Logicism and its Philosophical Legacy
Cambridge University Press, 1/3/2013
EAN 9781107029804, ISBN10: 1107029805
Hardcover, 281 pages, 22.8 x 15.2 x 2 cm
Language: English
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.