Isomorphisms in a Category of Propositions and Proofs

March 2, 2018

Abstract: In this talk, I show how a category of propositions and classical proofs can give rise to three different hyperintensional notions of sameness of content. One of these notions is very fine-grained, going so far as to distinguish $$p$$ and $$p\land p$$, while identifying other distinct pairs of formulas, such as $$p\land q$$ and $$q\land p$$; $$p$$ and $$\neg\neg p$$; or $$\neg(p\land q)$$ and $$\neg p\lor\neg q$$. Another relation is more coarsely grained, and gives the same account of identity of content as equivalence in Angell’s logic of analytic containment. A third notion of sameness of content is defined, which is intermediate between Angell’s and Parry’s logics of analytic containment. Along the way we show how purely classical proof theory gives resources to define hyperintensional distinctions thought to be the domain of properly non-classical logics.