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Mathematics without Numbers Geoffrey Hellman (Professor of Philosophy, Professor of Philosophy, University of Minnesota)

Mathematics without Numbers By Geoffrey Hellman (Professor of Philosophy, Professor of Philosophy, University of Minnesota)

Mathematics without Numbers by Geoffrey Hellman (Professor of Philosophy, Professor of Philosophy, University of Minnesota)

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Summary

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.

Mathematics without Numbers Summary

Mathematics without Numbers: Towards a Modal-Structural Interpretation by Geoffrey Hellman (Professor of Philosophy, Professor of Philosophy, University of Minnesota)

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.

Mathematics without Numbers Reviews

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 *

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

Additional information

NPB9780198240341
9780198240341
0198240341
Mathematics without Numbers: Towards a Modal-Structural Interpretation by Geoffrey Hellman (Professor of Philosophy, Professor of Philosophy, University of Minnesota)
Geoffrey Hellman (Professor of Philosophy, Professor of Philosophy, University of Minnesota)
Clarendon Paperbacks
New
Paperback
Oxford University Press
1993-11-25
168
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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