Naturalism isn't an arbitrary choice. By definition, the natural world is the world we can know anything about.
In order for knowledge of the world to be possible, the world must be consistent and governed by relatively fixed rules (laws of causality, in the broad sense of the term). These two axioms, consistency and causality, are the axioms of science and logical positivism. From consistency we get the laws of logic and mathematics, and from causality we get the scientific principles of mathematical modeling.
Is it possible to prove that the world is natural? I don't think that's possible. I cannot prove that the universe is consistent, nor that every event has a fixed cause. However, the natural world is the only world we can know anything about. Anything beyond naturalism (supernaturalism) must must violate either the axiom of consistency or axiom of causality (or both). That is, the supernatural must either be inconsistent or be exempt from any causal rules whatsoever.
I'll explain why this makes knowledge of the supernatural impossible.
Suppose we have a true proposition, P, about a supernatural cause. If the supernatural cause is not bound by consistency, then it is possible that the contradictory proposition NOT P (~P) is simultaneously true. For example, there is no reason why "God is good" could not simultaneously be true and false of a supernatural God. One cannot describe knowledge of both contradictory propositions as knowledge at all.
If the supernatural cause violates the axiom of causality, then there is no discoverable rule that relates a supernatural cause to experience. Any experience could equally well signify P as ~P. P can cause an effect E and also cause effect ~E. Likewise, ~P can cause an effect E and also cause effect ~E.
Furthermore, supernatural events would remain unexplained, and we would never know whether they were supernaturally caused or whether we just hadn't yet figured out the naturalistic cause.
You may have your own definition of naturalism. However, the definition presented here is precise and executable.
Now, given my definition, you may prefer to believe that God is not supernatural. In this case, God would be subject to certain rules, or perhaps be indistinguishable from those rules.
Naturalistic scenarios would include:
- God is an alien whose technology is so great that it simply appears like magic to us.
- God is another word for all the laws of the universe, or God actually is identifiable with the universe.
- We are living in a simulation created by a naturalistic being whom we call God.
However, few theologians subscribe to the view that God is a naturalistic phenomenon. The reason for this is that it's emotionally difficult to assign divinity to a naturalistic being. I think that few fans of Star Trek would say that Q was a God, despite his possession of God-like powers. He's just an evolved superbeing.
However, the supernaturalists are trapped. If they grant that their supernatural cause is knowable (logical and rule-based), then it automatically becomes a naturalistic automaton.
In order to give God the attributes that make him worthy of worship (e.g., perfect goodness), we end up making the concept incoherent or stretching language beyond all meaning.
In the end, I am an atheist for two reasons. First, we cannot have knowledge of the supernatural (propositions about God have no truth values). Second, I hold no Gods before me. That is, if there were a God-like alien (and so far there's no compelling evidence of this), then, while I might do what it forced me to do, I would not regard it as a God.
The two axioms I have described here are not exhaustive because there may be consistent, rule-based ystems that we still cannot know. That is, proposing that there is some consistent causal system that explains the world does you no good if you also posit that this consistent causal system is unknowable.