(For the purposes of this question, I am assuming that some form of physicalism holds.)
When I read about hard determinism and compatibilism, it struck me that they seem to be placing different labels on the same diagram. To use more standard terminology, they look (to my eye) like two differently-notated maps of the same territory.
- Is it possible to distinguish between a hard determinism universe and a compatibilist universe by some physical experiment?
- If not, what is the objective difference between them? Can one be true and the other false?
Since it has been asked, here are the definitions of these terms that I am familiar with:
- Hard determinism - The universe's future is either fully determined by its present state, or to the extent that it is not so determined, the nondeterminism manifests as randomness rather than some kind of cognitive process or other purposeful, non-random variation. Free will is thus excluded because there is no non-determinism in which it may exist.
- Compatibilism - Free will has nothing to do with non-determinism. Our choices are determined by our character, morals, memories, etc., none of which require or even benefit from non-determinism. Purposeful non-determinism is excluded because free will never involved non-determinism, so all non-determinism is purely incidental and non-purposeful (just as in hard determinism).
I have no objection to answers which challenge one or both of these definitions. I am not claiming that they are correct. They are merely the definitions that I happen to know.