God, Santa, and The Tooth Fairy

[Belacqua]

I realize there’s a possible false dichotomy here: ‘either a god is detectable via methodological naturalism, or god doesn’t exist.’ It may very well be the case that there are things which exist, that are also beyond our ability to investigate. But if carving out a unique, third set that contains god and only god[...]

Limited answer, to just the part quoted above.

A lot of people believe in things which are not detectable via methodological naturalism, yet seem to exist. 

The paradigm case is probably numbers. We can think and talk about the number two, we can use it to reason with, yet we cannot find it in the material world. It cannot be weighed, measured, or located. We know of the number two in two ways: first, by abstracting and extrapolating from the material world. Given enough cases of two thises and two thats, we can begin to discuss the number two separate from any material substantiation. Second, by fitting the number two into a logical and coherent system (i.e. mathematics) we can see that it is meaningful to discuss it without reference to the material world. 

The vehement materialists here [and I'm just going to pass over the fact that Vehement Materialists might make a good band name] will argue that numbers are just names we have for things and have no mind-independent existence. They might be right, but this turns out to be a trickier question than it first appears. There are some very serious people (Plato, Popper, Penrose, etc.) who hold that numbers are real. If they are right, then there are real things which are not detectable via methodological naturalism, but only through logic. 

So it appears that there may well be things that exist, inaccessible to methodological naturalism, which it is possible for us to investigate. But not through empirical methods. 

I bring this up because at least since the time of Plato and Aristotle, God is said to be more like numbers than like Bigfoot. His existence (they say) is known not by empirical evidence, but by extrapolation and abstraction from the material world. 

It is fair to say that in this system God is unique. He is not just another form or another number. He is held to be the sole member of his set, because all the other immaterial things (forms, numbers, etc.) require for their existence that there is one overriding, Logos-giving form. At the same time, saying he is unique is not to say that he is separate from the universe. As the saying goes: "God and the universe do not make two."