Not that I'm a (meta)mathemetics whiz or anything (although I have read not
only Godel, but also Ernst Nagel, Paul Benaserraf, and, most importantly,
John R. Lucas on "Godelian Incompleteness") but, J.R. Lucas to the contrary
not withstanding, Godelian Incompleteness with respect to (any) formal
systems (at least those robust enough to compute/instantiate elementary
arithmetic), including physical instantiations of such formal systems (e.g.,
discrete state, Turing machines) simply does *not* imply (much less entail)
"free will." Simply because such a Godelian system (including, e.g., human
beings) cannot (always) know what it will do/decide next, this does not inherently imply (much less entail) that said system is not utterly Laplacianly (or quasi-Laplacianly) determined down to the micro-level, and that the future behavior/decisions are not thereby utterly inevitable and incapable-of-being-otherwise. Godelian considerations are more of a (meta)epistemic element, rather than an ontological one. A system or entity can be utterly Godelianly epistemicly indeterminate, and still might be *physically* determinate down to a micro-level. Quantum-level uncertainty/randomness does nothing for the cause of free-will, either, without some theory linking it (say) to some sort of *agent-causation* (championed in this century in turn, by Rod Chisholm, Carl Ginet, Richard Taylor, and Peter Van Inwagan). On almost any current theory of quantum physics (Bohm/Hiley hidden variable/pilot wave [now somewhat passe], Everett/Tipler/Deutsch/McCall Multiverse Ensemble, etc.) free-will is not especially well-served. True, we no longer have Newtonian/classic-Laplacian determinism (replaced by Prigoginian dissipative emergence), but we don't have sufficient bridge-theory(s)---*yet*---to save free-will from quantum-randomness. And *randomness* is just as bad as strict determinism---you sure as hell don't get (what we [used to?] think of as)
"free-will" (which is actually agent-determination or agent-causation) out
What is needed is a robust theory of agent-causation which takes into account--indeed, incorporates--state-of-the-art quantum-cosmology (here broadly conceived to include Prigogine's stuff). No philosopher/scientist has yet done this (at least nowhere near completely and thorough-goingly), but some interesting groundwork has been laid by the philosophers Peter Van Inwagan and Storrs McCall (among a few others). I don't have specific citations handy, but I'll look 'em up and get 'em to whoever wants 'em. (I should note, however, that when I say groundwork, I mean, to extend the metaphor, only [so far] scratching the service!)
I'm all for freewill, but Godelian Incompleteness in and of itself doesn't get it for you.
P.S. Philosopher Edward Pols, of Bowdoin College in Maine, has also done some good stuff on the metaphysics of agency, extending the work of Whitehead, Polanyi, and others. See, e.g., his *Meditation on a Prisoner: Toward Understanding Action and Mind* (Carbondale, Il: S. Il. U. Pr., 1976), and his later stuff. He spins some interesting metaphysics--indeed, quite sound in my judgment--but fails to link it to contemporary physical concepts. Still worth reading, though.