It only remains to say something of the two forms in which a hedonistic doctrine is commonly held—Egoism and Utilitarianism. (§ 58 ¶ 1)

Egoism, as a form of Hedonism, is the doctrine which holds that we ought each of us to pursue our own greatest happiness as our ultimate end. The doctrine will, of course, admit that sometimes the best means to this end will be to give pleasure to others; we shall, for instance, by so doing, procure for ourselves the pleasures of sympathy, of freedom from interference, and of self-esteem; and these pleasures, which we may procure by sometimes aiming directly at the happiness of other persons, may be greater than any we could otherwise get. Egoism in this sense must therefore be carefully distinguished from Egoism in another sense, the sense in which Altruism is its proper opposite. Egoism, as commonly opposed to Altruism, is apt to denote merely selfishness. In this sense, a man is an egoist, if all his actions are actually directed towards gaining pleasure for himself; whether he holds that he ought to act so, because he will thereby obtain for himself the greatest possible happiness on the whole, or not. Egoism may accordingly be used to denote the theory that we should always aim at getting pleasure for ourselves, because that is the best means to the ultimate end, whether the ultimate end be our own greatest pleasure or not. Altruism, on the other hand, may denote the theory that we ought always to aim at other people’s happiness, on the ground that this is the best means of securing our own as well as theirs. Accordingly, an Egoist, in the sense in which I am now going to talk of Egoism, an Egoist, who holds that his own greatest happiness is the ultimate end, may at the same time be an Altruist: he may hold that he ought to love his neighbour, as the best means to being happy himself. And conversely an Egoist, in the other sense, may at the same time be a Utilitarian. He may hold that he ought always to direct his efforts towards getting pleasure for himself on the ground that he is thereby most likely to increase the general sum of happiness. (§ 58 ¶ 2)