How is free-will formally defined as distinct from determinism, randomness and determinism-randomness hybrid to support moral responsibility?

Question

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.

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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.

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

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

You have identified a conceptual problem that those who want to believe in libertarian free will suffer from. While physics itself appears to be underdetermined, based on the last century of both Chaos and Quantum Mechanics insights, this does not help libertarians, as you note. There IS no "formal definition" that allows a mind to be both a non-random agent of one's character, but not also CAUSED by one's character. All definitions provided for libertarian free will, if probed deeply enough, will boil down to caused or random, or some bounded/chaotic combo of the two.

Before you conclude that we cannot have free will, note this is actually a problem for almost every concept we work with. This was one of the key insights of Socrates, and he is famous for his dialogs that reveal the assumed, but invalid conception behind much of what we think.

Hume, continuing Socrates example, showed that "causation" has this same problem. One cannot show logical necessity behind something being caused, as causation applies to contingent things. Hume settled for "causation == correlation", which doesn't allow causation to do the things that you will need it to do in your coding/logical approach.

Popper's efforts to repair empiricism, post Hume, still run into the logic problems behind the meaning of causation. "Causation" is an inferred nature of indirectly postulated realty, where some aspect of the "laws" inferred for physics, logic, or psychology act in a controlling/constraining way to effectively necessitate a particular outcome. If one accepts that empiricism is a judgement call inference as to the nature of reality (indirect realism) based on the reliability/trustworthiness of boldly tested inferences, you STILL have multiple problems.

• "Judgement" is explicitly in this.
• the inference process is uncertain itself and needs to be adopted with hesitation
• plus the "reality" inferred to is itself contingent, not necessary
• AND -- the justification for this methodology is ITS EMPIRICAL SUCCESS -- IE its justification is explicitly circular

so as a logician/coder, you can't use Popper's empiricism to get to causation either.

These sorts of problems bedevil every aspect of the Analytic effort to logicize/mathematicise philosophy. Quine, for instance, in ""Two Dogmas of Empiricism", noted that NO language, either formal or natural, can ever have sufficient precision in its definitions to actually support analyticity!!!! And Godel showed there are logical limits of any logical method actually being able to establish "truth", even within its own arbitrary abstract framework, much less in the world. And meanwhile, the multiple geometries, and multiple logics that both mathematicians and logicians have discovered, show that there is nothing specials about either Cartesian geometry, or classical formal logic. They are just useful MODELS, which are in many cases not applicable to "reality".

The cumulative problems with logic/analytics have convinced me, at least, that formal "truth" is an impossible standard. We seem to be limited, forever, to pragmatic "good enough working model to trust within this local/bounded problem" judgment call approximation to "true". Pragmatic "truth" is, I believe, all we can ever hope to have.

So where does that leave one with "free will" and moral responsibility? What this discussion shows, is that logic frameworks are not definitive, constraining, or globally valid. Causation, in its ill-defined "strong" non Humean sense, is a super useful assumption for our understanding of the world. So is formal logic. But neither are definitive, so just because the combo of formal logic and strong ill-defined 'causation" exclude free will, does not mean that we cannot have free will. Because, after all, assuming "free will" is ITSELF a super useful assumption in doing morality, and morality is very important for us to be able to live in this world.

So we have pragmatic justification for multiple different and incompatible useful frameworks. That is actually a common situation in pragmatic and logically incomplete fields. These include the fields of science and engineering, literary interpretation and criticism, and theories of aesthetics. The world, and our pragmatic efforts to understand it, cannot be constrained by your effort to logicize or code our understanding, because none of our models can be more than local and pragmatically useful.

So -- I at least am comfortable using free will, and moral responsibility, despite my own inability to explicitly define them.

Answer 5

I don't usually reply to older questions even when the Community bot bumps them, on account of me not knowing whether the original poster will ever notice the reply. That being said, I would like to contribute to this question for external reasons, so this time, I'll bite.

"Preamble": to help refine the problem's formulation, one might check out the SEP article on chance and randomness, and see whether the distinction between these, and then secondary distinctions internal to either, can figure in a "way out" such as the OP was asking after.

Besides that, let us suppose a "volitional logic." I am nowhere near as competent at predicate logic as I am at propositional logic, so I will style this logic as having a basic operator on propositions. Let us say:

ẃS = "It is willed that S," e.g., "I willed that the door would open," and then, "It was willed that the door would open." This might sound ungrammatical but sometimes in English we do say things like, "Would that I had never been born!" so it does look like would/will can take propositions. At any rate, even if we could never make this sound normal in English, the notion of a will operator on propositions could be allowed formally, which is what we are looking for here.

A basic alternation over such an operator is deciding whether it is factive. In this case:

ẃS → S?

However, we seem capable of willing things that we fail to accomplish. For atomic actions, like (perhaps) blinking, I would say that the will operator is factive, or at least closer to factive, than with respect to "molecular" actions. So maybe we'd go with:

ẃS → ◊S

And then, to go in the direction we're looking for:

◊ẃS → ◊S

I am not really sure that we can iterate and permute these will and possibility operators to exactly land on an axiom or theorem expressive of, "There is free will," or, "Free will exists" (understanding free will in strong terms, modulo the OP's reference to the alternative-possibilities principle). However, consider a choice operation:

ḉ(A ∨ B)^EDIT

I would be hard pressed to say that this is intelligible without something like strong free will modulo "alternative possibilities." Eventually, my own argument turns into something like, "Strong free will is implicitly presupposed by the concept of disjunctive knowledge overall," i.e. unless the existence of strong free will is presupposed, skepticism would dominate our mental strategies inescapably (or we would never even have the concept of disjunctive knowledge at all). Whether this solves or circumvents the issue of defining strong free will relative to determinism, randomness, etc. remains to be seen.

^EDIT_{As far as determinism vs. causal chains goes, let's ask the question: "ḉ(ḉ(A ∨ B))?" That is, when choosing between A and B, do I have to choose to choose between them? And so on and on.}

Answer 6

Indeed a quite complicated question spanning many concepts... I will address one fact only, but I think is helpfull towards your goal. Suppose you made a bad choice in the past. If you understand your error, then in a similar case in the future, you can/will make a better choice. So, this is free-will, in the sense that from a random past event (bad choise) you "broke" determinism and the whole "determinism-randomness hybrid" cycle by understanding your error or changing your behaviour. And this is what moral responsibility is. Hope this helps.

Answer 7

There are many definitions for free will, none of which has any official status. The best definition I have found is simply: The ability to make decisions.

This definition sets free will as a concept completely outside physics and within psychology instead. There we will find also the concept of responsibility.

Trying to find responsibility in physics, determinism or randomness is quite pointless.