Logicism and Its Philosophical Legacy

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.Preface; Introduction; 1. Frege's analysis of arithmetical knowledge; 2. Carnap's thesis, on extending 'empiricism, semantics and ontology' to the realism-instrumentalism controversy; 3. Carnap's analysis of realism; 4. Bertrand Russell's The Analysis of Matter: its historical context and contemporary interest with Michael Friedman; 5. On the rational reconstruction of our theoretical knowledge; 6. Three views of theoretical knowledge; 7. Frege and the rigorization of analysis; 8. The philosophical basis of our knowledge of number; 9. The 1910 Principia's theory of functions and classes; 10. Ramsey's extensional propositional functions.