Could we ever come up with an experiment that is able to explain once and for all if free will exists or not? Another way to put it: given a universe and agents acting within it, is it possible for such agents to determine whether or not they possess free will? The more I think about this problem the more it seems undecidable to me, it seems structurally similar to the halting problem.
is it possible for such agents to determine whether or not they possess free will?
A precondition for answering this question is that the term "free will" is sufficiently well defined. IMHO, it is not, and the lack of adequate definition is the cause of much fruitless debate.
Since we do need a clear demarcation line between approval and rejection of a hypothesis, the lack of a definite, descriptive definition with empirically observable markers makes testing in the scientific sense impossible. Thus, the question/hypothesis is underdetermined and not scientifically answerable.
I don't really think it can ever be tested. Personally what convinces me there is no free will is the large amount of evidence that the chemistry of the brain determines our moods, even our personality. Some substances change our mood and behaviour. Brain trauma or surgery can change a personality beyond recognition. Electrodes in the brain can provoke emotions undifferentiated from genuine ones. And patients who are unaware of the mind alteration they are subjected to usually attribute their own thought and behaviour to themselves, going as far as inventing a personal reason for waving their hand when it is in fact the surgeon that made them wave it.
I could be convinced there is free will by the evidence that there are thoughts and actions that can't be explained by biochemistry, with the caveat that we would have to first rule out the gap between observation and theory is not due to a flaw of our theory, which is probably impossible. Note that it would not erase the massive amount of evidence that biochemistry at least influences most of what we do or think, so free will is already very limited.
This problem is similar to that of the creationist gap argument, according to which since we can't explain the beginning of the universe it must have been created: to come to this conclusion, we first would need to establish that our scientific knowledge is perfect, and it is obviously not.
Even a time machine wouldn't be enough. There are different definitions for free will, but in the end what they have in common (except notably for compatibilist free will, which is not really free anyway) is the idea that under the same circumstances, things could have gone a different way, other decisions could have been taken. If we could rewind time and observe the same situation to as if it has a different outcome, it would be an hint but only if we can rule out the possibility of randomness due to quantum effects. A proper study would have to fully understand this randomness and its probability distribution, then show that the same situation rewinded 1000 times did not match the previsions. And yet again, in that case I would suspect our understanding of the randomness first, so we are back to square one.
This is actually a question about philosophy of science. I'm surprised nobody has mentioned the criteria of falsifiability.
Simply put, for a hypothesis to even be suitable to be proven or disproven through scientific inquiry, it has to be falsifiable: it has to be conceivable that contradictory evidence could be observed, or reasoned from observation? The hypothesis that "All swans are white" is falsifiable, regardless of whether it is true or not. The hypothesis that "All solids have a melting point" is not falsifiable, because it is not possible to observe that a particular solid does not have a melting point, only that it has not reached a melting point.
So, let's look at your question, which, from your two formulations of it, I paraphrase as "Is it possible for us to prove whether or not we possess free will?"
"Possess" is vague, but what you're actually asking, is, "Are either the hypothesis 'We are capable of acting out of free will' or the hypothesis 'We are incapable of acting out of free will' falsifiable?"
The answer to this would then hinge on whether or not an action was precipitated by free will being something that can be observed, or, be deductively reasoned from observable phenomena.
Right at the outset, you can't conclusively prove a negative, so "We are capable of acting out of free will" is not falsifiable — to falsify it, you'd have to observe that we are never capable of acting out of free will. So that is not a valid hypothesis for scientific inquiry.
So, is "We are incapable of acting out of free will" falsifiable? Could we observe an example of a human acting out of free will?
Interestingly, Karl Popper, who first defined the notion of falsifiability, specifically addressed something very close to this question: whether the statement "We are incapable of acting out of altruism" is falsifiable. Quoting from the footnotes of the wikipedia page "Falsifiability":
"This theory ['All human actions are egotistic, motivated by self-interest'] is widely held: it has variants in behaviourism, psychoanalysis, individual psychology, utilitarianism, vulgar-marxism, religion, and sociology of knowledge. Clearly this theory, with all its variants, is not falsifiable: no example of an altruistic action can refute the view that there was an egotistic motive hidden behind"
(Popper, Karl (1983). Bartley, III (ed.).Realism and the Aim of Science: From the Postscript to The Logic of Scientific Discovery.)
So, for Popper, the answer to your question seems pretty simple: no. To his view, behavioral motivation is strictly unknowable, therefore questions about it are not falsifiable, therefore they cannot be proven or disproven. If you're ok with an appeal to authority, there's an answer for you.
Obviously, though, we can ask whether Popper's statement "no example of an altruistic action can refute the view that there was an egotistic motive hidden behind" is falsifiable (and I'm sure he thought hard about that, and was content that it wasn't." Would it be possible for someone to make a direct observation, or provided deduction from direct observation, that proved an action to be purely altruistic and not motivated by selfishness? Let's be careful here: the answer, to the best of my knowledge, is "I sure can't think of one". That doesn't mean there isn't one. We can't be sure.
So, I personally suspect Popper was doing what scientists often do: speaking in a manner that sounds definitive, but taking it as read that the listener understands that science doesn't describe reality or provide fact (even though the listener very often doesn't.) Science provides the best predictive model possible given the available information. That's all.
If I can digress: you hear some very ignorant people nowadays in the course of current events describing science as "just another religion". That's wrong in a lot of ways, but chief among them is that very misunderstanding. Scientists may state things in a manner that sounds like they consider what they're stating facts, but privately they know they're talking about likelihood, a model, not truth. They know that new evidence can upend the whole model tomorrow. The map isn't the territory. I think this concept gets lost in the popular mind. (Although it's important to say, a lot of people who do understand it then go on to make the converse mistake of trying to downplay the practical veracity of empirical scientific conclusions with statements like "It's all just theories". There's a slight misconception there, too, but that's beyond the scope of this answer.)
This is an important digression because it provides the correct answer to your question.
I know you were hoping for an argument concluding with "yes" or a "no", but the correct answer, based on current best-available evidence, is "it's unlikely."
Although I believe we have free will, it is actually impossible to ever prove it via any test whatsoever, because you cannot prove that the test results are meaningful at all. In particular, you cannot rely on randomization in the test because you have no proof that there is true randomness in reality, and so the test results may be deterministic, in which case you cannot provably exclude the possibility that even the test itself (the design and the execution) was just predetermined.
Ultimately the point is simply that if reality is deterministic, and we are stuck inside it, then everything we do is deterministic too, and so how can we possibly test for freedom of choice when we cannot even have freedom in testing?
From the Kant perspective, freedom is wanting what is necessary and unavoidable. From that position, an agent have the free will, if his actions are consistence with his intentions. This definition is independent from to which extend are those intentions determined or predictable.
You can disagree with that definition as far as you will, but doing so, you'd have to connect free will with the ability to act against the intentions (either because internal or external hurdles) which is quite the opposite of which people normally define as freedom.
Being predictable or determined is not contrary to the free will. If I let you choose between landing in a 5 star holiday resort, or North Korean concentration camp, I can quite assume your decision is both predictable and determined, and nevertheless, is the expression of what you'll call your free will.
Preface: I don't think we have free will. Or we only have it in a compatibilist sense. However:
First, consider a possible picture of "free will." In this picture, the universe might be compared to a video game where brains are controlled by external "players." The video game has its own internal logic, which we call the laws of physics, and the external players don't operate according to that logic. The external players might operate according to their own logic, which we set aside from the laws of the game and call "free will." I don't think this picture is accurate - I don't think there are external players - but that's a picture of how it could be. And in theory it could be possible to test for the accuracy of that picture.
So we could determine if there is free will according to this picture by first fully understanding the laws of physics for all non-brain objects - including any randomness inherent in those laws of physics. With powerful enough sensors and computers, we could use that to run a physically perfect simulation of the brain, giving physical error bounds on any randomness. If the brain consistently behaves outside the error bounds, that would be evidence that there is some external controlling factor not accounted for by our theory of physics, which is by hypothesis perfect on every non-brain object. And we could call that factor "free will."
Anyway I don't think it's likely we would find any such thing. It wouldn't be simple or elegant to have special laws of physics that are only for brains; it would violate Occam's razor.
It would also not mean that the external players have free will in their own external universe - they may have their own rules in their external universe that still dictate their behavior.
From physics Point of view
Everything is just particles and forces. All emergent behaviour can be explained from the underlying laws. The brain is made of particles that interact via forces. So:
Imagine a closed of environment (test room) with a human test subject. Now say we take a snapshot of the whole setup (test room and test subject) down to the finest granularity physics allows for so we have perfect information.
With a complete understanding of the laws of physics we can now (in principle) simulate the room and the test subject and compare to the actual behavior of the test subject. If free will does not exist, simulation and reality will be in accordance.
Note that this assumes that quantum effects can be neglected in the macroscopic workings of the brain. If not, these are just random anyway and is not an argument that free will can exist.
From an evolutionary PoV
We are placed somewhere in the tree of life. For those who think free will exist, they must place the introduction of it somewhere on the evolutionary tree and argue how the breaking of the laws of physics can be introduced by changes in DNA. This seems close to impossible to me.
Otherwise they must argue that all self-replicating molecules (or just molecules) contain a bit of free will. Both of these have absolutely no evidence, so I don't see why we should pursue the issue since there is no indication of free will other than the illusion of it, which some people just can't take for an answer.
First, let us define our terms. Assuming that by "free will" we mean acting in a manner that is not pre-determined, where somewhere inside our mind, an actual decision is being made that is not a simple causal chain. We will leave the details of how the mind works open, but we state that free will is proven if a being can make a decision that with infinite knowledge and processing power of the physical reality outside his mind could not be predicted.
The problem we need to solve is that our mind has an elaborate construction of agency that science has already disproven. There've been a number of experiments showing that fast actions can be measured in the brain quicker than consciousness can possibly work (according to our current knowledge), but the test persons report making a decision. Our current working model is that the brain acts and our consciousness then makes up a story of how it decided to act. This is not always true, however, as we can sit an deliberate on a course of action, obviously.
Our experiment would have to circumvent this illusion, and that means we cannot be judges of our own free will. Our mind will tell us that we acted intentionally, even when we clearly didn't, so it cannot be trusted on this question.
However, we also cannot judge from outside, as a) our infinite prediction machine doesn't include the mind itself and b) we hand-waived how exactly the mind works, so we have no way to measure it.
Under these conditions, it is impossible to devise such an experiment. We need a much better understanding of how the mind works before we can tackle the question of free will. Specifically, we must understand how decision processes work and which parts are deterministic and which parts are not and how that indeterminism works. If I speak of "conscious decision", what does that mean? Where does that consciousness reside and how does it make decisions?
Marvin Minski famously claimed that the mind is simply a hugely complex machine made of simple agents. No individual part is intelligent, intelligence is an emergent property. If that is the case then we will not find consciousness as the phenomenon we are looking for disappears under the microscope the way culture or fashion trends disappear when you examine a single painting or dress.
At the current state of our knowledge, we cannot imagine such an experiment because we do not know enough about the subject matter in question. "Free will" is a philosophical construct more than a scientific one.
As other answers mentioned, we should first define free will.
I suggest the following definition, which is not perfect though because it can be explained by other phenomena instead of free will.
Let put the question this way:
Are there systems in the universe whose evolution is not predictable (from within the universe) neither with deterministic, nor with probabilistic (Bayesian) laws?
The answer is yes. Thomas Breuer has shown mathematically that from the point of view of any given in-universe observer, the behavior of a system in which he is properly included, is unpredictable with any deterministic or probabilistic laws.
Now, does this necessarily certify the existence of free will? Actually it only certifies the existence of events without physical (measurable from within the universe) cause and that such events necessarily happen in any system which properly includes the observer himself (from his point of view).
Are there alternative explanations of this result besides free will? Yes. There are.
- Out-of-universe events affecting the physical world. This may be divine intervention, input ports, computer player for whom this world is a game, etc. But since the theorem would still work in the wider universe that includes those beings, we still will face the same question (for instance, we could conclude that God has free will and intervenes in the behavior of the observer, like player intervenes in the behavior of player-controlled character).
- Initial conditions of the universe affect events at present and in the future. In a sense, initial conditions are also a kind of input from outside the universe. And again, if our universe is a part of a greater world, the theorem will still apply to it. This rises the question, who and how set up the very first initial conditions? Was it a manifestation of some kind of free will of that being?
There are other questions that arise.
Is free will somehow connected with intellect? Yes, the observer finds himself unpredictable, but the theorem does not require an intelligent observer, it will work with a computer, for instance. Does our definition of free will require that the observer could affect universe in a way he desires rather than just physically unpredictable?
Is the existence of qualia needed for free will? What about states of the observer when he does not have qualia (unconscious or before formation of brain)? Does he have free will at those moments?
So, the questions still remain.
We would need an experiment with a result that is either possible with free will and impossible without free will or vice versa. (Better yet would be an experiment that forces such a result).
I think anything I could possibly do with free will I could do (be forced to do) without free will. There’s the possibility that there are things that I couldn’t do out of my free will but could do without free will. But then I never heard anyone claiming that Harold Shipman only could kill 200 people because it wasn’t his free will, so it is hard to say what exactly would be impossible if I had free will.
There are three broad categories of stance on free will: libertarian free will, no free will, and compatibilism.
Libertarian free will is generally a religious stance, premised on substance dualism - a supervenient but seperate layer, can generate 'acts of will' independent of the material world (eg, manifesting from our soul).
Those who deny free will, argue from our understanding of material causation, to say there can be no sources of causation that aren't material, so the sense we have of originating causes through deliberating, ie acts of will, must be an illusion. Notably, proponents of this view generally think that everyone arguing for free will is arguing for libertarian free will.
Compatibilism, the large majority view of professional philosophers, is the view that freedom of will is subjectively real, but operates through material causation. In the same way, identity is not pictured as the 'inextensible' realm like Descartes thought, information has material reality, even when considering substrate independence (and Turing completeness). It is useful to define conventional notions about identity, even accepting they are fundamentally reducible to atoms. The behaviour of atoms is a poor way to predict the behaviour of others, so we form a heuristic or explanatory layer, with identities in, in which human motivations are pictured as causal, from a supervenient layer.
To those who deny free will, this is seen as like the libertarian free will stance. But it is more like asserting biology has useful conceptual units and narrative groupings, even after accepting that the fundamental rules of the units involved are defined by physics. Identity, and will, and intentions, are useful narrative groupings, which allow us to better predict other humans, than knowing their position and momentum.
For a compatibilist, no test could 'prove' free will is not reducible to the behaviour of atoms, because they don't claim this. Asking for proof of free will in this view, is like asking for proof that cells exist - it just is a useful grouping, in it's own layer of explanation. Dunbar's number points to the neocortex as having evolved specifically to predict other humans, so we can go further to show how it is socially adaptive to understand intentions of ourselves & others, & this has substantially contributed to human cognitive & social complexity.
This is by no means a rigorous answer, but I find that this video is quite revealing about free will.
This was a scientific experiment done on a patient with epilepsy that uncovered the nature of free will. The part of this video containing the experiment runs from 11:38 to 17:50, and if you want, you can watch the rest of the video, it is really interesting. I love this video series and it's where all the big questions try to get answered, and I highly recommend it. Enjoy!
Summary of the video: There is an experiment done on a patient where they play a game where they try to mirror each other's moves (the patient and the other person who plays the game with them). If one of them predicts the other's move, then they win that round. There are electrodes planted on the patient's brain (due to brain surgery) and they collect and process the brain patterns to predict what move the patient will do next. As it turns out, when the patient makes a move, it was predicted beforehand about 300 milliseconds before the patient had done the move. Therefore, the patient did not consciously decide the move but rather it was made for them by their subconscious. The experimenter then concludes that free will is an illusion that we are not in control of.
This was a free-will experiment that reveals the nature of free will and it confirms that free will can be tested objectively.
This means that agents in the universe can, in fact, determine if they have free will by conducting an experiment like this one. Free will is not anymore a debate and intellectual challenge, but rather it can be experimentally verified.
I am not familiar with the halting problem and I have not put any thought into it, so it is something I cannot answer.
In principle, yes, it could be possible in future to prove the existence of free will. If we have free will, then our actions must be governed by something else in addition to the laws of physics. It might eventually be possible to study a living brain and body in sufficiently close detail to observe the necessary violation of physical laws. Note, however, that such an experiment could never disprove free will — you might just be unable to look closely enough.