What is the rigorous definition of free will? There has been, and will continue to be, a lot of debate around free will. These debates seem to go nowhere, and that is because (so I think, anyway) there is no definition of free will that all participants agree to. I have once read that free will is "the ability to make decisions", but of course that raises the question what the ability to make decisions means. So, my question is, has any philosopher defined free will in a rigorous way?
The general problem is that we know intuitively what free well is, though as of right now we still don't seem to have a clue how it works.
And without an understanding how it works we have a hard time fitting our intuition into words. Like free will is what you experience everyday of your waking life, it's the ability to make decisions by yourself. Any kind of action that is not instinctive, would be the result of free will.
At the same time our models of explaining how the world works rest upon the axiom of "cause and effect" and the idea of physicalism. And if we presuppose that everything is physical and that all physical things follow relations of cause and effect then free will creates a problem.
Because either it's an effect without a cause and thus potentially super-natural (outside and above the physical reality) or it's an illusion, we wouldn't have agency and only react but never act ourselves.
Now the supernatural is rather unwieldy, so people usually stick with the deterministic idea and either reject free will altogether, which is kinda problematic as it kinda puts pure reason over empiricism. Like we trust our models of reality more than we trust our own perception, which also is the foundation of these models... Or they try to define free will within the context of determinism so as something that is somehow compatible with it or that is emergent from a deterministic world.
Again we have not the faintest clue how such a phenomenon could emerge from determinism or how it would do that if it could. Our understandings of consciousness and agency are still very limited.
You of course can draw lines and that has and is being done, but usually these lines aren't really permanent or fixed. Like you can argue "free will makes people unpredictable". Sure. But so does randomness and you can have randomness without agency.
Likewise you can argue with the "freeness" of the will and interpret it to be "without constraints". "So if you're not in chains, you're free, right?". Well how about putting a gun to your head or showing you a picture of a loved one being in danger to coerce you. That is not so much a physical "coercion", as it is a "message". Like if you were to reorganize the pixels of the picture to keep the physical energy spectrum the same you'd have a very different reaction to it (it would just be gibberish) despite being the same in most aspects.
So is that nature pushing a button or is it you making a decision about a scenario presented by nature.
Even in a scenario of external coercion up to fatal consequences you could still "choose" to resist. People are able to subject themselves willingly to situations that are embarrassing, painful or even fatal. So the idea of us following a path of least resistance isn't necessarily true or at least it's not a path that we would consider obvious.
And even if you're in a scenario without options to chose from (unfree in your choice) you're still wandering around in your brain making internal choices. So a predictable outcome is not necessarily an absence of free will.
Yet even if you draw the line there, you could argue that your thinking is limited by your perception that your thoughts are fed to you by your subconsciousness, that you don't control your emotions but that your emotions control you (which is sometimes true, sometimes false and sometimes a mix of both).
So it's not that you can't come up with a definition of free will, but unless we find out how it works, setting one up and tearing it down will not necessarily result in the satisfying conclusion that you think it would.
The best definition I have found is that free will is the operation of agent causality, as detailed in this blog post from the Information Philosopher Bob Doyle: https://www.informationphilosopher.com/freedom/agent-causality.html
The key point is that agents do not act due to event causation, or randomness, but instead thru a different type of causal process. Free will is the term for the process of agent causation.
The development of a coherent idea of agent causation is a currently active project in philosophy. One such thinker is Helen Stewart, whose Metaphysics of Freedom is reviewed here: https://philosophynow.org/issues/105/A_Metaphysics_For_Freedom_by_Helen_Steward
I am not convinced that either Bob Doyle or Helen Stewart have cracked the definitional nut of Free Will, as I think that their approach will run afoul of repeated iteration of the Munchausen Trilemma. However, the rivals to Libertarian Free Will also suffer from definitional problems (even causation can handle more iterations of Munchausen than agency can, but event causation also appears to be fundamentally incoherent too, per our usual logic), or from science refutation (physics is not deterministic, so nothing is determined: Deterministic or stochastic universe?).
We now know that there are infinite logics that can be constructed. The problems formulating Libertarian Free Will using our standard logic, would suggest that we may need to explore further the space of alternative logics, to determine if Libertarian Free Will holds up better in a different logic framework, which can then also be evaluated against other aspects of our world to establish its general utility.
My definition is based on the opposition: free from whom? Absence of free will would mean that someone possesses ability to predict and/or influence our decisions. Impossibility of such a prediction is what I call free will.
Definitions are not cut in stone
Building an argument on clear definitions is good in mathematics or logic, but this is not how the real world works. Indeed, school teachers, University courses and even popular culture teach us to stick to clear definitions - the goal is to teach abstract thinking, and developing a logical argument. What is however forgotten, is that while clear definitions are necessary for making a clear argument, they are by no means universal or correct in any way - it is just with different definitions one may get to a very different conclusion about a different matter.
A classical example is special relativity: the math predicting the contraction of time and space was known well before Einstein, and many people as intelligent as him, tried to use deeper and deeper logical reasoning to explain the contradictions between these conclusions (following from the study of electromagnetism) and the classical mechanics. Einstein's achievement was in thinking out of the box, and questioning the very notions that seemed to be very clearly defined - those of space and time. Once the definitions were adjusted, everything easily fell in place - to the extent that special relativity is taught to high schoolers.
Likewise, the problem of free will is very much in understanding what it really means - i.e., in properly defining it.
Determinism vs. predictability
My approach to free will is admittedly that of a scientist: what matters/exists is what we know, what we can test, experience, and otherwise perceive. Any supernatural reality, that is not accessible to humans, and therefore cannot be studied does not exist for any practical purposes.
Thus, to the best of our knowledge the world is deterministic. This means, that, as far as we concerned, it is deterministic. Predicting someone's behavior requires knowledge and computational ability that are not available to humans, which means that such prediction is not possible - hence, we possess free will.
See also my answer to Determinism vs. prediction.
Emergent Moral Agency - The Concept of Human Will arising in the Context of Natural Cause
Due to circumstances beyond my control I am the master of my fate and the captain of my soul. - Original Source Unknown
Will - Legal Philosophy Professor Hugh Gibbons
In Spring 1991 I took Legal Philosophy with Professor Hugh Gibbons. He avoids using the words "free will" and prefers to use the word "will".
Justifying Law: An Explanation of the Deep Structure of American Law (116 page pdf)
Justifying Law - Page 7
There is no point, however, in explaining that which is unclear (law) in terms of something equally unclear (will), so I must explain what I mean by will.
Will refers to your experience of yourself as the cause of what happens to you.
Law is based upon the experience of each person that he is the cause of his actions and ideas. Whether or not that is true in any ultimate sense is irrelevant and probably unknowable. It is clear, however, that one's experience of himself as a subject can be eliminated by the will of another. That is the subject of law.
Law is, then, about liberty, not about freedom. A person is at liberty to the extent that he is free from the sensible constraints of others. It may well be that much or all of our lives emerges from the working out of imperatives in our genes and the playing out of past experiences. This causes the advocates of freedom a problem, but it presents no difficulty for liberty. Liberty simply requires that the particular cauldron of genes and experiences that is each one of us - if that is what we are - not constrain, as a result of our intentions, the will of others.
I cannot find the exact reference. I thought Gibbons defines will (somewhere in the text or footnotes of the above reference) in terms of an I-statement: I am the cause of desired perceptions.
The will of Hugh Gibbons, and the ego of Sigmund Freud, can both map to a human recognized source of cause. Gibbons describes will as the experience of self as the sole cause of desired perceptions. He maps other sources of cause to (1) unwilled constraints; and (2) willed constraints. Constraints limit or interfere with the effort of the will to be the cause of desired perceptions.
Gibbon's analysis of will, willed constraints, and unwilled constraints avoids the problems of defining freedom or free will but evokes both folk psychology and the simplified concept taken from perception control theory (PCT).
Free will has many definitions, none of which is universally accepted. You could say that the millennia long debate around free will is all about the definition. Once you have selected your definition, there is no longer any debate whether free will is real or imaginary.
Another problem is that there are some illogical and incomplete definitions going around. An example of an illogical definition is "the ability to have done otherwise than you just did". Incomplete definitions leave the question of reality vs. imaginary open, subject to debate. In other words, they don't actually define free will at all.
"The ability to make decisions" is the best one in my opinion. It makes most sense, leaves nothing unclear, gives the name free will to an ability we do have. No doubt, no more debate.
A decision is a "deliberately selected course of action". "Deliberately" means "for a purpose", "selected" means "picked one out of multiple alternatives", "course of action" means a controlled sequence of muscle moves.
In other words, free will is the ability to act for your own purposes (=goals in the future) instead of just reacting to past causes.