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Yeah, this is it.
And to take a slightly different tack, if the biochemical and electrical activity in your brain were not deterministic, how would you ever know? It's one thing to believe that you made a decision on your own "Free Will", but how could you possibly rewind the entire universe (or at least some sufficiently small portion of it), including your brain's exact atomic state, and re-run the experiment to know for sure? At that point, what would "Free Will" even mean?