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Excerpt from "A New Argument for Incompatibilism," Philosophical Perspectives, vol. 14, 2000, p. 168-72

II. "Proof" and a Formal Problem for Consequence Arguments

I will argue for incompatibilism by showing that necessarily, for all propositions X, if determinism is true and X, then no one is free to make it the case that ~X. Some parts of my argument will have a "formalistic" or "proof like" appearance. This appearance, however, should not lead anyone to think that I am trying in any literal sense to provide a proof of incompatibilism (or anything else).⁶ Rather, what I offer in Section III is merely an argument (a rather strong and convincing one in my view, but still, just an argument). The formalistic character of the presentation should not distract from this fact.

So far as I aware, all versions of the Consequence argument employ a "conditional proof" strategy; many also employ the terminology. Indeed, in most incompatibilist arguments the overall form of the argument is that of conditional proof. The argument typically looks like this: assume determinism and show that, given the assumption, no one has freedom. Most incompatibilists, however, either do not adequately understand or simply fail to adhere to a restriction relevant premises in such an argument must meet if the incompatibilist conclusion is to follow from such an argument. Most incompatibilists, to be precise, seem unaware that in order to get the incompatibilist conclusion that determinism and freedom are strictly incompatible (that no deterministic world is a world with freedom), their conditional proofs must not introduce or in any way appeal to premises that are merely contingently true in between the assumption of determinism and the step at which the "no freedom" conclusion is reached.

This is a simple point applying to any alleged conditional proof of a strict conditional. In general, to show by conditional proof that P strictly implies Q, one assumes the truth of P and derives the truth of Q, appealing only to P and necessary truths along the way to Q. In offering such an argument, one is restricted, on pain of modal fallacy, from appealing to merely contingent truths in between the assumption of P (which may be contingent) and the arrival at Q.

My evidence that typical proponents of the Consequence Argument are unaware of this restriction is that they defend only the truth, not the (broad logical) necessity, of the relevant steps of their arguments. To use the Consequence Argument displayed above as a model, incompatibilists typically defend the truth, but not the necessity, of (P1) of the argument. Introducing a merely contingently true premise into such an argument, however, weakens the justifiable conclusion of the argument considerably. Arguments weakened in this way show at most that the following conditional is true:

WEAK — If determinism is true then there is no freedom.

But this conclusion is strictly weaker than (it is implied by but does not imply) the proper incompatibilist conclusion:

INC — Necessarily, if determinism is true then there is no freedom.

Notice that (WEAK), if it is a material conditional, is true in every indeterministic world and is true in every world without freedom. While showing that the actual world is indeterministic would establish this reading of (WEAK), doing so would not establish the proper incompatibilist conclusion, (INC). One could defend a stronger contingent reading of (WEAK) as, for example, a counterfactual conditional, by arguing that the contingent premise appealed to in one's conditional proof is of suitable modal strength. Like (WEAK), however, such a conclusion would be strictly weaker than the proper incompatibilist conclusion. Finally, one could, in appealing to a contingent premise in one's conditional proof, defend a strict conditional asserting that the conjunction of determinism with some contingent truth, C, strictly implies the "no freedom" conclusion: necessarily, all deterministic worlds with C contain no freedom. But once again, this conclusion is strictly weaker than the proper incompatibilist conclusion. It is, I conclude, a mistake to appeal to a merely contingently true premise in the body of a "conditional proof" style argument for incompatibilism.⁷

This mistake, however, is apparently made by even the most prominent recent defenders of incompatibilism. Both Peter van Inwagen (1983) and Robert Kane (1996) defend the truth, but not the necessity, of relevant premises of their favorite versions of the Consequence argument. Both van Inwagen and Kane defend the truth, but not the necessity, of premises stating that, for example, "no one has a choice about the laws of nature." Indeed, van Inwagen has made it clear on more than one occasion that he is not even trying to defend the necessity of such premises.⁸ The Consequence arguments of van Inwagen and Kane therefore appear to be in danger.

Because this charge of modal fallacy is a serious one and is being made against the flagship argument of contemporary incompatibilists, it is worth pausing to display and explicitly examine the; influential version of the Consequence argument to see that my complaint is justified. The version I have in mind is, of course, the third version of the argument offered by my distinguished colleague Peter van Inwagen.

In an amusing passage beginning Chapter Three of An Essay on Free Will, van Inwagen dismisses much of the literature on the incompatibility of free will and determinism. Here's the passage:

Discussions of this question are usually not on a very high level. In the great majority of cases, they are the work of compatibilists and consist to a large degree in the ascription of some childish fallacy or other to incompatibilists... . It is not my purpose in this book to defend any previous writer against a charge of fallacious argument. My own arguments will be explicit, and any fallacies they commit should be correspondingly visible. (It is doubtful whether anyone has ever been seduced by the fallacies with which the incompatibilists are customarily charged; if anyone indeed has achieved such a level of philosophical incompetence, 1, at least, fall short of it). (1983, p.55)

Though I would never accuse van Inwagen of incompetence, I am making the charge of fallacy. Let's see if I can make the charge stick.

In An Essay on Free Will, van Inwagen offers the following argument for incompatibilism. Here are van Inwagen's abbreviations: Let "Np" abbreviate "p is true and no one has or ever had a choice about whether p", "❑" abbreviate broad logical necessity, "⊃" material conditional, "PO" abbreviate the complete state of the world at some time in the distant past, "L" abbreviate the conjunction of the laws of nature, and "P" abbreviate any truth. Here are van Inwagen's rules of inference:

ALPHA: From ❑P, derive NP;

BETA: From NP and N(P ⊃ Q), derive NQ.

With this set up in place van Inwagen argues as follows:

Another Consequence Argument (van Inwagen)

1.	❑ ((PO & L) ⊃ P)	Consequence of Determinism
2.	❑ (PO ⊃ (L ⊃ P))	1
3.	N (PO ⊃ (L ⊃ P))	2, Alpha
4.	N PO	Premise — "fixity of the past"
5.	N (L ⊃ P)	3,4, Beta
6.	N L	Premise — "fixity of the laws"
7.	N P	5,6, Beta

Having thus reached the conclusion that no one has or ever had any choice about any truth from his assumption of determinism, van Inwagen concludes that freedom and determinism are incompatible.

Whatever virtues this argument may have (and it has many), and whatever additional vices it may have (and it has some), this argument most certainly exhibits the modal fallacy I have been discussing.⁹ For the proper incompatibilist conclusion, (INC), to follow from the soundness of this argument, van Inwagen would need premises formally stronger than premises (4) and (6) above Among other things, van Inwagen needs to defend not merely the truth, but also the necessity, of his claim that no one has a choice about the laws of nature. Van Inwagen, that is, needs to defend the truth of ❑ NL, not just NL.¹⁰( Perhaps van Inwagen would be willing to defend this stronger premise (and the similarly strengthened version of premise 4). As the argument is presented it An Essay on Free Will, however, the argument, even if sound, does not establish the proper incompatibilist thesis. Instead it establishes only (WEAK) or some similarly weakened thesis. The time is ripe fora new and improved incompatibilist argument. I will provide such an argument in Section III.

As I stressed above, what I will offer in Section III is not a proof of incompatibilism. Rather, I will simply be offering a "semi-formal" argument for incompatibilism. I will, naturally enough, be quite interested to find out what step in the argument compatibilists wish to reject or call into question for I dc not think that there is a "defective" step in the argument. But I have no doubt that at least the craftiest philosophers in the compatibilist camp will find something in the arguments that they feel should be rejected. They had better, for if nothing else my argument is valid and, if sound, implies the falsity of compatibilism. It follows that one wishing to confront the argument and hold onto one's compatibilism must reject some step in the argument. This does not imply (at least not by itself) that my argument "begs the question" against the compatibilist." If it did, then, so far as I can tell, any formally valid argument would "beg the question" against those who do not accept its conclusion and all formally invalid arguments would, of course, be unsound: philosophical argumentation would thereby be reduced to absurdity.

Notes

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Bibliography

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