S
Scowler
Guest
The definition of “possible world” is a state of affairs, which is different from the existing world is some respect. Nothing more, nothing less. There are infinitely many possible worlds. “Possible existence” means that the entity in question exists in some world, but not all. “Necessary existence” means that the entity exists in all possible worlds. This must be the starting point for all discussions.Keep in mind that this is an english translation of a formal argument. So in this setting (the one where possibility and necessity are referring to the S5 modal system, although B is actually the minimal one needed), there’s pretty strict definitions. Specifically, under the S5 system, all possible worlds are reflexive, transitive, and symmetrical. “Necessity” here also refers strictly to ontological necessity, as opposed to other sorts of necessity (e.g. necessity under the laws of nature). In plain english the problem is that necessity refers to a bunch of different philosophical concepts.
To demonstrate that an entity exists “necessarily”, one must examine all the possible worlds and find that the entity exists in all of them. That is an impossible task. On the other hand it is easy to show that there is no “necessarily existing” entity. All one needs to do is to find two possible worlds, which have nothing in common, which have no intersection. That is all.