# Category Archives: logic

## A subset interpretation (with context morphisms) of the sequent calculus for predicate logic

The previous two posts used the sequent calculus with a subset interpretation: We work with sequents , and interpret the propositions (and ) as subsets of some universe set . We interpret the sequent itself as . While writing the … Continue reading

## Logic without negation and falsehood

In the last post, consideration related to partial functions lead us to present a logic without truth and implication, using the binary minus operation as a dual of implication and substitute for unary negation. But logic without implication and equivalence … Continue reading

Posted in logic | Tagged | 3 Comments

## Logic without truth

Pi is wrong! But so what? It is neither new, nor complicated enough to count as real math! And suggestions that  or  might be even better show that it not clear-cut either. I recently invested sufficient energy into some logical questions to … Continue reading

Posted in logic, partial functions | Tagged , | 6 Comments

## Gentzen’s consistency proof is more impressive than you expect

I recently said something about the impossibility to prove the consistency of PA, and that Gentzen proved just this in 1936. Because I got critizised quite a bit, and realized that even famous mathematicians get critizized if they dare to … Continue reading

Posted in logic | Tagged | 2 Comments