Frege S Philosophy Of Mathematics

Author : William Demopoulos
Publisher : Harvard University Press
Page : 492 pages
File Size : 52,7 Mb
Release : 1995
Category : Mathematics
ISBN : 0674319427

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Frege's Philosophy of Mathematics by William Demopoulos Pdf

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.

Author : Michael Dummett
Publisher : Harvard University Press
Page : 364 pages
File Size : 41,9 Mb
Release : 1991
Category : Mathematics
ISBN : 0674319354

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Frege by Michael Dummett Pdf

No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.

Author : Michael Beaney,Erich H. Reck
Publisher : Taylor & Francis
Page : 424 pages
File Size : 52,6 Mb
Release : 2005
Category : Philosophy
ISBN : 0415306043

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Gottlob Frege: Frege's philosophy of mathematics by Michael Beaney,Erich H. Reck Pdf

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.

Author : Michael Dummett
Publisher : Harvard University Press
Page : 756 pages
File Size : 50,9 Mb
Release : 1981
Category : Mathematics
ISBN : 0674319311

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Frege by Michael Dummett Pdf

No one has figured more prominently in the study of German philosopher Gottlob Frege than Michael Dummett. This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of analytic philosophy. Frege: Philosophy of Language remains indispensable for an understanding of contemporary philosophy. Harvard University Press is pleased to reissue this classic book in paperback.

Author : Patricia Blanchette
Publisher : OUP USA
Page : 207 pages
File Size : 52,8 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780199891610

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Frege's Conception of Logic by Patricia Blanchette Pdf

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.

Author : Tom Ricketts,Michael Potter
Publisher : Cambridge University Press
Page : 128 pages
File Size : 53,5 Mb
Release : 2010-09-02
Category : Philosophy
ISBN : 9781139825788

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The Cambridge Companion to Frege by Tom Ricketts,Michael Potter Pdf

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.

Author : Gottlob Frege
Publisher : John Wiley & Sons
Page : 146 pages
File Size : 55,8 Mb
Release : 1980
Category : Mathematics
ISBN : 9780631126942

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The Foundations of Arithmetic by Gottlob Frege Pdf

A philosophical discussion of the concept of number In the book, The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, Gottlob Frege explains the central notions of his philosophy and analyzes the perspectives of predecessors and contemporaries. The book is the first philosophically relevant discussion of the concept of number in Western civilization. The work went on to significantly influence philosophy and mathematics. Frege was a German mathematician and philosopher who published the text in 1884, which seeks to define the concept of a number. It was later translated into English. This is the revised second edition.

Author : Michael D. Resnik
Publisher : Unknown
Page : 258 pages
File Size : 40,5 Mb
Release : 1980
Category : Mathematics
ISBN : UCAL:B4246993

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Frege and the Philosophy of Mathematics by Michael D. Resnik Pdf

Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 51,7 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X

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Principia Mathematica by Alfred North Whitehead,Bertrand Russell Pdf

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

Author : Gottlob Frege
Publisher : Unknown
Page : 248 pages
File Size : 44,6 Mb
Release : 1980
Category : College student development programs
ISBN : PSU:000008707246

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Translations from the Philosophical Writings of Gottlob Frege by Gottlob Frege Pdf

Author : Gottlob Frege,Roy T. Cook
Publisher : Oxford University Press, USA
Page : 683 pages
File Size : 54,8 Mb
Release : 2013-10
Category : Mathematics
ISBN : 9780199281749

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Gottlob Frege: Basic Laws of Arithmetic by Gottlob Frege,Roy T. Cook Pdf

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.

Author : Joan Weiner
Publisher : Cornell University Press
Page : 344 pages
File Size : 54,6 Mb
Release : 2018-05-31
Category : Philosophy
ISBN : 9781501714955

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Frege in Perspective by Joan Weiner Pdf

Not only can the influence of Gottlob Frege (1848-1925) be found in contemporary work in logic, the philosophy of mathematics, and the philosophy of language, but his projects—and the very terminology he employed in pursuing those projects—are still current in contemporary philosophy. This is undoubtedly why it seems so reasonable to assume that we can read Frege' s writings as if he were one of us, speaking to our philosophical concerns in our language. In Joan Weiner's view, however, Frege's words can be accurately interpreted only if we set that assumption aside. Weiner here offers a challenging new approach to the philosophy of this central figure in analytic philosophy. Weiner finds in Frege's corpus, from Begriffsschrift (1879) on, a unified project of remarkable ambition to which each of the writings in that corpus makes a distinct contribution—a project whose motivation she brings to life through a careful reading of his Foundations of Arithmetic. The Frege that Weiner brings into clear view is very different from the familiar figure. Far from having originated one of the standard positions on the nature of reference, Frege turns out not to have had positive doctrines on anything like what contemporary philosophers mean by "reference." Far from having served as a standard-bearer for those who take the realists' side of contemporary disputes with anti-realists, Frege turns out to have had no stake in either side of the controversy. Through Weiner's lens, Frege emerges as a thinker who has principled reasons for challenging the very assumptions and motivations that animate philosophers to dispute these doctrines. This lucidly written and accessible book will generate controversy among all readers with an interest in epistemology, philosophy of language, history of philosophy, and the philosophy of mathematics.

Author : John P. Burgess
Publisher : Princeton University Press
Page : 270 pages
File Size : 42,8 Mb
Release : 2018-06-05
Category : Philosophy
ISBN : 9780691187068

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Fixing Frege by John P. Burgess Pdf

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.

Author : Bob Hale
Publisher : Oxford University Press
Page : 309 pages
File Size : 51,5 Mb
Release : 2013-09-19
Category : Philosophy
ISBN : 9780199669578

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Necessary Beings by Bob Hale Pdf

Bob Hale presents a broadly Fregean approach to metaphysics, according to which ontology and modality are mutually dependent upon one another. He argues that facts about what kinds of things exist depend on facts about what is possible. Modal facts are fundamental, and have their basis in the essences of things—not in meanings or concepts.

Author : Richard L. Mendelsohn
Publisher : Cambridge University Press
Page : 260 pages
File Size : 53,9 Mb
Release : 2005-01-10
Category : Philosophy
ISBN : 1139444034

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The Philosophy of Gottlob Frege by Richard L. Mendelsohn Pdf

This analysis of Frege's views on language and metaphysics in On Sense and Reference, arguably one of the most important philosophical essays of the past hundred years, provides a thorough introduction to the function/argument analysis and applies Frege's technique to the central notions of predication, identity, existence and truth. Of particular interest is the analysis of the Paradox of Identity and a discussion of three solutions: the little-known Begriffsschrift solution, the sense/reference solution, and Russell's 'On Denoting' solution. Russell's views wend their way through the work, serving as a foil to Frege. Appendices give the proofs of the first 68 propositions of Begriffsschrift in modern notation. This book will be of interest to students and professionals in philosophy and linguistics.