Wittgenstein S Philosophy Of Mathematics
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Wittgenstein S Philosophy Of Mathematics
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Author : Pasquale Frascolla
language : en
Publisher: Routledge
Release Date : 2006-12-05
Wittgenstein S Philosophy Of Mathematics written by Pasquale Frascolla and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-05 with Philosophy categories.
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'.
Wittgenstein S Philosophy Of Mathematics
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Author : Juliet Floyd
language : en
Publisher: Cambridge University Press
Release Date : 2021-08-12
Wittgenstein S Philosophy Of Mathematics written by Juliet Floyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-12 with Science categories.
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 S Philosophy Of Mathematics
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Author : V.H. Klenk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Wittgenstein S Philosophy Of Mathematics written by V.H. Klenk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
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 And The Turning Point In The Philosophy Of Mathematics
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Author : S.G. Shanker
language : en
Publisher: Routledge
Release Date : 2013-12-19
Wittgenstein And The Turning Point In The Philosophy Of Mathematics written by S.G. Shanker and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-19 with Philosophy categories.
First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.
Wittgenstein On Mathematics
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Author : Severin Schroeder
language : en
Publisher: Routledge
Release Date : 2020-12-29
Wittgenstein On Mathematics written by Severin Schroeder and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-29 with Philosophy categories.
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 Mathematics And World
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Author : Bob Clark
language : en
Publisher: Springer
Release Date : 2017-11-14
Wittgenstein Mathematics And World written by Bob Clark and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-14 with Mathematics categories.
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.
Wittgenstein S Philosophy Of Mathematics
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Author : V H Klenk
language : en
Publisher:
Release Date : 1976-09-30
Wittgenstein S Philosophy Of Mathematics written by V H Klenk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-09-30 with categories.
Wittgenstein S Lectures On The Foundations Of Mathematics Cambridge 1939
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Author : Cora Diamond
language : en
Publisher: University of Chicago Press
Release Date : 2015-05-14
Wittgenstein S Lectures On The Foundations Of Mathematics Cambridge 1939 written by Cora Diamond and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-14 with Philosophy categories.
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 On Philosophy And Mathematics
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Author : Christoffer Gefwert
language : en
Publisher:
Release Date : 1994
Wittgenstein On Philosophy And Mathematics written by Christoffer Gefwert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Philosophy categories.
Wittgenstein Finitism And The Foundations Of Mathematics
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Author : Mathieu Marion
language : en
Publisher: Oxford University Press
Release Date : 1998
Wittgenstein Finitism And The Foundations Of Mathematics written by Mathieu Marion and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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 thanon 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 adisjointed 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 alsodemonstrates that it has much to contribute to current debates about the foundations of mathematics.