Frege's Philosophy of Mathematics

by Demopoulos, William

• ISBN13: 9780674319431
• ISBN10: 0674319435
• Edition: Reprint
• Format: Paperback
• Copyright: 1997-03-25
• Publisher: Harvard Univ Pr

Summary

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.

Table of Contents

Preface

Introduction

Appendix

The Intellectual Background to flege's Logicism

Kant, Bolzano and the Emergence of Logicism

Frege: The Last Logicist

Frege and the Rigorization of Analysis

Frege and Arbitrary Functions

Frege: The Royal Road from Geometry Postscript

The Mathematical Content of Begriffsschrift

Reading the Begriffsschrift

Frege's Theory of Number Postscript

The Consistency of Frege's Foundations of Arithmetic

The Standard of Equality of Numbers

Grundgesetze der Arithmetik

The Development of Arithmetic in Frege's Grundgesetze der Arithmetik Postscript

Definition by Induction in Frege's Grundgesetze der Arithmetik

Eudoxus and Dedekind: On the Ancient Greek Theory of Ratios and its Relation to Modern Mathematics

Frege's Theory of Real Numbers

Frege's Theory of Real Numbers

On a Question of Frege's about Right-ordered Groups Postscript

On the Consistency of the First-order Portion of Frege's Logical System

Fregean Extensions of First-order Theories

Saving Frege from Contradiction George Boolos Index of Frege's Writings

General Index

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