RIP Saul Kripke

+Ryan Conti Thanks! And thanks for watching!

+SidewaysDeliverer At some point, yes. I do not have as much of a background in Continental philosophy, and therefore I generally focus on the analytics, but I would love to expand to the continentals at some point.

No worries! Thanks for watching. If V(◻q, w2) and V(~q, w3) are true, then R(w2,w3) must be false. As you have it framed, it is not necessarily the case that R(w1,w2) or R(w1,w3), and axiom 5 could possibly hold. You would need the claim that for all p V(◻p, w1) implies V(p, w2) and V(p, w3) (which would mean R(w1, w3) and R(w1, w2)). If we were in that situation, then Axiom 5 would not hold. If for all p, V(◻p, w2)=f (i.e. w2 has no necessary truths), then yes, for all worlds wn the relation R(w2, wn) would be true. If you assume Axiom 5 in such a situation, this would mean all worlds are accessible to each other.

These are all technically modal logics, but usually when people just say modal logic they mean alethic logic (the logic of possibility and necessity); deontic is the logic of what you ought do or may do; temporal is time; epistemic has to do with what you know. For each of these there are multiple systems that would fall under any of those above definitions, but most will have a common core of axiom system k

+Seth Apex Check out the first part of the map of philosophy (after the intro) where I go into a number of different kinds of logics. If you are interested in modal logics specifically, check out my series, the three months of modal logics. the other big modal one would be doxastic to add to your list. :)

+eammonful Yep. Exactly! Thanks!

World A has an elephant. World B has a tiger. Both Worlds are accessible to each other. As World A and World B can be same at same time. We can be talking about the same World or we can combine the 2 worlds like breaking a wall between 2 rooms. But let's say World A is a world where cows cannot fly. World B is a world where cows must fly . Now both World are not accessible to each other. Because both cannot be true at same time. They contradict each other. So taking above analogy. If we break the wall between these 2 rooms we will either find that one of statement is false or that it creates a paradox. And hence untrue.b

Nice question, i think it's fundamental try to answer

@@bimbumbam4434 if you're interested, combinatorialism offers an interesting answer that things that are necessarily impossible become possible in other worlds. It's more of an epistemic problem really but bassicly imagine a world where there are no colors, since there are no colors there is no way of identifying colors as a specific qualia, so to the black and white world it is impossible for there to be color, because there is no possible world (from the perspective of the black and white world) for there to be a world with colors. But the converse is not true, if you are in a world with colors, a black and white world is possible. wbw cannot acces wc but wc can access wbw. but that could just be an epistemic block and it's only one opinion. Witgensteinian combinatorialism, look into it, it's cool! I was just curious to hear these guys' opinion on the idea.

+Human Evolution Check out the first section (after the intro) of my video the map of philosophy for a list of most of the types of logic. For more in depth videos on modla logics, check out my series the three months of modal logics.

that's not irony, that's coincidence

I think that the standard definition of negation will work, i.e. has the opposite truth value as. ~[]p means that []p is false, regardless of what we mean by []. I don't think we need a separate definition, but I would be curious to hear more of why you think we do.

@@CarneadesOfCyrene So if the definion of the Valuation of ◻p is: (∀p)(∀w1)((V(◻p,w1)=t) ≡ (∀w2)(R(w1,w2) → (V(p,w2)=t)) then ~◻p is something like this: "(∃w2)(R(w1,w2) & (V(p,w2)=f))" ? Yeah, that seems right. I got confused and didn't know where to put the negation. I guess I just needed a nudge, thanks. Since you are reading this, let me make a video (series) request on modern theories of causation (ie. from Hume and on). You did that Aristotle's four causes, but well, he is kind of dated. In that video about counterfactuals you mentioned theories of causation but never took a deeper dive into it. I think that is kinda of important topic that is missing in the channel. Just a sugestion. I know that right now you are doing the set theory thing.

A key to remember is that Kripke is making a system for all modal logics (Deontic, epistemic, temporal, as well as alethic). Most people would say that alethically inaccessible worlds do not exist at all, but deontically, epistemically, temporally, inaccessible worlds do exist (kzfaq.info/get/bejne/hLh9mZBltarQmo0.html).

@@CarneadesOfCyrene thank you ❤

There are no inaccessible possible worlds. There is just one world. Take a step back and see the ridiculousness of the definitions.

@@CarneadesOfCyrene So if we are saying that all worlds are alethically accessible from one another, wouldn't that make S5 true?

+sparX Kuijper Thanks for coming! Ozzy is great, His promotion of my channel was one of the first big brreaks that we got!

Why? Is it useful in AI?

@@duartesilva7907 yea Language Models use (modal) logic

I'm sorry to hear that. What are you lost on? We have a series on modal logic that builds up more from the basics, though it is more focused on syntax than semantics (but could help out). kzfaq.info/sun/PLz0n_SjOttTfP_liEHPNCzvESZsh5eirP If you are looking for a more basic primer on logic, check out the 100 days of logic (kzfaq.info/sun/PLz0n_SjOttTcjHsuebLrl0fjab5fdToui). For more on Kripke check out this series (kzfaq.info/sun/PLz0n_SjOttTcnB00cGPznfNTuY1-3RJyE).

@@CarneadesOfCyrene like what is the point? Thats what im asking.

If you're interested in a more carried out and slow approach to modal logic, try Kane B.

Kripke is probably the worst face I've done. But overall I'm happy with the general aesthetic of most videos. If you don't like it, feel free to just listen. :)

@@CarneadesOfCyrene I think he was referring to the diagrams, and how they are hard to read due to the arrows being made of text.