This debate amongst neuroscientists and amongst commentators on Internet needs to look at the philosophical research on the matter. There are a variety of positions.
1. Fatalism. The universe's determinism ensures that everything comes out with a predetermined character, come what may. This is fatalism because it doesn't matter what you do, it will come out the way it's "meant to". Fatalism, I believe, is a primitive form of hard determinism.
2. Hard determinism. Your actions have antecedent causes over which you have no control, e.g. your country of birth, your language, your initial character formation, your genetic predispositions to react to stimuli and threats in a certain way. This ensures you always behave a certain way - within character. You are not free because you did not choose to be the way you are. This is a form of incompatibilism which states that free-will is not compatible with determinism: so much the worse for free will, it says. Freud was this sort of determinist. Another example is Pereboom, Living Without Free Will. Possibly also Ted Honderich.
3. Soft determinism or Compatibilism. Free-will is compatible with determinism. This is the status quo in Philosophy. The view is this: you are free if you act in such a way as to get what you want, and you get what you want because you wanted it. The fact that it originates in your character, which was deterministically created, is irrelevant. We speak of persons as free in the case where they get what they want because they wanted it. A person who is 'under duress' or 'forced' is not free because they either get what they don't want, or can't get what they do want. Example: Watson, G., Free Will, and also Frankfurt (1969), plus Daniel Dennett,1984, Elbow Room.
4. Libertarianism. This is the view that we live in a non-deterministic universe, and have free-will, and we have free-will because we're not determined. A form of incompatibilism which says, free-will is incompatible with determinism, and so much the worse for determinism. It's usually argued from quantum mechanics. However, quantum mechanics' effects apply only at the subatomic levels, eg with electron position and radioactivity. Neither affect our brains at all, since each neuron is made of millions of atoms. It's statistically irrelevant. Moreover, even if quantum mechanics caused our wills, our wills would be RANDOM, rather than what we will being caused by what we want. In order to say that our actions are ours, they have to be causally linked to what we want. So the question of free-will for a libertarian is just how to get our wills free of antecedent causation, for which they rely on quantum mechanics (these days). In the past, e.g. Sartre, they relied on phenomenology - ie I just feel like I am not constrained by my past. The trouble with libertarianism is it doesn't clearly link who I am with what I want and what I do. You need causal determinism to do that. Example: Robert Kane, Free Will, 1996. Other authors include Thomas Reid, and van Inwagen (1988).
5. Neuropsychology - .e.g Benjamin Libet, 1985, Journal: Behavioural and Brain Sciences, demonstrates that decisions are non-conscious or preconscious, and happen before we are aware of them. This means either our free-will is fully unconscious, as Freud said, or, we lack free-will, and really do act on instincts and desires, as Hume argued (Treatise on Human Nature, p460, Penguin Edition).
6. "Able to do otherwise". There is a debate about whether we need to be able to 'do otherwise' under the same circumstances in order to have free-will. Frankfurt (1969. “Alternative Possibilities and Moral Responsibility” in Journal of Philosophy, vol 45) gives an argument that we don't require alternative possibilities. But think about how often one says "If I were to live my life over again, I'd have done something different". But no: if you are who you are, and your life was the same up to that point in the second life, the circumstances leading to it would cause you to do the same thing, if determinism is true. If libertarianism is true, you could do otherwise, but then it wouldn't be YOU doing otherwise, it would be a quantum random antecedent cause.
7. Skepticism. Nietzsche argues that free-will is a christian concept invented in order to make people accountable to God. Modern skeptics, such as Richard Double, argue that Free-will is a nonsense concept. Double, R. (1991). The Nonreality of free-will. Oxford
I believe Libet is right that we can veto actions (control them) but I do not believe this means we are free. For, although, humans can and do respond to behavioural stimuli, as Skinner observed, we still do so because of prior circumstances and present opportunities. You can't want and will to be an astronaut if you live in Rural Africa and have never heard of such a thing. Therefore, even if we lack free will, we can still be controlled, incentivised, disincentivised, etc., and therefore society can function according to law without the need to assume delictual responsibility, or that retributive justice is merited.
In particular, I think that none of the following things demonstrate free-will, for the reasons stated below:
a) Quantum mechanics - just shows our actions would be random, which is not the same as free. Free means: without causal restraint or constraint. Randomness would be an antecedent cause over which we'd have no control, therefore, unfree.
b) "Able to do otherwise". Libet and Skinner show that we can choose to do otherwise. However, is it really we doing the choosing or is it another determinant, e.g. fear of jail, fear of a policeman, etc? Our ability to do otherwise is constrained by the availability of alternative options/possibilities plus our emotional proclivities, inclinations, etc. E.g. if I am starving, and I am told stealing is wrong, and there is no cake present, I will not steal cake. However, if cake is present, I will steal cake. The dictum "thou shalt not steal" will have zero motivational force; what determines whether I steal or not is simply the need (hunger) and the opportunity (cake is present). There are a grade of crimes which are less and less acceptable. So, for example, if cake was not present, but $20 was present, I might steal the $20. However, if $ 2000 was present, I'd probably still only take $20, i.e. just enough to get food. It's about how we're trained/brought up/raised/parented.
c) "Getting what you want because you wanted it" - this proves nothing. It just shows we can get what we want because we wanted it. It does not show that we did so freely, or, without constraint. So, the incompatibilist (myself) and the compatibilist (e.g. Watson) disagree on the meaning of "free". I take "free" to mean "lacking constraint" and Watson et al would take it to mean meeting one's goals. One can be forced at gunpoint to meet a goal and be willing too. This is what makes Leon's article "The willing addict" below quite interesting.
d) Phenomenologically free ala Sartre. This is naive. Just because something seems a certain way does not mean it is a certain way. The world looks flat, and tables seem to be solid. Yet we know quite well neither of these things are true; the world is a globe and tables are swarms of atoms.
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