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The usual argument against it is that if behavior of matter is not fully determined by its state then it has to be determined by something else, ergo dualism. This begs the question however, unless we insert determinism into the definition of matter its behavior can be causally gapped, there is no sufficient cause, no poltergeist, no "else".

What I think some libertarians about free will have in mind is something like this. We have basic level objects, fields and particles, we have weakly emergent high level objects, let me call them neutrally "collective states" (think of global patterns on a lattice grid). Basic level evolution is probabilistic, and there is a feedback channel that lets collective states influence distribution of outcomes in basic events, that is alter their probabilities. The influence is causal but lawless, not subject even to probabilistic laws, or partially lawless. One might object that there is no plausible mechanism for that. But we do not have a "mechanism" for matter "generating" gravity either, just an equation relating metric tensor to stress-energy tensor. Presumably the strength of the channel depends on complexity of emergents. With our present experimental capabilities, that require setup isolation, any such effects will be undetectable. But they may become detectable eventually as lawless deviations from pure QM predictions, etc. The scheme might require non-locality (although with some creativity one might be able to eliminate that), but it does not seem to require poltergeist.

This is only meant to give an idea, details are malleable. Think of the basic as physical, and collective as mental. One aspect usually assumed about reductionism will be missing: because of the feedback channel there will be no reduction of collective evolution to basic evolution, the basic states alone do not constrain it fully. But this concerns epistemological reduction only, ontologically there appears to be nothing but matter.

Would a materialist/physicalist accept this kind of reduction? The idea, as Davidson put it, is that mental events are physical events, but no laws relate mental to physical. He was a compatibilist though. Are there ways for a materialist to accept libertarian free will? If not what will be the arguments against (but please do not make them dependent on specifics of the above scheme)?

Conifold
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    I do not understand the scheme which makes up the most part of your question. It collects buzzwords like weakly(?) emergent, lattice grid, feedback channel, partially(?) lawless, QM predictions, non-locality, creativity, basic evolution, collective evolution. Does the scheme scetch your personal mind-body model? I consider the scheme to vague to relate any answer to this model. – Jo Wehler Dec 12 '15 at 08:50
  • @Jo Wehler No, I am averse to ontological models. This was my attempt to put together something that would do what libertarians say free will is supposed to do. For the purposes of the question you can ignore it and substitute any other scheme, or give an argument for or against independent of any specific scheme. The terminology is mostly from physics ("lawless" is what Brouwer calls "free choice" in his model of continuum), but perhaps there is too much of it :) – Conifold Dec 13 '15 at 23:52
  • If one can ignore the scheme for the purpose of your question, I would recommend to cancel your first question. Because it actually refers to the scheme. What about abandoning the scheme as a whole and stating just your interesting questions no.2 and no.3? - Why are you averse to ontological models? In my opionion all ontology is about models, because we do not have access to the thing in itself. – Jo Wehler Dec 14 '15 at 00:00
  • @Jo Wehler It refers to "this kind" of reduction, not to the scheme specifically, namely ontological reduction to matter without possibility of representing evolution of mental states in terms of physical states (I am guessing this would limit what neuroscience can be expected to accomplish). I am averse to ontology largely because I see no way around Quine's dim view of its "as if" nature (he calls ontologies of physical objects "myths" epistemologically). But I am intrigued to see libertarian materialism either criticized or defended, theories do need ontologies even if it is only "as if". – Conifold Dec 14 '15 at 03:58

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I don't see why not: must materialism entail determinism? One can still believe in only a natural world, without believing in spiritual substances of one kind or another whilst accepting indeterminism.

One could conceivably gesture towards the principle of plenitude, in that if Nature can in some ways be determined, then in other ways she is indetermined; then the burden of explanation falls on saying when and why, when she can be, and when she can't.

More practically, Intuitionistic mathematics takes dx to be only potentially zero, but not actually so - thus surely is a kind of indeterminism; and it makes the development of the calculus clearer.

And much more simply, a throw of the die in a game of blackjack shows simply hat something's are naturally understood as being indetermined.

All the above, I mean in the context of a physical ontology; and not taking into account how free-will can be constructed, which already presupposes that consciousness as such can be constructed (the hard problem); as free-will as standardly understood is intentional, and an aspect of consciousness.

Mozibur Ullah
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  • I disagree: A crucial distinction needs to be made between indeterminism from randomness and uncertainty (quantum, chaotic, or other) and indeterminism from freewill, which entails a certain intentionality about the future state of the agent. Saying that freewill lives in the gaps left by uncertainty and imprecision amount to a from of dualism, almost by definition, and I can't see how a materialist can work around that. – Alexander S King Dec 12 '15 at 02:48
  • @king: ok, I was simply talking about physical ontology - in the sense of physics; I wasn't talking about it as allowing freewill, that's a much more difficult problem - before one can talk about free-will in that context, one has to construct consciousness - the hard problem - that materialists take it as a de facto position. I'll update my answer to reflect this. – Mozibur Ullah Dec 12 '15 at 03:00
  • @AlexanderSKing Alternatively, a materialist may consider freewill to be an illusion, if the material laws simply randomness. – Cort Ammon Dec 12 '15 at 03:12
  • @ammon: that has a curious affinity with notions of *maya* that says the world itself is a kind of illusion. – Mozibur Ullah Dec 12 '15 at 03:25
  • MU the OP mentions freewill only once. Since a modern materialist or reductionist would trivially accept quantum indeterminism, I assumed the only other indeterminism "that matters" is metaphysical freewill induced indeterminism. @CortAmmon a materialist may consider freewill an illusion, but then she would no longer have to deal with indeterminism, so the OP's question is moot. – Alexander S King Dec 12 '15 at 05:48
  • @AlexanderSKing Does that imply that quantum indeterminism is a form of freewill? – Cort Ammon Dec 12 '15 at 15:24