| The important point is that Godel Incompleteness Theorem has to do with provability in logical systems, not with knowledge in general. |
| If one wants to express these constraints in terms of the provability of object language formulas, one naturally arrives at Aristotle's and Boethius' Theses. |
| He proved that the two notions of truth and provability do not coincide by discovering a formula about integers which is true but unprovable in elementary arithmetic. |
| Among the functions pursued are provability, optimization, and precision. |
| Thus, the question arises whether the provability of a crime is limited where the risk of contamination is low. |
| In provability logic, provability is not to be treated as a brand of necessity. |
