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.