Wittgenstein S Philosophy Of Mathematics

Author : Pasquale Frascolla
Publisher : Routledge
Page : 253 pages
File Size : 50,8 Mb
Release : 2006-12-05
Category : Philosophy
ISBN : 9781134974368

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Wittgenstein's Philosophy of Mathematics by Pasquale Frascolla Pdf

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'.

Author : Juliet Floyd
Publisher : Cambridge University Press
Page : 96 pages
File Size : 55,6 Mb
Release : 2021-08-12
Category : Science
ISBN : 9781108616539

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Wittgenstein's Philosophy of Mathematics by Juliet Floyd Pdf

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.

Author : Pasquale Frascolla
Publisher : Routledge
Page : 200 pages
File Size : 46,8 Mb
Release : 2006-12-05
Category : Philosophy
ISBN : 9781134974375

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Wittgenstein's Philosophy of Mathematics by Pasquale Frascolla Pdf

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'.

Author : Severin Schroeder
Publisher : Routledge
Page : 200 pages
File Size : 43,5 Mb
Release : 2020-12-30
Category : Philosophy
ISBN : 9781000318296

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Wittgenstein on Mathematics by Severin Schroeder Pdf

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.

Author : Mathieu Marion
Publisher : OUP Oxford
Page : 272 pages
File Size : 54,5 Mb
Release : 1998-12-17
Category : Philosophy
ISBN : 9780191568329

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Wittgenstein, Finitism, and the Foundations of Mathematics by Mathieu Marion Pdf

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.

Author : S.G. Shanker
Publisher : Routledge
Page : 373 pages
File Size : 45,6 Mb
Release : 2013-12-19
Category : Philosophy
ISBN : 9781317832041

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Wittgenstein and the Turning Point in the Philosophy of Mathematics by S.G. Shanker Pdf

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Ludwig Wittgenstein
Publisher : Unknown
Page : 204 pages
File Size : 46,5 Mb
Release : 1972
Category : Mathematics
ISBN : 0262730170

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Bemerkungen Über Die Grundlagen Der Mathematik by Ludwig Wittgenstein Pdf

Author : V.H. Klenk
Publisher : Springer Science & Business Media
Page : 128 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401013918

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Wittgenstein’s Philosophy of Mathematics by V.H. Klenk Pdf

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.

Author : Ludwig Wittgenstein
Publisher : Unknown
Page : 0 pages
File Size : 46,5 Mb
Release : 1989
Category : Mathematics
ISBN : OCLC:1391903096

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

Author : Crispin Wright
Publisher : Unknown
Page : 481 pages
File Size : 45,6 Mb
Release : 1994
Category : Mathematics
ISBN : 0751202959

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Wittgenstein on the Foundations of Mathematics by Crispin Wright Pdf

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.

Author : S.G. Shanker
Publisher : Routledge
Page : 479 pages
File Size : 54,6 Mb
Release : 2013-12-19
Category : Philosophy
ISBN : 9781317832034

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Wittgenstein and the Turning Point in the Philosophy of Mathematics by S.G. Shanker Pdf

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Gabriele M. Mras,Paul Weingartner,Bernhard Ritter
Publisher : Walter de Gruyter GmbH & Co KG
Page : 559 pages
File Size : 52,9 Mb
Release : 2019-11-18
Category : Philosophy
ISBN : 9783110657883

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Philosophy of Logic and Mathematics by Gabriele M. Mras,Paul Weingartner,Bernhard Ritter Pdf

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.

Author : Ian Hacking
Publisher : Cambridge University Press
Page : 212 pages
File Size : 43,9 Mb
Release : 2014-01-30
Category : Science
ISBN : 9781107729827

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Why Is There Philosophy of Mathematics At All? by Ian Hacking Pdf

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.

Author : Cora Diamond
Publisher : University of Chicago Press
Page : 301 pages
File Size : 53,5 Mb
Release : 2015-05-14
Category : Philosophy
ISBN : 9780226308609

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Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 by Cora Diamond Pdf

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.

Author : Bob Clark
Publisher : Springer
Page : 215 pages
File Size : 49,5 Mb
Release : 2017-11-14
Category : Mathematics
ISBN : 9783319639918

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Wittgenstein, Mathematics and World by Bob Clark Pdf

This book uses Ludwig Wittgenstein’s philosophical methodology to solve a problem that has perplexed thinkers for thousands of years: 'how come (abstract) mathematics applies so wonderfully well to the (concrete, physical) world?' The book is distinctive in several ways. First, it gives the reader a route into understanding important features of Wittgenstein’s writings and lectures by using his methodology to tackle this long-standing and seemingly intractable philosophical problem. More than this, though, it offers an outline of important (sometimes little-known) aspects of the development of mathematical thought through the ages, and an engagement of Wittgenstein’s philosophy with this and with contemporary philosophy of mathematics on its own terms. A clear overview of all this in the context of Wittgenstein’s philosophy of mathematics is interesting in its own right; it is also just what is needed to solve the problem of mathematics and world.