Freges Theorem

Paperback | October 29, 2014

byRichard G. Heck

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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 asingle 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 Theoremshows 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 languageand 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 discusschanges of mind, respond to published criticisms, and advance the discussion yet further.

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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 asingle principle: the number of these things ...

Richard G. Heck Jr is Romeo Elton Professor of Natural Theology at Brown University, where he has taught since 2005. He taught at Harvard University from 1991 to 2005 and was educated at the Massachusetts Institute of Technology, from which he received his PhD in 1991; at New College, Oxford (BPhil, 1987), where he was a Marshall Scho...

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Hardcover|Dec 29 2012

$60.02 online$63.00list price
Format:PaperbackDimensions:322 pages, 9.21 × 6.14 × 0.01 inPublished:October 29, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019870898X

ISBN - 13:9780198708988

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Table of Contents

PrefaceEditorial Notes1. Frege's Theorem: An Overview2. The Development of Arithmetic3. Die Grundlagen der Arithmetik SCSC82-834. Frege's Principle5. Julius Caesar and Basic Law V6. The Julius Caesar Objection7. Cardinality, Counting, and Equinumerosity8. Syntactic Reductionism9. The Existence of Abstract Objects10. The Consistency of Contextual Definitions11. Finitude and Hume's Principle12. A Logic for Frege's TheoremIndex

Editorial Reviews

"sets the standard for the serious study of Frege's logicism." --Manuel Bremer, Philosophy in Review