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Autor: Geoffrey Hellman
ISBN-13: 9780198240341
Einband: Taschenbuch
Seiten: 168
Gewicht: 236 g
Format: 216x139x13 mm
Sprache: Englisch
Erscheinungsdatum: 01.11.1993

Mathematics Without Numbers: Towards a Modal-Structural Interpretation

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This treatise 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, it addresses problems of application to the physical world.
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; Unboundedsentences: 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
Hellman here presents a detailed interpretation of mathematics as the investigation of "structural possibilities," as opposed to absolute, Platonic objects. After treating the natural numbers and analysis, he extends the approach to set theory, where he demonstrates how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.

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Autor: Geoffrey Hellman
ISBN-13:: 9780198240341
ISBN: 0198240341
Erscheinungsjahr: 01.11.1993
Verlag: OXFORD UNIV PR
Gewicht: 236g
Seiten: 168
Sprache: Englisch
Auflage Revised
Sonstiges: Taschenbuch, 216x139x13 mm