Logicism and its Philosophical Legacy

William Demopoulos

• Publisher: Cambridge University Press
• Year: 2013
• Print ISBN:
  9781107029804
• eBook ISBN:
  9781139604123
• Topic: Mathematics
• Subtopic: Logic in Mathematics
• Index: Mathematics

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

• Cover
• Contents
• Preface
• Introduction
• Chapter 1 Frege’s analysis of arithmetical knowledge
• Chapter 2 Carnap’s thesis
• Chapter 3 On extending “Empiricism, semantics and ontology” to the realism–instrumentalism controversy
• Chapter 4 Carnap’s analysis of realism
• Chapter 5 Bertrand Russell’s The Analysis of Matter: its historical context and contemporary interest
• Chapter 6 On the rational reconstruction of our theoretical knowledge
• Chapter 7 Three views of theoretical knowledge
• Chapter 8 Frege and the rigorization of analysis
• Chapter 9 The philosophical basis of our knowledge of number
• Chapter 10 The 1910 Principia’s theory of functions and classes
• Chapter 11 Ramsey’s extensional propositional functions
• Bibliography
• Index