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In possible world semantics, statements of the form "It is possible that P" are interpreted as meaning "There is some 'possible world' in which P is true". And if you're a modal realist, then these possible worlds are other universes in the multiverse, I guess.

So my question is about how this interacts with time.

Suppose there's a beautiful woman I want to be with, and I think "It's really possible that we'll be together." Now that means there is some universe where we're living happily together.

Then I say the wrong thing and blow my chances. It is no longer possible for us to be together. So It was possible but now it is impossible.

However, notice that the universe where we are living happily together is still there. My saying the wrong thing in this universe did not destroy it. So you can hopefully see the issue.

Benjamin Grange
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  • Another possibility is that your "beautiful woman" later decides that you intended to pay her a compliment but it was delivered wrongly. A decision tree may rejoin. – Weather Vane Mar 29 '24 at 19:23
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    Your 'Then I say the wrong thing and blow my chances' is just one possibility itself, you may still have other accessible branch(es) where this didn't happen to continue... – Double Knot Mar 29 '24 at 19:42
  • @DoubleKnot You mean that my memory in the present of having said that is erroneous? – Benjamin Grange Mar 29 '24 at 20:44
  • @WeatherVane Okay, maybe a different example would be better. Like "It is possible for me to win the race." Then I lose the race. It's no longer possible, but it was. – Benjamin Grange Mar 29 '24 at 20:44
  • There is additional piece of modal machinery called accessibility relation. "It is possible that P" is only true when it is true in a world accessible from the actual world. With time, the actual world changes, and so does the set of worlds accessible from it. After you "blew your chances", the happily ever after world does still exist, but it is no longer accessible from your actual world. In temporal logic, modal propositions, like non-modal ones, come with time stamps. So it was possible at one time but can become impossible later. – Conifold Mar 29 '24 at 20:45
  • Benjamin it was: on appeal the winner was disqualified, so long as "lose the race" means "finished second". – Weather Vane Mar 29 '24 at 20:47
  • @BenjaminGrange no memory error here, your 'saying wrong thing' is and was possible or even very likely, but still you have possibility you didn't say the wrong thing in some accessible PW at the same time where you uttered the wrong thing in this world. PWs can be interpreted as dynamically branched and evolved in its own partially ordered Kripke frame just in the similar manner as MWI interpretation of QM.. – Double Knot Mar 29 '24 at 21:19
  • So my question about "accessibility relations" is how can two distinct worlds have that kind of relation at all? If they have a relation, that relation could exist in a higher level universe containing both. The only kind of relation I can think of between totally separate universes would be symmetry.

    @DoubleKnot I will have to think about that...in what way is there an accessible PW in which event E didn't happen if I know that in this world E did happen? I know for a fact that E happened, I have no doubt about it. The possibility of non-E is no longer accessible.

     – Benjamin Grange Mar 29 '24 at 22:18
  • @BenjaminGrange remember somewhere you stated you’re assuming pw realism… – Double Knot Mar 30 '24 at 00:21
  • On standard interpretation, accessibility relations do not "exist" anywhere, they just codify conventions of our possibility talk. But if you want to reify them, accessible worlds are those reachable from the current actual world along the timelines that pass through it, see Branching time temporal logics. – Conifold Mar 30 '24 at 00:42
  • @Conifold by "universe" we're not talking about a physical universe but a logical one. PWs are sets of prop's, no? So a relation Rxy has to "exist" in some logical universe. It exists in ours (our actual world) because we're talking about it now...this leads to infinity/recursion but it might not be a "bad" infinity... – Benjamin Grange Mar 31 '24 at 13:22

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The solution has to do with something called an accessibility relation. Your explanation of possible world semantics is a bit simplistic. When one says "It is possible that P," it doesn't mean just that "such and such a possible world exists." It'd be better to say that "such and such a world is accessible from this one. So time is all about some worlds becoming accessible and others becoming inaccessible. The ocean of possibilities is out there but not all of them are accessible at any given time.

Benjamin Grange
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