Mill's proof of the principle of utility

Ethics 110 (2):282-310 (2000)
Abstract
Utilitarianism is a “consequentialist” doctrine: that actions are right or wrong in proportion as they produce good or bad consequences. Mill’s version is also a “hedonistic” doctrine. Consequences are good insofar as they have more happiness or less unhappiness; bad, as they have more unhap- piness or less happiness; and by happiness and unhappiness, Mill means pleasure and pain. In English, the words “happiness” and “unhappiness” do not have the same connotations as “pleasure” and “pain.” “Happiness” implies feeling good about one’s life as well as feeling good. “Happiness” is found in relationships with friends and loved ones and in a sense of accomplishment. “Pleasure” seems to be something that is momentary and more sensational. But according to Mill’s psy- chology, a happy life consists in many pleasures and few pains. The happiness of relationships with friends and loved ones is reducible to the joys and satisfactions in the moments of one’s life that arise from these relationships. The happiness of a sense of accomplishment consists of the pleasurable states of consciousness that arise from a sense of accomplishment. The happiness of self-respect and the unhap- piness of self-disrespect consist of the pleasurable and painful states of conscious- ness that these involve. This reduction of happiness and unhappiness to pleasures and pains is a controversial element in Mill’s philosophy. I leave it to the reader to think about that reduction. In what follows, it will be assumed
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