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Showing posts from June, 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.