Say that p and q are nomically equivalent provided that the laws of nature entail that p holds if and only if q does.
- If q is not up to you, and p is nomically equivalent to q, then p is not up to you.
Suppose determinism. Let L be the laws. Let t0 be 1000 years ago. Let p be a proposition reporting something you do. Let q be the disjunction of all the nomically possible states of the universe at t0 that evolve under L in such a way as to make p true. Then, plausibly:
- p and q are nomically equivalent.
Finally, observe that events a thousand years ago aren't up to you:
- q is not up to you.
We conclude that p is not up to you. So no actions are up to you if determinism holds.