Constructibility and mathematical existence / Charles S. Chihara.

Preface
Acknowledgements
Contents
I: The Constructibility Theory
1. The Problem of Existence in Mathematics
1. The Philosophical Problem
2. Quine's Platonism
3. Gödel's Platonism
4. Heyting's Intuitionism
2. The Constructibility Quantifiers
1. Introduction
2. The Language L
3. The Language L*
4. Some Objections Considered
3. Constructibility and Open-Sentences
1. The Constructibility of Open-Sentences
2. A Simple Type Theory for Open-Sentences
3. A Comparison with a Predicative System
4. The Logical Space of Open-Sentences.

5. The Kinds of Open-Sentences to be Discussed
6. Quine's Objections to Modality
4. The Deductive System
1. The Language Lt
2. The Theory Ct
3. Objections to Type Theory
4. Objections to the Constructibility Theory
5. Cardinality and Number Theory
1. Formal Developments
2. Philosophical Amplifications
6. Measurable Quantities and Analysis
1. A Standard Development of Real Analysis
2. A Theory of Lengths
3. Geometrical Representations of Functions
4. Putnam's Case for Realism
5. Complex Analysis
6. Applications by Means of Structural Identity.

II: Philosophical Developments
7. Mathematical Structuralism
1. Introduction
2. The Structuralist View of Applications
3. Resnik on the Nature of Structures
4. An Evaluation of Shapiro's Account of Mathematics
5. An Evaluation of Resnik's Account of Structures
8. Science without Numbers
1. Introduction to Field's Instrumentalism
2. The Conservation Theorem
3. Field's Cardinality Theory
4. Field's Nominalistic Physics
5. Some Doubts about the Adequacy of Field's View
6. A Comparison with the Constructibility Theory
7. A Re-examination of Resnik's Reasoning.

8. The Neo-Quinian Argument Reconsidered
9. Why Burgess Is a Moderate Realist
1. A Dilemma for the Nominalist
2. A False Dilemma
3. Burgess's Objection to Field's Preference for Nominalism
10. Maddy's Solution to the Problem of Reference
1. Involved Platonists
2. Problems of Reference for Mathematical Platonism
3. Maddy's Solution
4. Doubts about Maddy's Solution
5. Concluding Comments
11. Kitcher's Ideal Agents
1. Kitcher's Account of Mathematical Knowledge
2. An Analysis of Kitcher's View: Details and Doubts
12. Deflationism and Mathematical Truth.

1. Field's Deflationism
2. A Reconsideration of the Veridicality of Mathematics
Appendix: Field's Nominalistic Logical Theory
Postscript
Bibliography
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
V
W
Z.