The Reality of Numbers
A Physicalist's Philosophy of Mathematics
Samenvatting
This book casts new light on mathematics through its consideration of metaphysical materialism. The author identifies natural, real and imaginary numbers and sets with specified physical properties and relations.
However sets are construed numbers are not sets. Sets are important simply because they instantiate all the numbers and all the other properties and relations studied in mathematics. Set theory tempts us into misunderstanding the nature of mathematics; Bigelow challenges the myth that mathematical objects can be defined into existence.
By reconstruing numbers as real, non-linguistic, physical properties or relations, mathematics can be drawn back from its sterile, abstract exile into the midst of the physical world to which we belong.
Specificaties
Inhoudsopgave
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.