Download or read book Frege s Theorem written by Richard G. Heck and published by Oxford University Press, USA. This book was released on 2011-09-29 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Heck explores a key idea in the work of the great philosopher/logician Gottlob Frege: that the axioms of arithmetic can be logically derived from a single principle. Heck uses the theorem to explore historical, philosophical, and technical issues in philosophy of mathematics and logic, relating them to key areas of contemporary philosophy.
Download or read book Frege s Theorem written by Richard G. Heck and published by OUP Oxford. This book was released on 2011-09-29 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterly fundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that arithmetic follows, purely logically, from a near definition. As Crispin Wright was the first to make clear, that means that Frege's logicism, long thought dead, might yet be viable. Heck probes the philosophical significance of the Theorem, using it to launch and then guide a wide-ranging exploration of historical, philosophical, and technical issues in the philosophy of mathematics and logic, and of their connections with metaphysics, epistemology, the philosophy of language and mind, and even developmental psychology. The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues. There are also new postscripts to five of the essays, which discuss changes of mind, respond to published criticisms, and advance the discussion yet further.
Download or read book Reading Frege s Grundgesetze written by Richard G. Heck and published by Oxford University Press, USA. This book was released on 2012-11-29 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readership: Scholars and advanced students of philosophy of logic, philosophy of mathematics, and history of analytic philosophy
Download or read book Frege s Philosophy of Mathematics written by William Demopoulos and published by Harvard University Press. This book was released on 1995 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers. This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of The Basic Laws of Arithmetic. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of Frege's theory of arithmetic. Together they form an accessible and authoritative introduction to aspects of Frege's thought that have, until now, been largely missed by the philosophical community.
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Gottlob Frege Frege s philosophy of mathematics written by Michael Beaney and published by Taylor & Francis. This book was released on 2005 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection brings together recent scholarship on Frege, including new translations of German material which is made available to Anglophone scholars for the first time.
Download or read book Fixing Frege written by John P. Burgess and published by Princeton University Press. This book was released on 2005-07-25 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gottlob Frege's attempt to found mathematics on a grand logical system came to grief when Bertrand Russell discovered a contradiction in it. This book surveys consistent restrictions in both the old and new versions of Frege's system, determining just how much of mathematics can be reconstructed in each.
Download or read book From Frege to G del written by Jean van Heijenoort and published by Harvard University Press. This book was released on 1967 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathered together here are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege’s Begriffsschrift—which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory—begins the volume, which concludes with papers by Herbrand and by Gödel.
Download or read book The Foundations of Arithmetic written by Gottlob Frege and published by Northwestern University Press. This book was released on 1980-12 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.
Download or read book An Historical Introduction to the Philosophy of Mathematics A Reader written by Russell Marcus and published by Bloomsbury Publishing. This book was released on 2016-02-11 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.
Download or read book Gottlob Frege Basic Laws of Arithmetic written by Gottlob Frege and published by . This book was released on 2013-10 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (1893 and 1903), with introduction and annotation. As the culmination of his ground-breaking work in the philosophy of logic and mathematics, Frege here tried to show how the fundamental laws of arithmetic could be derived from purely logical principles.
Download or read book Importance and Legacy written by Matthias Schirn and published by Walter de Gruyter. This book was released on 2010-12-16 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cambridge Companion to Frege written by Tom Ricketts and published by Cambridge University Press. This book was released on 2010-09-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Gottlob Frege (1848–1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research.
Download or read book Frege s Conception of Logic written by Patricia Blanchette and published by OUP USA. This book was released on 2012-04-30 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic. She argues that the fruitfulness of Frege's conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the role of conceptual analysis in logical investigation. The first part of the book locates the role of conceptual analysis in Frege's logicist project. Blanchette argues that despite a number of difficulties, Frege's use of analysis in the service of logicism is a powerful and coherent tool. As a result of coming to grips with his use of that tool, we can see that there is, despite appearances, no conflict between Frege's intention to demonstrate the grounds of ordinary arithmetic and the fact that the numerals of his derived sentences fail to co-refer with ordinary numerals. In the second part of the book, Blanchette explores the resulting conception of logic itself, and some of the straightforward ways in which Frege's conception differs from its now-familiar descendants. In particular, Blanchette argues that consistency, as Frege understands it, differs significantly from the kind of consistency demonstrable via the construction of models. To appreciate this difference is to appreciate the extent to which Frege was right in his debate with Hilbert over consistency- and independence-proofs in geometry. For similar reasons, modern results such as the completeness of formal systems and the categoricity of theories do not have for Frege the same importance they are commonly taken to have by his post-Tarskian descendants. These differences, together with the coherence of Frege's position, provide reason for caution with respect to the appeal to formal systems and their properties in the treatment of fundamental logical properties and relations.
Download or read book Frege and the Logic of Sense and Reference written by Kevin C. Klement and published by Routledge. This book was released on 2017-09-25 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.
Download or read book The Reason s Proper Study written by Bob Hale and published by Oxford University Press. This book was released on 2003 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the most powerful presentation yet of a neo-Fregean program.
Download or read book Abstractionism written by Philip A Ebert and published by Oxford University Press. This book was released on 2016-12-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstractionism, which is a development of Frege's original Logicism, is a recent and much debated position in the philosophy of mathematics. This volume contains 16 original papers by leading scholars on the philosophical and mathematical aspects of Abstractionism. After an extensive editors' introduction to the topic of abstractionism, five contributions deal with the semantics and meta-ontology of Abstractionism, as well as the so-called Caesar Problem. Four papers then discuss abstractionist epistemology, focusing on the idea of implicit definitions and non-evidential warrants (entitlements) to account for a priori mathematical knowledge. This is followed by four chapters concerning the mathematics of Abstractionism, in particular the issue of impredicativity, the Bad Company objection, and the question of abstractionist set theory. Finally, the last section of the book contains three contributions that discuss Frege's application constraint within an abstractionist setting.
