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Logicism and its Philosophical Legacy
About This Book
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.
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Table of contents
- Cover
- Contents
- Preface
- Introduction
- Chapter 1 Fregeâs analysis of arithmetical knowledge
- Chapter 2 Carnapâs thesis
- Chapter 3 On extending âEmpiricism, semantics and ontologyâ to the realismâinstrumentalism controversy
- Chapter 4 Carnapâs analysis of realism
- Chapter 5 Bertrand Russellâs 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 Principiaâs theory of functions and classes
- Chapter 11 Ramseyâs extensional propositional functions
- Bibliography
- Index