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Single Idea 3355

[filed under theme 4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory ]

Full Idea

Von Neumann suggested that functions be pressed into service to replace sets.

Gist of Idea

Von Neumann wanted mathematical functions to replace sets

Source

report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23

Book Ref

Benardete,José A.: 'Metaphysics: The Logical Approach' [OUP 1989], p.188


The 3 ideas from 'works'

Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]