I'm a math student taking philosophy classes. So I have some math background but am absolutely unfamiliar with metaphysics&c. Recently I've come around the "Nothing Is Impossible" paper as a part of that course. The author is only constrained by S5. Here's the part I'm having trouble with:
Assume that it is possible for there to be something. If this is so, there are possible worlds (accessible from the actual world) in which beings exist.
The question basically is: why need't be accessible from the actual world?
I looked it up and found this SE answer about accessibility relation. It says:
The axioms of S5, for instance, require the relation to be an equivalence relation and so have the result that every world is accessible from every other world.
I'd rather conclude: "every world is accessible from every other world within its equivalence class" and I don't see why there would be exactly one class. Of course I might be missing some point in the definitions.
Some possible explanations I see:
- It might be meaningful to treat "$P$ is possible" as "$P$ is true is some accessible world". Doesn't explain the proposition from the SE answer I mentioned.
- Perhaps in S5 there can only be a single equivalence class and I missed it? Then why is it so? What's the purpose of such a trivial accessibility relation?