Now how to use philosophy to discuss God with a deeply logical atheist? Well St. Anselm's Ontological Argument is a very fine proof of God.
[link to plato.stanford.edu
8.2 Formulation 2
"The Fool understands the expression “the being than which no greater can be conceived”. (Premise)
If a person understands an expression “b”, then b is in that person's understanding. (Premise)
If a thing is in a person's understanding, then the person can conceive of that thing's existing in reality. (Premise)
Each thing which exists in reality is greater than any thing which exists only in the understanding. (Premise)
If a person can conceive of something, and that thing entails something else, then the person can also conceive of that other thing. (Premise)
If a person can conceive that a specified object has a given property, then that person can conceive that something or other has that property. (Premise)
Hence the being than which no greater can be conceived exists in reality. (From (1)-(6), by a complex series of steps here omitted.)"It is hard to argue that this logical proof is not without merit.