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Single Idea 10196

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX ]

Full Idea

Some mathematicians seem to think that talk of an Axiom of Choice allows them to choose a single member of a collection when there is no criterion of choice.

Gist of Idea

The Axiom of Choice needs a criterion of choice

Source

Max Black (The Identity of Indiscernibles [1952], p.68)

Book Ref

'Metaphysics - An Anthology', ed/tr. Sosa,E. /Kim,J. [Blackwell 1999], p.68

The 4 ideas from 'The Identity of Indiscernibles'

10193 The 'property' of self-identity is uselessly tautological [Black]
10195 If the universe just held two indiscernibles spheres, that refutes the Identity of Indiscernibles [Black]
10194 Two things can only be distinguished by a distinct property or a distinct relation [Black]
10196 The Axiom of Choice needs a criterion of choice [Black]