About Logic Interview with Graham Priest

See About Logic - Interview With Graham Priest. 

My comment:

13:31 "Does this affect the foundations of reasoning?" The answer steers this (not entirely reasonably, in my opinion) into foundations of mathematics. But Priest clearly has some notion of a foundation for mathematics but doesn't want to say what that is. For example it seems to be more than just a syntactic notion. But need it be endowed with formal semantics? It's not obvious to me that it is hopeless to attempt to define such an "ur language" which captures a bare minimum of the requirement that mathematical discourse is inter-interpretable by subjects in a consistent manner. That would be a foundation of reasoning and would apply to more than just mathematics.

Also this one: 

15:56 cf. My earlier comment, I'd like to have heard more about this. Gödel's First Incompleteness Theorem holds for HA (first order Heyting (Intuitionistic) Arithmetic) but it is itself not provable intuitionistically, is it? Doesn't that have implications for the Second Incompleteness Theorem?

34:21 On paraconsistent logics and Naïve Set Theory. I had never heard of Curry's Paradox before. 

36:17 on the idea of paraconsistent type theory and formalising higher category theory. See Emily Riehl on Univalent Foundations and Emily Riehl's "Infinity Categories for Undergraduates" Talk on Curt Jaimungal's Podcast. [Update: see also Emily Riehl on The Future of Mathematics where she talks a lot about formalising category theory proofs, including some in the Category of Categories].

40:29 On Hegelian logic. See Curt Jaimungal Interview With Urs Schreiber and Urs Schreiber on Hegel’s Logic and Category Theory. 

See the previous episode: About Logic - Theorem Proving, Constructive Mathematics and Type Theory. 

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