
Philosophy of Mathematics
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Content
- Intro
- Contents
- Introduction
- PART I: PERSPECTIVE
- 1 Mathematics and Its Philosophy
- 2 Object and Truth: A Realist Manifesto
- 1 Slogans
- 2 Methodology
- 3 Philosophy
- 4 Interlude on Antirealism
- 5 Quine
- 6 A Role for the External
- PART II: STRUCTURALISM
- 3 Structure
- 1 Opening
- 2 Ontology: Object
- 3 Ontology: Structure
- 4 Theories of Structure
- 5 Mathematics: Structures, All the Way Down
- 6 Addendum: Function and Structure
- 4 Epistemology and Reference
- 1 Epistemic Preamble
- 2 Small Finite Structure: Abstraction and Pattern Recognition
- 3 Long Strings and Large Natural Numbers
- 4 To the Infinite: The Natural-number Structure
- 5 Indiscernibility, Identity, and Object
- 6 Ontological Interlude
- 7 Implicit Definition and Structure
- 8 Existence and Uniqueness: Coherence and Categoricity
- 9 Conclusions: Language, Reference, and Deduction
- 5 How We Got Here
- 1 When Does Structuralism Begin?
- 2 Geometry, Space, Structure
- 3 A Tale of Two Debates
- 4 Dedekind and ante rem Structures
- 5 Nicholas Bourbaki
- PART III: RAMIFICATIONS AND APPLICATIONS
- 6 Practice: Construction, Modality, Logic
- 1 Dynamic Language
- 2 Idealization to the Max
- 3 Construction, Semantics, and Ontology
- 4 Construction, Logic, and Object
- 5 Dynamic Language and Structure
- 6 Synthesis
- 7 Assertion, Modality, and Truth
- 8 Practice, Logic, and Metaphysics
- 7 Modality, Structure, Ontology
- 1 Modality
- 2 Modal Fictionalism
- 3 Modal Structuralism
- 4 Other Bargains
- 5 What Is a Structuralist to Make of All This?
- 8 Life Outside Mathematics: Structure and Reality
- 1 Structure and Science-the Problem
- 2 Application and Structure
- 3 Borders
- 4 Maybe It Is Structures All the Way Down
- References
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- Z
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