The “Principle of Utility” is that happiness is desirable, and the only thing desirable, as an end; all other things being only desirable as means to that end. In Chapter 4 of Utilitarianism, Mill addresses himself to the question: “Of What Sort of Proof the Principle of Utility Is Susceptible.” In Chapter 1, Mill has explained that “this cannot be proof in the ordinary and popular meaning of the term. Questions of ultimate ends are not amenable to direct proof. Whatever can be proved to be good, must be so by being shown to be a means to something admitted to be good without proof.” If “it is asserted that there is a comprehensive formula, including all things which are in themselves good,” the formula “is not subject of what is commonly understood by proof …” (208 [I, 5]). But he then goes on to say, “We are not, however, to infer that its acceptance or rejection must depend on blind impulse or arbitrary choice. … The subject is within the cognizance of the rational faculty; and neither does that faculty deal with it solely in the way of intuition. Considerations may be capable of determining the intellect either to give or withhold its assent to the doctrine, and this is equivalent to proof” (208 [I, 5]).

The twelve paragraphs of Chapter 4 present an argument that, if successful, is one of the most important arguments in all of moral philosophy, for it would establish hedonism, in the broad meaning that Mill attaches to pleasure, as the valuational foundation for all of life and for morality as a part of that.