Modal Correspondence Theory | Logic Tutorial | Attic Philosophy

Modal logic is the logic of possibility and necessity, past and future, knowledge and belief, and dynamic change. It's one of the most exciting areas of logic to learn, and one of the best for philosophers and linguists. In this tutorial video, we'll see how different modal logics correspond to the different modal semantics. We'll see how placing different conditions on the accessibility relation - like reflexivity, or transitivity - gives us new valid theorems.
00:00 - Intro
01:38 - Corresponding logics
02:38 - Entailment
04:38 - Modal Axioms
09:02 - Modal Correspondence
10:27 - Wrap-up
More videos on modal 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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[@FffffffffffffffffffffffffffffL]

Hey I'm a philosophy major who really wants to advance my knowledge in philosophy. I love that you have a channel dedicated to philosophy, I liked this video a lot and will certainly watch more. Subscribed and liked :)

[@AtticPhilosophy]

Thanks! Glad it helped.

[@MrGamerFann]

If only my professor could explain this clearly... Your videos make modal logic accessible and not as overwhelming :)

[@AtticPhilosophy]

Aw thanks! Glad it helped.

[@quantum-atom]

Hi Mark! Thanks for the video! At 7:45, you mentioned a logic system with KTB; In the context of doxastic logic, would that describe a reasoner who never believes any false proposition (T) and also believes that their beliefs are never inaccurate (B)?

[@quantum-atom]

Also, does KB describe the doxastic logic for a reasoner who believes that their beliefs are never inaccurate (B)?

[@AtticPhilosophy]

Yes, KTB would describe someone whose beliefs are always true (so, more usually applied to knowledge) and, for any truth p, always believes they don't believe ~p. Or, to put it another way, for any falsehood, they believe they don't believe it. T is implausible for belief but plausible for knowledge. But B (p -> K~K~p) is implausible for knowledge: it implies, for any falsehood, you know you don't know it. How could the mere fact that something is false give you positive knowledge? Interestingly, B is linked to the other 'introspection' principles: 4, or 'positive introspection' (Kp -> KKP) and 5, 'negative introspection (~Kp -> K~Kp). Given B, 4 and 5 are equivalent. Some have argued that 4 but not 5 is plausible for knowledge.

[@marcomarabello9318]

Hi Mark, thanks for the video! I knew that the D in axiom D stands for "deontic", if this is true then we have two axioms whose names make sense ;) But I don't know whether D really stands for that...

[@AtticPhilosophy]

Yeah I think D is for Deontic. D ensures no contradictions are necessary: it's equivalent to []T. In alethic logic, it ensures necessity implies possibility. In deontic logic, it means obligations imply permissions.
Other axiom names: B is for Brouwer, the Dutch intuitionist logician. 4 and 5 come from CI Lewis's system numbering (systems 1-5), hence the logic names S4 and S5. Still a pain to remember!