I think when we get to this level of reasoning it’s less about actual arguments and more about trying to tease out intuitions and develop intuition pumps. Actual arguments are usually the easy part, the hard part is finding an intuition on which to hang an argument!
While I might agree that the metaphysics of S5 is strange, I don’t think that’s really a function of S5 as much as it is a function of any coherent metaphysics.
For example consider again the accessibility relation over possible worlds. I suspect we all agree it is reflexive, but to deny S5 is to deny that it is transitive or reflexive. I think a possibility relation which is not transitive or reflexive also very weird!
Surely, my intuition says, if world A is possible from B, and B is possible from C, then A is possible from C. Surely, my intuition says, if A is possible from B, then B is possible to A.
I’d have some sympathy for the denial of symmetry if we were talking about a possible future, so maybe you can get to future A from here and future B from here, but you can’t get to here from B, or from A, and can’t get from A to B or vice versa. Ok, but we are talking about whole worlds rather than future, so I don’t think that’s the right logic to use here.
Which I think is really my point in the intuitions in my first comment—this is less about whether S5 is true or not, and more about whether it’s the right system for the type of objects we are dealing with. Since the type of objects we are dealing with a kind of “universal”, my intuition is we should use the most “universal” logic, which is S5.
I read that other thread you referenced and didn’t find the arguments particularly compelling, perhaps because I am coming from more of a platonist perspective where I think formal systems exist regardless of what concrete objects exist which might instantiate them. If I didn’t think that, I’d likely deny that necessary existence was a coherent concept at all, and so the argument falls apart much earlier!
Thank you for your kind words.
I think when we get to this level of reasoning it’s less about actual arguments and more about trying to tease out intuitions and develop intuition pumps. Actual arguments are usually the easy part, the hard part is finding an intuition on which to hang an argument!
While I might agree that the metaphysics of S5 is strange, I don’t think that’s really a function of S5 as much as it is a function of any coherent metaphysics.
For example consider again the accessibility relation over possible worlds. I suspect we all agree it is reflexive, but to deny S5 is to deny that it is transitive or reflexive. I think a possibility relation which is not transitive or reflexive also very weird!
Surely, my intuition says, if world A is possible from B, and B is possible from C, then A is possible from C. Surely, my intuition says, if A is possible from B, then B is possible to A.
I’d have some sympathy for the denial of symmetry if we were talking about a possible future, so maybe you can get to future A from here and future B from here, but you can’t get to here from B, or from A, and can’t get from A to B or vice versa. Ok, but we are talking about whole worlds rather than future, so I don’t think that’s the right logic to use here.
Which I think is really my point in the intuitions in my first comment—this is less about whether S5 is true or not, and more about whether it’s the right system for the type of objects we are dealing with. Since the type of objects we are dealing with a kind of “universal”, my intuition is we should use the most “universal” logic, which is S5.
I read that other thread you referenced and didn’t find the arguments particularly compelling, perhaps because I am coming from more of a platonist perspective where I think formal systems exist regardless of what concrete objects exist which might instantiate them. If I didn’t think that, I’d likely deny that necessary existence was a coherent concept at all, and so the argument falls apart much earlier!