The Ontological Argument

The ontological argument relies on the following premises.

1. That than than which nothing greater can be conceived, can be conceived.
2. Anything that can be conceived, can be conceived to exist.
3. All else being equal, a thing is greater if it exists than if it does not exist.
4. God is that than which nothing greater can be conceived.

From these premises, the existence of God is deduced as follows. From premise 1, that than which nothing greater can be conceived can be conceived. By premise 2, that than which nothing greater can be conceived can, moreover, be conceived to exist. By premise 3, if it did not exist, it would not be that than which nothing greater can be conceived, which contradicts its definition. Thus that than which nothing greater can be conceived exists. By premise 4, God exists.

Since the premises of this argument are all self-evidently true, and the argument employing them is valid, the ontological argument is sound.

On the contrary...

Objection 1

The first premise is not self-evidently true. For it is possible that than which nothing greater can be conceived is not itself conceivable. By way of example, every natural number (the counting numbers 1,2,3... and so on) can be conceived, but it is not possible to conceive of a natural number which is greater than every other natural number, for it is part of the very definition of a natural number that it must admit a successor number which is greater than it by one. Thus, if we cannot conceive of a greatest member in the set of all natural numbers, it is not at all clear that the set of all conceivable entities contains a greatest member. Thus the first premise requires further proof.

Objection 2

Even if the first three premises are true, the fourth premise requires the assumption that God exists. For if God does not exist, then the first three premises imply that He cannot be that than which nothing greater can be conceived. But this renders the argument circular.