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.

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.

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.

Wittgenstein est mort en 1951 et on attend toujours une édition de ses œuvres complètes. Ce n'est qu'en 1994 que sont parus, accompagnés d'un volume d'introduction à l'ensemble du projet d'édition de la main du directeur de publication, Michael Nedo, les deux premiers d'une série de quinze volumes, les Wiener Ausgabe, qui reproduiront l'intégralité des écrits de Wittgenstein, de son retour à Cambridge en janvier 1929 à la première version du Big Typescript en 1933, avec index et concordances. D'après le catalogue établi par Georg Henrik von Wright, il s'agit des articles suivants: MS 105 à 114 et 153 à 155, TS 208 à 218. Ces deux premiers volumes reproduisent les manuscrits écrits entre janvier ou février 1929 et l'été 1930, soit les MS 105, 106, 107 et 108. Ils constituent l'aboutissement d'une véritable saga entourant l'œuvre posthume de Wittgenstein, dont il vaut la peine de rapporter ici quelques-uns des faits marquants.

The relation between logic and knowledge has been at the heart of a lively debate since the 1960s. On the one hand, the epistemic approaches based their formal arguments in the mathematics of Brouwer and intuitionistic logic. Following Michael Dummett, they started to call themselves `antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to unify both traditions by means of what is now known as `explicit epistemic logic'. Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference. The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume believe that in the age of Alternative Logics, where manifold developments in logic happen at a breathtaking pace, this debate should be revisited. Contributors to this volume happily took on this challenge and responded with new approaches to the debate from both the explicit and the implicit epistemic point of view.