The God quantifier

Hypothesis: There is no fundamental quantifier that includes within its domain both God and something other than God. (Obviously, this is inspired by Jon Jacobs' work on apophaticism.)

The hypothesis is compatible with saying in ordinary English that both God and human beings exist, and that nothing (not even God) is a unicorn. But if we speak Ontologese, a language where all our quantifiers are fundamental, we will need to modify these locutions. Perhaps we will have a fundamental divine existential quantifier D and a fundamental creaturely quantifier ∃, and if in Ontologese we want to give the truth conditions for the ordinary English "Nothing is a unicorn", we may say something like:

• ~Dx(Unicorn(x)) & ~∃x(Unicorn(x)).

And if we want to give truth conditions for "Something is alive", we may say something like:

• Dx(Alive(x)) or ∃x(Alive(x)).

(Assuming that Alive(x) is a predicate of Ontologese.)

Of course, it could be that Ontologese doesn't just have a single quantifier for creatures. It might, for instance, have "metaphysically Aristotelian quantification": a quantifier ∃ over (created) substances and a subscripted quantifier ∃_x over the accidents of the substance x. In that case, "Nothing is a unicorn" will have truth conditions:

• ~Dx(Unicorn(x)) & ~∃x(Unicorn(x)) & ~∃x∃_xy(Unicorn(y)).

(It might seem excessive to say that no accident is a unicorn, but better be safe than sorry.) Likewise, "Something is alive" has the truth conditions:

• Dx(Alive(x)) or ∃x(Alive(x)) or ∃x∃_xy(Alive(x)).

Now, it may seem wacky to think of a quantifier D that quantifies only over God. But it shouldn't seem so wacky if we recall that Montague-inspired linguistic classifies names as quantifiers (they correspond to functors that lower the arity of a predicate, after all).

Now this leads to an interesting question. Speaking in the ontology room, where we insist that our language cut at the joints, should we say "God exists"? That's a choice. We could adapt the English "exists" when used in the ontology room to go with the fundamental quantifier D or the fundamental quantifier ∃.

We might want to, this being the ontology room after all, make the decision that we will adapt words to the most fundamental meanings we can. But in some sense surely the divine quantifier D is more fundamental than the creaturely quantifier ∃, so in the ontology room we could say: "Only God exists." It is said that Jesus said to St Catherine of Siena: "I am he who is, and you are she who is not." Maybe St Catherine's mystical theology room wasn't that different from the ontology room.

Or we might want to keep as many of the ordinary existence claims unchanged, and so say "Photons exists". Then we might want to say something like "God does not exist but divinely-exists."

But since the ontology room isn't the ordinary context, this is really a matter of decision. My own preference would be to say "Only God exists" in the maximally fundamental ontology room, but to spend a lot of time in less fundamental ontology rooms, ones in which one can say "God exists" and "Photons exist" but not "Holes exist" or "Tables exist."