math wouldn’t provide such a useful tool for modeling reality. 2+2 really could be equal to mashed potato. Such a universe would be governed by illogic.

Could a universe governed by illogic even exist? I don't really see the reason why 2+2 could equal something different or even absurd. The whole point of something like 2+2 is that its value holds true in any conceivable universe, whether there is a god or not. And I don't know theological opinions on it, but could God make 2+2 equal 5 or make a square circle?

The reason for these processes playing out by logical, coherent rules is ultimately the observable fact that our universe is governed by logic.

Right, but rules do not necessarily imply a rulemaker. There is such a thing as spontaneous order. In this case, any universe where life exists probably would have to have some laws, or at least, I don't see any reason why the existence of laws implies a divinity.

I’m not trying to be tautological

I didn't mean it like that, more like that any view of the universe ultimately boils down to some assumptions which are taken as axiomatic. One can be 'parallel lines cannot cross'. Or that 'the origin of mathematics is a divinity'.

The key point is that there is no reason why mathematics should be so applicable to reality

The whole reason we discover mathematics and do apply it to reality, is because we created it based on our experiences with reality - not the other way around. It's not as if mathematics was something that just coincidentally happened to be applicable to reality, correct?

It is, like Plato’s forms, an idealized abstraction that exists only in the minds of humans (as far as we know), right?

Technically, Plato's forms would be an actual reality in the real world.

So for math to be “real”, that means this idealized, non-physical form must also be real, but somehow existing outside of the universe. If one can accept this, God is basically just a name given by us to this underlying order and meaning which exists outside of, and was wholly responsible for shaping, the universe itself.

But if we give a name to an 'underlying order', that is quite different from attributing agency or the creation of the world to that. Suppose that we did agree to label the underlying order of the universe, which we can agree on, 'god'. Would that imply that this is a personal god that is responsible for creating the universe? On the other hand, does agreeing to such a minimalistic idea of god not undermine the theist or deist? He is reducing the idea of a god to an 'underlying order', after all.

One of the most interesting versions I’ve seen even applied the logic to the evolution of universes themselves

You seem very interested in abstract ideas and metaphysics. Less so for me. I tried reading a book on the alleged nature of time recently, and it just befuddled me.

Yes, this is effectively the “Anthropic Principle”, which is admittedly the best attempt at a counter-argument I’ve come across, but I agree with Roger Penrose that to invoke it provides no explanatory power at all, and is in fact the far more tautological option than concluding a higher order intelligence behind the universe (imo at least).

Ultimately, we're just in a cage with no way to definitively figure out what is beyond. Either way, it's absurd. And I'll freely admit that having a higher intelligence is less absurd than there being no time and a singularity at the time of the big bang. At least that would make some sense. But are natural processes obliged to make sense to us puny humans?

Glad to find a subject we have so much agreement on. Maybe we can sharpen each others arguments to better effect!

Not that much agreement yet, but at least good conversation.