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Mathematics without Numbers: Towards a Modal-Structural Interpretation de Geoffrey Hellman

Mathematics without Numbers: Towards a Modal-Structural Interpretation: Clarendon Paperbacks

Autor Geoffrey Hellman
en Limba Engleză Paperback – 25 noi 1993
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.
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Specificații

ISBN-13: 9780198240341
ISBN-10: 0198240341
Pagini: 168
Dimensiuni: 138 x 216 x 13 mm
Greutate: 0.24 kg
Ediția:Revised
Editura: OUP OXFORD
Colecția OUP Oxford
Seria Clarendon Paperbacks

Locul publicării:Oxford, United Kingdom

Cuprins

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

Recenzii

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.
rich, subtle, and insightful