Mathematics without Numbers: Towards a Modal-Structural Interpretation

by Geoffrey Hellman

Overview

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.

Product Details

ISBN-13:	9780191520112
Publisher:	Oxford University Press
Publication date:	10/12/1989
Series:	Clarendon Paperbacks
Sold by:	Barnes & Noble
Format:	eBook
Lexile:	1490L (what's this?)
File size:	1 MB

About the Author

University of Minnesota

Table of Contents

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

Editorial Reviews

"An exciting and intriguing book, rich in ideas and not short on technical ingenuity, that will doubtless repay careful study."—Philosophical Review

"A breath-taking blend of philosophy, mathematics, and logic....Rich, subtle, and insightful."—Nous

"Several important insights are woven together and brought to bear on the nature of mathematics in this signal contribution to the philosophy of the field."—Mathematical Reviews

From the Publisher