Paul Rubin wrote:
Historically (in "naive set theory") we didn't bother with any of this. We could write { S : S \not\in S } for the set of all sets that are not members of themselves. Is S a member of itself ("Russell's paradox")? Either way leads to contradiction. So the comprehension axiom schemas for set theory had to be designed to not allow formulas like that.
Personally I think mathematicians worry overly much about that. What it means is that not every predicate can be used to define a set. A manifestation of the same thing in computing is that not every program you can write down will terminate. But we don't warp our languages in an effort to make non-terminating programs impossible; we just accept them as a fact of life and move on. -- Greg -- https://mail.python.org/mailman/listinfo/python-list