I will prove to you that God exists

[Angrboda]

It's not clear that people are speaking correctly about infinity and the transfinite.  These terms have specific meaning that is often ignored in favor of intuitive but incorrect senses.  But then, the intuitive sense predates the mathematical one, so a choice has to be made about whether the older usages are constrained by the mathematics.  If not, it would seem that infinity and the transfinite do not possess the behaviors that our/their intuitions attributed to them.

I guess if you allow for mathematical sense infinities (i.e. in a mathematical hierarchy of infinities) than either god is or is not the biggest infinity. I suspect the latter is not endorsed by christianity (god is GOAT). If the christian god is GOAT than my counterproof leads to the same result. If not, the christian god definition is breached. Maybe there is a hierarchy of gods all the way up, as there are turtles all the way down. Solves the fine tuning of the christian god.

Somewhat reminiscent of Kripke's concept of truth, I would guess there are infinite infinities, and thus speaking of a greatest would also be intuitive but incoherent.

[LoneWolf]

As I understand it, the Christian God is not said to "radiate" temperance, modesty, or any of the other virtues. Those virtues are habits people develop through their behavior, but God has no behavior. As the Form of the Good (for Neoplatonic Christians) and as actualization without potentiality (for the more Aristotelian kind) a Christian would attempt to become in line with God through such behaviors. Though God, being ideal, wants nothing, people say metaphorically "God wants you to be temperate." This really means that it's in one's own best interest to be temperate, in order to be as good as possible.

How can god act in the world if he has no behavior? Without action/behavior it becomes very difficult to put on your socks, let alone create a universe. Another argument getting us deeper in illogical reasoning.
As for temperance, it was adopted by the church as one of the seven holy virtues. If the holy virtues are not an indication of what is meant with doing/being "good", than what is? At least it was the interpretation of the church at the time that those things belonged in the category "good". Or do we have different categories of good, one for gods and one for mortals? Further in the trench we go.

As for Giordano Bruno, he was an early adopter of lots of newish ideas, but that's not what got him killed. He was executed for going to Rome and loudly advocating the overthrow of the Catholic Church, so it could be replaced with a set of even wilder ideas supposedly recovered from an ancient tablet, which even then was identified as a forgery. If he had published his cosmological speculations as speculation, and not poked his thumb in the pope's eye he would have been OK. 
...
From our modern perspective, Bruno's fake-ancient beliefs may be no better than what Catholics believe. But it wasn't the science-y part that got him in trouble.

I never said Bruno "radiated" science and was therefore burned. The point is there were and still are a lot of views within christianity that go against doctrine. In fact christianity (say the Catholic Church) nowadays evolved from a vast array of different opinions competing in the early church. Power and politics certainly played a role. So, how can we discern who's proof of the christian god we should take seriously?

[LoneWolf]

Somewhat reminiscent of Kripke's concept of truth, I would guess there are infinite infinities, and thus speaking of a greatest would also be intuitive but incoherent.

Well mathematics indeed developed a hierarchy of infinities and found that you can say that one type of infinity is greater than another. This started with Georg Cantor in the late 1800s and developed further with Richard Dedekind, David Hilbert, Kurt Godel, Paul Cohen and Ernst Zermelo, no small potatoes. Sometimes what seems intuitively incoherent can be proven mathematically. But maybe I misunderstood you.