Lester Zick wrote: > Tautological combinations such as "A, not A" exhaust all possibilities > for truth unless I'm very much mistaken.
Good thing you admit it. Yes you are very much mistaken. For example take A be the statement: "Is P(N) = aleph_1 true in ZFC". Simple enough statement. However, neither "A" nor "not A" is true. You must be VERY careful what kind of statement you make A. Further the fact that either A or not A is true is an AXIOM (given that A is a well defined statement that is either true or false in some system)! It is an ASSUMPTION! Further some people reject this assumption, for it leads to non constructive proofs.