Download or read book Wittgenstein on Mathematics written by Severin Schroeder and published by Routledge. This book was released on 2020-12-30 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Wittgenstein s Philosophy of Mathematics written by Juliet Floyd and published by Cambridge University Press. This book was released on 2021-08-12 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Wittgenstein s Philosophy of Mathematics written by Pasquale Frascolla and published by Routledge. This book was released on 2006-12-05 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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'.
Download or read book Wittgenstein s Lectures on the Foundations of Mathematics Cambridge 1939 written by Ludwig Wittgenstein and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wittgenstein Finitism and the Foundations of Mathematics written by Mathieu Marion and published by OUP Oxford. This book was released on 1998-12-17 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Wittgenstein on the Foundations of Mathematics written by Crispin Wright and published by . This book was released on 1994 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this detailed account, Crispin Wright offers a systematic account of Wittgenstein's later philosophy of mathematics and establishes its links with his later philosophy of language. In line with this, he examines Wittgenstein's Remarks on the Foundations of Mathematics.
Download or read book Wittgenstein and the Turning Point in the Philosophy of Mathematics written by S.G. Shanker and published by Routledge. This book was released on 2013-12-19 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.
Download or read book Bemerkungen ber Die Grundlagen Der Mathematik written by Ludwig Wittgenstein and published by . This book was released on 1972 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wittgenstein s Annotations to Hardy s Course of Pure Mathematics written by Juliet Floyd and published by Springer Nature. This book was released on 2020-08-31 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein’s remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized. The authors first establish the context behind the annotations and discuss the historical role of Hardy’s textbook. They then go on to outline Wittgenstein’s non-extensionalist point of view on real numbers, assessing his manuscripts and published remarks and discussing attitudes in play in the philosophy of mathematics since Dedekind. Next, coverage focuses on the annotations themselves. The discussion encompasses irrational numbers, the law of excluded middle in mathematics and the notion of an “improper picture," the continuum of real numbers, and Wittgenstein’s attitude toward functions and limits.
Download or read book Philosophy of Logic and Mathematics written by Gabriele M. Mras and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-18 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Günther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Mühlhölzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Woleński and Richard Zach.
Download or read book The Oxford Handbook of Wittgenstein written by Oskari Kuusela and published by Oxford University Press. This book was released on 2011-10-27 with total page 839 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Why Is There Philosophy of Mathematics At All written by Ian Hacking and published by Cambridge University Press. This book was released on 2014-01-30 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.
Download or read book Wittgenstein written by Severin Schroeder and published by Polity. This book was released on 2006-03-31 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a lucid and highly readable account of Wittgenstein's philosophy, framed against the background of his extraordinary life and character. Woven together with a biographical narrative, the chapters explain the key ideas of Wittgenstein's work, from his first book, the Tractatus Logico-Philosophicus, to his mature masterpiece, the Philosophical Investigations. Severin Schroeder shows that at the core of Wittgenstein's later work lies a startlingly original and subversive conception of the nature of philosophy. In accordance with this conception, Wittgenstein offers no new philosophical doctrines to replace his earlier ones, but seeks to demonstrate how all philosophical theorizing is the result of conceptual misunderstanding. He first diagnoses such misunderstanding at the core of his own earlier philosophy of language and then subjects philosophical views and problems about various mental phenomena understanding, sensations, the will to a similar therapeutic analysis. Schroeder provides a clear and careful account of the main arguments offered by Wittgenstein. He concludes by considering some critical responses to Wittgenstein's work, assessing its legacy for contemporary philosophy. Wittgenstein is ideal for students seeking a clear and concise introduction to the work of this seminal twentieth-century philosopher.
Download or read book Wittgenstein on Mathematics written by Severin Schroeder and published by Routledge. This book was released on 2020-12-29 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Cambridge Companion to Wittgenstein written by Hans Sluga and published by Cambridge University Press. This book was released on 2018 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updated edition of this important book, charting the development of Wittgenstein's philosophy of the mind, language, logic, and mathematics.
Download or read book Wittgenstein s Lectures on the Foundations of Mathematics Cambridge 1939 written by Cora Diamond and published by University of Chicago Press. This book was released on 2015-05-14 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.
Download or read book Essays on the philosophy of Wittgenstein written by Volker Munz and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
