Comment on Shrader-Frechette's "Parfit and Mistakes in Moral Mathematics

Abstract

In a recent article in this journal' Shrader-Frechette discusses Parfit's arguments in Reasons and Persons2 with respect to issues in moral calculation. Although her analysis is reasonable, aspects of it need elaboration. The present note is an attempt to flesh out her response to Parfit. The issues are best illustrated with an example such as the one used by Parfit. He describes a scenario in which a thousand wounded soldiers in the desert need water, while in a second group of one thousand each individual is deciding whether or not to contribute his or her pint of water to be divided equally among the thirsty men. The effect of the equal division is that the pint contributed by a given altruist adds one thousandth of a pint to the amount each man receives. If it is assumed that this tiny fraction of the pint each person has to contribute is too small to be perceived by even a very thirsty individual, then each contributor may feel that his or her pint would avail nothing if distributed. The fact that many soldiers would each get slightly more water is irrelevant if none of them perceives any change. One thousand non-effects still constitute a non-effect. Yet, the benefit from the full contribution of the second thousand would certainly produce a noticeable alleviation of thirst. In a manner reminiscent of the Sorites problem, this is a situation in which each additional fraction of a pint makes at most an difference, but the sum of all such differences is quite perceptible. Parfit argues that there are indeed imperceptible benefits and that they must be counted as benefits in spite of this property. ShraderFrechette suggests that an analysis in terms of thresholds and probabilities of benefit would avoid the need to count them in this way. I agree, but I find her discussion somewhat preliminary. She does not spell out clearly how this might work.