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in favor of physics because biological explanations are more complex than physics explanations? Or economists to give up economics because physics provides simpler explanations of the price of oil?
You're assuming that science itself is completely reductionistic, but that itself is far from being established. It's certainly not clear that from a complete knowledge of physics, one could predict the emergence of higher level properties such as life or consciousness or culture. For one thing, there are serious doubts about whether determinism is true. For another, it's possible that higher level properties supervene on physical properties in virtue of laws that are not themselves laws of physics. And that's just for starters.
So harking on with this complaint that theism posits something of a higher order of complexity is like complaining that mathematicians posit sets to explain numbers.
Nor do I need to accept that God is more complex than the world. In classical theism, God is a simple, not a composite being. God is immaterial substance, i.e. is not composed of parts. Matter, by contrast, always seems to possess a complex essence, with a variety of measurable properties such as position, velocity, momentum, angular momentum, etc. Simplicity is really a vague, not a well-defined, notion, and I suspect that when used to characterize explanations, it's inherently subjective. But when we use it to characterize, not explanations, but beings, then I think that rational consciousness is less obviously complex (in the sense of being composite or divisible into discrete parts or properties) than is material reality. It's certainly not obvious that mind is more ontologically complex than matter.
But even if mind or God was more ontologically or explanatorily complex than material reality, one would still have to show why a correct explanans of any given thing has to be less complex than the explanandum. It seems to me that in science, we often explain something by positing something more complex than the thing being explained. For example, we see an apple fall from a tree. When along comes Einstein with his General Theory of Relativity, do we say, "YOU'RE WRONG, ALBERT. YOUR THEORY IS A LOT MORE COMPLEX AND HARDER TO UNDERSTAND THAN A FALLING APPLE!"????
No, we don't, is the short answer to that. Same with explaining WELCOME TO SCOTLAND signs by reference to conscious rational minds acting purposively.
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