Frege's Theorem

Frege's Theorem
Author: Richard G. Heck
Publisher: Oxford University Press, USA
Total Pages: 322
Release: 2011-09-29
Genre: Mathematics
ISBN: 0199695644

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.

Reading Frege's Grundgesetze

Reading Frege's Grundgesetze
Author: Richard G. Heck
Publisher: Oxford University Press, USA
Total Pages: 315
Release: 2012-11-29
Genre: Mathematics
ISBN: 0199233705

Readership: Scholars and advanced students of philosophy of logic, philosophy of mathematics, and history of analytic philosophy

Frege's Philosophy of Mathematics

Frege's Philosophy of Mathematics
Author: William Demopoulos
Publisher: Harvard University Press
Total Pages: 492
Release: 1995
Genre: Mathematics
ISBN: 9780674319424

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.

Gottlob Frege: Frege's philosophy of mathematics

Gottlob Frege: Frege's philosophy of mathematics
Author: Michael Beaney
Publisher: Taylor & Francis
Total Pages: 424
Release: 2005
Genre: Philosophy
ISBN: 9780415306041

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.

Frege's Theorem

Frege's Theorem
Author: Richard G. Heck
Publisher: Oxford University Press, USA
Total Pages: 0
Release: 2014-10-02
Genre: Philosophy
ISBN: 9780198708988

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.

An Historical Introduction to the Philosophy of Mathematics: A Reader

An Historical Introduction to the Philosophy of Mathematics: A Reader
Author: Russell Marcus
Publisher: Bloomsbury Publishing
Total Pages: 849
Release: 2016-02-11
Genre: Philosophy
ISBN: 1472529480

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.

Gottlob Frege: Basic Laws of Arithmetic

Gottlob Frege: Basic Laws of Arithmetic
Author: Gottlob Frege
Publisher:
Total Pages: 683
Release: 2013-10
Genre: Mathematics
ISBN: 0199281742

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.

Fixing Frege

Fixing Frege
Author: John P. Burgess
Publisher: Princeton University Press
Total Pages: 276
Release: 2005-07-25
Genre: Mathematics
ISBN: 9780691122311

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.

Importance and Legacy

Importance and Legacy
Author: Matthias Schirn
Publisher: Walter de Gruyter
Total Pages: 477
Release: 2010-12-16
Genre: Philosophy
ISBN: 3110813041

The Reason's Proper Study

The Reason's Proper Study
Author: Bob Hale
Publisher: Oxford University Press
Total Pages: 470
Release: 2003
Genre: Language Arts & Disciplines
ISBN: 0199266328

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.