Proposed new syntax

[Gregory Ewing]

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