Lot's of semantic nuances there: I certainly believe, as I think you
mean to point out here, that the thing I call free will resides
solely in the matter of my brain and its arrangement, and is manifested
by understandable physical processes. There is plenty of evidence
for that (neurobiology), but to call these processes "deterministic"
just begs the question of what free will means. I experience it; it
is there. So far, the chemical properties of the brain that we can
understand don't explain it, so we must not know everything about how
those atoms behave. I don't have to postulate that there is something
other than them ("soul" or whatever), just that I don't yet know what
it is about them that creates what I experience as free will.