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 : 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 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 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 On Mathematics

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Author : Severin Schroeder
language : en
Publisher: Routledge
Release Date : 2020-12-30

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 2020-12-30 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 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.

Ludwig Wittgenstein Dictating Philosophy

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Author : Arthur Gibson
language : en
Publisher: Springer Nature
Release Date : 2020-12-13

Ludwig Wittgenstein Dictating Philosophy written by Arthur Gibson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-13 with Philosophy categories.

In this volume we witness Wittgenstein in the act of composing and experimenting with his new visions in philosophy. The book includes key explanations of the origin and background of these previously unknown manuscripts. It investigates how Wittgenstein’s philosophical thought-processes are revealed in his dictation to, as well as his editing and revision with Francis Skinner, in the latter’s role of amanuensis. The book displays a considerable wealth and variety of Wittgenstein’s fundamental experiments in philosophy across a wide array of subjects that include the mind, pure and applied mathematics, metaphysics, the identities of ordinary and creative language, as well as intractable problems in logic and life. He also periodically engages with the work of Newton, Fermat, Russell and others. The book shows Wittgenstein strongly battling against the limits of understanding and the bewitchment of institutional and linguistic customs. The reader is drawn in by Wittgenstein as he urges us to join him in his struggles to equip us with skills, so that we can embark on devising new pathways beyond confusion. This collection of manuscripts was posted off by Wittgenstein to be considered for publication during World War 2, in October 1941. None of it was published and it remained hidden for over two generations. Upon its rediscovery, Professor Gibson was invited to research, prepare and edit the Archive to appear as this book, encouraged by Trinity College Cambridge and The Mathematical Association. Niamh O’Mahony joined him in co-editing and bringing this book to publication.

Why Is There Philosophy Of Mathematics At All

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Author : Ian Hacking
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-30

Why Is There Philosophy Of Mathematics At All written by Ian Hacking 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 2014-01-30 with Mathematics categories.

Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.

The Oxford Handbook Of Wittgenstein

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Author : Oskari Kuusela
language : en
Publisher: Oxford University Press
Release Date : 2011-10-27

The Oxford Handbook Of Wittgenstein written by Oskari Kuusela 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 2011-10-27 with Philosophy categories.

Since the middle of the 20th century Ludwig Wittgenstein has been an exceptionally influential and controversial figure wherever philosophy is studied. This is a comprehensive volume on Wittgenstein where 35 scholars explore the whole range of his thought, offering critical engagement and original interpretation.