Utilitarianism opens by noting that philosophy has never settled the question of what makes actions right or wrong. Mill argues that the utilitarian answer, the Greatest Happiness Principle, has in fact shaped moral thinking across rival schools without being clearly acknowledged. His aim is to correct common misunderstandings and then offer such grounds for accepting the principle as the subject admits.
Chapter II defines the doctrine. Utility is not opposed to pleasure; it is pleasure itself and the absence of pain. Mill then introduces the crucial distinction between higher and lower pleasures. Those who are competently acquainted with both give a decided preference to the pleasures of the intellect, imagination, and moral feeling. The famous formulation follows: it is better to be a human being dissatisfied than a pig satisfied, better to be Socrates dissatisfied than a fool satisfied. Utilitarianism therefore requires cultivating nobleness of character, both because noble character makes others happier and because the standard is the greatest happiness of all, not of the individual agent alone.
Chapter III addresses motivation. The external sanctions of social approval, legal pressure, and the fear of God attach to utilitarian morality as readily as to any other. The deeper, internal sanction is conscience itself: the subjective pain that accompanies the violation of duty. Mill argues that the feeling of unity with other human beings, when fully cultivated through education, supplies all the motive force that utilitarian morality requires.
Chapter IV takes up proof. Ultimate ends cannot be demonstrated by direct argument, but they can be shown to be what people actually desire. Each person desires their own happiness; therefore the general happiness is desirable as a good to the aggregate of all persons. Mill further argues that other apparent ends (virtue, money, fame, power) are either already parts of happiness or have become so through association, so that nothing is ultimately desired except happiness.
Chapter V is the longest and addresses justice. Mill surveys the many things called just or unjust (respecting legal rights, meeting moral rights, giving desert, keeping faith, maintaining impartiality) and finds that what distinguishes justice from other moral duties is the presence of a right residing in an individual who can claim it. The sentiment of justice, he argues, is the natural impulse of self-defence and sympathy, widened by intelligence and sympathy to cover all persons. Justice is utility concentrated on the interest of security, the most vital of all interests, which is why the demand of justice feels absolute while ordinary calculations of expedience feel provisional.