The Anatomy and Ultimate Nature of "True-But-Unprovable" Propositions

The class of all complementary pairs of propositions of Classical Logic is partitioned as {{U}, {K}, {N}}, where both {U} and {K} are recursively-enumerable. This leaves {N} as non r.e. and hence necessarily the "home" of the class of all "True-but-Unprovable" propositions B [together with their negations ~B]. These "True-but-Unprovable" propositions B are true by virtue of being n-valid [ = valid on all-and-only-finite domains] and unprovable because ~B has an infinite model. These B's are further characterized by containing some "item" of extra-logical information, often of an existential nature, which comprises a condition which is incapable of being determined by purely logical means. Hence the truth of these B's is contingent upon the truth of that "item" of extra-logical information, and this fact is "witnessed" by the model of an alternate universe in which the contingency is false, and which is characterized by ~B. A concrete example, Cantor's Theorem, is given, and the counter-model is constructed via a predicative definition