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Single Idea 18270

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

Full Idea

The axiom of choice was an assumption that implicitly questioned the necessity of intensions to guarantee the presence of classes.

Clarification

'Intensions' here are concepts which generate the classes

Gist of Idea

Choice suggests that intensions are not needed to ensure classes

Source

J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 7 'Log')

Book Ref

Coffa,J.Alberto: 'The Semantic Tradition from Kant to Carnap' [CUP 1993], p.114

A Reaction

The point is that Choice just picks out members for no particular reason. So classes, it seems, don't need a reason to exist.

The 5 ideas from 'The Semantic Tradition from Kant to Carnap'

18279 Relativity is as absolutist about space-time as Newton was about space [Coffa]
18263 The semantic tradition aimed to explain the a priori semantically, not by Kantian intuition [Coffa]
18266 Mathematics generalises by using variables [Coffa]
18270 Choice suggests that intensions are not needed to ensure classes [Coffa]
18272 Platonism defines the a priori in a way that makes it unknowable [Coffa]