more on this theme | more from this text
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.
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] |