Constructibility and Mathematical Existence

Erscheinungsjahr 2001
ISBN: 978-0-19-823975-8
Verlag: OUP Oxford

Buch, Englisch, 298 Seiten, Format (B × H): 140 mm x 216 mm, Gewicht: 426 g

Reihe: Clarendon Paperbacks

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 through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.

Autoren/Hrsg.

Chihara, Charles S.

Fachgebiete

• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie

Inhaltsverzeichnis

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.