Wittgenstein On Philosophy And Mathematics

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Wittgenstein's Philosophy of Mathematics

Author : Juliet Floyd
Publisher : Cambridge University Press
ISBN 13 : 1108616534
Total Pages : 96 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Wittgenstein's Philosophy of Mathematics by : Juliet Floyd

Download or read book Wittgenstein's Philosophy of Mathematics written by Juliet Floyd and published by Cambridge University Press. This book was released on 2021-08-12 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics (1934–1951) grew from his Early (1912–1921) and Middle (1929–33) philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.

Wittgenstein on Mathematics

Author : Severin Schroeder
Publisher : Routledge
ISBN 13 : 100031829X
Total Pages : 200 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Wittgenstein on Mathematics by : Severin Schroeder

Download or read book Wittgenstein on Mathematics written by Severin Schroeder and published by Routledge. This book was released on 2020-12-30 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Philosophy of Mathematics

Author : Pasquale Frascolla
Publisher : Routledge
ISBN 13 : 1134974361
Total Pages : 253 pages
Book Rating : 4.1/5 (349 download)

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Book Synopsis Wittgenstein's Philosophy of Mathematics by : Pasquale Frascolla

Download or read book Wittgenstein's Philosophy of Mathematics written by Pasquale Frascolla and published by Routledge. This book was released on 2006-12-05 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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'.

Bemerkungen Über Die Grundlagen Der Mathematik

Author : Ludwig Wittgenstein
Publisher :
ISBN 13 : 9780262730174
Total Pages : 204 pages
Book Rating : 4.7/5 (31 download)

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Book Synopsis Bemerkungen Über Die Grundlagen Der Mathematik by : Ludwig Wittgenstein

Download or read book Bemerkungen Über Die Grundlagen Der Mathematik written by Ludwig Wittgenstein and published by . This book was released on 1972 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Wittgenstein, Finitism, and the Foundations of Mathematics

Author : Mathieu Marion
Publisher : OUP Oxford
ISBN 13 : 0191568325
Total Pages : 272 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Wittgenstein, Finitism, and the Foundations of Mathematics by : Mathieu Marion

Download or read book Wittgenstein, Finitism, and the Foundations of Mathematics written by Mathieu Marion and published by OUP Oxford. This book was released on 1998-12-17 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 by philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any other indicates its centrality in his thought. 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. Marion shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy; and he also demonstrates that it has much to contribute to current debates about the foundations of mathematics.

Wittgenstein and the Turning Point in the Philosophy of Mathematics

Author : S.G. Shanker
Publisher : Routledge
ISBN 13 : 1317832035
Total Pages : 571 pages
Book Rating : 4.3/5 (178 download)

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Book Synopsis Wittgenstein and the Turning Point in the Philosophy of Mathematics by : S.G. Shanker

Download or read book Wittgenstein and the Turning Point in the Philosophy of Mathematics written by S.G. Shanker and published by Routledge. This book was released on 2013-12-19 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

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

Author : Ludwig Wittgenstein
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)

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Book Synopsis Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 by : Ludwig Wittgenstein

Download or read book Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 written by Ludwig Wittgenstein and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Wittgenstein on the Foundations of Mathematics

Author : Crispin Wright
Publisher :
ISBN 13 : 9780751202953
Total Pages : 481 pages
Book Rating : 4.2/5 (29 download)

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Book Synopsis Wittgenstein on the Foundations of Mathematics by : Crispin Wright

Download or read book Wittgenstein on the Foundations of Mathematics written by Crispin Wright and published by . This book was released on 1994 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this detailed account, Crispin Wright offers a systematic account of Wittgenstein's later philosophy of mathematics and establishes its links with his later philosophy of language. In line with this, he examines Wittgenstein's Remarks on the Foundations of Mathematics.

Wittgenstein's Philosophy of Mathematics

Author : Pasquale Frascolla
Publisher : Routledge
ISBN 13 : 113497437X
Total Pages : 200 pages
Book Rating : 4.1/5 (349 download)

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Book Synopsis Wittgenstein's Philosophy of Mathematics by : Pasquale Frascolla

Download or read book Wittgenstein's Philosophy of Mathematics written by Pasquale Frascolla and published by Routledge. This book was released on 2006-12-05 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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'.

Philosophy of Logic and Mathematics

Author : Gabriele M. Mras
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110657880
Total Pages : 559 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Philosophy of Logic and Mathematics by : Gabriele M. Mras

Download or read book Philosophy of Logic and Mathematics written by Gabriele M. Mras and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-18 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Günther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Mühlhölzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Woleński and Richard Zach.

Wittgenstein on Mathematics

Author : Severin Schroeder
Publisher : Routledge
ISBN 13 : 1000318273
Total Pages : 238 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Wittgenstein on Mathematics by : Severin Schroeder

Download or read book Wittgenstein on Mathematics written by Severin Schroeder and published by Routledge. This book was released on 2020-12-29 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Why Is There Philosophy of Mathematics At All?

Author : Ian Hacking
Publisher : Cambridge University Press
ISBN 13 : 1107729823
Total Pages : 212 pages
Book Rating : 4.1/5 (77 download)

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Book Synopsis Why Is There Philosophy of Mathematics At All? by : Ian Hacking

Download or read book Why Is There Philosophy of Mathematics At All? written by Ian Hacking and published by Cambridge University Press. This book was released on 2014-01-30 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

Author : Cora Diamond
Publisher : University of Chicago Press
ISBN 13 : 022630860X
Total Pages : 301 pages
Book Rating : 4.2/5 (263 download)

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Book Synopsis Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 by : Cora Diamond

Download or read book Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 written by Cora Diamond and published by University of Chicago Press. This book was released on 2015-05-14 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Remarks on the Foundations of Mathematics

Author : Ludwig Wittgenstein
Publisher : Wiley-Blackwell
ISBN 13 : 9780631125051
Total Pages : 448 pages
Book Rating : 4.1/5 (25 download)

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Book Synopsis Remarks on the Foundations of Mathematics by : Ludwig Wittgenstein

Download or read book Remarks on the Foundations of Mathematics written by Ludwig Wittgenstein and published by Wiley-Blackwell. This book was released on 1991-01-08 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

A Companion to Wittgenstein's Philosophical Investigations

Author : Garth Hallett
Publisher : Cornell University Press
ISBN 13 : 1501743406
Total Pages : 816 pages
Book Rating : 4.5/5 (17 download)

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Book Synopsis A Companion to Wittgenstein's Philosophical Investigations by : Garth Hallett

Download or read book A Companion to Wittgenstein's Philosophical Investigations written by Garth Hallett and published by Cornell University Press. This book was released on 2019-06-30 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: "One of the most impressive pieces of scholarship I have ever encountered."-W. E. Kennick, Amherst College There is nothing in the literature on the Philosophical Investigations comparable to this learned and exhaustive commentary. Offering both information and interpretation, it is a remarkable book that fills a recognized need for a close study of one of the world's major works of philosophy. After a general introduction, Father Hallett divides the text of the Investigations into forty-one units, and then provides an introduction to each section, along with detailed comments on individual paragraphs, statements, and expressions. His use of paragraph numbers in the general introduction and in the sectional introductions permits ready reference downward, for detailed development or illustration of a general observation, or upward, from a particular passage to its wider context. To clarify the philosophical point of Wittgenstein's remarks, Father Hallett makes frequent references to other parts of the Investigations; to Wittgenstein's other writings, both published and unpublished; and to the works which Wittgenstein knew and often had in mind, such as those of Frege, Russell, Moore, James, Augustine, Plato, Schlick, and Kohler. Father Hallett also cites and quotes secondary sources, and he includes an appendix relating Wittgenstein to more than 150 authors, particularly those of his own generation or earlier whom he read, or knew personally, and who are mentioned in this commentary. Written in straightforward and lucid prose, this outstanding book reveals continuities in Wittgenstein's thought over long periods of time. It is an indispensable guide for those preparing courses on the Investigations and a useful tool for students taking those courses.

Wittgenstein’s Philosophy of Mathematics

Author : V.H. Klenk
Publisher : Springer Science & Business Media
ISBN 13 : 9401013918
Total Pages : 128 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Wittgenstein’s Philosophy of Mathematics by : V.H. Klenk

Download or read book Wittgenstein’s Philosophy of Mathematics written by V.H. Klenk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wittgenstein's remarks on mathematics have not received the recogni tion they deserve; they have for the most part been either ignored, or dismissed as unworthy of the author of the Tractatus and the I nvestiga tions. This is unfortunate, I believe, and not at all fair, for these remarks are not only enjoyable reading, as even the harshest critics have con ceded, but also a rich and genuine source of insight into the nature of mathematics. It is perhaps the fact that they are more suggestive than systematic which has put so many people off; there is nothing here of formal derivation and very little attempt even at sustained and organized argumentation. The remarks are fragmentary and often obscure, if one does not recognize the point at which they are directed. Nevertheless, there is much here that is good, and even a fairly system atic and coherent account of mathematics. What I have tried to do in the following pages is to reconstruct the system behind the often rather disconnected commentary, and to show that when the theory emerges, most of the harsh criticism which has been directed against these re marks is seen to be without foundation. This is meant to be a sym pathetic account of Wittgenstein's views on mathematics, and I hope that it will at least contribute to a further reading and reassessment of his contributions to the philosophy of mathematics.

Wittgenstein

Author : Severin Schroeder
Publisher : Polity
ISBN 13 : 0745626165
Total Pages : 286 pages
Book Rating : 4.7/5 (456 download)

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Book Synopsis Wittgenstein by : Severin Schroeder

Download or read book Wittgenstein written by Severin Schroeder and published by Polity. This book was released on 2006-03-31 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a lucid and highly readable account of Wittgenstein's philosophy, framed against the background of his extraordinary life and character. Woven together with a biographical narrative, the chapters explain the key ideas of Wittgenstein's work, from his first book, the Tractatus Logico-Philosophicus, to his mature masterpiece, the Philosophical Investigations. Severin Schroeder shows that at the core of Wittgenstein's later work lies a startlingly original and subversive conception of the nature of philosophy. In accordance with this conception, Wittgenstein offers no new philosophical doctrines to replace his earlier ones, but seeks to demonstrate how all philosophical theorizing is the result of conceptual misunderstanding. He first diagnoses such misunderstanding at the core of his own earlier philosophy of language and then subjects philosophical views and problems about various mental phenomena understanding, sensations, the will to a similar therapeutic analysis. Schroeder provides a clear and careful account of the main arguments offered by Wittgenstein. He concludes by considering some critical responses to Wittgenstein's work, assessing its legacy for contemporary philosophy. Wittgenstein is ideal for students seeking a clear and concise introduction to the work of this seminal twentieth-century philosopher.