Tuesday, November 7, 2017

Adding infinite guilt

Bob has the belief that there are infinitely many people in a parallel universe, and that they wear numbered jerseys: 1, 2, 3, …. He also believes that he has a system in a laboratory that can cause indigestion to any subset of these people that he can describe to a computer. Bob has good evidence for these beliefs and is (mirabile!) sane.

Consider four scenarios:

  1. Bob attempts to cause indigestion to all the odd-numbered people.

  2. Bob attempts to cause indigestion to all the people whose number is divisible by four.

  3. Bob attempts to cause indigestion to all the people whose number is either odd or divisible by four.

  4. Bob yesterday attempted to cause indigestion to all the odd-numbered people and on a later occasion to all the people whose number is divisible by four.

In each scenario, Bob has done something very bad, indeed apparently infinitely bad: he has attempted infinite mass sickening.

In scenarios 1-3, other things being equal, Bob’s guilt is equal, because the number of people he attempted to cause indigestion to is the same—a countable infinity.

But now we have two arguments about how bad Bob’s action in scenario 4 is. On the one hand, in scenario 4 he has attempted to sicken the exact same people as in scenario 3. So, he is equally guilty in scenario 4 as in scenario 3.

On the other hand, in scenario 4, Bob is guilty of two wrong actions, the action of scenario 1 and that of scenario 2. Moreover, as we saw before, each of these actions on its own makes him just as guilty as the action in scenario 3 does. Doing two wrongs, even two infinite wrongs, is worse than just doing one, if they are all of the same magnitude. So in scenario 4, Bob is guiltier than in scenario 3. One becomes the worse off for acquiring more guilt. But if 4 made Bob no guiltier than 3 would have, it would make Bob no guiltier than 1 would have, and so after committing the first wrong in 4, since he would already have the guilt of 1, Bob would have no guilt-avoidance reason to refrain from the second wrong in 4, which is absurd.

How to resolve this? I think as follows: when accounting guilt, we should look at guilty acts of will rather than consequences or attempted consequences. In scenario 4, although the total attempted harm is the same as in each of scenarios 1-3, there are two guilty acts of will, and that makes Bob guiltier in scenario 4.

We could tell the story in 4 so that there is only one act of will. We could suppose that Bob can self-hypnotize so that today he orders his computer to sicken the odd-numbered people and tomorrow those whose number is divisible by four. In that case, there would be only one act of will, which will be less bad. It’s a bit weird to think that Bob might be better off morally for such self-hypnosis, but I think one can bite the bullet on that.

No comments: