The timing on this video is impeccable! You truly are helping the emerging philosophers in the world like myself. Your videos are awesome, keep it up!!!
Amazing tutorial on intuitionistic logic as always. Do you have any recommended websites/books/pdfs on where I can practice proof solving with examples in intuitionistic logic?
Thanks! Graham Priest's book 'Introduction to non-classical logic' is good on intuitionistic proof trees. Tbh not many people like intuitionist proof trees as they're very fiddly, preferring a natural deduction system or the sequent calculus. There's plenty of online natural deduction proof checkers, e.g.: proofs.openlogicproject.org. There's also online proof tree checkers, e.g. www.umsu.de/trees/, but I haven't found one which covers intuitionistic trees.
Short answer: yes (for using Kripke semantics), one ordering relation for interpreting ~ and ->, and one accessibility relation for modalities. Longer answer: there's lots of different candidates for 'intuitionistic modal logic'. One issue is that []A needn't be equivalent to ~~A, so there's a question of how the accessibility relations should interact, or even whether Kripke-style semantics is the right way to go at all.
Categories are all about the commuting arrows, which you don't have here. But there is a link (kind of): category theory (specifically, cartesian closed categories) is a natural semantics for intuitionistic type theory.
The timing on this video is impeccable! You truly are helping the emerging philosophers in the world like myself. Your videos are awesome, keep it up!!!
Thanks! That's the idea, so I'm glad.
Would I like to? Some day probably, not yet.
Amazing tutorial on intuitionistic logic as always. Do you have any recommended websites/books/pdfs on where I can practice proof solving with examples in intuitionistic logic?
Thanks! Graham Priest's book 'Introduction to non-classical logic' is good on intuitionistic proof trees. Tbh not many people like intuitionist proof trees as they're very fiddly, preferring a natural deduction system or the sequent calculus. There's plenty of online natural deduction proof checkers, e.g.: proofs.openlogicproject.org. There's also online proof tree checkers, e.g. www.umsu.de/trees/, but I haven't found one which covers intuitionistic trees.
Would there have to be two different accessibility relations for Intuitionistic Modal Logic?
Short answer: yes (for using Kripke semantics), one ordering relation for interpreting ~ and ->, and one accessibility relation for modalities. Longer answer: there's lots of different candidates for 'intuitionistic modal logic'. One issue is that []A needn't be equivalent to ~~A, so there's a question of how the accessibility relations should interact, or even whether Kripke-style semantics is the right way to go at all.
@@AtticPhilosophy thank you, that helps a lot.
The whole reflexive/transitive relation makes me think about category theory.
Categories are all about the commuting arrows, which you don't have here. But there is a link (kind of): category theory (specifically, cartesian closed categories) is a natural semantics for intuitionistic type theory.
for the love of god get rid of that cancer intro, or at least decrease the volume