(From an e-mail.)
I see science as working within the assumptions of metaphysics - so that before any science is done there is an implicit metaphysics of causality. And science cannot investigate what it assumes by its very existence.
Scientific reasoning studies cause and effect processes, as you say - which means it cannot use cause and effect reasoning to challenge the validity of cause and effect reasoning.
This is also the argument why it is incoherent to challenge free will - but CS Lewis states it much better than I could in Mere Christianity and elsewhere; and indeed I'm sure you have felt the force of it yourself when engaged in such arguments. If free will does not exist, then what are we arguing for or about?
I don't think science has made any contribution at all to understanding of free will, quite the opposite - it has led to great confusion.
Before any discourse, before science, we must assume free will - we assume that there is something possessed by humans that is not determined and not random but an expression of our individual ... essence (hard to think of a suitable word).
At least we must assume free will among the participants in the discourse, and of course we would need to exclude those who did not have it else the discourse would be invalidated.
In general, I have behind this a metaphysic that humans come into the world gifted with reason and free will (and other attributes), and these are divine gifts and upon their validity depends... well everything else.
Like CSL I argue that reason and free will cannot be challenged coherently because the challenge itself depends on the validity of reason and free will. In fact this is obvious!
But the problem for modern people is that in denying God they deny the validity of free will and reason - because if free will and reason are nothing more than evolutionary products - the products of random variation and differential reproduction - then of course free will and reason are mere contingent and temporary accidents and naturally have zero validity, and no real knowledge is possible of any kind - including exactly this knowledge about the evolutionary causes of free will and reason...
Which is nonsense.
Therefore we must believe in 'god' (albeit not necessarily the Christian God, but something much simpler, with metaphysical properties), or we cannot believe anything at all.
The ancient Greeks perceived this - that 'god' is necessary to underwrite the validity of every inference; doubt god and you are (know it or not) plunging into impossible and intractable paradox.
This is probably the deep reason why godless philosophers cannot comprehend even the most basic philosophy, cannot comprehend the stuff that was worked out two and a half thousand years ago.