Extensional equivalence of simple and general utilitarian principles.
Donald E. Nute · Notre Dame Journal of Formal Logic · 1979
In the third chapter of his Forms and Limits of Utilitarianism, 1 David Lyons attempts to answer the following question: For the purpose of comparing value, does it make any difference whether we assess acts according to their general utilities or tendencies rather than according to their simple utilities?In presenting his answer, Lyons first argues for causal linearity, then for utilitarian linearity, and finally for the extensional equivalence of non-comparative 2 pairs of simple and general utilitarian principles which are identical in all other respects.Since his equivalence argument depends upon considering the behaviour of others in deciding the utility of our own actions, he next argues that such considerations do not conflict in any way with the notion of general utilitarian relevance.He then completes his answer by extending his equivalence thesis to include pairs of corresponding simple and general comparative 2 utilitarian principles.In the next few pages, I will examine Lyon's arguments and show that the final step leading to the conclusion that corresponding pairs of comparative utilitarian principles are equivalent fails and that this conclusion is, in fact, false.I will also present a weaker equivalence result which Lyons' argument does establish.The notion of causal linearity which Lyons maintains is this: Let A be some act, E the effect of a single occurrence of A, and T the total effect of n occurrences of A. Then T = nxE expresses the condition of causal linearity and T ^nxE expresses the corresponding condition of causal nonlinearity.Analogous to this is the notion of utilitarian linearity: Let A be some act, S the utility of a single occurrence of A, and G the total utility of n occurrences of A. Then G = nxSexpresses the condition of utilitarian linearity and G •£ nxS the corresponding condition of utilitarian nonlinearity.Lyons holds that a complete description of actions, taking into account threshold-related effects, will always yield T= nxE, and a complete description of the relevant utilitarian properties of actions, taking into account threshold-related utilities, will always yield G = nxS.It is only when thresholds are considered in evaluating one side of the equation