Good idea! Here's a simple alethic example: P1 It's necessary that either p or q P2 Not p C Therefore, q Some good examples come from epistemic modalities: 'If one knows that p, then p' as Kp -> p And temporal modalities: 'If it's always going to be p or q, and today isn't p, then today is q' As to why we might prefer one system to another, it depends on how we read [] and . If alethic ('necessary' and 'possible'), then S5 is very plausible: what's necessary is necessarily necessary; what's possible is necessarily possible. But 5 is not so plausible for epistemic uses: we don't know all the things we don't know (~Kp doesn't seem to imply K~Kp).

@@AtticPhilosophy What does epistemic Kp correspond to in alethic modal logic? Box p or Diamond p?

[]p. It's saying: in all epistemic possibilities (for the agent in question), p.

@@AtticPhilosophy The alethic example only works if we assume that every world has an arrow that connects back to itself. Otherwise there could be some world W such that "p v q" is true in every world that W can see, but false in W itself.

@@Nicoder6884 That's right. Nearly everyone believes that 'necessarily' is factive, which amounts to reflexivity (every world has an arrow to itself). But as you say, it's perfectly ok to have logical systems which lack this feature.

Thanks! Much appreciated!

@@AtticPhilosophy Hey Attic philosophy! Very much like your work and videos explaining this not so taught subject :) Id be happy to give my 2 cebts with some constructive critisicm ^^ Your presentation is very clear, and well communicated, and the visuals are spot on. Theres a bit of a feeling of hopping from subject to subject, from trees to axioms to proofs back to trees again semantics though there were semantics before but again... a bit jumbled up, maybe a bit more of a transition from a topic to another or a table of contents. The explination of each subject feels messy with to few examples, leaves quite a bit to be desired, and to be frank - I don't know if I could say I actually learned how to properly reiterate the skills you introduce, even in the most simplest of way, it seems lacking. Apologies if it seems harsh a bit, thats my feedback and hope it helps!😁

Thanks!

Thanks, I’ll try!

Thanks!

Valuations assign true or false to each sentence letter, p,q,r etc., not to every sentence of the language. Complex sentences get assigned a truth-value by the recursive clauses, based on a valuation. There are (usually) countably many sentence letters p,q,r… (and so countably many sentences is total). Countable = same size infinity as the natural numbers.

@@AtticPhilosophy Thanks, so does V assign a truth value to every single primitive sentence in the whole language L (and never just a finite subset of Lp)? (Lp is the subset of L containing all and just the primitive sentences of L)

@@user-wt7vb4yv1s Yes, otherwise, for some p, pv~p wouldn't be true.

Epistemic modalities are really tricky! The issue is known as 'the problem of logical omniscience': just because something is valid, or necessarily true, doesn't mean we automatically know it. And relatedly, you can know p->q and know p without knowing q. (Although some people deny this!) If you want to do epistemic modalities without these features, you need to go beyond possible world semantics. Either impossible worlds (my favourite), or use some other approach entirely.

Already ahead of you! Try these ones: Paraconsistent logic kzfaq.info/get/bejne/osWinMZ3rszefaM.html Three-valued logic: kzfaq.info/get/bejne/mNungrGXusCxiHk.html No fact of the matter: kzfaq.info/get/bejne/nMB8mpSjluDFoJs.html

Sure, language is often vague, but logical sentences are meant to be perfectly precise.

Philosophy is counter intuitive- if you wanted to be a philosopher you need to train yourself for all the people who will oversimplify just because they have preconceived notions about it.

​@@AtticPhilosophyI'm gonna have to rewatch to see wtf I meant by my comment, on a video about modal logic 😂😂🥰