Single Idea 13441

[catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets]

Full Idea

'Comprehension' is the assumption that every predicate has an extension. Naïve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety.

Gist of Idea

Naïve set theory has trouble with comprehension, the claim that every predicate has an extension

Source

William D. Hart (The Evolution of Logic [2010], 1)

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.4


A Reaction

This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions.