Geoffrey (Professor of Philosophy, Professor of Philosophy, University of Minnesota) Hellman
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Geoffrey (Professor of Philosophy, Professor of Philosophy, University of Minnesota) Hellman,
,
Geoffrey Hellman
e druk, 1993
9780198240341
Mathematics without Numbers
Towards a Modal-Structural Interpretation
Specificaties
Paperback, 168 blz.
|
Engels
|
e druk, 1993
ISBN13: 9780198240341
Rubricering
Onderdeel van serie
Clarendon Paperbacks
Verwachte levertijd ongeveer 11 werkdagen
Samenvatting
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.
Specificaties
Inhoudsopgave
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