Reality of Numbers: A Physicalist's Philosophy of Mathematics

ISBN-13: 9780198249573 / Angielski / Twarda / 1988 / 202 str.

John Bigelow

Opis

Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.

Recenzje

'This is what philosophy ought to be: a grand vision combined with original and careful work on the details. It is presented with lucidity and modesty and good humour, and without bedazzling technicalities. An admirable book.' David Lewis, Princeton University, Australasian Journal of Philosophy

Spis treści

Part I - Metaphysics contains chapter on: Mathematics and universals; Recurrence Part II - Mathematics contains chapters on: Natural Numbers - Pebbles and Pythagoras; Numbers as properties; Numbers as paradigms; Numbers as relations; Numbering sets Real Numbers - Approximations; Arithmetic and Geometry; Proportions; Ratios; Real Numbers Complex Numbers - Imaginary numbers; Complex proportions Sets - From universals to sets; Sets and Essences; Sets and Consistency Part III - Truth and Existence contains chapters on: The Problem - Functions and arguments; Truth and essence; The Fox paradox Wholes and Parts - Counterparts and accidents; Property-instances; Robinson's merger; States of affairs Anyhow to Something - Categories of being; The second-order Fox; Platonism and necessity.