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

Author: Ludwig Wittgenstein

Publisher: University of Chicago Press

ISBN: 022630860X

Category: Philosophy

Page: 300

View: 5614

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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,R. G. Bosanquet,Cora Diamond

Publisher: University of Chicago Press

ISBN: 9780226904269

Category: Mathematics

Page: 300

View: 3766

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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, Finitism, and the Foundations of Mathematics

Author: Mathieu Marion

Publisher: Oxford University Press

ISBN: 9780198235163

Category: Mathematics

Page: 260

View: 5542

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Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking from the 1920s through to the 1950s, in the context of themathematical 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. He shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy,and also that it can do much to illuminate current debates about the foundations of mathematics.

Lecture on Ethics

Author: Ludwig Wittgenstein

Publisher: John Wiley & Sons

ISBN: 1118887131

Category: Philosophy

Page: 152

View: 2428

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The most complete edition yet published of Wittgenstein’s 1929 lecture includes a never-before published first draft and makes fresh claims for its significance in Wittgenstein’s oeuvre. The first available print publication of all known drafts of Wittgenstein’s Lecture on Ethics Includes a previously unrecognized first draft of the lecture and new transcriptions of all drafts Transcriptions preserve the philosopher’s emendations thus showing the development of the ideas in the lecture Proposes a different draft as the version read by Wittgenstein in his 1929 lecture Includes introductory essays on the origins of the material and on its meaning, content, and importance

Ludwig Wittgenstein

The Duty of Genius

Author: Ray Monk

Publisher: Random House

ISBN: 1448112672

Category: Biography & Autobiography

Page: 704

View: 9156

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'Monk's energetic enterprise is remarkable for the interweaving of the philosophical and the emotional aspects of Wittgenstein's life' Sunday Times 'Ray Monk's reconnection of Wittgenstein's philosophy with his life triumphantly carries out the Wittgensteinian task of "changing the aspect" of Wittgenstein's work, getting us to see it in a new way' Sunday Telegraph 'This biography transforms Wittgenstein into a human being' Independent on Sunday 'It is much to be recommended' Observer 'Monk's biography is deeply intelligent, generous to the ordinary reader... It is a beautiful portrait of a beautiful life' Guardian

Seeing Wittgenstein Anew

Author: William Day,Victor J. Krebs

Publisher: Cambridge University Press

ISBN: 0521838436

Category: Language Arts & Disciplines

Page: 393

View: 8768

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Seeing Wittgenstein Anew is a collection which examines Ludwig Wittgenstein's remarks on the concept of aspect-seeing, showing that it was not simply one more topic of investigation in Wittgenstein's later writings but rather a pervasive and guiding concept in his efforts to turn philosophy's attention to the actual conditions of our common life in language. The essays in this 2010 volume open up novel paths across familiar fields of thought: the objectivity of interpretation, the fixity of the past, the acquisition of language, and the nature of human consciousness. Significantly, they exemplify how continuing consideration of the interrelated phenomena of aspect-seeing might produce a fruitful way of doing philosophy in a new century.

Bemerkungen über die Philosophie der Psychologie

Author: Ludwig Wittgenstein

Publisher: University of Chicago Press

ISBN: 9780226904368

Category: History

Page: 424

View: 9066

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Wittgenstein finished part 1 of the Philosophical Investigations in the spring of 1945. From 1946 to 1949 he worked on the philosophy of psychology almost without interruption. The present two-volume work comprises many of his writings over this period. Some of the remarks contained here were culled for part 2 of the Investigations; others were set aside and appear in the collection known as Zettel. The great majority, however, although of excellent quality, have hitherto remained unpublished. This bilingual edition of the Remarks on the Philosophy of Psychology presents the first English translation of an essential body of Wittegenstein's work. It elaborates Wittgenstein's views on psychological concepts such as expectation, sensation, knowing how to follow a rule, and knowledge of the sensations of other persons. It also shows strong emphasis on the "anthropological" aspect of Wittgenstein's thought. Philosophers, as well as anthropologists, psychologists, and sociologists will welcome this important publication.

Culture and Value

Author: Ludwig Wittgenstein

Publisher: University of Chicago Press

ISBN: 9780226904351

Category: Philosophy

Page: 181

View: 2099

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Selections from the notebooks of the distinguished philosopher discuss subjects such as music, religion, thinking, science, architecture, and civilization

Big Typescript

TS 213

Author: Ludwig Wittgenstein

Publisher: John Wiley & Sons

ISBN: 1118394259

Category: Philosophy

Page: 1056

View: 4986

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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

Notebooks, 1914-1916

Author: Ludwig Wittgenstein

Publisher: University of Chicago Press

ISBN: 9780226904474

Category: Philosophy

Page: 234

View: 3953

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The Austrian philosopher works out his theories of mathematical logic, the meaning of life, happiness, and death

The Voices of Wittgenstein

The Vienna Circle : Ludwig Wittgenstein and Friedrich Waismann

Author: Ludwig Wittgenstein,Gordon P. Baker,Friedrich Waismann

Publisher: Psychology Press

ISBN: 0415056446

Category: Philosophy

Page: 558

View: 2302

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This work brings in both the original German and English translation of over one hundred short essays in philosophical logic and the philosophy of mind of historical importance to understanding Wittgenstein's philosophical thought and development in the 1930's. Transcribed from the papers of Friedrich Waismann and dating from 1932-35, the majority are highly important dictations by Wittgenstein to Waismann, but also includes texts of redrafted material by Waismann closely based on the dictations. Many of these texts become the ultimate sources of material on philosophy of language that constitutes the bulk of Waismann's book Logic, Sprache, Philosophy (The Principles of Linguistic Philosophy). The transcriptions throw light on the development of Wittgenstein's thought in this period and some of the topics are not covered in any of the existing publications of his writings, in particular his detailed attention to causal theories of meaning. They also contain texts covering psychological concepts such as expecting, intending and experience; these have no counterparts in Waismann's publications.

Wittgenstein's Remarks on the Foundations of AI

Author: Stuart G. Shanker

Publisher: Routledge

ISBN: 1134859910

Category: Philosophy

Page: 296

View: 9234

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Wittgenstein's Remarks on the Foundations of AI is a valuable contribution to the study of Wittgenstein's theories and his controversial attack on artifical intelligence, which successfully crosses a number of disciplines, including philosophy, psychology, logic, artificial intelligence and cognitive science, to provide a stimulating and searching analysis.

Wittgenstein: Lectures, Cambridge 1930–1933

From the Notes of G. E. Moore

Author: David G. Stern,Brian Rogers,Gabriel Citron

Publisher: Cambridge University Press

ISBN: 1316432130

Category: Philosophy

Page: N.A

View: 6710

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This edition of G. E. Moore's notes taken at Wittgenstein's seminal Cambridge lectures in the early 1930s provides, for the first time, an almost verbatim record of those classes. The presentation of the notes is both accessible and faithful to their original manuscripts, and a comprehensive introduction and synoptic table of contents provide the reader with essential contextual information and summaries of the topics in each lecture. The lectures form an excellent introduction to Wittgenstein's middle-period thought, covering a broad range of philosophical topics, ranging from core questions in the philosophy of language, mind, logic, and mathematics, to illuminating discussions of subjects on which Wittgenstein says very little elsewhere, including ethics, religion, aesthetics, psychoanalysis, and anthropology. The volume also includes a 1932 essay by Moore critiquing Wittgenstein's conception of grammar, together with Wittgenstein's response. A companion website offers access to images of the entire set of source manuscripts.

Wittgenstein's Tractatus

An Introduction

Author: Alfred Nordmann

Publisher: Cambridge University Press

ISBN: 9780521850865

Category: Philosophy

Page: 234

View: 5315

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

Why Is There Philosophy of Mathematics At All?

Author: Ian Hacking

Publisher: Cambridge University Press

ISBN: 1107729823

Category: Science

Page: 212

View: 435

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This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

Philosophical Explorations of the Legacy of Alan Turing

Turing 100

Author: Juliet Floyd,Alisa Bokulich

Publisher: Springer

ISBN: 3319532804

Category: Science

Page: 361

View: 970

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This volume presents an historical and philosophical revisiting of the foundational character of Turing’s conceptual contributions and assesses the impact of the work of Alan Turing on the history and philosophy of science. Written by experts from a variety of disciplines, the book draws out the continuing significance of Turing’s work. The centennial of Turing’s birth in 2012 led to the highly celebrated “Alan Turing Year”, which stimulated a world-wide cooperative, interdisciplinary revisiting of his life and work. Turing is widely regarded as one of the most important scientists of the twentieth century: He is the father of artificial intelligence, resolver of Hilbert’s famous Entscheidungsproblem, and a code breaker who helped solve the Enigma code. His work revolutionized the very architecture of science by way of the results he obtained in logic, probability and recursion theory, morphogenesis, the foundations of cognitive psychology, mathematics, and cryptography. Many of Turing’s breakthroughs were stimulated by his deep reflections on fundamental philosophical issues. Hence it is fitting that there be a volume dedicated to the philosophical impact of his work. One important strand of Turing’s work is his analysis of the concept of computability, which has unquestionably come to play a central conceptual role in nearly every branch of knowledge and engineering.