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 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 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 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 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 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 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 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 Remarks on the Foundations of Mathematics written by Ludwig Wittgenstein and published by Wiley-Blackwell. This book was released on 1991-01-08 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.
Download or read book Foundations of Mathematics and other Logical Essays written by Frank Plumpton Ramsey and published by Routledge. This book was released on 2013-10-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Volume V in a series of eight on the Philosophy of Logic and Mathematics. Originally published in 1931, this study offers a collection of logical essays around the topic of the foundations of mathematics. Though mathematical teaching was Ramsey's profession, philosophy was his vocation. Reared on the logic of Principia Mathematica, he was early to see the importance of Dr. Wittgenstein's work (in the translation of which he assisted); and his own published papers were largely based on this. But the previously unprinted essays and notes collected in this volume show him moving towards a kind of pragmatism, and the general treatise on logic upon which at various times he had been engaged was to have treated truth and knowledge as purely natural phenomena to be explained psychologically without recourse to distinctively logical relations.
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 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 Philosophical Remarks written by Ludwig Wittgenstein and published by University of Chicago Press. This book was released on 1980-10-15 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: When in May 1930, the Council of Trinity College, Cambridge, had to decide whether to renew Wittgenstein's research grant, it turned to Bertrand Russell for an assessment of the work Wittgenstein had been doing over the past year. His verdict: "The theories contained in this new work . . . are novel, very original and indubitably important. Whether they are true, I do not know. As a logician who likes simplicity, I should like to think that they are not, but from what I have read of them I am quite sure that he ought to have an opportunity to work them out, since, when completed, they may easily prove to constitute a whole new philosophy." "[Philosophical Remarks] contains the seeds of Wittgenstein's later philosophy of mind and of mathematics. Principally, he here discusses the role of indispensable in language, criticizing Russell's The Analysis of Mind. He modifies the Tractatus's picture theory of meaning by stressing that the connection between the proposition and reality is not found in the picture itself. He analyzes generality in and out of mathematics, and the notions of proof and experiment. He formulates a pain/private-language argument and discusses both behaviorism and the verifiability principle. The work is difficult but important, and it belongs in every philosophy collection."—Robert Hoffman, Philosophy "Any serious student of Wittgenstein's work will want to study his Philosophical Remarks as a transitional book between his two great masterpieces. The Remarks is thus indispensible for anyone who seeks a complete understanding of Wittgenstein's philosophy."—Leonard Linsky, American Philosophical Association
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Logical Must written by Penelope Maddy and published by Oxford University Press. This book was released on 2014-08-01 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Logical Must is an examination of Ludwig Wittgenstein's philosophy of logic, early and late, undertaken from an austere naturalistic perspective Penelope Maddy has called "Second Philosophy." The Second Philosopher is a humble but tireless inquirer who begins her investigation of the world with ordinary perceptual beliefs, moves from there to empirical generalizations, then to deliberate experimentation, and eventually to theory formation and confirmation. She takes this same approach to logical truth, locating its ground in simple worldly structures and our knowledge of it in our basic cognitive machinery, tuned by evolutionary pressures to detect those structures where they occur. In his early work Tractatus Logico-Philosophicus, Wittgenstein also links the logical structure of representation with the structure of the world, but he includes one key unnaturalistic assumption: that the sense of our representations must be given prior to-independently of-facts about how the world is. When that assumption is removed, the general outlines of the resulting position come surprisingly close to the Second Philosopher's roughly empirical account. In his later discussions of logic in Philosophical Investigations and Remarks on the Foundations of Mathematics, Wittgenstein also rejects this earlier assumption in favor of a picture that arises in the wake of the famous rule-following considerations. Here Wittgenstein and the Second Philosopher operate in even closer harmony-locating the ground of our logical practices in our interests, our natural inclinations and abilities, and very general features of the world-until the Second Philosopher moves to fill in the account with her empirical investigations of the world and cognition. At this point, Wittgenstein balks, but as a matter of personal animosity rather than philosophical principle.
Download or read book Wittgenstein on the Foundations of Mathematics written by Crispin Wright and published by . This book was released on 1980 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Philosophy of Mathematics written by Øystein Linnebo and published by Princeton University Press. This book was released on 2020-03-24 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
