Constructibility and Mathematical Existence by Chihara, Charles S. -- Read -- Imperial Library of Trantor

Index

Book title The Problem of Existence in Mathematics

2. Quine's Platonism 3. Gödel's Platonism 4. Heyting's Intuitionism

The Constructibility Quantifiers

2. The Language L 3. The Language L* 4. Some Objections Considered Constructibility and 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

The Deductive System

2. The Theory Ct The Axiom of Extensionality Identity Axioms The Axiom of Abstraction The Hypothesis of Infinity 3. Objections to Type Theory 4. Objections to the Constructibility Theory

Cardinality and Number Theory

2. Philosophical Amplifications

Measurable Quantities and Analysis

2. A Theory of Lengths Fundamentals Rational Lengths Real Lengths 3. Geometrical Representations of Functions 4. Putnam's Case for Realism 5. Complex Analysis 6. Applications by Means of Structural Identity

Mathematical Structuralism

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

Science without Numbers

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

Why Burgess Is a Moderate Realist

2. A False Dilemma 3. Burgess's Objection to Field's Preference for Nominalism

Maddy's Solution to the Problem of Reference

2. Problems of Reference for Mathematical Platonism 3. Maddy's Solution 4. Doubts about Maddy's Solution 5. Concluding Comments

Kitcher's Ideal Agents

2. An Analysis of Kitcher's View: Details and Doubts Are the Theorems of Mathematics Known to be True? Do People Believe What Kitcher Implies that They Do? Kitcher's Theory of Arithmetic Kitcher's Version of Set Theory Kitcher's Explanation of how Mathematics is Applied Has Kitcher Accounted for Our Mathematical Knowledge? Zermelo's Axioms

Deflationism and Mathematical Truth

Field's Nominalistic Logical Theory Postscript Bibliography Index