Wittgenstein and the Turning Point in the Philosophy of Mathematics PDF Download

Author: S.G. Shanker
Publisher: Routledge
ISBN: 1317832043
Category : Philosophy
Languages : en
Pages : 373

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

Author: S. G. Shanker
Publisher:
ISBN: 9780709923848
Category : Mathematics
Languages : en
Pages : 358

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Author: Stuart Shanker
Publisher: SUNY Press
ISBN: 9780887064821
Category : Philosophy
Languages : en
Pages : 380

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Shanker exposes the confusions underlying the currently prevailing interpretations of Wittgenstein. He shows how such approaches and their underlying critical frameworks are incapable of coming to terms with Wittgenstein's arguments in the philosophy of mathematics. This book explains not only Wittgenstein's approach, which was justly heralded as causing a turning point in the philosophy of mathematics, but also the philosophy of mathematics in general.

Author: Juliet Floyd
Publisher: Cambridge University Press
ISBN: 1108616534
Category : Science
Languages : en
Pages : 96

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Book Description
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
ISBN: 113497437X
Category : Philosophy
Languages : en
Pages : 200

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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: Stewart Shapiro
Publisher: OUP USA
ISBN: 0195148770
Category : Mathematics
Languages : en
Pages : 850

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Covers the state of the art in the philosophy of maths and logic, giving the reader an overview of the major problems, positions, and battle lines. The chapters in this book contain both exposition and criticism as well as substantial development of their own positions. It also includes a bibliography.

Author: Hans D. Sluga
Publisher: Cambridge University Press
ISBN: 9780521465915
Category : Philosophy
Languages : en
Pages : 528

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Book Description
The essays in this volume address central themes in Wittgenstein's writings on the philosophy of mind, language, logic, and mathematics.

Author: Severin Schroeder
Publisher: Routledge
ISBN: 1000318273
Category : Philosophy
Languages : en
Pages : 238

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Book Description
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: Christoffer Gefwert
Publisher: Routledge
ISBN: 1351731424
Category : Philosophy
Languages : en
Pages : 349

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This title was first published in 2000: What was Wittgenstein's relation to "theory of meaning" in his post-1937 writings and what was his characterization of "philosophy" ? How does "philosophy" in Wittgenstein's later writings differ from what is usually accepted in modern academic 'analytic' philosophy? This book discusses problems encountered in looking at Wittgenstein's texts after-1937, focusing particularly on whether the problem of philosophy amounts to a systematic or a theoretical activity. Arguing that philosophy can be characterized as a form of conceptual investigation, Gefwert aims to demonstrate that a theoretical view does not correspond to Wittgenstein's conception of philosophy. For example, philosophy is not transcendental as he thought it was before 1929. Neither is philosophical language universal as Wittgenstein 1929-1936 thought it was. Proposing that a philosophical conceptual investigation is analogous to a psychotherapeutical session of Freud, with the common aim to dissolve the conceptual problems in language that haunt us in our everyday life, Gefwert's examination of the post-1937 writings of Wittgenstein concludes that "philosophical investigation" is a very different activity than that assumed by the Logical Positives and others adhering to a theoretical view.

Author: Stuart Shanker
Publisher: Psychology Press
ISBN: 9780415149150
Category : Philosophy
Languages : en
Pages : 352

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Book Description
Wittgenstein scholarship has continued to grow at a pace few could have anticipated - a testament both to the fertility of his thought and to the thriving state of contemporary philosophy. In response to this ever-growing interest in the field, we are delighted to announce the publication of a second series of critical assessments on Wittgenstein, emphasising both the breadth and depth of contemporary Wittgenstein research.As well as papers on the nature and method of Wittgenstein's philosophy, this second collection also relates to a broader range of topics, including psychology, politics, art, music and culture.