Mathematics without Numbers
Towards a Modal-Structural Interpretation
Published on 25. November 1993
Book
Paperback/Softback
168 pages
978-0-19-824034-1 (ISBN)
Description
Geoffrey Hellman presents a detailed interpretation of mathematics as the investigation of structural possibilities, as opposed to absolute, Platonic objects. After dealing with the natural numbers and analysis, he extends his approach to set theory, and shows how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.
Reviews / Votes
Without doubt this volume is a major contribution to recent philosophy of mathematics and should be read by anyone interested in this difficult but philosophically central field. * Peter Clark, Times Higher Education Supplement * rich, subtle, and insightful * Stewart Shapiro, Nous *More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 216 mm
Width: 140 mm
Thickness: 10 mm
Weight
220 gr
ISBN-13
978-0-19-824034-1 (9780198240341)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Content
Introduction; Chapter 1: The natural numbers and analysis; Introduction; The modal-structural framework: The hypothetical component; The categorical component: An axiom of infinity and a derivation (inspired by Dedekind with help from Frege); Justifying the translation scheme; Justification from within; Extensions; The question of nominalism; Chapter 2: Set theory; Introduction; Informal principles: Many vs. one; The relevant structures; Unbounded sentences: Putnam semantics; Axioms of infinity: Looking back; Axioms of infinity: Climbing up; Appendix; Chapter 3: Mathematics and physical reality; Introduction; The leading ideas; Carrying the mathematics of modern physics: RA2 as a framework; Global solutions; Metaphysical realist commitments? `Synthetic Determination' relations; A role for representation theorems