system
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human
Are there ontological arguments against the existence of God?

Since metaphysics has, traditionally, as a discipline, been fertile soil for theism, and the most metaphysical of metaphysical arguments for the existence of God is the ontological one, I recently became interested in proofs of this kind that go against the grain.

So far, I have identified three:

1. Spinoza's claim that there cannot be multiple substances, which rules out traditional theistic conceptions of a God causing a world distinct from itself.

2. The traditional omnipotence paradox.

3. Sartre's claim that God, if he existed, would simultaneously be in-itself and for-itself; since that a
being like that would be contradictory, God does not exist.

Can we call these "ontological arguments against the existence of God"? If so, are there others? 

Of course, I exclude other traditional arguments for atheism like the *problem of evil* since it is not ontological at all. An ontological argument would be concerned with the essence of a thing, and therefore, the *a priori* necessity of its existence or inexistence. 

I am also curious of what a Hegelian response to Sartre's argument could be, since, although I know very little of both, it seems suspiciously Hegelian to join the two aforementioned principles.
gpt
> Spinoza's claim that there cannot be multiple substances, which rules out traditional theistic conceptions of a God causing a world distinct from itself.

It doesn't: the theist is typically inclined to accept this argument, which Spinoza largely appropriates from traditional philosophical theology. You can find stuff like this in Aquinas, for example.

> The traditional omnipotence paradox.

It's not clear how this is an ontological argument, and it doesn't have much history of being taken seriously so it would probably be somewhat trivialized even if it were.

> Sartre's claim that God, if he existed, would simultaneously be in-itself and for-itself; since that a being like that would be contradictory, God does not exist.

Does Sartre give this argument? It's not clear why the category of the in-and-for-itself, which does receive constructive use quite significantly, would be self-contradictory. 

> An ontological argument would be concerned with the essence of a thing, and therefore, the a priori necessity of its existence or inexistence.

The terminology of "ontological" argument doesn't imply merely that the argument has to do with being, nor merely that it happens to be a priori -- features it shares with the other two arguments of transcendental theology, the cosmological argument and the physicotheological argument. Rather, the term "ontological" has here a narrow, technical meaning of referring to a very particular kind of argument in transcendental theology.