## Thursday, June 4, 2009

### A bad argument against determinism

Consider this fairly popular argument. If determinism were true, then it would be possible that Jane knows what Jake will do, and Jane tells Jake what he will do. But human beings contrary creatures, as we well know, Jake likely will not do what Jane says he will do.

We can even formalize the argument. Suppose Jake is determined to do A, and Jane tells him so. Then:

1. (Premise) Jake is determined to do A
2. (Premise) Jake is told he will do A
3. (Premise) If x is determined to do A, then P(x does A) = 1
4. (Premise) If x is told he will do A, then P(x does A) < 1/2.
5. P(Jake does A) = 1 (by 1 and 3)
6. P(Jake does A) < 1/2 (by 2 and 4)
7. 1<1/2 (by 5 and 6)
Observe that in the formalization, the claim that Jane knows what Jake will do has dropped out. This is good, because determinism is compatible with nobody (except God) being able to know what will happen. All we need for the argument is the possibility that Jane will correctly tell Jake what he will in fact do, and that possibility is there even if Jane does not know what Jake will do—she might guess right.

Where the argument fails is in a step prior to the formalization above, namely the step that says that if determinism is true, it is possible that Jane will correctly tell Jake what he will do. To see the failure, consider the conditional:

1. Were Jane to tell Jake that Jake would do u, then Jake would do v,
which I will abbreviate T(u,v). Determinism by itself says nothing about what the truth values of T(u,v) are for different choices of u and v. In fact, determinism by itself is prima facie compatible with these conditionals being all false as well as with none of them having a truth value. But Jane can correctly tell Jake what he will do only if there is a u such that T(u,u). And the existence of such a u is not guaranteed.

Let's be more concrete. Suppose Jake is choosing between A and B. Then there are four relevant conditionals: T(A,A), T(A,B), T(B,A) and T(B,B). The fact of determinism tells us nothing about the truth values of these: they could all lack truth value, or they could have any of the fourteen possible combinations of truth values TFTF, TFFT, FTTF, FTFT, FFTF, FFFT, TFFF, FTFF, FFFF, NNTF, NNFT, TFNN, FTNN and NNNN (I may have missed something) where "N" means no truth value (assuming A and B are incompatible, and that the antecedents are all possible). On views of counterfactuals on which subjunctive conditionals must have truth value, NNTF, TFNN and FTNN are ruled out. On views of counterfactuals on which conditional excluded middle holds, FFTF, FFFT, TFFF, FTFF and FFFF are ruled out. But in any case, on no view of counterfactuals are we guaranteed that there is u such that T(u,u). That would require excluding the possibility FTTF (i.e., T(A,A) is false, T(A,B) is true, T(B,A) is true and T(B,B) is false), which no purely formal considerations of determinism and counterfactuals can rule out.

But perhaps one can try to rescue the original argument as follows. It seems vastly improbable that there be no situation in which T(u,u) is true for some u. So, probably, there is some situation in which Jane can correctly tell what Jake will do. I agree. But in that case, the determinist will deny (4). The determinist can say: "Look: by your own admission, people are contrary creatures. They are unlikely to do what they are told they will do. Therefore, situations where there is u such that T(u,u) are relatively rare. Now, our support for (4) is empirical data about human contrariness. But this empirical data is quite compatible with the existence of relatively rare situations where people are not contrary—and it is only in those situations in which there is a u such that T(u,u). When we condition on the specifics of the situation, the probability of Jake doing u given that he was told he would do u will in fact be 1. But because such situations are relatively rare, without conditioning on the specifics of the situation, we can still say that it is unlikely that Jake would do what he was told he would do."

Perhaps the libertarian can say that even in such a situation of non-contrariness, surely our experience teaches us that the probability of Jake doing what he was told he would do is less than one. But our determinist friend will say that this is because in practice there are always hidden deterministic factors.

Of course the libertarian could say that her reason for thinking that Jake always has a probabity less than one of doing what he was told he would do is not empirical—she just has that intuition. I think this is a fine reason for denying determinism—but it doesn't need the special case of being told what one will do. All one needs is the intuition that in any choice where one option does not dominate all the others, the probability of choosing any particular option is less than one. But this intuition is, alas, probably not shared by the determinist.