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Philosofags of /his/, I need your help.
I have a good background in propositional, first order and temporal logic (LTL, CTL) and now I want to study modal logic. In doing so, I came across the semantics of possible worlds and I'm confused. While formally it makes sense and is easy to handle, I don't understand ontologically what a "possible world" is supposed to be.
In my understanding the underlying intent is to prove that some things (of which we might not know yet whether they are true or false) are possible in our world (or necessary, which would imply they have to be true). But how does our world relate to other possible worlds and what constraints do we have on those worlds? Also what does the transition relation in the logical model mean in our reality, if we can't actually move between possible worlds? Doesn't the idea of a transition relation contradict the concept of possible worlds, since those should be assumed to be independent of each other?
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Here is a great YouTuber who will help you out:
https://www.youtube.com/watch?v=EaCLZ9OZzAg&list=PLXKKIUdnOESGk43pUg3NTkRWjglvKXKi7
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>>2466374
Thanks anon. I'll have a look.
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The trouble you have stems from the modern positivism of today's education.
Namely a super empirical philosophy we all inherit where science and material evidence provides the basis of our understanding of viewing the world.
However, if you could somehow leave the paradigm of the modern world view and implant yourself in the Aristotelian worldview you could make more sense of this and this is as Aristotelian philosophy is based around logic.
Without you going back to Aristotle its I think, difficult to understand especially becase we are taught in the verificationism/falsifiable mode of thought where the only logic that matters is comparing the variable to the control.
Ill try to make the obvious example to explain quickly but youll have to expand on it on your own.
Basically modal logic is a more powerful propositional logic.
So for example propositional logic can tell you
if P -> Q
And we could say P is fire and Q is oxygen because if you have fire you necessarily have oxygen. (reminder that combustion requires oxygen and carbon for the reaction to go through). But if you have oxygen don't necessarily have fire.
Modal logic expands on this.
Because now you can say if I have oxygen then I possibly have a fire. You could say if I don't have oxygen then I necessarily don't have a fire. You could say I have fire I necessarily have oxygen.
You've added anther dimension to what you can say is logically true. You expand this whole new analytic tool in a complex way and you'll find out things like Goddel's proof about God or whatever you were looking into.
A lot of people don't understand modal logic, Dawkins comes to mind because their understanding of logic is simply limited to science.
Modal logic is complex and hard to understand while at the same time its as simple and always right.
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