Joseph Raz on number problems in morality
Imagine that there are two people drowning on one side of a lifeguard and three people drowning on another. The lifeguard cannot save all of the people. He must choose a side and let the people on the other side drown. The lifeguard is not related to any of them, none of them were likely to die soon prior to drowning, etc. In this kind of situation, one might think that the lifeguard should try to save the three, rather than the two. In his paper Numbers With and Without Contractualism, Raz agrees, but he arrives at this conclusion by a different route to the standard route.
The standard route
The standard route to the conclusion that the lifeguard should try to save the three involves the premise that if a person has reason to do something, then it must be possible for them to do that thing. We do not have reason to perform impossible actions. Thus it cannot be the case that the lifeguard has reason to save all five drowning people, since that is impossible for him to do.
The standard route also involves the premise that when it comes to saving from death, the value of human lives can be added together. Three lives are worth more than two. Thus the lifeguard has reason to save the three on one side. (Some people who think the lifeguard should try to save the three will want to rely on a qualified version of the premise that the value of human lives can be added together, while accepting the first premise. I count them as also proceeding by the standard route. Raz, in contrast, denies the first premise and does not transparently rely on the second.)
Despite the fact that it is impossible for the lifeguard to save all five of the drowning people, Raz thinks that the lifeguard has reason to save all five. Since each life is of value, the lifeguard has a reason to save each person and so has reason to save all five. Raz also thinks that compliance with reason comes in degrees. Even if there cannot be complete compliance, there can be partial compliance. Partial compliance is better than no compliance. Greater compliance is better than less.
If the lifeguard did nothing, he would not be complying at all with reason. If he saved two, he would be partially complying, but if he saved three he would be partially complying and be closer to complete compliance. Raz therefore thinks that the lifeguard should set off in the direction of the three drowning on one side, since saving three will bring him closest to complete compliance.
Denying ought implies can
Raz denies the first premise of the standard route: that if a person has reason to do something, then it must be possible for them to do that thing. It sounds as if he is denying the principle that ought implies can. According to this principle, if a person ought to do something, this implies that they can do it. (A necessary condition for a course of action being something that they ought to do is that they can do it.) But Raz does not explicitly refer to the principle that ought implies can in his paper.
Raz, J. 2003. Numbers, With and Without Contractualism. Ratio 16: 346-367.