Re: Mathematical objects and Discernment


I'm not sure I have quite understood you, but, for all I can gather,
you propose to conceive of sets not really as collections
(extensionally) but in a pure intensional way: a set should perhaps be
identified with the concept its name includes? I assume all names
including the same conceptual content are to be considered the same
name (?).

You discard the first (so to say) axiom of the usual set theory.

If I have correctly understood you, your proposal seems highly
problematic. Sets are extensional from their very definition. If we are
to disregard its extensional nature, what is the use of keeping them;
can we not do with just concepts (or names)?

Regards

.