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

Hellman, Geoffrey

 
9780198240341: Mathematics without Numbers: Towards a Modal-Structural Interpretation (Clarendon Paperbacks)
Brossura
ISBN 10: 0198240341 ISBN 13: 9780198240341
Casa editrice: Oxford University Press, 1993

Sinossi

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Recensione

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)

Contenuti

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

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Editore
Oxford University Press
Data di pubblicazione
1993
Lingua
Inglese
ISBN 10 
0198240341
ISBN 13 
9780198240341
Rilegatura
Copertina flessibile
Numero di pagine
168
Contatto del produttore
Messaggerie Libri
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Assago Milano
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Italia

Altre edizioni note dello stesso titolo

9780198249344: Mathematics Without Numbers: Towards a Modal-Structural Interpretation

Edizione in evidenza

ISBN 10:  0198249349 ISBN 13:  9780198249344
Casa editrice: Oxford Univ Pr, 1989
Rilegato