A Proof of Free Will

by Michael Huemer

ABSTRACT: A modest free will thesis, stating that at least sometimes, someone has more than one course of action open to him, can be derived from three premises: first, the proposition that we should believe only what is true; second, the 'ought' implies 'can' principle; and third, the proposition that I believe I have free will. The first of these is the only one that is at all controversial; however, I argue that it is a necessary presupposition of rational thought and discourse. As a result, one cannot rationally accept hard determinism.

The minimal free will thesis (MFT) holds that at least some of the time, someone has more than one course of action that he can perform.(1) This is the least that must be true in order for it to be said that there is free will. It may be disputed whether the truth of MFT is sufficient for us to 'have free will,'(2) but there is no doubt that the main philosophical challenge to the belief in free will has come from the thesis of universal determinism, so understood as to exclude MFT. A proof of MFT is therefore of considerable philosophical interest, whether or not it constitutes a full proof of free will. In any case, it is the minimal free will thesis of which I have a proof to offer.

It will be convenient to have a name for the contradictory of MFT. With apologies to compatibilists, I use the label "determinism." Hereinafter, then, determinism is the thesis that the only thing anyone can ever do is the thing he actually does, where by stipulation, "can" is used in the sense (whatever that is) that is relevant to free will.

My proof requires four premises. First: with respect to the free-will issue, we should believe only what is true; that is, we should refrain from believing false propositions. We should not accept determinism unless it is true; likewise, we should not accept the free-will thesis unless it is true. This is a presupposition of rational discourse on the topic of free will. When we sit down to talk about this issue, or any philosophical issue, there is a tacit assumption that we are all interested in finding out the truth, and we accept this goal as governing the discussion. This does not mean that all of us will always think in the manner that is in fact most truth-conducive, for we may occasionally make mistakes or be unknowingly influenced by biases. What we may not do, consistent with rational discourse, is to accept mistakes or biases as such. That is, we are at least committed in theory to renouncing such mistakes and biases, even if that commitment is sometimes difficult to implement in practice. Thus, if someone announces that he thinks that we should believe what is false, or that having a false belief would be just as good as having a true belief on this matter, then, I think, that person has explicitly disavowed rational discourse on the topic of free will. I will therefore assume that my audience accepts this first premise.

My second premise is the "'ought' implies 'can'" principle: that is, to say that something should be done implies that it can be done. For example, suppose a student explains to me that he could not make it to class because his car broke down. One way I might respond would be by telling him that he could have made it to class some other way. But it would be nonsensical of me to say, "Yes, I understand that you could not have come to class, but you should have come anyway." In general, it is not the case that you should do the impossible. This is equivalent to saying that if you should do something, then you can do that thing.

The third premise states that, if determinism is true, then whatever can be done is actually done. This follows directly from the definition of determinism given above: determinists hold that any person, at any given time, has one and only one course of action open to him. Thus, according to determinists, if a person fails to perform an action, that means he literally was unable to perform it. Which implies that if a person is able to perform an action, then he performs it.

Finally, the fourth premise states that I, personally, believe in free will. This is an empirical fact, which I know on the basis of introspection. Of course, there will be those who dispute my belief, in the sense that they think it is a false belief, but I assume no one will question the mere fact that I have such a belief; I assume, that is, that none will wish to accuse me of lying when I say I believe I have free will. Incidentally, any other example of an individual who believes MFT will do just as well for purposes of my argument.

Given these premises, now, we can deduce the truth of the minimal free-will thesis:

1. With respect to the free-will issue, we should refrain from believing falsehoods. (premise) 2. Whatever should be done can be done. (premise) 3. If determinism is true, then whatever can be done, is done. (premise) 4. I believe MFT. (premise) 5. With respect to the free-will issue, we can refrain from believing falsehoods. (from 1,2) 6. If determinism is true, then with respect to the free will issue, we refrain from believing falsehoods. (from 3,5) 7. If determinism is true, then MFT is true. (from 6,4) 8. MFT is true. (from 7)

The validity of steps 5-8 should be uncontroversial.(3) In step 7, we see that, if determinism is true, then MFT is not a falsehood, since if it were, we would (step 6) refrain from believing it, whereas some in fact believe it (step 4). Thus, we see that determinism is self-refuting, in the sense that, modulo certain true premises, determinism implies its own contradictory (MFT). Any proposition that thus implies its own contradictory is false, so determinism is false, and MFT true.

Despite the unquestionable validity of my proof and its highly plausible premises, in my experience, few people are prepared right away to accept it. Therefore, I shall discuss some of the objections which have been raised against it.

Objection #1:

Premise (1) begs the question, because, if determinism is true, then it is never the case that a person 'should' do anything, because in order for it to be true that S should do A, it must be true both that S can do A and that S can refrain from doing A. Determinism implies that S is never both able to do A and able to refrain from doing A. Therefore, a determinist would obviously reject (1).

Reply:

Consider the following possible definitions of 'begging the question':

BQ1: An argument begs the question iff the premises contain the conclusion. BQ2: An argument begs the question iff, if the conclusion were false, one of the premises would have to be false. BQ3: An argument begs the question iff one or more of the premises depend for their plausibility on the conclusion.

Which view of begging the question might the objector have in mind? Start with BQ1. One can see by inspection that MFT is not contained in (1). (1) only says that we should not believe what is false with respect to the free-will issue; that by itself does not say anything about which position is in fact true or false. Nor does (1) by itself even entail MFT; (1) must be combined with premises (2), (3), and (4) in order to derive MFT. Alternately, it may be combined with (2), (3), and the premise, "Whatever a person should do, he can fail to do." But presumably if (1) 'contained' MFT (in any decent sense of 'contain'), then (1) alone would be logically sufficient for MFT.

Next, consider BQ2. I freely admit that my argument 'begs the question' according to definition BQ2, because every valid argument 'begs the question' in that sense. An argument is valid if and only if: it is logically impossible that the premises are all true and the conclusion false. The second half of that biconditional is equivalent to the following: it is logically necessary that if the conclusion is false, then the premises are not all true. This certainly implies that if the conclusion were false, at least one of the premises would have to be false. Therefore, BQ2 implies that all valid arguments beg the question.(4) Presumably, validity is not a defect in an argument, so 'begging the question' in this sense is not a defect.

Likewise for the proposal that my argument begs the question because a consistent determinist would reject (1): of course, since my argument is valid, anyone who denied the conclusion, and was consistent, would have to deny one of the premises. Again, this is not a logical defect in the argument.

Lastly, consider BQ3. (1) does not seem to depend for its justification on MFT, nor does the above objection give any reason to think that it does. I did not cite MFT as a reason for believing (1). What I actually said on behalf of (1) was that it was a presupposition of rational discourse.

Nor is it clear how MFT could serve as a reason, or even part of a reason, for believing (1). The objector claims that the plausibility of (1) depends on MFT, so he should be able to explain how (1) could be inferred from MFT, perhaps in conjunction with some other plausible premises. I do not see how this can be done.

In fact, the case is just the reverse of what the objector claims: it is the determinist who is begging the question if he makes this objection. Premise (1) is initially plausible, and no reason has been given for doubting it other than that (1) (allegedly) conflicts with determinism. Those who have no commitment either to determinism or to its denial would find (1) plausible. In fact, I believe that those who accept determinism would also find (1) plausible, provided they did not see the potential conflict with determinism. The determinists, at least superficially, appear to believe that we should accept determinism because it is true; that is the natural position to take with respect to any position one holds (i.e., that people should accept that position because it is true). A determinist who says otherwise does so only because he sees that he has to in order to maintain his determinism (alongside other things he takes to be true).

In my experience, having presented this argument informally to both students and colleagues, those who press the 'begging the question' objection never object to (1) before they see that it leads to the denial of determinism (or that determinism leads to the denial of (1)), and they give no objection to (1) other than that it is allegedly inconsistent with determinism.(5) Thus, their reasoning seems to be something like this: I haven't refuted determinism, because (1) is unacceptable as a premise. Why is (1) unacceptable? Because it's not compatible (given other premises which are obviously true) with the truth of determinism. In fine, it is unacceptable because if accepted, it refutes determinism. Objection #2:

The argument involves an equivocation, since the "should" in premise (2) is the "should" of morality, while (1) employs the "should" of epistemic rationality.

Reply:

I do not believe that there exist these different senses of "should." What there are, admittedly, are different reasons why a person should do a particular thing. One reason for doing A might be that A advances your own interests. Another might be that A helps out a friend of yours. Another might be that A fulfills a promise. Etc. I do not see that these different possible reasons why an action should be performed generate different senses of the word "should."

Be that as it may, even if there are different senses of "should," there is no reason why (2) must employ the moral "should." Any relation to a potential action worthy of the name "should" must at least have this feature: it is normative, i.e., to say one "should" do A is to in some manner recommend in favor of A. This is sufficient for (2) to be true, for it is nonsensical to recommend the impossible. That is, he who recommends a thing is committed to its being possible to follow his recommendation. If he admits the thing recommended to be impossible, he must withdraw the recommendation.

For example, suppose a Bayesian recommends that we always conform our degrees of belief to the probability calculus. One implication of this is that we should accord to every necessary truth the highest possible degree of belief. The Bayesian says we are irrational for not doing so. Now suppose an objector argues that we have no feasible way of identifying all the necessary truths as such, and therefore no feasible way of taking the Bayesian's advice.(6) (Compare: not knowing the combination to the lock, I cannot open the safe. Likewise, not knowing what all the necessary truths are, I cannot assign degree of belief 1 to all of them.) It seems to me that the objector has a valid point. The Bayesian cannot sensibly respond, "Yes, I know that people cannot identify all of the necessary truths and believe them with certainty. But we should do so anyway. Since my recommendation was epistemic in nature rather than moral or prudential, the impossibility of what I suggest is no excuse for not doing it." Such a response sounds no more reasonable than my telling my student that he should have come to class even though he couldn't. Of course, the Bayesian could still say some related things about the practice of conforming degrees of belief to the probability calculus: He might say that this is how an ideal reasoner would or should behave (the ideal reasoner having capabilities that normal humans lack). He might also say that we should do our best to approximate to this kind of reasoning. But he cannot sensibly criticize us for not succeeding in attaining this ideal, provided he grants that we literally cannot do so. Objection #3:

Premise (1) falsely claims that we should believe only what is true. Rather, we should believe only what is justified.

Reply:

First, we care about justification because we care about truth. Believing only justified propositions is desirable, as our best means to believing truths and avoiding errors.(7) One might even define an epistemically justified belief as a belief that is rational to accept, from the standpoint of our goals of attaining truth and avoiding error. Accepting only justified propositions constitutes the rational pursuit of truth (just as maximizing expected utility constitutes the rational pursuit of utility).(8)

But surely it is false that we should undertake means to a goal that is impossible to attain.(9) So, given the assumption, granted by the present objection, that we should believe only justified propositions (concerning the issue of free will), it follows that we can avoid error (with respect to the issue of free will). This gives us step (5), and the argument can continue on as before without appealing to (1).

Furthermore, even if we give in to the objector and replace (1) with

1'. We should believe only propositions for which we have adequate justification.

the argument will still be damaging to the determinist. Instead of leading to (8) "MFT is true," the argument will lead to

8'. I have adequate justification for MFT.

And though the determinist would no longer be involved in a logical contradiction if he affirmed this, the view that everyone who believes in free will (which is almost everyone) is justified in doing so is at least an uncomfortable one to combine with the belief in determinism.

Objection #4:

(1) is false as used with the epistemic sense of "should," because people have no control over their beliefs. When a belief is epistemically irrational, there is a sense in which the believer "should not" hold it. However, since people never have a choice about what they believe, this cannot be taken to imply that the believer has it within his power to refrain from holding that belief.(10) To show that people cannot control their beliefs, perform this experiment: try believing that you are a safety pin.(11) You will find that you can't do it.

Reply:

I think people have freedom with respect to their beliefs, in the same sense that they have freedom with respect to their choices. At the least, a person can refrain from accepting a belief that is not adequately justified, which is all that the argument requires when (1') is used. I do not see, otherwise, how it would be possible to criticize people for their irrational beliefs.(12) The above objection contains no account of this, nor any real response to the intuition that "ought" implies "can."

There are two things to say in response to the "experiment." First, it is not an example of an inability to refrain from believing an unjustified proposition. At best, it instances the inability to accept an unjustified proposition, when the negation of that proposition is strongly justified. The fact that there is no reason to believe I am a safety pin--indeed, that it is obviously false that I am a safety pin--is essential to the case: no similar intuition is found in cases where it is proposed that I accept a well justified proposition or refrain from accepting an unjustified one. So the argument does not weaken my premise that we ought to refrain from accepting unjustified propositions.

Second, there is empirical evidence that people can choose to accept or reject propositions, particularly with regard to matters where the available evidence is inconclusive. Choosing to accept a proposition for which there is no strong evidence is known as 'taking a leap of faith.' This practice is widely advocated among religious individuals and seemingly widely adopted. It is often difficult to explain, otherwise, why they believe as they do.

There is also the phenomenon of refusal to accept well justified propositions (a form of self-deception). For example, a man, presented with evidence that his son is guilty of a serious crime, might refuse to accept the conclusion. He might even say, "I refuse to accept that." The reasons for his refusal would be similar to the reasons one might have for performing an (ordinary) action--a sense of loyalty, desire to avoid personal distress, and so on--which lends credibility to the claim that we can control our beliefs in the same sense that we control our actions. People might argue with the man, telling him he should accept his son's guilt. They might, intelligibly, criticize or praise the man (morally) for his decision to believe in his son. This, too, lends support to the idea that we can control our beliefs in the same sense that we control our actions.

I think at this point that I have done everything to refute determinism that could reasonably be expected. I have presented an argument, the premises of which are highly plausible, do not contain the conclusion (except in the sense in which the premises of any valid argument 'contain' the conclusion), and entail that determinism is false. It would, of course, be open to a determinist to reject one of my premises in order to avoid my conclusion. But this can be said of any philosophical argument. It is always open to a philosopher, when presented with an apparent refutation of one of his views, to reject one of the premises on which that apparent refutation depends. Such a move, however, should be used sparingly; otherwise, it becomes a path to dogmatism.

I would like in conclusion to elaborate on the idea that reasoning presupposes freedom just as deliberation about actions does,(13) an idea which is obviously closely related to my premise (1). Suppose I am in the process of deciding whether to accept the existence of free will or not. I realize that if determinism is true, then the outcome of my deliberation, whatever it shall be, is determined. So if determinism is true and I accept the free will thesis, this will mean that I was determined to accept the free will thesis; I could not have done otherwise. This, in turn, will mean that it was not the case that I should accept determinism, and that I could not be criticized for accepting free will. Similarly, if determinism is true and I accept determinism, then I could not be criticized for accepting determinism. If determinism is true, then no choice could be wrong, in the sense that no choice could be one that I shouldn't have made.

This fact--namely, that determinism implies that we can never violate epistemic norms (nor any other kind of norm)--is reflected in step (6) (or (6'), "If determinism is true, then with respect to the free will issue, we refrain from believing unjustified propositions") in my deduction. If we assume certain epistemic norms, then determinism implies that whatever we are going to do, we will have satisfied those norms; in particular, for example, if I accept free will, I will have satisfied the norms of epistemic rationality. But if, on the other hand, we do not assume any epistemic norms, then the very process of deliberation about what to believe--and in particular, about what to believe on the issue of free will and determinism--breaks down. Rationality in forming beliefs consists in the at least implicit acceptance of certain norms--norms such as that truth is to be preferred to error, that degrees of belief should be proportioned to degrees of evidence for those beliefs, that one should not contradict oneself, and so on. This does not entail that those norms are true; but it does entail that one could not rationally reject them.(14)

Notes

1. Following Peter van Inwagen's terminology in An Essay on Free Will (Oxford: Clarendon Press, 1983), p. 91.

2. The main problem is that, if some human actions were mere random events, this would seem to be sufficient for MFT to be true, but it would not be sufficient for any actions to be free. A less interesting objection is that "we have free will" would normally be taken to mean that all normal people perform free actions reasonably often.

3. The premises can be symbolized: 1. (x)(Fx → S[~Bx]), 2. (x)(S[x] → C[x]), 3. (Fm → (x)(C[x] → D[x])), 4. Bm; using the following symbolism: Fx = x is false, S[x] = I should do x, C[x] = I can do x, D[x] = I do x, m = the minimal free-will thesis. Premises 1-3 imply (Fm → D[~Bm]), which says that if MFT is false, then I do refrain from believing it ("[~Bm]" denotes the 'action' of not believing MFT). With the tautological premise (suppressed in the text) that (Bm → ~D[~Bm]) (if I believe MFT, then it is not the case that I refrain from believing it), one can infer ~Fm. Given the tautological premise (suppressed in the text) that (~Fm → Tm) (if MFT isn't false, then it's true), one can infer Tm.

4. This explains why the charge of begging the question frequently appears against otherwise unanswerable arguments. For a similar observation, see Peter van Inwagen's "Reply to Christopher Hill," Analysis 52 (1992): 56-61.

5. Leaving aside another objection that I will discuss below.

6. Note that this objection is distinct from the objection that human beings have been known periodically to mis-identify propositions as necessary or impossible through errors in reasoning.

7. This is a widely-accepted view in epistemology. See for example, Laurence BonJour, The Structure of Empirical Knowledge (Cambridge: Harvard University Press, 1985), pp. 5-8. See also note 8 below.

8. This is my understanding of Richard Foley's position in his Working without a Net (New York: Oxford University Press, 1993).

9. Assuming, of course, that these means are not themselves intrinsically valuable and that they also do not lead to some other goal that is attainable by them.

10. David Owens defends this view in his Reason without Freedom (London: Routledge, 2000).

11. I owe this example to Brian McLaughlin (in conversation).

12. Philip Pettit and Michael Smith make this argument in "Freedom in Belief and Desire," Journal of Philosophy 93 (1996): 429-49.

13. J. R. Lucas makes this claim in the course of an argument closely related to my own. See The Freedom of the Will (Oxford: Clarendon Press, 1970), pp. 114-6.

14. I would like to thank J. R. Lucas for his comments on an earlier version of this paper.