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What I am asking is this: does the notion of free will require
as necessary conditions? Does this entail that not everything which is a physical effect have a physical cause?
Note: I am merely asking if those are necessary conditions, not if free will does, indeed, exist.
The notion of free will does not require either dualism where mental activity controls physical effects nor top-down causality. That is, there exist descriptions of free will that could be called "causal indeterminist or event-causal libertarian" views of free will as Robert Kane describes his own position.
The overview to Mark Balaguer's Free Will as an Open Scientific Problem describes a similar position to Kane's:
...contrary to the traditional wisdom, the libertarian question reduces to a question about indeterminacy—in particular, to a straightforward empirical question about whether certain neural events in our heads are causally undetermined in a certain specific way; in other words, Balaguer argues that the right kind of indeterminacy would bring with it all of the other requirements for libertarian free will.
That indeterminacy is present at the quantum level implies that it cannot be ruled out at the human level and so the problem of free will is open and from a physicalist perspective is a scientific problem.
References
Mark Balaguer, Free Will, MIT Press, 2014.
Mark Balaguer, Free Will as an Open Scientific Problem, MIT Press, 2012
Robert Kane, "Free Will: New Foundations for an Ancient Problem", Proceedings of the British Academy: 48 (1962), pp. 1-25, (Reprinted 2009 in Hackett Readings in Philosophy, Free Will)
The biofunctional analogy may help: biofunctional explanations are causal, involving interactions among the concepts of inhertitance, random mutation, and natural selection. Yet it seems undeniable that lower level causes - biochemical, physical - can fully account for these biofunctional events. We observers detect the biochemical causes, but they don't seem to have any other function; they aren't part of what the emergentist Lloyd Morgan aptly called the "Go of the world". And yet if the lower level causes are there, so, automatically given the nature of reality, are the higher.
Can we carry this reasoning to the case of mental causation? Suppose my wanting a drink and as a result filling a glass just is another description of an immensely complex lower level causal process - it is not caused by that process but simply is that process. I don't think that renders beliefs and desires epiphenomenal in a perjorative sense; they are both real, being the same thing, and not only that but the higher level, intentional characterization is very much richer, more informationally compressed, more meaningful than the lower. I think it should strike us as awesome that the basic stuff of the universe evidently has the ability to organize itself in this way
