Logical proof of god´s existence... I don´t think so.
While I won´t claim to be a Ph D. in mathematics, and not event a self proclaimed Platonist Philosopher as Dr. Hatcher
But I know what´s wrong with his proof.
While it doesn´t fall into the infinite regress, it falls into something similar.
Since the universe is a composite and can not be the cause of its components, there must be an external cause... ok.
By definition, if there is the universe and Dr. Hatcher´s G element, then there is a second metauniverse, containing G and our universe.
In that metauniverse, G can not be created by the metauniverse, since it´s a component of it. So there must be a G´ which created G.
If we decide, as he did, that G is self-created instead, why can´t every quark be self-created?
Why can´t there be just a dozen quarks, moving through time, and we see him many times because he crossed our position in time many times?
Are you willing to have a quark as your god? :-)
The real issue, I propose, is not whether the Common Prayer should be rewritten "Our quarks, who art in sub-space, hallowed be thy spin..."
;-).
The real issue is that our "vision" of G has evolved. God wasn't ALWAYS this abstract, omnipotent force. Pagan gods were often quite limited in power; humans could affect them with prayer and sacrifice (sometimes of human blood, yuck!).
But around the time the concept of the One All-Powerful God came around, he became more abstract. And as mankind learned that the cosmos was always BIGGER than we'd imagined - perhaps even infinite - God became infinitely remote and abstract. The "humanoid" component of G faded out.
Let's say that we prove the existence of G. Will this mean a revival of religion everywhere? I don't think so. Because this G will be utterly removed from us, that we wouldn't praying to "it". We'd know better... G can create universes, so why would G care about incense and prayer on one tiny planet among many?
I'm not saying this is the way it IS... but quarks don't have the emotional pull of a man on a cross. It's awfully hard to gather people around an elementary particle. :)
As for Dr. Hatcher... I'll just say this: Platonism gave birth to Romanticism, which gave birth to Fascism. Plato despises reality. Plato is an evil elitist. :(
Well, I am an evil elitist myself, and I find it hard to blame Plato for what happened 2300 years after he died ;-)
As for Plato despising reality... well, think about it. No internet access, no soap, no hamburgers. Really despicable reality!