Meaning in Intuitionistic Logic | Attic Philosophy

Intuitionistic logic rejects one of the central building blocks of classical logic: that we can always say 'true or false', A-or-not-A. In this video, we start to look at what it means, by presenting the Kripke (relational model) semantics.
00:00 - Intro
01:14 - History
02:13 - States of Information
04:42 - Conjunction and Disjunction
05:25 - Implication
07:47 - Negation
09:13 - Avoiding Excluded Middle
10:13 - Validity
10:31 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: markjago.net
My book What Truth Is: bit.ly/JagoTruth
Most of my publications are available freely here: philpapers.org/s/Mark%20Jago
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#logic #philosophy #semantics

[@CristianGonzalez-zc9nt]

Whyyyyy don't you have more views? It''s a shame I did not discover this channel before. Wonderful content, wonderful explanation for anyone who hasn't had close contact with this formal topic.

[@AtticPhilosophy]

Thanks very much! Hopefully the views are coming in time. Glad this was useful!

[@JosiahWarren]

No people care about logic like us

[@toe_fans]

Very interesting indeed

[@woosix7735]

This is just what i was looking for , thanks!

[@vitusschafftlein77]

Very nice explanation. I'm looking forward to your next video!

[@AtticPhilosophy]

Thank you!

[@Bobby-bz8bk]

Too few views! This is a really helpful video on a much-neglected subject.

[@AtticPhilosophy]

Thanks Bobby, glad you liked it!

[@alexandersanchez9138]

How is this related to the Heyting algebra approach?

[@AtticPhilosophy]

This is the kripke-style semantics, which is an alternative to Heyting algebras. There’s a feeling that, while formally good, the algebraic approach doesn’t make much philosophical sense in giving the meaning of intuitionistic logic.

[@Guz579N]

haha im writing a chapter in my uni work on this right now

[@AtticPhilosophy]

Good luck!

[@madvorakCZ]

OK but can we ever get x->y without obtaining y?

[@AtticPhilosophy]

Sure, you don’t need y to be verified to verify x->y. In a proof, deriving y on the assumption of x proves x->y.

[@ReflectiveJourney]

Is this equivalent to finite state automata?

[@AtticPhilosophy]

They look similar but they’re up to different things. Logical models are fixing what sentences are valid. Automata are abstract models of computation. There *are* connections: automata over modal models is a technique for showing why modal logics are decidable. That’s more advanced stuff!

[@toe_fans]

The idea of only having a state of information at-a-particular-state weirdly reminds me of like whitehead's process philosophy

[@rookiedoesevrythng9222]

Make a series on the logical arguments for and against god

[@AtticPhilosophy]

Good idea! I'm planning a series on religion, but it's not something I want to rush.