Constructibility And Mathematical Existence

Constructibility and Mathematical Existence

This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach in an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.

Constructibility and Mathematical Existence

Concerned with the problem of existence in mathematics, this volume develops a mathematical system in which there are no existence assertions but only assertions of constructibility. It explores the philosophical implications of such an approach in the writings of Field, Burgess, Maddy and Kitcher.

Constructibility and Mathematical Existence: The Constructibility Theory – 1. The Problem of Existence in Mathematics – 2. The Constructibility Quantifiers – 3. Constructibility and Open Sentences – 4. The Deductive System – 5. Cardinality and Number Theory – 6. Measurable Quantities and Analysis – Part II: Philosophical Developments – 7. Mathematical Structuralism – 8. Science Without Numbers – 9. Why Burgess Is a Moderate Realist – 10. Maddy’s Solution to the Problem of Reference – 10. Kitcher’s Ideal Agent – 12. Deflationism and Mathematical Truth