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Usually free-will is assumed by most faith traditions as a prerequisite for moral responsiblity in order to justify eternal punishment. The argument goes as "you are truly responsible for your immoral deeds because you were perfectly capable of acting morally, but chose not to, and therefore you are guilty and deserve punishment". In other words, there is an assumption of a self capable of having chosen otherwise. But this definition sounds kind of handwavy to me. What do they really mean by "capable of having chosen otherwise"? Does this mean that if we somehow go back in time and press the "univere's play button" again, a different decision would have come out of the same self? But how would that be different from randomness?

I would appreciate a formal (hopefully, mathematical if you can) definition of free-will that clearly differentiates it from determinism, randomness and any kind of determinism-randomness hybrid. Furthermore, I would love to read a logical discussion of how the formal definition provided would support the existence of true moral responsibility. Let me explain why. If the only options available were determinism, randomness and determinism-randomness hybrid, I cannot see any hope for true moral responsibility:

  1. Determinism: your actions, either moral or immoral, are just the ripple effect of past events, you cannot help but do what the laws of Physics make you do, you had no choice, it's not your fault, therefore there is no true moral responsibility on your part.
  2. Randomness: your actions are random, chaotic, there is no control, you are lucky/unlucky that you behave morally/immorally by random chance (e.g. because of weird quantum randomness in the brain, for example). In other words, it's just a matter of luck, a matter of winning the morality lottery. If you behave immorally, it's not really your fault, it's just your bad luck. Therefore there is no true moral responsibility on your part either.
  3. Determinism-Randomness Hybrid: your actions are the result of a combination of deterministic rules applied to past events combined with random quantum noise or something along those lines. Depending on how strong are the causal ripple effects from past events and how strong are the random noises altering them, you end up acting either morally or immorally. In part you are unlucky, in part you have no choice. Anyway, it's not your fault. Therefore there is no true moral responsibility on your part either.

So, somehow, free-will is supposed to have a mysterious formal definition that distinguishes it from determinism, randomness and determinism-randomness hybrid that allows for true moral responsibility in a way that these other concepts can't. I would really appreciate such a formal definition.


EDIT: my question was tagged as possible duplicate of Is free will a third option aside from chance and necessity?, but that's clearly not the case, because there is no formal/mathematical definition of free-will on that post, leaving aside any discussion of moral responsibility.


EDIT2: with respect to what I mean by "formal/mathematical definition of free will", this question might be of interest.

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    What you are asking for does not exist: if one had a model of free will that satisfies libertarian wish list and is consistent with the laws of physics (as currently understood) controversies surrounding it would likely cease. All we know is that determinism, pure chance and (classical) mixtures of the two, featured in most traditional arguments, do not exhaust the possibilities because quantum mechanical randomness is unsplittable due to the Bell inequalities. Just as we know that odd perfect numbers are not ruled out by known theorems, but have no explicit example of one. – Conifold May 12 '18 at 4:23
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    free will and eternal punishment is accepted by monotheistic religions that assert an extra-cosmic God. It is not accepted by 'many' religions. Eternal barbecuing is not accepted by all monotheistic religions. Free will is a dilemma that all monotheistic religions face. Monastic traditions face no free will controversy and have no eternal barbecuing. – Swami Vishwananda May 12 '18 at 4:49
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    Possible duplicate of Is free will a third option aside from chance and necessity? – jbyseribpngf May 12 '18 at 14:36
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    It is hard, if at all possible, to set free-will or liberty of consciousness in math or logic formalizations because those formalizations are themselves based on the preassumption that there is only determinism in the end. – ttnphns May 13 '18 at 6:44
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    @ttnphns, I would not be so sure, Quantum Mechanics is formalized in mathematics and as far as I understand Quantum Mechanics supports indeterminism. – xwb May 13 '18 at 14:37
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What you are looking for does not exist.

First off, there is no one formal definition for freewill. Not everyone agrees on what free will is beyond generally agreeing that humans have it. There are myriad variants, each with their own little twists.

One variant that will give you trouble is the metaphysical freewill approach, which explicitly states that freewill is something beyond the physical world. When you make that statement, you skip past all of physics, by necessity. These arguments are distinguished from determinisim/chaos/etc by simply not being connected to them in any way. If you find a layer of physics in their definition of freewill, they will redefine it to not include that physics. Because they value this freedom to redefine freewill, they must only provide it descriptive phrasings.

Another variant that will give you trouble is the compatibilists, who argue that there is no fundamental need to differentiate metaphysical freewill from physical processes. They argue that our "self" may be one, or the other, but that there is no way to discern the difference. These individuals, by necessity, will not provide you a distinction because they don't believe one exists.

One thing I have found helpful, myself, is to break free of the shackles of the statistical definition of randomness. As you noticed in your question, statistical randomness requires the idea of being able to create more than one universe, where things play out differently but it all stems from the same random variable. These arguments are enormously difficult to work with because we don't really know anything about other universes. We don't even know whether they exist at all, and certainly don't know anything about them. We can only conjecture.

If one recognizes the existence of an "inside" and an "outside," such as we often apply at the edges of our skin, it does open the door for something to be "unpredictable" by anything outside, even if it isn't statistically random. If the information needed to predict the action only exists inside, the outside simply cannot make any useful predictions.

As a compatabalist myself, I find that construction convenient. If there is no metaphysical self, this pattern still is useful for defining morality in a subjective sense: its related to what the "outside" is permitted to predict about what will happen inside. This boundary can be shrunk however arbitrarily small, yielding constructs which look more and more like a metaphysical self (more formally, looks like a P-Zombie). If there is a metaphysical self, then the construction naturally permits things like morality in an objective sense. Thus, in all reasonable situations, the two behave identically, even though they come to markedly different conclusions. I find that is close enough to a formal definition for me to work with.

  • I've found that chaos theory solves the issue for me, in much the way you're describing. Choices are a product of people's minds, and the choices are made in full accordance with the deterministic (or random) laws of nature, but the chaotic structure of the brain means that they cannot be predicted. The decision may be deterministic in the grand sense, but it cannot be determined except by having the individual actually make the decision. A simulation complex enough to predict accurately what the decision would be would be a person in it's own right. – kbelder May 14 '18 at 18:13
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First, I'm not sure exactly what you expect by a "formal" definition of free will.

However, I will try to report about a conception of free will that "clearly differentiates it from determinism, randomness and any kind of determinism-randomness hybrid."

This sort of conception of free will, which tends to be called "libertarian" free will, often means that a person's actions are caused only by that person's "self", with that self being decoupled from the world's causality. The actions are therefore not determined by physical events in the world. But the actions are also not random. The actions are, instead, chosen by the self. As such, that self becomes morally responsible for those actions.

Philosopher Robert Kane has attempted to say this is possible in a purely physicalist view of persons, but I have yet to understand how that could be possible. It seems to me that in order for this "self"-caused concept of free will to even have a chance to be possible, the self has to be supernatural, something like a soul, and that the causal nature of self-causing agents has to be (at least at this point, possibly forever) entirely mysterious. Some Christian philosophers, such as philosopher/theologian J.P. Moreland, put forth just this view. This is also a doctrine of, for example, the Catholic Church.

  • By formal, I mean something ideally as close to a mathematical definition as possible. Anyways, do you know / can you elaborate more on how the "choosing by the self" works? How does that "choosing" operate in a way that is neither random, deterministic nor a combination of both? – xwb May 12 '18 at 19:10
  • @xwb I'm having trouble imagining redescribing what I wrote above in language that is similar to mathematical definitions without it seeming gratuitous ("Call an act, A, an act of free will, if and only if a world, B, at time t,", etc.). As far as elaborating on how the choosing by the self works, I already wrote that this remains "entirely mysterious". But if that is unsatisfying, so is the origin of the universe/multiverse, or why causality holds at all (cf. Hume). – Chelonian May 12 '18 at 19:54
  • Regarding your trouble redescribing what you said in mathematical terms, I think this question I just posted might be relevant: philosophy.stackexchange.com/questions/52107/… – xwb May 12 '18 at 23:57
  • Agree with the "soul decoupled from causality". However, if that supernatural "soul" has to be (exist) as an absolute, i.e. on its own grounds, it must be God or its emanation. God will not tolerate another absolute to exist besides himself. So, if one wants to secure the "soul" from God or to remove God from the scene they should say the soul does not be (is not a being) - it is not a "substance". It is possible: consciousness exists by the mode of non-being. – ttnphns May 13 '18 at 9:43
  • @xwb Papers that use that sort of language abound in philosophy. Some quick searches pulled up this: eprints.lse.ac.uk/46931/1/… as well as this: andrewmbailey.com/pvi/FormalApproach.pdf You will have to scan through them to find the symbol-heavy parts (obviously, they aren't entirely symbolized, but either are math papers). – Chelonian May 13 '18 at 11:56
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Mark Balaguer (Free Will, MIT, 2014 (FW)) claims that “we can distinguish many kinds of free will” (FW 50), that is, there are many different ways to define free will. He looks at two very different definitions: Hume-style free will used by compatibilists and not-predetermined free will which he wants to use within a materialist context like that of the OP’s question.

He claims that compatibilists define free will as Hume-style free will, that is, you have free will if “You did want you wanted to do”. (FW 46) This sets up your desires as the cause of your choices which allows them to be determined. Since they are caused or predetermined by something they aren’t free.

To get around that predetermination, he defines free will as explicitly not-predetermined free will (FW 75-6):

For a decision to be a product of my free will (in the sense of not-predetermined free will, as opposed to Hume-style free will), two things need to be true. First, it needs to have been me who made the decision; and second, my choice needs to have not been predetermined by prior events. In other words, it needs to be the case that (a) I did it, and (b) nothing made me do it.

This second definition of free will does not allow determinism to provide a cause. Balaguer wants to fit this definition into a materialist view of reality where we are the neural processes of our brains. He has to find a way to make his view of free will fit in with the “determinism, randomness and determinism-randomness hybrid” mentioned by the OP. He thinks this can be done by allowing free will to happen intermittently during periods where we make “torn decisions” (FW 76):

In particular, we only exercise free will (if we have it at all) when we make torn decisions--when we’re in situations where we’re confronted with multiple options that seem equally good to us, and we stop and think for at least a brief moment about what we should do, and then we settle the matter with a conscious choosing.

Balaguer claims that neuroscience “leaves open the possibility of indeterminism”. (FW 94) However we are "nowhere near ready" (FW 122) to say that we have this kind of free will or not.

Balaguer provides a definition of free will that fits it into a materialist perspective distinguishing it from the "determinism, randomness and determinism-randomness hybrid" mentioned in the OP. He leaves it open for future neuroscience to decide if we have free will or not. His perspective is not a religious or spiritual one.

Robert Kane, whom Chelonian mentioned in his answer, (see “Free Will: New Foundations for an Ancient Problem” in Free Will (Hackett Readings in Philosophy)) uses "self-forming actions" to construct an "event-causal libertarian view of free will" that may offer something similar.

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