Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939

Author: Cora Diamond
Publisher: University of Chicago Press
ISBN: 022630860X
Category : Philosophy
Languages : en
Pages : 301

Book Description
For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939

Author: Ludwig Wittgenstein
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 314

Book Description

Wittgenstein's Tractatus

Author: Alfred Nordmann
Publisher: Cambridge University Press
ISBN: 9780521850865
Category : Mathematics
Languages : en
Pages : 256

Book Description
This introduction, first published in 2005, considers the philosophical and literary aspects of Wittgenstein's 'Tractatus' and shows how they are related.

Philosophical Remarks

Author: Ludwig Wittgenstein
Publisher: University of Chicago Press
ISBN: 0226904318
Category : Philosophy
Languages : en
Pages : 357

Book Description
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

Wittgenstein's Philosophy of Mathematics

Author: Pasquale Frascolla
Publisher: Routledge
ISBN: 1134974361
Category : Philosophy
Languages : en
Pages : 318

Book Description
Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the `community view of internal relations'.

The Cambridge Quintet

Author: J. L. Casti
Publisher:
ISBN: 9780316642811
Category : Artificial intelligence
Languages : en
Pages : 181

Book Description
By 1949, the idea of duplicating human thought processes in a computer was starting to surface, as the outgrowth of code-breaking work done by Alan Turing and others in Britain during the Second World War. This ingenious work of speculative scientific fiction reconstructs what might have been said during the animated conversation flowing around Snow's rooms that fateful in Cambridge. The quintet's debate anticipates all of the basic questions which have surrounded artificial intelligence in the fifty years since. Can a machine think or merely process information? Is the brain simply a symbol-processing machine, as Turing suggests, and if so, what is the nature of meaning? Can there be, as Wittgenstein proposes, no thought without language, and no language without the social interaction of human beings?

Wittgenstein on Mathematics

Author: Severin Schroeder
Publisher: Routledge
ISBN: 100031829X
Category : Philosophy
Languages : en
Pages : 200

Book Description
This book offers a detailed account and discussion of Ludwig Wittgenstein’s philosophy of mathematics. In Part I, the stage is set with a brief presentation of Frege’s logicist attempt to provide arithmetic with a foundation and Wittgenstein’s criticisms of it, followed by sketches of Wittgenstein’s early views of mathematics, in the Tractatus and in the early 1930s. Then (in Part II), Wittgenstein’s mature philosophy of mathematics (1937-44) is carefully presented and examined. Schroeder explains that it is based on two key ideas: the calculus view and the grammar view. On the one hand, mathematics is seen as a human activity — calculation — rather than a theory. On the other hand, the results of mathematical calculations serve as grammatical norms. The following chapters (on mathematics as grammar; rule-following; conventionalism; the empirical basis of mathematics; the role of proof) explore the tension between those two key ideas and suggest a way in which it can be resolved. Finally, there are chapters analysing and defending Wittgenstein’s provocative views on Hilbert’s Formalism and the quest for consistency proofs and on Gödel’s incompleteness theorems.

Wittgenstein's Whewell's Court Lectures

Author: Yorick Smythies
Publisher: John Wiley & Sons
ISBN: 1119166381
Category : Philosophy
Languages : en
Pages : 347

Book Description
Wittgenstein’s Whewell’s Court Lectures contains previously unpublished notes from lectures given by Ludwig Wittgenstein between 1938 and 1941. The volume offers new insight into the development of Wittgenstein’s thought and includes some of the finest examples of Wittgenstein’s lectures in regard to both content and reliability. Many notes in this text refer to lectures from which no other detailed notes survive, offering new contexts to Wittgenstein’s examples and metaphors, and providing a more thorough and systematic treatment of many topics Each set of notes is accompanied by an editorial introduction, a physical description and dating of the notes, and a summary of their relation to Wittgenstein’s Nachlass Offers new insight into the development of Wittgenstein’s ideas, in particular his ideas about certainty and concept-formation The lectures include more than 70 illustrations of blackboard drawings, which underline the importance of visual thought in Wittgenstein’s approach to philosophy Challenges the dating of some already published lecture notes, including the Lectures on Freedom of the Will and the Lectures on Religious Belief

Wittgenstein

Author: Ludwig Wittgenstein
Publisher: Univ of California Press
ISBN: 9780520013544
Category : Biography & Autobiography
Languages : en
Pages : 84

Book Description
In 1938 Wittgenstein delivered a short course of lectures on aesthetics to a small group of students at Cambridge. The present volume has been compiled from notes taken down at the time by three of the students: Rush Rhees, Yorick Smythies, and James Taylor. They have been supplemented by notes of conversations on Freud (to whom reference was made in the course on aesthetics) between Wittgenstein and Rush Rhees, and by notes of some lectures on religious belief. As very little is known of Wittgenstein's views on these subjects from his published works, these notes should be of considerable interest to students of contemporary philosophy. Further, their fresh and informal style should recommend Wittgenstein to those who find his Tractatus and Philosophical Investigations a little formidable.

Wittgenstein

Author: William Child
Publisher: Routledge
ISBN: 1136731369
Category : Philosophy
Languages : en
Pages : 359

Book Description
Ludwig Wittgenstein (1889-1951) is considered by most philosophers - even those who do not share his views - to be the most influential philosopher of the 20th century. His contributions to the philosophy of language, mind, meaning and psychology - as well as to logic, mathematics and epistemology - permanently altered the philosophical landscape, and his Tractatus Logico Philosophicus and Philosophical Investigations continue to be studied in philosophy departments around in the world. In this superb introduction and overview of Wittgenstein’s life and work, William Child discusses: Wittgenstein’s early work, Tractatus Logico-Philosophicus, including his account of language and thought Wittgenstein’s subsequent rejection of some of the central doctrines of the Tractatus Wittgenstein’s later philosophy intentionality and rule-following philosophy of mind and psychology in Philosophical Investigations knowledge and certainty, and Wittgenstein’s final work philosophy of religion the legacy and influence of Wittgenstein’s ideas in philosophy, and beyond. Including a chronology, glossary, and helpful conclusions to each chapter, Wittgenstein is essential reading for anyone coming to Wittgenstein's philosophy for the first time.