Frege S Theorem
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Frege S Theorem
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Author : Richard G. Heck
language : en
Publisher: Oxford University Press
Release Date : 2011-09-29
Frege S Theorem written by Richard G. Heck and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-29 with Mathematics categories.
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.
Frege S Philosophy Of Mathematics
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Author : William Demopoulos
language : en
Publisher: Harvard University Press
Release Date : 1995
Frege S Philosophy Of Mathematics written by William Demopoulos and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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.
Fixing Frege
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Author : John P. Burgess
language : en
Publisher: Princeton University Press
Release Date : 2018-06-05
Fixing Frege written by John P. Burgess and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-05 with Philosophy categories.
The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics. This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured.
Importance And Legacy
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Author : Matthias Schirn
language : en
Publisher: Walter de Gruyter
Release Date : 2010-12-16
Importance And Legacy written by Matthias Schirn and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-16 with Philosophy categories.
Gottlob Frege Frege S Philosophy Of Mathematics
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Author : Michael Beaney
language : en
Publisher: Taylor & Francis
Release Date : 2005
Gottlob Frege Frege S Philosophy Of Mathematics written by Michael Beaney and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Philosophy categories.
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.
From Frege To G Del
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Author : Jean van Heijenoort
language : en
Publisher: Harvard University Press
Release Date : 2002-01-15
From Frege To G Del written by Jean van Heijenoort and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-15 with Philosophy categories.
The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded by Leibniz, may be said to have been initiated by Boole, De Morgan, and Jevons, but it was the publication in 1879 of Gottlob Frege’s Begriffsschrift that opened a great epoch in the history of logic by presenting, in full-fledged form, the propositional calculus and quantification theory. Frege’s book, translated in its entirety, begins the present volume. The emergence of two new fields, set theory and foundations of mathematics, on the borders of logic, mathematics, and philosophy, is depicted by the texts that follow. Peano and Dedekind illustrate the trend that led to Principia Mathematica. Burali-Forti, Cantor, Russell, Richard, and König mark the appearance of the modern paradoxes. Hilbert, Russell, and Zermelo show various ways of overcoming these paradoxes and initiate, respectively, proof theory, the theory of types, and axiomatic set theory. Skolem generalizes Löwenheim’s theorem, and he and Fraenkel amend Zermelo’s axiomatization of set theory, while von Neumann offers a somewhat different system. The controversy between Hubert and Brouwer during the twenties is presented in papers of theirs and in others by Weyl, Bernays, Ackermann, and Kolmogorov. The volume concludes with papers by Herbrand and by Gödel, including the latter’s famous incompleteness paper. Of the forty-five contributions here collected all but five are presented in extenso. Those not originally written in English have been translated with exemplary care and exactness; the translators are themselves mathematical logicians as well as skilled interpreters of sometimes obscure texts. Each paper is introduced by a note that sets it in perspective, explains its importance, and points out difficulties in interpretation. Editorial comments and footnotes are interpolated where needed, and an extensive bibliography is included.
Frege S Theorem
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Author : Richard G. Heck
language : en
Publisher: OUP Oxford
Release Date : 2011-09-29
Frege S Theorem written by Richard G. Heck and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-29 with Philosophy categories.
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.
Reading Frege S Grundgesetze
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Author : Heck Jr.
language : en
Publisher: OUP Oxford
Release Date : 2012-11-29
Reading Frege S Grundgesetze written by Heck Jr. and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-29 with Philosophy categories.
Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy. Part I of Reading Frege's Grundgesetze develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses his notorious 'Basic Law V' and attempts to secure its status as a law of logic. Part II examines the mathematical basis of Frege's logicism, explaining and exploring Frege's formal arguments. Heck argues that Frege himself knew that his proofs could be reconstructed so as to avoid Russell's Paradox, and presents Frege's arguments in a way that makes them available to a wide audience. He shows, by example, that careful attention to the structure of Frege's arguments, to what he proved, to how he proved it, and even to what he tried to prove but could not, has much to teach us about Frege's philosophy.
Frege And The Logic Of Sense And Reference
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Author : Kevin C. Klement
language : en
Publisher: Routledge
Release Date : 2017-09-25
Frege And The Logic Of Sense And Reference written by Kevin C. Klement and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Philosophy categories.
First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.
The Foundations Of Frege S Logic
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Author : Pavel Tichy
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-25
The Foundations Of Frege S Logic written by Pavel Tichy and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-25 with Philosophy categories.