I am assured by logicians that in any axiomatic system rich enough to include number theory, there are propositions that can be neither proved nor disproved, regardless of whether they are "really" true or "really" false. A common example that may be of this type is the twin primes conjecture (TWP). Now suppose that TWP is really of this kind -- that it can neither be proved nor disproved (with a conventional finite proof in number theory). Then we have the right to choose to add either TWP or its negation to the existing axioms and the resulting system will be consistent*. And so there exists a model for this new system. And so it (apparently) "exists". BUT -- what if a hypothetical infinite check of all possible twin primes shows that TWP is true . . . yet we choose to add as an additional axiom its negation ~TWP. Then there is a model of this system, despite the fact that it is WRONG. Would that system really exist? I.e., spiritually, it's inconsistent, but we could not prove it thus with a conventional finite proof. --Dan __________________________________________________ * If we assume Number Theory is consistent, which we shall do. _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele