User:Gregbard/Nontheorem

A nontheorem is a formula of a formal system that is not a theorem. A nontheorem is distinct from a negation of a theorem. Of the validly formed formulas of a formal language, some can be derived as theorems, and some can be shown to be the negation of some theorem. However this does not account for all possible formulas. Some formulas may be validly formed according to the formation rules of the language, and yet still be nonsense.