Reading Frege's Grundgesetze

by Heck, Jr., Richard G.

• ISBN13: 9780199233700
• ISBN10: 0199233705
• Format: Hardcover
• Copyright: 2013-02-07
• Publisher: Oxford University Press

Summary

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 moremathematical 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 wideaudience. 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.

Author Biography

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 through 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 Scholar; and at Duke University (BS, 1985). Professor Heck has worked on the philosophies of language, logic, mathematics, and mind, and is is one of the world's foremost experts on the philosophy of Gottlob Frege. He lives in Canton, Massachusetts, with his wife, daughter, and five cats.

Table of Contents

Preface

Editorial Notes

Introduction

The Logic Behind Frege's Logicism

Frege and Semantics

Grundgesetze I SCSC29-32 (I)

Grundgesetze I SC10

Grundgesetze I SCSC29-32 (II)

The Mathematics Behind Frege's Logicism

The Development of Arithmetic

Definition by Recursion

Frege on Finitude

The Finite and the Infinite

The Definition of Addition

Further unto the Infinite

Appendices

Bibliography

Index

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