The paper presents an interpretation of the thinking behind the early Wittgenstein's "general form of the proposition." It argues that a central role is played by the assumption that all domains of discourse are governed by the same laws of logic. The interpretation is presented partly through a comparison with ideas presented recently by Michael Potter and Peter Sullivan; the paper argues that the above assumption explains more of the key characteristics of the "general form of the proposition" than Potter (...) and Sullivan suppose, including, in particular, its claim that the bases from which all other propositions are derived must be elementary propositions. (shrink)

The early Schlick developed an evolutionary biological account of play. He contrasted play with work. Where work encompasses all activity that is undertaken for the sake of some practical outcome, play renders what was previously a mere means into an end enjoyable in itself. Schlick thus distinguished between aesthetic, religious, scientific, and ethical game types. This paper shows that this typology underlies his later attempts to naturalize these fields, and allows us to clarify the relation between object-games and their description (...) within the scientific game. Schlick's demarcation between aesthetic and scientific games arguably prefigures the Vienna Circle's anti-metaphysical stance. (shrink)

This book attempts to explicate and expand upon Frank Ramsey's notion of the realistic spirit. In so doing, it provides a systematic reading of his work, and demonstrates the extent of Ramsey's genius as evinced by both his responses to the Tractatus Logico-Philosophicus , and the impact he had on Wittgenstein's later philosophical insights.

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...

Philosophical Investigations, Volume 45, Issue 3, Page 320-333, July 2022.

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)

In conversations with Schlick and Waismann from June and December 1930, Wittgenstein began to turn his attention to the topic of games. This topic also centrally concerned Schlick. In his earliest philosophical output, Schlick had relied on the results of evolutionary biology in setting out an account of the emergence of the human species’ ability to play [Spiel] as a prerequisite for the genesis of scientific knowledge. Throughout his subsequent works one finds fragmentary appeals to this early view, e.g. in (...) his oft misunderstood claim that play constitutes the meaning of life. Wittgenstein’s turn to the topic of games in 1930 not only happened while Professor Schlick was in the room, but was also coupled with an explicit response to Schlick’s 1930 book Fragen der Ethik. Schlick here employs the example of chess to distinguish between rules and their application – a distinction which underlies his whole attempt to naturalise ethics as a descriptive psycho-sociological discipline. This paper investigates the relation between Wittgenstein’s and Schlick’s accounts of games in light of Wittgenstein’s criticisms of Schlick’s ethics. Wittgenstein’s objections can be answered by taking Schlick’s theory of play into consideration. (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)

pour l'autre en nous et parmi nousAn apologia seeks to cover up the revolutionary moments in the course of history. The establishment of continuity is dear to its heart. It only gives importance to those elements of a work that have already generated an after-effect. It misses those points at which the transmission breaks down and thus misses those jags and crags that offer a handhold to someone who wishes to move beyond them.I am all the same convinced that these (...) notes [in Culture and Value] can be properly understood and appreciated only against the background of Wittgenstein’ s philosophy and, furthermore, that they make a contribution to our understanding of that philosophy. (shrink)

Dans cet article, j’essaie de montrer que le dépassement et le rejet du dogmatisme sont un aspect décisif du changement dans la pensée de Wittgenstein qui a eu lieu au début des années 30, quand il commence à mettre en valeur l’autonomie de la grammaire du langage et à parler d’images grammaticales et de jeux de langage en tant qu’objets de comparaison. En examinant certains traits fondamentaux de ce changement, je mettrai en évidence l’impulsion et les idées décisives que Wittgenstein (...) a reçues des nouveaux développements dans les mathématiques et la science naturelle du début du 20e siècle.It will be argued that the overcoming and avoiding of dogmatism is a decisive feature of the change in Wittgenstein’s thinking that takes place in the beginning of the 1930’s when he starts to emphasise the autonomy of the grammar of language and to talk about grammatical pictures and language games as objects of comparison. By examining certain crucial features in this change in Wittgenstein’s thinking, it will be shown that he received decisive impulses and ideas from new developments in mathematics and natural science in the early 20th century. (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)

Does it follow from Wittgenstein's views about indeterminism that irregularities of nature could take place? Did he believe that chairs could simply disappear and reappear, that water could behave differently than it has, and that a man throwing a fair die might throw ones for a week? Or are these things only imaginable? Is his view simply that if we adopted an indeterministic point of view we would no longer look for causes, or would not always look for causes, because (...) we would no longer assume that there must be a cause of each event? (shrink)

Contrary to a widespread interpretation, Wittgenstein did not regard credal statements as merely metaphorical expressions of an attitude towards life. He accepted that Christian faith involves belief in God's existence. At the same time he held that although as a hypothesis, God's existence is extremely implausible, Christian faith is not unreasonable. Is that a consistent view? According to Wittgenstein, religious faith should not be seen as a hypothesis, based on evidence, but as grounded in a proto‐religious attitude, a way of (...) experiencing the world or certain aspects of it. A belief in religious metaphysics is not the basis of one's faith, but a mere epiphenomenon. Given further that religious doctrine is both falsification‐transcendent and that religious faith is likely to have beneficial psychological effects, religious doctrine can be exempt from ordinary standards of epistemic support. An unsupported religious belief need not be unreasonable. However, it is hard to see how one could knowingly have such an unsupported belief, as Wittgenstein seems to envisage. How can one believe what, at the same time, one believes is not likely to be true? This, I argue, is the unresolved tension in Wittgenstein's philosophy of religion. (shrink)

In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse (...) different evaluative standards for theories. We evaluate the distinction between pure and applied mathematics from a late Wittgensteinian perspective. We note that the classical exegesis of the later Wittgenstein’s philosophy of mathematics, due to Maddy, leads to a clear-cut but misguided demarcation. We then turn our attention to a more niche interpretation of Wittgenstein by Dawson, which captures aspects of the aforementioned distinction more accurately. Building on this newer, maverick interpretation of the later Wittgenstein’s philosophy of mathematics, and endorsing an extended notion of meaning as use which includes social, mundane uses, we elaborate a fuzzy, but more realistic, demarcation. This demarcation, relying on family resemblance, is based on how direct and intended technical applications are, the kind of evaluative standards featured, and the range of rhetorical purposes at stake. (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.

En el prefacio al Tractatus, Wittgenstein establece que la cuestión del sinsentido tiene que ver con trazar los límites del lenguaje. Las expresiones sinsentido van más allá de los límites del lenguaje significativo y residen “del otro lado” de lo que puede ser dicho. Aún así, al final del libro declara que sus propias proposiciones son, hablando de manera estricta, sinsentidos. El presente trabajo pretende analizar la estrategia de auto-refutación del primer Wittgenstein como un modo de trascender los límites del (...) lenguaje, comparando su concepto de “sinsentido” con la visión de Kierkegaard acerca de la comunicación indirecta y de la ironía socrática. (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 his Tractatus, Wittgenstein maintained that arithmetic consists of equations arrived at by the practice of calculating outcomes of operations$\Omega ^{n}(\bar {\xi })$defined with the help of numeral exponents. Since$Num$(x) and quantification over numbers seem ill-formed, Ramsey wrote that the approach is faced with “insuperable difficulties.” This paper takes Wittgenstein to have assumed that his audience would have an understanding of the implicit general rules governing his operations. By employing the Tractarian logicist interpretation that theN-operator$N(\bar {\xi })$and recursively defined arithmetic (...) operators$\Omega ^{n}(\bar {\xi })$are not different in kind, we can address Ramsey’s problem. Moreover, we can take important steps toward better understanding how Wittgenstein might have imagined emulating proof by mathematical induction. (shrink)

Ayer’s Language, Truth and Logic (1936) was immediately regarded as a clear and faithful presentation of the views of the Vienna Circle to English-speaking readers. Since Ayer wrote this book after his visit to Vienna, where he participated in the meetings of the Circle, one may often hear to this day that he brought logical positivism to England. However, while Ayer’s conception was a form of logical positivism, it significantly differed from its Viennese counterpart(s). The key discrepancies are related to (...) verificationism: this article aims to analyse these discrepancies. It will be claimed that upon his return from Vienna Ayer assumed positions that were no longer, or had never been, held in the Circle: regarding the verification principle, test-statements, phenomenalist reductionism and analyticity. (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.

The paper undertakes an in-depth analysis of the early phase of Ludwig Wittgenstein’s writings in Notebooks, Tractatus Logico Philosophicus and “A Lecture on Ethics” in order to present an exposition of some of the central themes, and to extrapolate his views on ethics. To this end, the paper analyses Wittgenstein’s understanding of the nature of philosophical inquiry, significance and centrality of ethics, the model of language, saying/showing distinction, notions of will, happiness, good and evil, use of relative and absolute values (...) and several others. Early Wittgenstein’s views on ethics are peculiar in so far as they are implied by his views on language with the study of which he was centrally concerned. He claims that language, thought and reality are isomorphic; therefore, language is the basis of all speculation about morality. In TLP, Ethics is transcendental and transgresses the limits of language. The paper begins with a discussion of the importance of ethics, as explicated in his early writings. (shrink)

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)

The paper analyzes the ontological meaning of mood in Heidegger’s conception of Attunement, in order to relate this notion of Stimmung specifically to our “attunement” to a form of life, as conceived in Wittgenstein’s philosophy of language. It claims that moods spell out the constitutive impossibility to grasp and found the human experience as such. However, this impossibility is not a lack of human knowledge, but rather corresponds to the necessary opacity, indeterminability and groundlessness of every human experience, which make (...) it possible as such. The paper argues that the ontological mood of anxiety in Heidegger’s thought cannot be understood as a dark feeling, since it points to a constitutive sense of disorientation, which involves the impossibility to found and ensure the very familiarity of our ordinary experience. Moreover, the paper claims that the same impossibility is also involved in our “attunement” to language and to a form of life, as described by Wittgenstein in his Philosophical Investigations. By analyzing the mood of trust sketched out by Wittgenstein in On Certainty, the paper suggests that the ontological mood of trust, as the groundless certainty of our praxis, points to the very impossibility to found and ensure every human experience. From this perspective, moods reveal the groundlessness of human experience and make us acknowledge it. (shrink)

Philosophical Investigations, Volume 44, Issue 4, Page 403-425, October 2021.

An investigation of the concept of “surveyability” as traced through the thought of Hilbert, Wittgenstein, and Turing. The communicability and reproducibility of proof, with certainty, are seen as earmarked by the “surveyability” of symbols, sequences, and structures of proof in all these thinkers. Hilbert initiated the idea within his metamathematics, Wittgenstein took up a kind of game formalism in the 1920s and early 1930s in response. Turing carried Hilbert’s conception of the “surveyability” of proof in metamathematics through into his analysis (...) of what a formal system (what a step in a computation) is in “On computable numbers, with an application to the Entscheidungsproblem” (1936). Wittgenstein’s 1939 investigations of the significance of surveyability to the concept of “proof “in Principia Mathematica were influenced, both by Turing’s remarkable everyday analysis of the Hilbertian idea, and by conversations with Turing. Although Turing does not use the word “surveyability” explicitly, it is clear that the Hilbertian idea plays a recurrent role in his work, refracted through his engagement with Wittgenstein’s idea of a “language-game”. This is evinced in some of his later writings, where the “reform” of mathematical notation for the sake of human surveyability (1944/45) may be seen to draw out the Hilbertian idea. For Turing, as for Wittgenstein, the need for “surveyability” earmarks the evolving culture of humans located in an evolving social and scientific world, just as it had for Hilbert. (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 offers a Marxist reading of Wittgenstein and juxtaposes his famous dictum that philosophy ‘leaves everything as it is’ with the idea of transformative action. I seek to align the later philosophy of Wittgenstein with Marx’s 11th thesis on Feuerbach. I advance an unorthodox view interpreting Wittgenstein as an advocate for social and political reform. Wittgenstein’s philosophy encourages us to imagine alternatives and contemplate concrete possibilities for changing the world. The debate operates within the philosophy of education and draws (...) inspiration from related inquiries in political thought and, more specifically, from Marxist connections with Wittgenstein. (shrink)

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

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

ABSTRACT: This article explores Wittgenstein's little known remarks on colour from his notebooks of the early 1930s. It emphasizes the importance of the notion of logical multiplicity contained in these remarks. The notion of logical multiplicity indicates that Wittgenstein, as in the years of the Tractatus, is committed to a theory of logical space in which every colour is embedded. However, logical multiplicities in his remarks of the early 1930s do not depend on an apparatus of simple objects, states of (...) affairs, and elementary propositions. I suggest that, in this period, the logical multiplicity of colour space is a matter of how we see colours.RÉSUMÉ: Cet article examine les remarques trap peu connues de Wittgenstein sur les couleurs dans ses cahiers du début des années 1930. Je souligne l'importance qu'y prend la notion de multiplicité logique, qui est le signe que Wittgenstein souscrivait alors, tout autant que dans les années du Tractatus, à une théorie de l'espace logique propre à chaque couleur. Dans ces remarques du début des années 1930, les multiplicités logiques ne dépendent toutefois pas du dispositif conceptuel constitué par les objets simples, les états de choses et les propositions élémentaires. Mon propos est de montrer que, dans cétte periode, la multiplicité logique de l'espace chromatique est relative à la manière dont nous voyons les couleurs. (shrink)

I demonstrate that analogies, both explicit and implicit, between Wittgenstein’s discussions of rituals, aesthetics, and aspect-perception, have important payoffs in terms of understanding his notion of a “surveyable representation” (übersichtliche Darstellung) as it applies to phenomena that are not exclusively grammatical in nature. In particular, I argue that a surveyable representation of certain anthropological and aesthetic facts allows us to see, qua form of aspect-perception, internal relations and formal connections, so that the inner nature of a ritual or the solution (...) of an aesthetic puzzle is exhibited. This particular form of seeing both explains why Wittgenstein thought that hypothetical explanations about the origins of a ritual are irrelevant to appreciating its meaning and elucidates his understanding of rituals, which involves seeing “internal relations” and “formal connections.” The upshots of the account for work in anthropology are discussed. (shrink)

External obstacles to properly understanding Wittgenstein’s philosophy of mathematics are not lacking, either. For one thing, there is the piecemeal way that his mathematical manuscripts have been made available. The editors of Remarks on the Foundations of Mathematics write that “the time has not yet come to print the whole of Wittgenstein’s MSS on these... topics”. One wonders what sorts of reasons there could be for that editorial choice.

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)

Wittgenstein did not write very much on the topic of probability. The little we have comes from a few short pages of the Tractatus, some 'remarks' from the 1930s, and the informal conversations which went on during that decade with the Vienna Circle. Nevertheless, Wittgenstein's views were highly influential in the later development of the logical theory of probability. This paper will attempt to clarify and defend Wittgenstein's conception of probability against some oft-cited criticisms that stem from a misunderstanding of (...) his views. Max Black, for instance, criticises Wittgenstein for formulating a theory of probability that is capable of being used only against the backdrop of the ideal language of the Tractatus. I argue that on the contrary, by appealing to the 'hypothetical laws of nature', Wittgenstein is able to make sense of probability statements involving propositions that have not been completely analysed. G.H. von Wright criticises Wittgenstein's characterisation of these very hypothetical laws. He argues that by introducing them Wittgenstein makes what is distinctive about his theory superfluous, for the hypothetical laws are directly inspired by statistical observations and hence these observations indirectly determine the mechanism by which the logical theory of probability operates. I argue that this is not the case at all, and that while statistical observations play a part in the formation of the hypothetical laws, these observations are only necessary, but not sufficient conditions for the introduction of these hypotheses. (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.