Mathieu Marion

In this paper, we argue against Göran Sundholm’s claim that the Tractatus is the “finest exposition of realism in logic”. We do not directly criticize the basis of his reading, but try and put forward two aspects of the book that point in the other direction, antirealism. In both cases our arguments rely on later remarks which we claim only express ideas that were in nuce in the Tractatus. First, we claim that readings of the latter in terms of simple language–world relations should be replaced by a semiotic triad, and that the “method of projection” is the source of Wittgenstein’s later remarks on “verificationism”. Secondly, we present Wittgenstein’s explicitly antirealist account of arithmetical equations, for which no logical calculus applies. We conclude showing that this account brought Wittgenstein in 1929 closer to Brouwer’s “epistemic realism”, coupled with an “ontological idealism”, than Sundholm’s own standpoint, which is rather the coupling of “epistemic idealism” with “ontological Platonism”.

This volume brings into focus the unique philosophical and historical importance of Wittgenstein's pre-Tractatus writings. These contributed essays show that Wittgenstein’s earliest writings are worth studying for their own sake. They also reveal how much one can still learn about the Tractatus, if we are to study these early writings not as documenting one’s prior interpretation of the Tractatus, but as a series of steps in Wittgenstein’s thought, some down paths that are later abandoned, some leading towards it. The volume thus offers not only a fresh perspective on the pre-Tractatus writings, but also a comprehensive reading of a wide range of central topics from the very first letters, the “Notes on Logic”, the “Notes dictated to G.E. Moore” to the three surviving war-time notebooks.

We argue that the proper context for understanding Collingwood’s The Principles of Art is his claim that it has bearing “upon the condition of art in England in 1937”. We thus argue that he formulated a philosophical argument that underpins avant-garde dramatic poetry and theatrical practices (Eliot, Auden and the Group Theatre), taking his interpretation of Spinoza’s Ethics 5 prop. 3 to be the book’s central thesis: it is through art that one knows, against the ‘corruption of consciousness’, what emotions one feels and recognizes them as one’s own. Collingwood further believed that this could only be achieved through collaboration between the artist and the community, validating new theatrical practices involving interaction with the audience. We analyse these views in the context of England in 1937: in an era marked by the rise of Fascism and Nazism, Collingwood believed that art thus conceived could help restoring emotional support for the defense of liberal democracies. We conclude with an exploration of parallels with and divergences from the Spinozist idea of ‘mobilizing affects’ in contemporary ‘left populism’ (Mouffe).

In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in the context of dialectical games. One consequence of our approach is a novel explanation of the doctrine of the existential import of the quantifiers in dialectical terms. After a brief survey of Lorenzen's dialogical logic, we offer a set of rules for dialectical games based on previous work by Castelnérac and Marion, to which we add here the rule for the universal quantifier, as interpreted in terms of its counterpart in dialogical logic. We then give textual evidence of the use of that rule in Plato's dialogues, thus showing that Aris...

Friedrich Waismann (1896–1959) was one of the most gifted students and collaborators of Moritz Schlick. Accepted as a discussion partner by Wittgenstein from 1927 on, he functioned as spokesman for the latter’s ideas in the Schlick Circle, until Wittgenstein’s contact with this most faithful interpreter was broken off in 1935 and not renewed when exile took Waismann to Cambridge. Nonetheless, at Oxford, where he went in 1939, and eventually became Reader in Philosophy of Mathematics (changing later to Philosophy of Science), Waismann made important and independent contributions to analytic philosophy and philosophy of science (for example in relation to probability, causality and linguistic analysis). The full extent of these only became evident later when the larger (unpublished) part of his writings could be studied. His first posthumous work The Principles of Linguistic Philosophy (1965, 2nd edn.1997; German 1976) and his earlier Einführung in das mathematische Denken (1936) have recently proved of fresh interest to the scientific community. This late flowering and new understanding of Waismann’s position is connected with the fact that he somewhat unfairly fell under the shadow of Wittgenstein, his mentor and predecessor. Central to this book about a life and work familiar to few is unpublished and unknown works on causality and probability. These are commented on in this volume, which will also include a publication of new or previously scattered material and an overview of Waismann’s life.

Dans ce texte, je pars de l’analyse intuitionniste de la vérité mathématique, « A est vrai si et seulement s’il existe une preuve de A » comme cas particulier de l’analyse de la vérité en termes de « vérifacteur », et je montre pourquoi Wittgenstein partageait celle-ci avec les intuitionnistes. Cependant, la notion de preuve à l’oeuvre dans cette analyse est, selon l’intuitionnisme, celle de la « preuve-comme-objet », et je montre par la suite, en interprétant son argument sur le caractère « synoptique » des preuves, que Wittgenstein avait plutôt en tête une conception de la « preuve-comme-trace ».In this paper, I start with the intutionist analysis of mathematical truth, « A is true if and only if there exists a proof of A », as a particular case of the analysis of truth in terms of « truth-makers », and I show why Wittgenstein shared it with the intuitionists. However, the notion of proof at work in this analysis is, according to intuitionism, that of « proof-as-object », and I then show, with an interpretation of his argument on the « surveyability » of proofs, that, instead, Wittgenstein had in mind a notion of « proof-as-trace »

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.’

Après avoir présenté les grandes lignes de la réflexion phénoménologique de Wittgenstein en 1929 et son abandon de Vidée d'un langage phénoménologique, je montre qu'il fait face à un dilemme à propos de la notion de règle. Si on regarde l'expression symbolique d'une règle sous le mode physicaliste, on ne peut pas voir le lien entre celle-ci et ses applications. Comment peut-elle, de par elle-même, servir de guide à nos actions ? Il faut une intention, une interprétation, ce qui fait de la règle un objet phénoménologique. L'abandon du langage phénoménologique doit cependant forcer Wittgenstein à reconnaître qu'une règle en tant qu'objet phénoménologique ne peut pas être comparée à ou être utilisée pour déclencher une action qui se déroule dans le monde physique. Je montre que c'est en tentant de sortir de ce dilemme que Wittgenstein en viendra aux conceptions exposées dans ses remarques sur « suivre une règle ». J'examine en dernier lieu quelques conséquences de cette interprétation sur celle de la philosophie des mathématiques de Wittgenstein.After presenting a broad sketch of Wittgenstein's phenomenology; in 1929, and of his abandonment of the idea of a phenomenological language, it is shown that the notion of a rule left him with a dilemma, if the symbolical expression of a rule is understood in a physicalist mode, one cannot see the link between it and its applications. How could it, of itself guide our actions? One needs an intention or interpretation, thus turning the rule into a phenomeno/ogica I object. The abandonment ofthe p he nojne no logical language must have foiled Wittgenstein to recognize that a rule, qua phenomenological object, cannot be compared to or used to trigger an action in the physical world. It is then shown how Wittgenstein reached, while trying to solve this dilemma, the conception of rules presented in the remarks on 'following a rule". Lastly, some of the consequences of this new reading on the interpretation of Wittgenstein's philosophy of mathematics are examined

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

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.

Waismann’s writings can be divided into three periods. The fi rst corresponds to his early work in Vienna under the aegis of Schlick, thus mainly to his collaboration with Wittgenstein on the fi rst drafts of Logik, Sprache, Philosophie, out of which came not only the book itself many years later but also transcriptions of conversations with Schlick and Wittgenstein and numerous dictations reworked by Waismann, now published under the title The Voice of Wittgenstein. The Vienna Circle. Waismann also did at that stage independent work, albeit largely infl uenced by Wittgenstein, on probability and identity. The second period runs roughly from the moment relations with Wittgenstein were severed – towards the end of 1934 – to his arrival in Oxford, where he started lecturing in Michaelmas Term 1939

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.

É fácil mostrar que, no Tractatus, atribuições de cor não podem ser proposiçõeselementares. Mas já não é tão fácil determinar que tipo de análise poderia ser feita dejuízos de percepção do tipo “a é vermelho”. Wittgenstein nos dá uma indicação vaga noaforismo 6.3751. Ele pede que o leitor tenha em mente o modo pelo qual lidamos com aexclusão das cores no campo da física. Mesmo assim, é difícil determinar o que exatamenteele estava tentando dizer ali. Ofereço uma interpretação do aforismo que associa o problemada exclusão mútua das cores ao tratamento dado aos números e à noção de “sériede formas” (Formenreihe). Algumas passagens das Philosophische Bemerkungen são usadasem apoio a esta linha interpretativa.

Mathematics is one of the many domains where the adoption of a form of realism has traditionally been challenged. Behaviorism and phenomenalism, opposed to realism about, respectively, mental entities and the existence of material objects, are other well‐known examples. The realism debate, as initiated by Dummett's challenge, appears to have run its course, at least on its original terms, and difficulties have been raised with respect to both antirealist and anti‐antirealist readings of Wittgenstein within that debate. Realism about meaning did not remain unchallenged, however, as successor debates took its place, surrounding Robert Brandom's “inferentialism” or Price's generalized form of quasi‐realism, called “pragmatism”. Brandom also espouses “non‐representationalism” and predictably made use of Wittgenstein, with a reading akin to Kripke's of the rule‐following argument. He was criticized by McDowell largely for failing to account for Wittgenstein's quietism.