Constructibility and Mathematical Existence

ISBN-13: 9780198239758 / Angielski / Miękka / 1991 / 304 str.

Charles S. Chihara

Opis

Chihara here develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. He utilizes this system in the analysis of the nature of mathematics, and discusses many recent works in the philosophy of mathematics from the viewpoint of the constructibility theory developed. This innovative analysis will appeal to mathematicians and philosophers of logic, mathematics, and science.

Recenzje

'an important work in the philosophy of mathematics, well deserving of more careful study and analysis than there has been room for here' John P. Burgess, Princeton University, The Philosophical Review, Vol. 101, No. 4, (October 1992)

Spis treści

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.