In his “The Foundations of Mathematics”, Ramsey attempted to marry the Tractarian idea that all logical truths are tautologies and vice versa, and the logicism of the Principia. In order to complete his project, Ramsey was forced to introduce propositional functions in extension (PFEs): given Ramsey's definitions of 1 and 2, without PFEs even the quantifier-free arithmetical truth that 1 ≠ 2 is not a tautology. However, a number of commentators have argued that the notion of PFEs is incoherent. This (...) response was first given by Wittgenstein but has been best developed by Sullivan. While I agree with Wittgenstein and Sullivan's common conclusion, I believe that even the most compelling of Sullivan's arguments is importantly mistaken and that Wittgenstein's remarks are too opaque to be left as the end of the matter. In this article I uncover the fault in Sullivan's argument and present an alternative criticism of PFEs which is Wittgensteinian in spirit without being too mystifying. (shrink)

When in May 1930, the Council of Trinity College, Cambridge, had to decide whether to renew Wittgenstein's research grant, it turned to Bertrand Russell for an assessment of the work Wittgenstein had been doing over the past year. His verdict: "The theories contained in this new work . . . are novel, very original and indubitably important. Whether they are true, I do not know. As a logician who likes simplicity, I should like to think that they are not, but (...) from what I have read of them I am quite sure that he ought to have an opportunity to work them out, since, when completed, they may easily prove to constitute a whole new philosophy." "[ Philosophical Remarks ] contains the seeds of Wittgenstein's later philosophy of mind and of mathematics. Principally, he here discusses the role of indispensable in language, criticizing Russell's The Analysis of Mind . He modifies the Tractatus 's picture theory of meaning by stressing that the connection between the proposition and reality is not found in the picture itself. He analyzes generality in and out of mathematics, and the notions of proof and experiment. He formulates a pain/private-language argument and discusses both behaviorism and the verifiability principle. The work is difficult but important, and it belongs in every philosophy collection."--Robert Hoffman, Philosophy "Any serious student of Wittgenstein's work will want to study his Philosophical Remarks as a transitional book between his two great masterpieces. The Remarks is thus indispensible for anyone who seeks a complete understanding of Wittgenstein's philosophy."--Leonard Linsky, American Philosophical Association. (shrink)

Long awaited by the scholarly community, Wittgenstein's so-called Big Typescript (von Wright Catalog # TS 213) is presented here in an en face English–German scholar’s edition. Presents scholar’s edition of important material from 1933, Wittgenstein’s first efforts to set out his new thoughts after the publication of the Tractatus Logico Philosophicus. Includes indications to help the reader identify Wittgenstein’s numerous corrections, additions, deletions, alternative words and phrasings, suggestions for moves within the text, and marginal comments.

This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Understanding Wittgenstein's Tractatus provides an accessible and yet novel discussion of all the major themes of the Tractatus. The book starts by setting out the history and structure of the Tractatus. It then investigates the two main dimensions of the early Wittgenstein's thought, corresponding to the division between what language can say by means of its propositions and what language can only show. It goes on to discuss picture theory, logical atomism, extensionality, truth-functions and truth-operations, semantics, metalogic and mathematics, solipsism (...) and value, metaphysics, and finally, Wittgenstein's idea of the duty of maintaining silence. Frascolla also proposes a new interpretation of the ontology of the Tractatus. Based on the identification of objects with qualia, the argument put forward in the book challenges the currently prevalent ideas of the ‘New Wittgenstein'. The paradoxical nature of the Tractatus itself, and the theme of "throwing away the ladder", are thus revisited in a new key. _Understanding Wittgenstein's Tractatus_ is essential reading for anyone wishing to further their insight into one of the most influential works of twentieth-century philosophy. (shrink)

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.

Reuben Louis Goodstein (1912-1985) foi aluno de Wittgenstein em Cambridge de1931 a 1934. Neste artigo, faço uma breve descrição de seu trabalho na lógica matemática,no qual se percebe a influência das idéias de Wittgenstein, inclusive a substituição,em seu cálculo equacional, da indução matemática por uma regra de unicidade de umafunção definida por uma função recursiva. Esse último aspecto se encontra no Big Typescriptde Wittgenstein. Também mostro que as idéias fundamentais do cálculo equacionalpodem ser encontradas não apenas no período intermediário, mas, (...) in nuce, nas observaçõessobre matemática do Tractatus Logico-philosophicus. A partir disso, procuro desenvolverum argumento contra uma leitura corrente daquele livro, o assim chamado “NovoWittgenstein”. Outra conexão entre Goodstein e Wittgenstein se encontra na rejeição dateoria da quantificação; na parte final do artigo, recorro às observações críticas de Goodsteinsobre a Lei do Terceiro Excluído (que também incluem uma crítica a Brouwer e à suarejeição “pela metade” dessa lei) para lançar luz sobre as observações do próprioWittgenstein a esse respeito. (shrink)

Wittgenstein's Tractatus has generated many interpretations since its publication in 1921, but over the years a consensus has developed concerning its criticisms of Russell's philosophy. In Wittgenstein's Apprenticeship with Russell, Gregory Landini draws extensively from his work on Russell's unpublished manuscripts to show that the consensus characterises Russell with positions he did not hold. Using a careful analysis of Wittgenstein's writings he traces the 'Doctrine of Showing' and the 'fundamental idea' of the Tractatus to Russell's logical atomist research program, which (...) dissolves philosophical problems by employing variables with structure. He argues that Russell and his apprentice Wittgenstein were allies in a research program that makes logical analysis and reconstruction the essence of philosophy. His sharp and controversial study will be essential reading for all who are interested in this rich period in the history of analytic philosophy. (shrink)