Geoffrey Hellman

Mathematics Without Numbers

Towards a Modal-Structural Interpretation

• Broschiertes Buch

Produktbeschreibung

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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Produktdetails

• Verlag: OUP Oxford
• Seitenzahl: 168
• Erscheinungstermin: 25. November 1993
• Englisch
• Abmessung: 216mm x 140mm x 9mm
• Gewicht: 220g
• ISBN-13: 9780198240341
• ISBN-10: 0198240341
• Artikelnr.: 21776357

Inhaltsangabe

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