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 A subset interpretation (with context morphisms) of the sequent calculus for predicate logic September 24, 2017
 Logic without negation and falsehood December 11, 2016
 Logic without truth September 3, 2016
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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
Posted in category theory, logic, partial functions
Tagged category theory, gentzen, logic
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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
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 clearcut either. I recently invested sufficient energy into some logical questions to … Continue reading
Posted in category theory, logic, partial functions
Tagged category theory, gentzen, logic
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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