A common philosophical question revolves around the existence of free will, but these debates gloss over the concept of "free will" itself, either taking it as a given (that everyone understands what the term really means), or proceeding with a murky and unspecific definition. Have there been attempts to provide a rigorous, mathematical definition of what specific conditions would constitute a free choice? What are the necessary conditions for an action to be regarded as a free choice, rather than a determined one?

This doesn't have to be confined to a particular world. The formalized explanation of "free will" could be valid in any kind of world, where the laws of "physics" can be different from the ones in our world, and where one could point to a process which would constitute a free choice.

For comparison, there is a mathematical explanation of a deterministic will. Conway's Game of Life constitutes a world where for any process or change in state, you can point to it as a deterministic process, because it is rule-bound, and the future is predictable from the current state. What change would I have to do to be able to point to a process and say that it was a free process?

When these processes are involved in a choice, the determinacy of the choice inherits the determinacy of the process. If a brain makes a choice, and the brain is contained within a deterministic universe, the choice itself becomes deterministic. How could one constitute a universe so the processes behind the choice were constituted in such a way that the choice would become free?

The reason for me asking is that I always find myself dissatisfied with the definitions of "free will" I get, just as I never can wrap my head around the concept of objective values. It's just something you're supposed to intuitively have a concept of and if you don't, you seem to be on your own.

If I speak to somebody who doesn't know what "deterministic" means, I can give a precise, clear, mathematical definition. Since the free will-claim is on a direct collision course with determinism, all I want is for someone in the free will-camp to return the favor. So far, this hasn't happen and since I can't begin to understand what "free will" would be, I haven't been able to produce anything myself.

I'm not asking how one could look at the outcome of a system and decide whether it was generated by free choice or not. I'm also not looking for a proof of free will. I'm simply asking for a way that it could be implemented in some possible world, regardless of whether that is actually the case. We can do this in regard to determinism, for example, without also saying that the world works deterministically (e.g the statement "if every state of the world is fully determined by the previous state, the world is deterministic" doesn't imply that the world also works deterministically).

To better 'illustrate' my point (with the help of Sidney Harris):

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    I like this question, not sure why it was closed so fast. However, while it makes sense to me, I doubt anyone will have answer for you, because although I sure people have tried to "mathematically" formulate free will, none (as far as I know) have even remotely succeeded, because if they had, it would be HUGE. The determinism / free will debate is critical to many theories in philosophy and other sciences; the discovery of a mathematical proof for the opposite would not be something that is likely to go unnoticed.
    – stoicfury
    Commented Aug 5, 2011 at 15:03
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    I agree that it is not a real question: in fact, it is a nonsensical question-- but in this case, it does have a real answer. The answer is: no philosophers have tried to do this, for reasons best found in Wittgenstein on rule following (cf. the Philosophical Investigations). Put simply: given the output of the "game of life" example, there is no rigorous way that one could determine what rules (if any) were followed. Thus, there is no mathematically formalizable structure that would allow one to examine a set of actions and determine whether they came about via free will or determinism. Commented Aug 5, 2011 at 21:39
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    (Related Meta discussion regarding this question: meta.philosophy.stackexchange.com/questions/190/…) Commented Aug 9, 2011 at 11:44
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    @Joseph: I think this is an excellent question. It is related to how discussions of logical thinking and argumentation, logical rules, the idea of truth, has eventually boiled down to mathematical logic, where the vague narrative rules that were used before can be replaced by operators that can be manipulated mechanically (for example, there is no worry about the paradoxes of material implication because it is accepted as the way to deal with implication.
    – Mitch
    Commented Aug 9, 2011 at 19:21
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    From the wording of this question and examples, it is still not clear if what you want is either 1) a way to tell if a given system (as a black box) is behaving deterministically or with free will, or 2) if of a known system and known properties, can you say the system (or entities within it) is deterministic or has freewill. Or some other possibility?
    – Mitch
    Commented Aug 9, 2011 at 19:24

13 Answers 13


"Free will" as broadly defined is "a particular sort of capacity of rational agents to choose a course of action from among various alternatives" (SEP). Although there are extreme views, such as Descartes' where "the will is by its nature so free that it can never be constrained," most people accept that our will can at the very least be influenced by factors external to ourselves, if not wholly controlled by it. The challenge, as you point out, is finding how to explain a notion of freedom through non-causation.

In a strict sense, the answer to your question is no. There have been no successful logical explanations for free will as traditionally defined. The problem lies with the fact that to be free requires non-causation, or indeterminacy. Proponents of free will often invoke abstruse theories about the quantum indeterminacy or the Heisenberg Uncertainty principle as examples of where the secret of free will lies, but the major problem which undercuts each of these theories is a lack of an explanation of how free will can be obtained through seemingly random processes.

Concordantly, I think it is more appropriate at this time—given our current understanding of the universe—to relax our notion of free will instead of trying to stretch it to afford an as of yet an indescribable freedom. To this end, the notion of free will in a deterministic system can be explained as an illusory sense of control that occurs when it appears there is more than one possible future before us.

Long-winded explanation

The distinct feeling of freedom of action is not foreign to us, and even if we would call ourselves determinists we all still act under the assumption that we actually can control our own decisions and actions. We still talk and move around assuming our bodies operates under our own volition – if we did not we may as well simply collapse under the futility of it all. It is readily apparent that despite our understanding of determinism, our perceived control over our own actions completely permeates every moment of our lives — and thus the temptation to embrace free will. But closer inspection brings forth the actual degree of control we actually have, which is in my view broken into two distinct types of control: universal control and human control. Universal control is the notion that we are able, through whatever mechanisms, to break ourselves free of physical causation; this is impossible. In other words, it’s just an affirmation of standard causal determinism: that “every event, including human cognition and behavior, decision and action, is causally determined by an unbroken chain of prior occurrences” (Van Inwagen, 1983). This type of control we do not have. However, we do have human control; that is, we have the ability to predict (or rather, inability to perfectly predict) the outcome of events which provides us with the illusion that there is a “possibility” between choices. Note that it is not the freedom to “decide” whether or not we predict or not; it is simply the distinct feeling of comfort and peace that comes from a sense of control, i.e., from one’s sense that he or she understands the future well enough such that his or her desires are favorably in-line with the likely future. Stated differently, we do not have control in the sense that we are agents free from causation, but we do have control in the sense that, given our inability to calculate the precise outcome of all the causal factors leading to a particular event, we are able to—with a fair degree of accuracy, especially for common events—predict at least a set of outcomes that will likely occur. While only one outcome is truly inevitable for any event, our limited intellects can often only narrow down the factors to several “possible” outcomes. The control we feel is the degree to which our predicted outcome is expected to match the inevitable outcome. Dennett (1984), illustrates this best with his remote-control airplane example:

When you control your plane perfectly, you don’t do it by controlling all the causes that influence it. The weather, the density of the air, and the force of gravity, for instance, are all beyond your control, and they are the largest forces that act on your plane. The fact that your plane is constantly under the influence of gravity does not prevent you from controlling it–in fact in some regards gravity helps you, just so long as you know its effects on the plane. But a sudden and unanticipated gust of wind may upset your control, either temporarily or permanently. What is important about the difference between the gust of wind and gravity is not the steadiness of the latter and the suddenness of the former, but the (relative) unexpectability of the former. … Foreknowledge is what permits control.

–Dennett, Daniel (1984). Elbow Room: The Varieties of Free Will Worth Having. Cambridge. MA: MIT Press.

Thus, the nature of human control is not “real” control; it is the measure of our desires against our prediction of the future. At best, this leaves us with the illusion of free will. In this way (regarding the OP's question), free will can be quantified in a deterministic system without breaking any rules of causation.

In an effort to avoid some of the inevitable pro-"free will" comment backlash this post will generate, I just to want to add that I understand that people don't want to give up the idea of freedom of action; they don't want to be reduced purely physical automata. What they don't realize is that—if this is the way we really are—nothing really has to change. It's not like the slight alteration of our conceptual understanding of the free will flips our entire world upside down. At the end of the day, we still get up in the morning, we still take showers, eat breakfast and go to work. We still hang out with our friends when we want and watch our favorite TV shows as we please. Ice cream and brownies still taste delicious, the night sky full of stars still fills us with awe and wonder, and the pain of losing a loved one is still real to us. If determinism is true, no one has to give up anything.

  • I don't understand the plane example. Sure, I don't control gravity and can't fly in any arbitrary way I wish -- but I can direct the plane to any destination I wish, right?
    – Joseph Weissman
    Commented Aug 12, 2011 at 14:20
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    The point of the airplane example is to highlight the fact that control is not a measure of how much or how little we influence the actions of the plane, but rather a measure of our understanding of what will occur when those influences do act on the plane. E.G., you might fly your plane high and then dive straight down; during this downward flight you needn't do anything with your joystick (you needn't yourself personally influence the plane) because gravity and other forces do the work for you. But you would still feel in control of the plane. (cont.)
    – stoicfury
    Commented Aug 12, 2011 at 18:48
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    Control (and thus free will) then is not a measure of our influence in a decision or action (how much our "will" plays a role in a choice); it is a measure of our understanding — our predictions of the future vs. what will inevitably happen. We feel in control when our predictions are accurate (when the plane goes as we think it will based on our actions). We feel out of control when our predictions are consistently inaccurate (I press left on the joystick, plane goes in a random direction. I would feel not in control because I could not predict its actions.) Foreknowledge is control.
    – stoicfury
    Commented Aug 12, 2011 at 18:55
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    Thanks, I think I see what you are getting at here; though this perhaps raises another issue: is predictability actually fore-"knowledge"? Even given that a process is predictable doesn't imply that our predictive model is "true" -- just that it has been accurate enough up until now. In other words we may have justified confidence in our predictions, but still not (strictly speaking) "know the truth" of the phenomena. Probably nitpicking, however; this is a great answer.
    – Joseph Weissman
    Commented Aug 12, 2011 at 19:36

If I speak to somebody who doesn't know what "deterministic" or "random" means, I can give a precise, clear, mathematical definition.

No, you can't, really. Saying "Any live cell with fewer than two live neighbours dies with a probability of 0.5" is an example of a rule that defines a random process simply substitutes one undefined term ("random") with another ("probability"). If that's the kind of definition you want, we can just as easily say "Any live cell with fewer than two live neighbours dies if it chooses to" is a definition of free will. In other words, if "random" means "chance", and "determined" means "rule-bound", then "free will" means "choice"-- but all we've done here is to shift the terms: now we have to define "Rule", "Chance", and "Choice". And, as you might imagine, there is no "precise, clear, mathematical definition" for any of those terms, in a philosophical setting.

You can see an overview of some common conceptions of free will here, but you'll notice that none of them come close to the mathematization you desire.

Similarly, efforts to define rule-based behavior fail, for the reasons found in Wittgenstein's Philosophical Investigations (but also intimated in Hume.)

  • No, I totally agree with you. I have come to "accept" random as a fundamental concept that doesn't need to be explained even though I've never understood how something can be random. So, basically, the only process I can accept is a deterministic one. To make it hard for a random process doesn't make it easier for a free process though.
    – Speldosa
    Commented Aug 9, 2011 at 16:12
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    Ah, but even the "determined" process is difficult to understand from a philosophical standpoint-- because then you are getting into the problem of causality, with all of the Humean (and Wittgensteinian) complications that follow. For me, the more interesting question is: why would it matter? Since we certainly appear to have some form of conscious choice available to us, does it really matter if that choice is merely apparent, as long as we act as if we had it? Commented Aug 9, 2011 at 20:16
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    You have demonstrated that you cannot (or did not) give a precise mathematical definition of "random". But you have hardly shown that it cannot be done; your answer is at best incomplete, and closer to a straw-man argument as it stands presently.
    – Rex Kerr
    Commented Aug 10, 2011 at 17:32
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    I did say the same for "deterministic". There may be a "precise, clear, mathematical definition" for "randomness" within the domain of mathematics, but mathematics is a constructed domain based on a certain set of unquestioned axioms. Any properly philosophical definition of randomness would not be able to rely on those axioms. Philosophy aims at clarity, but also attempts to grapple with the world as we find it, and not solely an artificially constructed world like the world of mathematics. Commented Aug 10, 2011 at 19:48
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    Sorry, several problems arise. First of all, "it happens the same way each time" isn't going to fly, since we don't have a means to try the same state multiple times. So, this will only work with a trivial "toy universe", and offers no knowledge regarding the universe we happen to inhabit. Second, and more critically, even if we were to overcome the first objection, we still have no way of knowing whether it indeed "happens the same way each time" based on observation. How many times would we need to repeat the experiment to get absolute certainty? Commented Aug 11, 2011 at 8:07

Only when 'effect' is not linked to a 'cause', it is possible. The perfect Random! So is it possible to have effect not preceded by cause? Yes certain theories does support this-see Retrocasuality.

Also universe is not deemed to be deterministic. You cannot predict the momentum and position of an electron with utmost accuracy simultaneously-says Heisenberg’s uncertainty principle. So I guess there are ‘worlds’ in which free will happens-beyond the world we experience and define through Newtonian mechanics and that seems to be the very nature of our universe at micro and cosmic levels of abstractions.”’ 'God' does play dice with the world’ and free will occurs!


The problem here is not the definition of 'choice' or 'free will' - we all know free will from choosing ice-cream in vanilla flavour or chocolate, walnut or no ice-cream at all.

The problem comes from the boundary to yourself - what is YOU, and what is not? If you're genetically disposed to prefer in most situations bananas over apples, is it you, or is it your genes?

Is it YOU or is it your brain? Is it only a nervous reaction?

Freedom of choice means, that you have the possibility to choose to follow your preferences (banana) or maybe a diet plan (no banana, no apple). It doesn't mean that every choice you make has an equal distribution, not related to genes, not related to your history and experiences, not related to your brain and its universe, where decisions seem meaningful from a limited perspective.

That limited brain IS you (and is me, of course). You are your brain and your body, and in contrast to a brick, rolling down a mountain, you have free will.

Don't get confused by language. I'm following Wittgenstein too, here.

  • A reference to or brief citation of the particular Wittgensteinian arguments that you're following would do a lot to improve this answer. Commented Aug 10, 2011 at 4:02
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    Wittgenstein only in so far, that you have to be careful, not to be fooled by language. It's from the 'Tractatus', but I don't have it by hand. Commented Aug 10, 2011 at 4:33
  • @user I think free will generally refers to the idea that a person's actions, decisions, and beliefs are not determined by physical causality. Thus brains/people don't have free will: given a totally defined context, the brain can, must, and will follow only one tack. In contrast, what you are saying, is just that brains are capable of a wide spectrum of thought and action, and that the subset of that spectrum that is a manifest at any time is determine partly by immediate context and partly by static biopsychological factors (the latter actually being reducible to a facet of the context). Commented Aug 24, 2011 at 20:49
  • @Matt: You can easily perform an experiment. The rules are as following: You throw a dime, and if it shows 'number', you clap with your left hand on the desk, if it shows 'head', you don't. You repeat it 10 times (to not get bored). You have the free will to perform this experiment according to the rules or not, but only if you perform it, you enter the second level of freedom: the freedom to follow slavishly an absurd ruleset, where you and nobody else can predict what will happen - number or head? But if you do so, the chances are low, that you performed the clapping ... Commented Aug 25, 2011 at 2:07
  • ... as stated by the rules just by chance is 1/(2^10)=1/1024. You can perform the experiment solely in your head, but I promise you, it is a different experience to perform it for real. You have 10 times the chance to prove your free will and abandon the experiment, and 1 times the chance to follow the rules. After performing the experiment, we can talk again. Commented Aug 25, 2011 at 2:14

The following is an excerpt from Bertrand Russell's Our Knowledge of the External World. With the exception of the concept of sense-data, which was abandoned by the Author in latter works, the rest of the book is still good. I hope it answers your question.

The apparent indeterminateness of the future, upon which some advocates of free will rely, is merely a result of our ignorance. It is plain that no desirable kind of free will can be dependent simply upon our ignorance; for if that were the case, animals would be more free than men, and savages than civilised people. Free will in any valuable sense must be compatible with the fullest knowledge. Now, quite apart from any assumption as to causality, it is obvious that complete knowledge would embrace the future as well as the past. Our knowledge of the past is not wholly based upon causal inferences, but is partly derived from memory. It is a mere accident that we have no memory of the future. We might—as in the pretended visions of seers—see future events immediately, in the way in which we see past events. They certainly will be what they will be, and are in this sense just as determined as the past. If we saw future events in the same immediate way in which we see past events, what kind of free will would still be possible? Such a kind would be wholly independent of determinism: it could not be contrary to even the most entirely universal reign of causality. And such a kind must contain whatever is worth having in free will, since it is impossible to believe that mere ignorance can be the essential condition of any good thing. Let us therefore imagine a set of beings who know the whole future with absolute certainty, and let us ask ourselves whether they could have anything that we should call free will.

Such beings as we are imagining would not have to wait for the event in order to know what decision they were going to adopt on some future occasion. They would know now what their volitions were going to be. But would they have any reason to regret this knowledge? Surely not, unless the foreseen volitions were in themselves regrettable. And it is less likely that the foreseen volitions would be regrettable if the steps which would lead to them were also foreseen. It is difficult not to suppose that what is foreseen is fated, and must happen however much it may be dreaded. But human actions are the outcome of desire, and no foreseeing can be true unless it takes account of desire. A foreseen volition will have to be one which does not become odious through being foreseen. The beings we are imagining would easily come to know the causal connections of volitions, and therefore their volitions would be better calculated to satisfy their desires than ours are. Since volitions are the outcome of desires, a prevision of volitions contrary to desires could not be a true one. It must be remembered that the supposed prevision would not create the future any more than memory creates the past. We do not think we were necessarily not free in the past, merely because we can now remember our past volitions. Similarly, we might be free in the future, even if we could now see what our future volitions were going to be. Freedom, in short, in any valuable sense, demands only that our volitions shall be, as they are, the result of our own desires, not of an outside force compelling us to will what we would rather not will. Everything else is confusion of thought, due to the feeling that knowledge compels the happening of what it knows when this is future, though it is at once obvious that knowledge has no such power in regard to the past. Free will, therefore, is true in the only form which is important; and the desire for other forms is a mere effect of insufficient analysis.

Russell, Bertrand. Our Knowledge of the External World. George Allen & Unwin Ltd.: 1922


Free will, in the sense that you are asking about, is the opposite of deterministic, so mathematically, the definition would be akin to "division by 0." (original work, no citation.)


There are many ways to answer this.

  • mathematically

    • there is the concept of determinism and non-determinism with respect to computations (which one can see as an analogy with motivation and action). These are stipulated definitions and may not correspond exactly to what you are thinking of. A start can be had at Turing machines.
    • in a system like the Game of Life, the rules are purely deterministic: for a given input there is exactly one possible output (at any stage). One could modify the game such that a 'random' process or a willful demon makes some arbitrary, -inherently- unpredictable choices (i.e. the rules might allow more than one possibility). This allowance can be stipulated mathematically (as a probability distribution, say or oracle).
  • in physics, one may question whether objects (at a particular scale, namely sub-atomic particles) act deterministically. At first I wondered if your question was asking if there were a scientific test to distinguish free will and determinism. Anyway, 20th century quantum physics says there is experimental evidence that subatomic particles do not behave deterministically.

To me it is difficult to judge if the technical antonym to determinism, which is either probabilistic or non-deterministic (the latter two are not identical mathematically), corresponds well to what we informally refer to as free-will. That would be the philosophical question left unanswered for me.

But to summarize for your titled question, one necessary condition (but possibly not sufficient), is that the causes of the action not be 'functional' (which is to say almost tautologically, that the cause can't have a single possible outcome).


First we have to understand that we are:

  • dependence upon something else, or
  • not dependence upon something else

Freedom within Dependence upon Something


But since mostly we are dependence to something else, then in general, we are within boundaries.

Free is an escape. Escape from what? Free is an escape from dependence to something. But if we can escape from dependence to something then we have to stay within another boundary. If that so, then where is our freedom? Is freedom an escape from all boundaries? Surely no!

It's an escape from one boundaries to another boundaries. The qualities of an escape is determined by how can we get new boundaries without something as found on previous boundaries.

Adjusting Level

Imagine a basketball is being played by an untrained people - people A. This shows the freedom of moving the basketball as far as can be done by an untrained people generally. Now put this person A on the maintenance of another basketball trainer (assuming that person A will be trained by a basketball trainer and really affects person A), and let person A plays with the same basketball, and soon the basketball will have the possibilities more than before. It’s just a basketball.

Secondly, this already trained person A will be trained by another people for further entertaining. Then person A will get even more expertise in playing basketball. Then the basketball will experience freedom greater than before. It’s just a basketball.

For those who feel they have no free will, then he should link “the will” to something more powerful in the assumption to get more freedom than before.

Someone should put the chances of the expansion of freedom to the wider domination who is considered to have the possibility of free will is much broader than anything, so it is enough to realize that freedom in the process of the future will be more extensive than what can be imagined.

No matter whether you can select or all of them is in accordance with what should happen, the important thing is, we have to realize that free will is a process of exploration as far as strength within ourselves or as far as the extent of power that are considered higher than ourselves where we rely on it.

From just a baskeball to display the impression of freedom just because it was propped on something that has the possibility of more widespread. Therefore if we want to get freedom better, then we must rely our hope to something that has the possibility of more widespread (I consider it God).

It's adjusting level. The qualities of adjusting level is determined by how can we get new boundaries with wider domination than previous boundaries.

Freedom within Dependence upon Ourselves


Psychologically speaking

Our domination within boundaries is strongly dependence to our ego. Each time our ego is being threatened, then our domination is being threatened.

And our ego have ability to push ourselves to dominate as far our own available functions (potential) that can be realized without obstacle.

If our ego are being threatened and this threat restricts our ego to release our functions as human, then ourselves will try to find something better to support our functions as human.

If our ego was failed to dominate, further our Id will not be satisfied, and we need another chance (freedom) to fulfill our needs

There must be better synchronizing in between our functionality as human and something to support ourselves. Without this, our domination will be threatened easily, and our ego will be threatened, further our freedom (to fulfill our needs) will be restricted.

It's freedom for our determination.

Pleaser refer to SuperEgo, Id and Ego for further understanding. I am not supporting exactly what Sigmund freud said, but part of his work has the closer principle as mine and it can be used as citation to make a clear understanding on this case. I have different point of view (Bending Consciousness) regarding on this.

The points are:

We can always trace back our current choices to previous events with limitations that dominate us and lead us to current decisions. Therefore, what does it mean to have freedom as a human?

It means to explore to the possible extent within our ability to make progress, as far as on whom we rely.

  • This can be expressed in two different ways (to provide necessary conditions for an action to be regarded as a free choice) within two different perspectives.

    These are the closest ways (various degrees) to freedom:

    • From fairness:
    • Our ability to get supports to fulfill our functionality as human, to be specifically our own functionality that typical to ourselves,

    • It's fulfilling to the specific extent within fairness.

    • From our ego:
    • Our ability to satisfy our ego to dominate.

    • It's fulfilling such domination to satisfy our ego to create sense of freedom.

Because, there is no way for us to get freedom beyond any boundaries, since it's unreasonable. Whether we believe causalities or not, but no matter how hard we try to be free, we are still within boundaries.

  • Is there any chance I might be able to persuade you to back some of this up, ideally with citations?
    – Joseph Weissman
    Commented Jul 26, 2012 at 18:59
  • Hi @JosephWeissman, i edited (without changing the essence) by adding citation to fulfill your requirement and more with additional assertions. Thank you for suggesting it.
    – Seremonia
    Commented Jul 27, 2012 at 0:22
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    By the way, citations are not a general requirement -- just sometimes helpful in certain cases. Thanks for adding a few links in; I might encourage you to go a bit further here, and maybe cite support for particular claims you're making here. Please keep in mind StackExchange is like a wiki: we need to try to back up what we're saying, even when it's subjective.
    – Joseph Weissman
    Commented Jul 27, 2012 at 0:28
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    Sometimes we need citation when our point of view might not be understood clearly. Citation may be used as another illustration or similar to popular understanding that help others closer to what we intend to. But sometimes, citation is crucial not only to make a clear understanding but further for an assertion (premise). Yes, i agree.
    – Seremonia
    Commented Jul 27, 2012 at 0:36

"Freedom" is an ordinary language term. It does not have a very precise meaning.

Your question presumes that freedom means causal indeterminacy of the will. This interpretation of freedom is not very useful. The will is not causal undetermined and this is not the common interpretation of the term.

"Free" as in "free choice" is not usually understood as the opposite of undetermined. In this context it usually means the opposite of "forced or obliged".

The conditions for a free action in this sense are:

  • an action (regarding action as a meaningful behavior),
  • the absence of coercion

The fact that the will is causally determined does not affect in any way the fact that it is not "forced or obliged" in certain circumstances.

Let's consider a man who wants to eat meat.

If he is forced to do so, he is not free.
If he is forced not to do so, he is not free.
If he is obliged to do so, he is not free.
If he is obliged not to do so, he is not free.

It doesn't matter if he eats or doesn't eat meat. If he wants, do it and is obliged to do it, than he is not free. I want to work, I do work and I am obliged to work, than I am not free. I don't want to work, I do work, I am neither obliged nor forced to do it, I am free.


A simple response from a dualist perspective:

A free action is one that is able to act on a given system in a way that is not determined by (or within) that system.


Looking at Conway's game of life, some examples of free actions would be:

  • The original seeding of the cells
  • A user which adds, removes, or moves cells "at will", while the game is running
  • A user modifying the rules of the game

Scope: Whether the user's actions are determined within the broader system that the user exists in is a completely separate question. A free action is defined from the perspective of the deterministic system (or causal chain) under investigation only.

Random Actions: A random action may or may not be free, depending on whether it is defined/required/constrained to work in a random manner by the system itself. I think of most random effects as pseudo-determined or statistically determined.

Detectability: It may be impossible to detect and/or prove what actions are free from the perspective of an actor within the system in question.

Postscript: I think where most people get tripped up is by assuming the entire universe is one big integrated causal/determined system and nothing can/does exist outside the universe, and deny any form of dualism (or separate causal chains) within the universe. If that is true, then I believe there are no free actions/free will actions because nothing exists outside of the system under inspection. Of course, it is currently impossible to prove that is the state of the universe.

  • 1) Original seeding of cells could arise purely deterministically out of a zero point field. 2) A 'user' may have a model within the system thus is a predicate of a specific system, not independent of it in any formal sense. 3) the same goes for the modification of rules.
    – Vivek Iyer
    Commented Oct 18, 2018 at 18:53

How could one constitute a universe so the processes behind the choice were constituted in such a way that the choice would become free?

There is no free will. There is only chaos.

That aside, believing in free will deterministically sets different boundaries for which actions can occur.

I guess for a more compatibilist view you'd could think of free will as relative concept where some entities have more 'choice' then others. In that case you could consider a salmon in two parallel worlds swimming up a river to lay eggs and die, and in the same worlds a person going to that river and one world fights back against a bear and in the other world pretends to be dead. Although both actions of the person are deterministically achieved, it has more variation than the actions of the salmon. I think you could describe free will as having more available programs that chaotically can be elicited.

So, if there is free will (compatibilist view), for an action to be regarded as a free choice you would at least need more than one available path that can be chaotically elicited. And you would like the trigger to come from within the entity itself as it were being the agent making the 'choice'.


I think information theory could give a perspective on defining "free will". Assuming there is some capability to "make choices" (abstracting away what system enables that), what seems relevant is the distinct number of choices. Using some sort of compositional ontology, we could mathematically quantify how much distinct "substance" there is in a particular universe, and how much of it is possible or available under some given choice (i.e., you cannot choose to have a unicorn as a pet, because it does not exist.)

I can add to my answer to make clearer and more robust what I am saying.


"Free will by a newbie"

I think that our actions are determined by our genetics and environment and I don't believe in a "separate mind or soul" making choices. I believe it is all contained in our brain and our mind is one and the same as our brain. However, lets consider a possibility that our complex brain has evolved higher order functions that include a "choice engine". The engine has evolved as it can give people a survival edge to act differently given the same environment. The engine is a set of complex interacting and self modifying algorithms obeying all the law of nature. The unique thing about the engine is that given any set of inputs it does not give the same answer every time and nor does it give a random answer. It's rules allow it to make a considered choice. At this point, I don't think we can construct such a machine, but that doesn't preclude its existence in our brains.

Humans need to "invent" a "choice engine" in a super computer and demonstrate that it's choices are neither random nor pre-determined. In fact they will have to have two of them side by side and show that they produce differing results with the same input without randomness.

The other point worth mentioning is that if there is no free will and all is determined, we are still unlikely to ever be able to make accurate predictions beyond statistical probabilities (i.e. certainties) that will be useful. So where does one go with determinism, if we'll never be smart enough to pre-determine anything that is even slightly complex - say what direction will a microbe travel in a solution in a petri dish. Obviously, that doesn't change how "true" determinism is, but it also makes it a rather useless truth.

I listened to an excellent radio podcast last week between 3 neuroscientists (BBC In our Time - Neuroscience). They describe the brain in 3 sections, in increasing order of evolutionary development and from low to high function. The inner brain, nearest the spinal system, deals with motor functions and direct response to sensory input. This is the "reptilian" brain, dealing with simple stuff. It's the engine of a machine. No free will going on here, just survival impulse. The next layer is the "mammalian" brain that deals for more complex sensory input, interpretation, learning, emotions, etc. Sort of stuff that makes a chimpanzee so human in its behaviour. The last layer is the surface areas of the brain, uniquely human. Here is where the human high order functions happen. This is where "planning", sorting through large amounts of data and distilling this into strategies far more complex than "man kill, man make fire, man eat" - the most commonly given example is, what college shall I go to?

It's not a low order impulse driven decision. It's a high order, complex decision, based on many variables, where the variables themselves are not senses and are not definitive. Indeed, the variables will change - you might change your opinion based on your mood on a particular day.

Because of all of this complexity and variability, the decisions taken ("free will?") are not easily predicted not easily replicated. If they can't be predicted and replicated, then, even with deterministic physics at the ultimate root, this can be considered "free will" - at least its a candidate for free will.

So my "newbie" definition of free will is "actions that cannot be predicted and are not random". I suspect this is full of holes and tautology, but I like it for now.

  • Please consider trying to cite some sources for your primary claims here -- maybe give us a link to the BBC podcast you were watching? (In passing, please don't "title" your posts; though of course do feel free to make section headers if necessary.)
    – Joseph Weissman
    Commented Nov 21, 2011 at 17:55
  • Apologies for missing a direct link. The BBC does not have a way of hearing old shows. The only way I know to get archived shows is via free membership of this site radioarchive.cc . I cannot provide a direct link to the file, as you need to be a member to get it. I have no other citations to make regarding my proposed definition of free will as, as far as I am aware, it is my own. Clearly, there are very few original ideas left in this world and no doubt one of the great philosophers will have covered my idea (and dismissed it), but I don't know who that would be.
    – andrewfd
    Commented Nov 21, 2011 at 20:47
  • 1
    @andrewfd: I think you just need to clarify some things for us. How the end of the first paragraph reads is very confusing—the last sentence throws me off. The whole point of your answer seems to indicate that paragraph 2 is impossible, yet you seem to think that it is there? Paragraph 3 is fine. The end of paragraph 4 is wrong - planning is not a uniquely human trait nor do humans have some part of the brain that no other animals has — ours just tends to be larger or with greater surface area. P5 is distinct from 4 but talks about the same thing? Why is it separate? P6 last sentence = ???
    – stoicfury
    Commented Nov 22, 2011 at 0:01
  • How would a "choice engine" be neither random nor pre-determined? Maybe it could have a human providing that part of the input. Oh hang on, we're trying to mimic human choice making, so that might be circular logic... Commented Jun 26, 2012 at 7:08
  • Not random nor pre-determined, but I can see how it could be neither random nor PREDICTABLE, which I think is what the poster is getting at. If something is deterministic, but there is no method of predicting the outcome, it is 'effectively' non-deterministic. The human mind can take fixed inputs and respond to them in ways that you can't predict without recreating, in exact detail, the structure and status of the brain. This may not be possible, because the sensitivity and chaotic nature of the brain can amplify very small effects (sometimes atomic scale) into macroscopic effects. Commented Jan 29, 2013 at 16:13

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