This definition you provide here only eliminates free will if you start out with the assumption that free will must entail the ability to have done otherwise in exactly the same circumstances. It is this assumption that you don't even attempt to justify.
This the core of the matter, but I would put it slightly differently. A subject
does have the ability to do otherwise in exactly the same circumstances; however, the subject
will not do otherwise, in exactly the same circumstances.
The hard determinist believes, evidently, that every fact about the world is a necessary truth. In fact, as I’ve repeatedly pointed out, the only facts about the world that are necessary truths are truths of
logical necessity; e.g., that all triangles have three sides.
Earlier, DBT quoted the opening paragraph of
this paper, but then does not seem to have read the entire essay, which concludes:
[Necessity must be limited to its proper use in logic, and disambiguated from its close relatives
causality,
determinism,
certainty, and
predictability.]
In practice, when the compatibilist speaks of “could have done otherwise,” he/she means, “would have done otherwise, if …”
If what?
If antecedent circumstances had been different.
This morning I had eggs for breakfast. But using modal logic’s possible worlds heuristic, it’s easy to show that there is a
possible world, very “near” the actual world, at which I had pancakes for breakfast. Conversely, there is no possible world at which triangles have four sides.
All actual truths about the world, including its entire history, are contingent truths, unless they are logically necessary truths. Since having eggs is not a logical truth, its a contingent truth. Contingent on what? On my choice to have eggs, which is a free act insofar as no one coerced me to have eggs against my will.
This is my only (minor, mainly terminological) dispute with Marvin, who otherwise has done such an outstanding job in this thread. I do not recognize any such modal category as “causal necessity.” I only recognize “causal determinism,” which is always a set of contingent (could have been otherwise) outcomes.