How is free-will formally defined as distinct from determinism, randomness and determinism-randomness hybrid to support moral responsibility?
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Julian Baggini has written a book called Freedom Regained: the Possibility of Free Will. In it the idea emerges that Philosophers working on free will and moral responsibility proceed almost exclusively by appealing to intuitions.
Richard Oerton in his book The Nonsense of Free Will gives, I think, a good,
not-too-technical-for-the-average-reader discussion of the incoherence of the
free will idea. When something is essentially illogical it means that the sort of formal mathematical definition you seek is actually impossible. That's the thing about free will, it is free of formal definition. If we could define it it would not be free. It just fills a gap people want to fill. The human will is not free of how God made it or why God made it. We are free to be ourselves but not free to be anything else. We make choices based on who we are. Who we are depends upon how we were made. Nothing has ever made itself. All our choices depend on how we were made. Free will needs a gap between what we are and how we behave. This gap does not exist.
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