Remarks On The Foundations Of Mathematics Revised Edition
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Remarks On The Foundations Of Mathematics Revised Edition
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Author : Ludwig Wittgenstein
language : en
Publisher: National Geographic Books
Release Date : 1983-05-10
Remarks On The Foundations Of Mathematics Revised Edition written by Ludwig Wittgenstein and has been published by National Geographic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-05-10 with Philosophy categories.
Wittgenstein's work remains, undeniably, now, that of one of those few philosophers who will be read by all future generations. The Remarks analyzes in depth such topics as logical compulsion (the “must”) and mathematical conviction; calculation as experiment; mathematical surprise, discovery, and invention; Russell's logic, Gödel's theorem, Cantor's diagonal procedure, Dedekind's cuts; the nature of proof and contradiction; and the role of mathematical propositions in the forming of concepts. Wittgenstein's later philosophy was much involved with the concept of “language-games,” of which mathematics was one. It was his feeling that a proper analysis of the use of language would clarify concepts and lead to the solution of (what seem to be) philosophical problems. Sometimes, Wittgenstein's expository method is pre-Socratic: a flow of disconnected statements, not unlike Heraclitean fragments, that range from clear aphorisms to cryptic oracles. Elsewhere, there are brief Socratic dialogues with imaginary persons, opponents of equally severe seriousness, representatives of the other half of Wittgenstein strove for total clarity of language as a means of solving philosophical problems, but some of his most meaningful statements here are expressed suggestively, subjectively, poetically.
New Foundations In Mathematics
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Author : Garret Sobczyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-28
New Foundations In Mathematics written by Garret Sobczyk 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 2012-10-28 with Mathematics categories.
The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
Remarks On The Foundations Of Mathematics
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Author : Ludwig Wittgenstein
language : en
Publisher: Wiley-Blackwell
Release Date : 1991-01-08
Remarks On The Foundations Of Mathematics written by Ludwig Wittgenstein and has been published by Wiley-Blackwell this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-08 with Philosophy categories.
Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.
Wittgenstein S Lectures On The Foundations Of Mathematics Cambridge 1939
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Author : Ludwig Wittgenstein
language : en
Publisher:
Release Date : 1989
Wittgenstein S Lectures On The Foundations Of Mathematics Cambridge 1939 written by Ludwig Wittgenstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Conceptions Of Set And The Foundations Of Mathematics
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Author : Luca Incurvati
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-23
Conceptions Of Set And The Foundations Of Mathematics written by Luca Incurvati 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 2020-01-23 with History categories.
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Wittgenstein And The Moral Life
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Author : Cora Diamond
language : en
Publisher: MIT Press
Release Date : 2007
Wittgenstein And The Moral Life written by Cora Diamond and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Philosophy categories.
Essays by leading scholars that take as their point of departure Cora Diamond's work on the unity of Wittgenstein's thought and her writings on moral philosophy.
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 Mathematics 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 Finitism And The Foundations Of Mathematics
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Author : Mathieu Marion
language : en
Publisher: OUP Oxford
Release Date : 1998-12-17
Wittgenstein Finitism And The Foundations Of Mathematics written by Mathieu Marion and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-17 with Philosophy 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.
Reflections On The Foundations Of Mathematics
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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Reflections On The Foundations Of Mathematics written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.
The Creation Of Wittgenstein
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Author : Thomas H. Wallgren
language : en
Publisher: Bloomsbury Publishing
Release Date : 2023-02-23
The Creation Of Wittgenstein written by Thomas H. Wallgren and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-23 with Philosophy categories.
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.