Arithmetic and goodness

Abstract

The idea of a sum (or even average) of pleasure or value occurs in a number of philosophical discussions, But it has been challenged, and it seems to lead to paradoxical conclusions. Rashdall defended it by citing cases where it clearly applied; but it turns out hard to assign quantities to values without being arbitrary. It is argued here that we can only ‘do sums’ where like is being compared with like. In other cases, we begin by judging which of two possible states of affairs would be the better, and only then are in a position to speak (if we choose) of sums of goodness. The implications of this for certain forms of utilitarianism and theodicy are briefly considered.