Frege

Philosophy of Mathematics

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Author: Michael A. E. Dummett

Publisher: Harvard University Press

ISBN: 9780674319356

Category: Philosophy

Page: 331

View: 4164

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.

Frege's Philosophy of Mathematics

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Author: William Demopoulos

Publisher: Harvard University Press

ISBN: 9780674319424

Category: Mathematics

Page: 464

View: 3683

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.

Frege

Philosophy of Language

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Author: Michael Dummett

Publisher: Harvard University Press

ISBN: 9780674319318

Category: Mathematics

Page: 708

View: 8743

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.

The Reason's Proper Study

Essays Towards a Neo-Fregean Philosophy of Mathematics

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Author: Bob Hale,Crispin Wright

Publisher: Oxford University Press

ISBN: 9780199266326

Category: Philosophy

Page: 455

View: 8627

Bob Hale and Crispin Wright draw together here the key writings in which they have worked out their distinctive neo-Fregean approach to the philosophy of mathematics. The two main components in Frege's mathematical philosophy were his platonism and his logicism - the claims, respectively, that mathematics is a body of knowledge about independently existing objects, and that this knowledge may be acquired on the basis of general logical laws and suitable definitions. The central thesis ofthis collection is that Frege was - his own eventual recantation notwithstanding - substantially right in both claims. Where neo-Fregeanism principally differs from Frege is in taking a more optimistic view of the kind of contextual explanation (proceeding via what are now commonly called abstraction principles) of the fundamental concepts of arithmetic and analysis which Frege considered and rejected. On this basis, neo-Fregeanism promises defensible and attractive answers to some of the most important ontological and epistemological questions in 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 programme and the contributions made to it by the various papers; a postscript explaining which issues most require further attention; and bibliographies both of references and of further useful sources. The Reason's Proper Study will be recognized as the most powerful presentation yet of the neo-Fregean programme; it will prove indispensable reading not just to philosophers of mathematics but to all who are interested in the fundamental metaphysical and epistemological issues on which the programme impinges.

Gottlob Frege: Frege's philosophy of mathematics

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Author: Michael Beaney

Publisher: Taylor & Francis

ISBN: 9780415306041

Category:

Page: 416

View: 1482

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.

Philosophy of Mathematics

Selected Readings

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Author: Paul Benacerraf,Hilary Putnam

Publisher: Cambridge University Press

ISBN: 1107268133

Category: Science

Page: N.A

View: 5885

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

The Foundations of Arithmetic

A Logico-Mathematical Enquiry Into the Concept of Number

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Author: Gottlob Frege,J. L. Austin

Publisher: Northwestern University Press

ISBN: 0810106051

Category: Mathematics

Page: 119

View: 3599

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.

Frege

Philosophy of Mathematics

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Author: Michael A. E. Dummett

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 331

View: 8449

Fixing Frege

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Author: John P. Burgess

Publisher: Princeton University Press

ISBN: 0691187061

Category: Philosophy

Page: N.A

View: 5479

Frege's Logic

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Author: Danielle MACBETH,Danielle Macbeth

Publisher: Harvard University Press

ISBN: 0674040392

Category: Philosophy

Page: 218

View: 740

For many philosophers, modern philosophy begins in 1879 with the publication of Frege's Begriffsschrift, in which Frege presents the first truly modern logic in his symbolic language, Begriffsschrift, or concept-script. Macbeth's book, the first full-length study of this language, offers a highly original new reading of Frege's logic based directly on Frege's own two-dimensional notation and his various writings about logic.

Phenomenology, Logic, and the Philosophy of Mathematics

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Author: Richard L. Tieszen

Publisher: Cambridge University Press

ISBN: 9780521837828

Category: Mathematics

Page: 357

View: 2703

In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.

Logicism and the Philosophy of Language

Selections from Frege and Russell

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Author: Arthur Sullivan

Publisher: Broadview Press

ISBN: 1551114712

Category: Philosophy

Page: 304

View: 6099

Logicism and the Philosophy of Language brings together the core works by Gottlob Frege and Bertrand Russell on logic and language. In their separate efforts to clarify mathematics through the use of logic in the late nineteenth and early twentieth century, Frege and Russell both recognized the need for rigorous and systematic semantic analysis of language. It was their turn to this style of analysis that would establish the philosophy of language as an autonomous area of inquiry. This anthology gathers together these foundational writings, and frames them with an extensive historical introduction. This is a collection for anyone interested in questions about truth, meaning, reference, and logic, and in the application of formal analysis to these concepts.

Gottlob Frege: Basic Laws of Arithmetic

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Author: Gottlob Frege

Publisher: Oxford University Press (UK)

ISBN: 0199281742

Category: Mathematics

Page: 33

View: 942

This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (originally published in two volumes, 1893 and 1903), with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to allintents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework within which his technical contributions were conceived and developed has been so deep that he has astrong case to be regarded as the inventor of much of the agenda of modern analytical philosophy itself. Two of Frege's three principal books - the Begriffsschrift (1879) and Grundlagen der Arithmetik (1884) - have been available in English translation for many years, as have all the most important of his other, article-length writings. Grundgesetze was to have been the summit of Frege's life's work -a rigorous demonstration of how the fundamental laws of the classical pure mathematics of the natural and real numbers could be derived from principles which, in his view, were purely logical. A letter received from Bertrand Russell shortly before the publication of the second volume made Fregerealise that Axiom V of his system, governing identity for value-ranges, led to contradiction. But much of the main thrust of Frege's project can be salvaged. The continuing importance of the Grundgesetze lies not only in its bearing on issues in the foundations of mathematics but in its model of philosophical inquiry. Frege's ability to locate the essential questions, his integration of logical and philosophical analysis, and his rigorous approach tocriticism and argument in general are vividly in evidence in this, his most ambitious work.

Frege's Theorem

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Author: Richard G. Heck

Publisher: Oxford University Press

ISBN: 0199695644

Category: Mathematics

Page: 307

View: 1388

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.

Philosophy of Arithmetic

Psychological and Logical Investigations with Supplementary Texts from 1887–1901

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Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 9401000603

Category: Mathematics

Page: 515

View: 2804

This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.

Principia Mathematica

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Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: N.A

View: 3237

Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals)

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Author: Donald Gillies

Publisher: Routledge

ISBN: 113672107X

Category: Mathematics

Page: 118

View: 2628

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic.