Mathematics without Numbers (Clarendon Paperbacks) de Geoffrey Hellman

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

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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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