Tuesday, June 27, 2017

Semantics and provability


Hypothesis 1: False formulas are unprovable.
Hypothesis 2: Formula A is unprovable.

3. If A is false then A is not-unprovable.
4. Then, by modus tollens H2 and 3.: A is true.
5. Ergo, when A is true it is unprovable.

We cannot define provability in semantical terms.
The concept of provability has only syntactical meaning, therefore is useless for life.