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Abstract, “Thresholds from the Bottom Up”
Many hold that, ceteris paribus, you may not kill one innocent to prevent more but not far more than one other innocent from being killed but may kill one innocent to prevent far more than one other innocent from being killed. Suppose this is right. Extremely roughly, the threshold problem is the problem of giving a principled, unified explanation of this fact, as well as of analogous facts concerning harm-types other than killing.
In this paper, I propose the beginning of a solution to the threshold problem as it applies to killing, which likely generalizes to many other harm-types, as well.
My argument comprises five main steps.
First, I defend without argument the Small Harm Claim, according to which you may give one innocent person a paper cut to prevent exactly one other innocent person from being killed.
Second, I defend the No Worse Than Claim, according to which death is no more than a googolplex times worse for its victim than a paper cut is for its victim. A sizeable portion of the paper is devoted to clarifying and motivating the No Worse Than Claim. I argue for the No Worse Than Claim in part by proposing and motivating a sufficient condition on harm x’s being no more than n times worse for its victim than harm y is for its victim, namely that (a) there exists some harm z such that z is less than n times worse for its victim than y is for its victim and (b) x is substantially less bad for its victim than z is for its victim. This sufficient condition, combined with some additional plausible comparative evaluative claims, yields the No Worse Than Claim.
Third, I defend the Worse Than Claim, according to which death is more than 2 times as bad for its victim as any harm that I may inflict on an innocent to prevent another innocent from being killed.
Fourth, I propose the following claim:
Threshold Thesis. Ceteris paribus, I may kill innocent person P to prevent n or more other innocent persons from being killed if and only if, and because, there is some harm h such that (a) death would be no more than n times worse for P than h would be for P and (b) I would be permitted to inflict H on P to prevent exactly one other innocent person from being killed.
If the Threshold Thesis and the three preceding claims are all true, then because they are all true, you may not kill one innocent to prevent 2 other innocents from being killed but may kill one innocent to prevent a googolplex of other innocents from being killed. Those who defend the above four claims therefore have at least the beginning of a solution to the threshold problem as it applies to killing.
Fifth, I give an independent argument for the Threshold Thesis, which proceeds in three steps.
First, I invite the reader to imagine some harm-type H that meets the following three conditions:
(a) One instance of H is considerably more than negligibly bad for the victim.
(b) It seems likelier than not that one instance of H is sufficiently small that it would be permissible to inflict one instance of H on one innocent to prevent one other innocent from being killed.
(c) It is possible to inflict instances of H on the same person indefinitely, in rapid succession, until that person dies.
An example of a harm-type that meets these conditions might be successfully shooting a medicine ball of not-very-great weight at not-very-high velocity at a person.
In what follows, let “Hn” refer to the act of inflicting n instances of H on one innocent in rapid succession to save n other innocents from being killed.
Second, I suggest that your credence that some act Hn is permissible ought, as n increases, to descend for a while and then to ascend. For example, you ought to be less confident that H6 is permissible than that H1 is permissible, but more confident that H300 is permissible than that H6 is permissible. (I mean these particular numbers to be merely illustrative of the credence curve’s “down-up” shape.)
Third, I propose an explanation of the fact that your credence curve ought to have this down-up shape, which strongly suggests that the Threshold Thesis is true. I also suggest that alternative explanations will be either unmotivated or unsuccessful.
Very roughly and briefly, the explanation goes as follows: Ceteris paribus, the total amount of harm that you may inflict on one innocent to prevent n other innocents from being killed is (n)(X), where X is the greatest amount of harm that you may inflict on one innocent to prevent one other innocent from being killed. Call this claim the “Linear Claim.” Furthermore, there are good reasons having to do with risk of severe harm to suspect that in any real-life case of inflicting multiple instances of H in rapid succession on an innocent, H1 will inflict less than X on him, H6 will inflict more than 6X on him, and H300 will inflict less than 300X on him. This is why you should be less confident in H6’s permissibility than in H1’s and in H300’s.
If the Linear Claim is true, then it is very plausible that the Threshold Thesis is true. Hence the present explanation tells strongly in favor of the Threshold Thesis.