Remarks on the Foundation of Mathematics PDF Download

Author: Ludwig Wittgenstein
Publisher:
ISBN:
Category :
Languages : en
Pages : 204

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Parallel dual language text (German and English).

Author:
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Category :
Languages : en
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Author: Alois Pichler
Publisher: Walter de Gruyter
ISBN: 3110328917
Category : Philosophy
Languages : en
Pages : 465

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This wide-ranging collection of essays contains eighteen original articles by authors representing some of the most important recent work on Wittgenstein. It deals with questions pertaining to both the interpretation and application of Wittgenstein’s thought and the editing of his works. Regarding the latter, it also addresses issues concerning scholarly electronic publishing. The collection is accompanied by a comprehensive introduction which lays out the content and arguments of each contribution. Contributors: Knut Erik Tranøy, Lars Hertzberg, Georg Henrik von Wright, Marie McGinn, Cora Diamond, James Conant, David G. Stern, Eike von Savigny, P.M.S. Hacker, Hans-Johann Glock, Allan Janik, Kristóf Nyíri, Antonia Soulez, Brian McGuinness, Anthony Kenny, Joachim Schulte, Herbert Hrachovec, Cameron McEwen.

Author: Thomas H. Wallgren
Publisher: Bloomsbury Publishing
ISBN: 135012110X
Category : Philosophy
Languages : en
Pages : 417

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Making extensive use of unique archival resources this collection presents, for the first time, an in-depth study of the work and influence of Wittgenstein's original literary heirs, Rush Rhees, Elizabeth Anscombe and Georg Henrik von Wright as editors of Wittgenstein's posthumous writings. Presenting philosophical portraits of Rhees, Anscombe and von Wright, a team of international contributors provide a history of their collaboration and discuss how the individual philosophical views of the literary heirs shaped what we now know as the works of Wittgenstein. They consider the link between philosophically relevant aspects of their biography, their friendship with Wittgenstein and the development of their philosophical personalities, offering us a new appreciation of the dynamics of their editorial collaboration and how each of the heirs worked individually as an editor to create Wittgenstein's philosophy. Each chapter reveals what the editors did to enrich and shape our understanding of Wittgenstein's philosophical contribution on topics such as rule-following, logical necessity, aesthetics and the methods and aims of philosophy. This thorough critical analysis of the editorial history of Wittgenstein's works allows us to finally appreciate the profound impact the editors have had on our understanding of his philosophy, his views and his cultural significance.

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

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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: Charles D. Parsons
Publisher: Cornell University Press
ISBN: 1501729322
Category : Mathematics
Languages : en
Pages : 367

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This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics. A common point of view, that mathematical thought is central to our thought in general, underlies the essays. In his introduction, Parsons articulates that point of view and relates it to past and recent discussions of the foundations of mathematics. Mathematics in Philosophy is divided into three parts. Ontology—the question of the nature and extent of existence assumptions in mathematics—is the subject of Part One and recurs elsewhere. Part Two consists of essays on two important historical figures, Kant and Frege, and one contemporary, W. V. Quine. Part Three contains essays on the three interrelated notions of set, class, and truth.

Author: Volker Munz
Publisher: Walter de Gruyter
ISBN: 3110330598
Category : Philosophy
Languages : en
Pages : 399

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This first of two volumes brings together invited papers of the 32nd International Wittgenstein Symposium (Kirchberg/W. (Austria), 2009). The relation between language and the world was undoubtedly one if not the central issue in Wittgenstein’s whole philosophical oeuvre. His one hundred and twentieth birthday provided an occasion for foregrounding this aspect of his work. A special workshop was dedicated to new aspects of Wittgenstein’s Nachlass. In this volume Frank Cioffi, Peter Hacker, Ian Hacking, Roy Harris, Lars Hertzberg, Jaakko Hintikka, Marie McGinn, Danièle Moyal-Sharrock, Hans Sluga among others provide substantial contributions on various aspects of Wittgenstein’s writings such as the philosophy of mathematics, the problem of rule following or the relation between meaning and use.

Author: Charles Parsons
Publisher: Harvard University Press
ISBN: 0674419502
Category : Philosophy
Languages : en
Pages : 331

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In this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century. Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl’s idea of a “vicious circle” in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Gödel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell’s mathematical logic—Gödel’s first mature philosophical statement and an avowal of his Platonistic view. Philosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine’s early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. Parsons attempts to tease out Putnam’s views on existence and ontology, especially in relation to logic and mathematics. Wang’s contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Gödel are examined, as are Tait’s axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures.

Author: Angelika Bikner-Ahsbahs
Publisher: Springer
ISBN: 3319425897
Category : Education
Languages : en
Pages : 56

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This survey provides an overview of German meta-discourse on theories and mathematics education as a scientific discipline, from the 1970s to the 1990s. Two theory strands are offered: a semiotic view related to Peirce and Wittgenstein (presented by Willibald Dörfler), and the theory of learning activity by Joachim Lompscher (presented by Regina Bruder and Oliver Schmitt). By networking the two theoretical approaches in a case study of learning fractions, it clarifies the nature of the two theories, how they can be related to inform practice and renew TME-issues for mathematics education as a scientific discipline. Hans-Georg Steiner initiated the first of five international conferences on Theories of Mathematics Education (TME) to advance the founding of mathematics education as a scientific discipline, and subsequently German researchers have continued to focus on TME topics but within various theory strands.

Author: Anne Siegetsleitner
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110702258
Category : Philosophy
Languages : en
Pages : 485

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Contemporary deep-reaching changes – whether in financial or real economy, in Europe’s political conditions, in the context of scientific theories, in the field of global (environmental) security, or gender relations – are also a challenge to philosophy. The volume comprises cutting-edge scholarly articles from renowned philosophers with various geographical backgrounds and from different philosophical strands. Next to investigating general questions as to the relation of philosophy and critique (What is philosophical critique and which philosophical concepts of critique are of importance today? Where do we need it most? Where are its limits?), the articles focus on issues like theories of democracy and modes of election; the roles of emotions in the political realm; challenges from a widespread discontent in society to politics and science; changes to social identities and different theoretical approaches to social identity formation. The book is indispensable for all who are interested in what contemporary philosophy has to say on crucial issues of our time.