Abstract

PART I: THE CONSTRUCTIBILITY THEORY: The Problem of Existence in Mathematics The Constructibility Quantifiers Constructibility and Open-Sentences The Deductive System Cardinality and Number Theory Measurable Quantities and Analysis. PART II: PHILOSOPHICAL DEVELOPMENTS: Mathematical Structuralism Science Without Numbers Why Burgess is a Moderate Realist Maddy's Solution to the Problem of Reference Kitcher's Ideal Agents Deflationism and Mathematical Truth. Appendix Field's Nominalistic Logical Theory.

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