There are infinitely many people. A random process causes each one to independent develop a cancer, either of type A or of type B. The chance that a given individual develops a type A cancer is 9/10 and the chance that she develops a type B cancer is 1/10. It is not possible to diagnose whether an individual has type A or type B cancer. There are two drugs available, either of which—but not both, because they are toxic when combined—could be distributed by you en masse to all of the infinitely people. There is no possibility of distributing different drugs to different people—the logistics only make it possible for you to distribute the same drug to everyone. Drug Alpha cures type A cancer but does not affect type B, and drug Beta cures type B cancer but does not affect type A.
What should you do? Clearly, you should distribute Alpha to everyone. After all, each individual is much more likely to have type A cancer.
But now suppose that an angel reveals to everyone the following interesting fact:
- (F) Only finitely many people have type A cancer.
The obvious answer is that you should distribute Beta to everyone. After all, if you distribute Alpha, finitely many people will be cured, while if you distribute Beta, infinitely many will be. Clear choice!
But not so fast. Here is a plausible principle:
- (I) If you're choosing between intrinsically morally permissible options X and Y and for every relevant individual x, option X is in x's best interest, then option X is the best option to choose.
- (Fx) Among people other than x, only finitely many have type A cancer.
- Necessarily, if I is true, then in the infinitary case above, you should distribute Alpha.
But at the same time it really was quite obvious that you should save infinitely many rather than finitely many people, so you should distribute Beta. So it seems we should reject I.
Yet I seems so very obviously true! So, what to do?
There are some possibilities. Maybe one can say deny I in cases of incomplete knowledge, as this one is. Perhaps I is true when you know for sure how the action will affect each individual, but only then. Yet I seems true without the restriction.
A very different suggestion is simply to reject the case. It is impossible to have a case like the one I described. Yet surely it is possible for the outcome of the random process to satisfy F. So where lies the impossibility? I think the impossibility lies in the fact that one would be acting on fact F. And the best explanation here is Causal Finitism: the doctrine that there cannot be infinitely many things among the causal antecedents of a single event. In the case as I described it, the angel's utterance is presumably caused by the infinitary distribution of the cancers.