Contents
Preface
Introduction
Chapter 1 Frege’s analysis of arithmetical knowledge
1.1 Frege’s interest in rigor
1.2 The significance of a derivation of arithmetic from logic
1.3 The problem of apriority
1.4 Analysis versus justification
1.5 Summary and conclusion
Chapter 2 Carnap’s thesis
2.1 Background to the thesis
2.2 Two strategies
2.3 Applying geometry
2.4 Applying arithmetic
2.5 Recapitulation: the analysis of equinumerosity and simultaneity
2.6 Centrality
Acknowledgments
Chapter 3 On extending “Empiricism, semantics and ontology” to the realism–instrumentalism controversy
3.1 The nature of the problem
3.2 The realism–instrumentalism controversy and the atomic hypothesis
3.3 A recent criticism of ESO
3.4 Carnap and the realism–instrumentalism controversy
Acknowledgments
Chapter 4 Carnap’s analysis of realism
4.1 Constructive empiricism and its discontents
4.2 Friedman’s observation
4.3 Carnap’s neutrality
4.4 The role of metaphysics in the realism–instrumentalism controversy
Appendix: Empiricist structuralism
Chapter 5 Bertrand Russell’s The Analysis of Matter: its historical context and contemporary interest
5.1
5.2
5.3
5.4
Chapter 6 On the rational reconstruction of our theoretical knowledge
6.1 Introduction
6.2 Russell’s theory of propositional understanding
6.3 Ramsey’s primary and secondary systems
6.4 Carnap’s reconstruction of the language of science and an observation of Newman
6.5 Extension of the foregoing to constructive empiricism
6.6 Putnam’s model-theoretic argument and the semantic view of theories
6.7 The problem clarified and resolved
Acknowledgments
Chapter 7 Three views of theoretical knowledge
7.1 Introduction
7.2 Ramsey sentences and Craig transcriptions
7.3 Ramsey sentences and the applications of a theory
7.4 Extensions and expansions of models and Russell’s structuralism
7.5 Ramsey on theories
7.6 Carnap’s synthesis
7.7 The structuralist thesis
Acknowledgments
Chapter 8 Frege and the rigorization of analysis
8.1 Introduction
8.2 Rigor and spatio-temporal intuition
8.3 Spatio-temporal intuition and abstraction
8.4 Frege’s theory of sequences
Acknowledgments
Chapter 9 The philosophical basis of our knowledge of number
9.1
9.2
9.3
9.4
9.5
9.6
9.7
Appendix
Acknowledgments
Chapter 10 The 1910 Principia’s theory of functions and classes
10.1 The status of classes
10.2 Types and orders
10.3 Principia’s model of our knowledge of classes
10.4 The concept of a propositional function
10.5 Reducibility
Appendix: russell’s propositional paradox
Acknowledgments
Chapter 11 Ramsey’s extensional propositional functions
11.1 Introduction
11.2 The Tractarian background to Ramsey’s extensional propositional functions
11.3 Infinity without extensional propositional functions
11.4 Infinity with extensional propositional functions
11.5 Extensional propositional functions and logicism
Acknowledgments
Bibliography
Index
