There is no set of all perfections

I was examining Bertrand Russell's take on the ontological 'proof' and that prompted this:

P is the set of all perfections, no matter how each perfection is defined.

P is the apex of perfections and so is a perfection.

Is P a member of itself?

Well, I know we have various axioms which do not permit P e P. Yet, that prohibition does not seem logically reasonable since P fulfills the criterion for membership in P.

My response is to say that P neither exists nor subsists because it implies a contradiction, to wit, Russell's paradox. There is no finite or infinite set that contains all perfections, just as, if the power set axiom is accepted, there is no set that contains all sets, because if so, we have Cantor's paradox.

In my terminology, which I will elucidate in future, objects that are describable but imply contradiction are said to negexist or n-exist. That is, because they are describable one cannot say they do not exist at all. They have n-existence and are members of the E_N set of objects.

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