Logicism and Its Philosophical Legacy

by Demopoulos, William

• ISBN13: 9781107029804
• ISBN10: 1107029805
• Format: Hardcover
• Copyright: 2013-02-25
• Publisher: Cambridge Univ Pr

Summary

The idea that mathematics is reducible to logic has a long history, but it was Frege who gave logicism an articulation and defense that transformed it into a distinctive philosophical thesis with a profound influence on the development of philosophy in the twentieth century. This volume of classic, revised and newly written essays by William Demopoulos examines logicism's principal legacy for philosophy: its elaboration of notions of analysis and reconstruction. The essays reflect on the deployment of these ideas by the principal figures in the history of the subject - Frege, Russell, Ramsey and Carnap - and in doing so illuminate current concerns about the nature of mathematical and theoretical knowledge. Issues addressed include the nature of arithmetical knowledge in the light of Frege's theorem; the status of realism about the theoretical entities of physics; and the proper interpretation of empirical theories that postulate abstract structural constraints.

Table of Contents

Preface

Introduction

Frege's analysis of arithmetical knowledge

Carnap's thesis, on extending 'empiricism, semantics and ontology' to the realism-instrumentalism controversy

Carnap's analysis of realism

Bertrand Russell's The Analysis of Matter: its historical context and contemporary interest with

On the rational reconstruction of our theoretical knowledge

Three views of theoretical knowledge

Frege and the rigorization of analysis

The philosophical basis of our knowledge of number

The 1910 Principia's theory of functions and classes

Ramsey's extensional propositional functions

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