What is Augustine's proof of God's existence?

Answer 1

At first, St. Augustine considered that the existence of God should simply be taken for granted. It was regarded as a matter so self-evident that a proof of God's existence would be entirely superfluous. He subsequently proposed an ontological argument to prove his case.

Augustine began by proving that human reason exists, something with which no one could argue. He then asked his listener to accept that if he can prove there is something greater than human reason, that it must be God. This was a weak point in his argument and, unless the listener agreed, Augustine could not continue.

Augustine would then point out the mathematical truth that seven plus three equals ten, arguing that this is true, whether or not human reason exists. Therefore there is something out there, some truth, which is greater than human reason. The statement is true, not because we say it is, but because it is a truth that exists in this world and that truth must come from somewhere. Since this truth is greater than human reason, and does not depend on us to be true, there must be a God.

Answer 2

St Thomas Aquinas relied on what is known as the Cosmological Argument for the existence of God. He claimed that there were five valid ways to prove God exists, although thre of them are essentially restatements of the same things. Essentially his view was that some contingent beings exist; contingent beings require a noncontingent ground of being (a "necessary thing") in order to exist; therefore a noncontingent ground of being exists. This is not a great deal different to the Ontological Argument.

Aquinas' theological positions involved making unprovable assumptions from which to prove the unprovable.