Pruss answers in the affirmative: Yes, because the statement "God is a necessary being" can be claimed to be a necessary proposition (as in the ontological argument).
But, it is often claimed, the notion of a necessary being is absurd. For it is propositions that are necessary, not beings, and hence talk of a necessary being is a category mistake. However, this is an uncharitable argument, since the claim that A is a necessary being can be translated into the claim that the proposition ∃x(x=A) is necessarily true, or perhaps that there is some individual essence E of A that is a property that only A can have and that is such that ∃x(x has E) is necessarily true. Talk of necessary and contingent beings will henceforth usually be understood in this way, though there is also a Thomistic model on which a necessary being is one whose esse and essentia are identical.1The second objection proceeds from conceivability. If one can conceive anything to exist, one can also conceive the same to not exist. However, Pruss counters this by raising the fact that there are propositions which are necessarily true, and their veracity implies their existence.
A better argument against the existence of a necessary being is that by a principle of Hume, anything that can coherently be thought to exist can also be thought not to exist. This by itself does not yield a satisfactory argument, however. It is not obvious that the totality of all existing things can be thought not to exist, that it could have been that there is nothing in existence. Moreover, this would imply that propositions, mathematical objects, and properties have merely contingent existence, an implication that may well be thought to be absurd since the proposition that 2+2=4 would be true no matter what, and it could not be true unless it existed, as nonexistent things lack properties, even properties such as truth. Moreover the proposition that there is a solution to the equation 3x2+x−7=0 is also necessarily true.2Pruss, of course, notes that this only established the existence of abstract objects, not the nonabstract God.
Of course, even mathematical propositions cannot be co-eternal with God if the doctrine of divine aseity is to be maintained; they are only true with respect to the world we are in and are contingently related to it, in which sense they don't possess necessity in the absolute sense of existing "necessarily", even abstractly. In fact, they have no existence or being of themselves. We find very conflicting results when we attempt to overstretch mathematical tools to understand reality (cf. Zeno's paradoxes vs. Pythagoreanism, Kantian antinomies), proving their epistemic limits of applicability. A rival cosmology would be Platonism that believes in the existence of eternal, immutable, plural ideas, which Christian theologians do not at all find to be compatible with the Biblical doctrine of creation.
1Alexander R. Pruss, The Principle of Sufficient Reason (Cambridge University Press, 2006), p.84
Modified Feb 20, 2016