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Single Idea 10149

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

Full Idea

The Axiom of Choice seems clearly true from the Platonistic point of view, independently of how sets may be defined, but is rejected by those who think such existential claims must show how to pick out or define the object claimed to exist.

Gist of Idea

Platonist will accept the Axiom of Choice, but others want criteria of selection or definition


Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I)

Book Reference

Feferman,S/Feferman,A.B.: 'Alfred Tarski: life and logic' [CUP 2008], p.47

A Reaction

The typical critics are likely to be intuitionists or formalists, who seek for both rigour and a plausible epistemology in our theory.