possibility can be different from possible-worlds semantics

A predicate calculus that asserts its own existence would appear to exist to itself, and that notion of existence would be indistinguishable from our current notion of actual existence.




Predicate calculus P



P exists in the sense of P, i.e. P asserts qua P that there is something that exists which is P i.e. PP.



This notion of existence is the same notion as actual existence, i.e. if our universe is P we could not tell the difference between existence-in-the-sense-of-P and the kind of existence that is actual.



Because of this, it is plausible that all we need is the possible existence of P.



I will give an example from quantum mechanics where the possible existence of something is different from a possible-worlds interpretation. In the many-worlds semantics, one says it could be the case that it does not exist and it could be the case that it exists. We want to say instead that it is possible that P exists, perhaps using a kind of intentional logic/model. An example of this phenomenon comes from quantum mechanics: we can write y-spin up when any value of x-spin is possible,



(1)



but we cannot decompose this situation into one where there is a set of possible worlds where y-spin is up and x-spin is up, together with a set of possible words where y-spin is up and x-spin is down:



(2)



If we can find such a P, and we can show that our universe is P (by making predictions from P about physical phenomena), then we would have a rational explanation for existence.



(It is not germane that we can also define a set of possible worlds in which the electron is in a superposition.)