Girdle's Incompleteness Theorems

Girdle's incompleteness theorems say there are statements that are true in mathematics, but which cannot possibly prove. The laws of physics are such that what can be proved prohibits us from ever finding the proof of those things. Curing's version of this is that there are some statements that are not computable or dicidable. And by the way, you can have systems such as so called sentential or propositional logic. In these systems, the axioms allow you to prove everything that is true within that system.