Agnosticism IS the most dishonest position

[Belacqua]

I think I disagree that you can separate science and logic in that way. Logic is grounded in the physical realty we experience. The laws of logic are descriptive of that realty. Consider the law of identity. A, meaning “a thing,” must be identical to itself. Without a physical reality where things exist, there is nothing to describe or identify.  Many of the common logical arguments for god still depend on the truth or likely truth of their premises, and many of those premises are commenting on some purported truth or truths about the physical, detectable universe.

I didn't mean to say that in thinking carefully about the world we can separate science and logic. We use them together, though a given case may demand more of one than the other. 

A paradigm case is maybe Zeno's logical arguments as to why motion is impossible. Though the conclusions are obviously false -- because motion happens -- it's surprisingly hard to show why his logic is bad. Demonstrating through logic that Zeno is wrong led Aristotle to develop his whole system of act and potency, which has ever since affected the way we think about both theology and science. 

Another way to approach it might be to think about math as a form of logic. It seems likely that math began for purely practical reasons in the real world. (If your tribe has 34 members, and consumes one wooly mammoth per month, how many mammoths do we need to make it to spring, assuming that as always one third of the tribe will die from disease during the winter?) But the logical development of math has led to negative, irrational, and imaginary numbers, which may have very little relevance to the material world. Math tells us that there are infinities of different sizes, which seems pretty unrelated to any mammoth problem I can think of. 

Natural theology works entirely as you say: it begins with purported truth about the world as we see it, and works from there. If people's logic seems wrong to us, then we either point to the empirical world as a rebuttal, or show that the logic is wrong. 

But our knowledge of the empirical world is often flawed. And our logic is often wrong as well. So it's an ongoing problem to use them in dialectic to improve out thinking.