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Author: S.G. Shanker
Publisher: Routledge
Published: 2013-12-19
Total Pages: 373
ISBN-13: 1317832043
DOWNLOAD EBOOKFirst published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.
Author: Juliet Floyd
Publisher: Cambridge University Press
Published: 2021-08-12
Total Pages: 96
ISBN-13: 1108616534
DOWNLOAD EBOOKFor 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
Published: 2006-12-05
Total Pages: 200
ISBN-13: 113497437X
DOWNLOAD EBOOKWittgenstein'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: Stuart Shanker
Publisher: SUNY Press
Published: 1987-01-01
Total Pages: 380
ISBN-13: 9780887064821
DOWNLOAD EBOOKShanker 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: Stewart Shapiro
Publisher: OUP USA
Published: 2005-02-10
Total Pages: 850
ISBN-13: 0195148770
DOWNLOAD EBOOKCovers 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: S. G. Shanker
Publisher:
Published: 1987
Total Pages: 358
ISBN-13: 9780709923848
DOWNLOAD EBOOKAuthor: Carl Posy
Publisher: Springer Nature
Published: 2023-05-05
Total Pages: 404
ISBN-13: 3031216555
DOWNLOAD EBOOKThis book provides a survey of a number of the major issues in the philosophy of mathematics, such as ontological questions regarding the nature of mathematical objects, epistemic questions about the acquisition of mathematical knowledge, and the intriguing riddle of the applicability of mathematics to the physical world. Some of these issues go back to the nascent years of mathematics itself, others are just beginning to draw the attention of scholars. In addressing these questions, some of the papers in this volume wrestle with them directly, while others use the writings of philosophers such as Hume and Wittgenstein to approach their problems by way of interpretation and critique. The contributors include prominent philosophers of science and mathematics as well as promising younger scholars. The volume seeks to share the concerns of philosophers of mathematics with a wider audience and will be of interest to historians, mathematicians and philosophers alike.
Author: Hans D. Sluga
Publisher: Cambridge University Press
Published: 1996-10-28
Total Pages: 528
ISBN-13: 9780521465915
DOWNLOAD EBOOKThe essays in this volume address central themes in Wittgenstein's writings on the philosophy of mind, language, logic, and mathematics.
Author: A. Biletzki
Publisher: Springer Science & Business Media
Published: 2012-09-14
Total Pages: 276
ISBN-13: 940070822X
DOWNLOAD EBOOKThis book tells the story of Wittgenstein interpretation during the past eighty years. It provides different interpretations, chronologies, developments, and controversies. It aims to discover the motives and motivations behind the philosophical community's project of interpreting Wittgenstein. It will prove valuable to philosophers, scholars, interpreters, students, and specialists, in both analytic and continental philosophy.
Author: Severin Schroeder
Publisher: Routledge
Published: 2020-12-29
Total Pages: 238
ISBN-13: 1000318273
DOWNLOAD EBOOKThis 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.
