandonment of the analysis of number that had been given in the Tractatus. Wittgenstein realizes that numbers should be brought back to the basis of language, as part of the structure of the elementary propositions themselves. At the same time, he realizes that it is impossible to give the logic underlying our language before the process of logical analysis is carried out. He undertakes the project of a logical investigation of phenomena even after giving up the idea of a phenomenological language. (shrink)

This paper argues that the problematic of rule following in Wittgenstein's Philosophical Investigations and Heidegger's analysis of anxiety in Being and Time have analogous structures. Working through these analogies helps our interpretation of both of these authors. Contrasting sceptical and anti-sceptical readings of Wittgenstein helps us to resolve an interpretive puzzle about what an authentic response to anxiety looks like for Heidegger. And considering the importance of anxiety to Heidegger's conception of authenticity allows us to locate in Wittgenstein's later philosophy (...) a covert appeal to something resembling Heideggerian authenticity. (shrink)

This article analyses in detail Wittgenstein’s ‘Cambridge period’ from his return to Cambridge in 1929 until his decease in 1951. Within the ‘Cambridge period’, scholars usually distinguish the ‘middle’ (1929–1936) and the ‘late’ (1936–1951) periods. The trigger point of Wittgenstein’s return to Cambridge and philosophy was his visit to Brouwer’s lecture on ‘Mathematics, Science, and Language’ in Vienna in March 1928. Dutch mathematician Brouwer influenced not only Wittgenstein’s ability to do philosophy again but also the development of some of his (...) ideas. Namely, for Brouwer, language was a natural development of the social history of human beings. With the help of his friends, F. P. Ramsey, J. M. Keynes, G. E. Moore, and B. Russell, in 1929 Wittgenstein returned to Cambridge. The author argues that this was the crucial turning point in his philosophy that led to the revision of some of his ideas. Wittgenstein returned from self-isolation in remote villages of Lower Austria to the intellectual academic environment, where he could discuss his ideas with intellectual interlocutors and receive their valuable remarks and comments. This article is organised in chronological order: it describes the very ‘early’ middle period of 1929–1935 involving the development of Wittgenstein’s ‘phenomenology’ and the origin of the ‘language-games’ concept in the Blue and Brown Books; 1935–1936 period of ‘romantic’ enthusiasm for Soviet Russia and a trip there; Wittgenstein’s life and work during the WWII-time; resign from teaching in Cambridge in 1947 to finally finish his Philosophical Investigations. The author suggests that the ‘romantic areal’ about the USSR was formed by Wittgenstein’s predilection for Russian poetry and literature of the nineteenth century, i.e., Tolstoy, Dostoevsky, and Pushkin. Analysing the development of Wittgenstein’s ideas on language in his Cambridge period, the author mentions the influence of N. Bakhtin and P. Sraffa. Also, the author touches upon the topic of the possibility of Marxism’s influence on Wittgenstein’s life and thought. (shrink)

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

This dissertation investigates the origin, intellectual development and use of a semantic variant of the idea of logical space found implicitly in Kant and explicitly in early Wittgenstein and van Fraassen. It elucidates the idea of logical space as the idea of images or pictures representative of reality organized into a logico-mathematical structure circumscribing a form of all possible worlds. Its main claim is that application of these images or pictures to reality is through a certain conception of self. The (...) first chapter presents a novel interpretation of Kant’s semantic theory of schemata in the Critique of Pure Reason, showing that a structure of the imagination induced by the transcendental self informs an implicit idea of logical space. The second chapter offers an intellectual history of the idea through developments in the organization of images introduced by Helmholtz and Hertz. The third chapter reveals early Wittgenstein’s idea of logical space to be his notion of the self, demonstrating how this serves to unify propositions of the Tractatus Logico-Philosophicus concerning solipsism, realism, ethics, aesthetics and mysticism with those pertaining to the picture theory of meaning. The fourth chapter provides a historical overview of the development of van Fraassen’s empiricism in relation to his adaptation of logical space, and evaluates his recent proposal in Scientific Representation: Paradoxes of Perspective that the problem of coordination in the semantic view of theories is dissolved through self-location in logical space. After identifying a number of problems this proposal creates for his empiricism, a brief suggestion is made about how van Fraassen might improve upon his conception of logical space, and how an empiricist view of scientific representation might be understood as a result. (shrink)

This thesis argues that Heidegger’s existential analytic of human existence challenges the traditional understanding of responsibility as lying in the power or mastery of the subject. In contrast to secondary literature that attempts to read Heidegger as showing that we take responsibility through some kind of self-determination or control, I argue that Heidegger’s account of our thrownness, and its first-personal manifestation in our attunement, contests such understandings and points to an account of responsibility that does not find its locus in (...) the power of the subject. In light of this, I argue that taking responsibility for our being-in-the-world should be understood as becoming attentive. By emphasizing the ‘movement’ of thrownness and the meaning of this as finding ourselves always already gripped by way of being attuned, my analysis demonstrates the pervasive power of that which is beyond the subject. I show that we must always already find ourselves submitted to particular possibilities and, more fundamentally, to the enigma of being Dasein. From this analysis, and via the work of Harry Frankfurt, I demonstrate how our thrownness speaks against seeing responsibility for our being-in-the-world in terms of choice, rational judgement, or wholeheartedness. A further analysis of anxiety, contrasting with accounts which read it as manifesting a privileged space for freedom and self-determination, emphasizes the revelation of the ‘I’ as essentially bound to what is beyond it. I then argue that a Heideggerian account of responsibility should be understood in terms of attention or attentiveness, a notion that is developed through phenomenological analysis, and in dialogue with the work of Iris Murdoch. Through the use of the examples of the film 'Locke' and the novel 'Disgrace', I propose that attentiveness, with its accent on that which is beyond the subject, is a more appropriate way of conceiving responsibility on a Heideggerian account. (shrink)

The "standard account" of Wittgenstein’s relations with the Vienna Circle is that the early Wittgenstein was a principal source and inspiration for the Circle’s positivistic and scientific philosophy, while the later Wittgenstein was deeply opposed to the logical empiricist project of articulating a "scientific conception of the world." However, this telegraphic summary is at best only half-true and at worst deeply misleading. For it prevents us appreciating the fluidity and protean character of their philosophical dialogue. In retrospectively attributing clear-cut positions (...) to Wittgenstein and his interlocutors, it is very easy to read back our current understanding of familiar distinctions into a time when those terms were used in a much more open-ended way. The paper aims to to provide a broader perspective on this debate, starting from the protagonists’ understanding of their respective positions. Too often, the programmatic statements about the nature of their work that are repeated in manifestoes, introductions, and elementary textbooks have occupied center stage in the subsequent secondary literature. Consequently, I focus on a detailed examination of a turning point in their relationship. That turning point is Wittgenstein's charge, in the summer of 1932, that a recently published paper of Carnap's, "Physicalistic Language as the Universal Language of Science", made such extensive and unacknowledged use of Wittgenstein's own ideas that Wittgenstein would, as he put it in a letter to Schlick, "soon be in a situation where my own work shall be considered merely as a reheated version or plagiarism of Carnap’s." While the leading parties in this dispute shared a basic commitment to the primacy of physicalistic language, and the view that all significant languages are translatable, there was a remarkable lack of mutual understanding between them, and deep disagreement about the nature of the doctrines they disputed. Three quarters of a century later, we are so much more conscious of the differences that separated them than the points on which they agreed that it takes an effort of historical reconstruction to appreciate why Wittgenstein once feared that his own work would be regarded as a pale shadow of Carnap’s. (shrink)

Review of the translation of Ludwig Wittgenstein book: Observações Filosóficas. São Paulo: Edições Loyola, 2005. Tradução (do inglês) por Adail Sobral e Maria Stela Gonçalves.

Questions about the possibility of thought as an activity directed to reality, are deeper than those concerning the possibility of knowledge. These deeper questions have found intuitive expression in the Agrippan Trilemma, particularly in the trope of arbitrary presupposition. This trope can be raised as a criticism of current varieties of hinge epistemology inspired by Wittgenstein, mainly by virtue of the fact that Wittgensteinian hinges are foundational principles governing our epistemic practice. As such, they are necessarily unsupportable, being thus dificult (...) to see how it would be possible to conciliate the hinges’ lack of support with their being not bare, arbitrary assertions. Facing up to this challenge, hinge epistemologists have proposed practical --though not pragmatic-- arguments according to which hinges are either postulates legitimately demanded to every epistemic agent or rules constitutive of quotidian practices. It is the aim of this article to show that practical arguments for hinges fall short, necessarily so. (shrink)