> > As is, with your '...' being syntactically unformalized, then Yes, > the followings are possible: > > (a) U is finite: containing only finite elements. > (b) U is finite: containing also infinite elements. > (c) U is infinite: containing only finite elements. > (d) U is infinite: containing also infinite elements. > > _All_ those are the possibilities. _Which of those 4 possibilities_ > can you _specifically construct that one can verify_ ? > > You might have (c) in mind, but then from the unformalized and > _unverifiable_ notion of (c), how could you _verify_ the existences > of certain predicate and function sets, hence _verify_ as true or > false the truth values of certain formulas?
Are you a strict finist? Is all this stuff about things being unknowable an objection to reasoning about finite sets? Or maybe you're an ultrafinitist like Esenin-Volpin.
-- I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne