The first edition of The Methods of Ethics, published in 1874, ended by admitting that its argument had failed at the last step. Its author, a lecturer at Trinity College, Cambridge, had set out in 1862 to reconcile the two camps of English moral philosophy, and twelve years later he had found that reason gave two answers to the question of what to do. One said: act for the greatest happiness of everyone, because from the point of view of the universe no one's good counts for more than anyone else's. The other said that it is reasonable for each person to put their own happiness first. Both seemed to him self-evident. When they collided, reason could not settle the case. Unless some moral order in the world made the two coincide, he concluded, duty fell apart into chaos. Later editions softened the tone and kept the conclusion, which philosophers now call the dualism of practical reason.
Henry Sidgwick came to ethics by way of a problem of honesty. He had been elected a fellow of Trinity in 1859, the year he graduated at the head of the classical list. In the 1860s he lost his hold on Anglican doctrine. He tried to settle the matter as a historian would: in 1862 he spent some weeks in Dresden beginning Arabic, and he worked at Arabic and Hebrew for a comparative study of the Semitic religions. Then he gave the research up, convinced it would not answer the fundamental questions. His fellowship required assent to the Thirty-Nine Articles, the doctrinal statement of the Church of England. In October 1869 he resigned it. His colleagues let him keep his lectureship, and his example strengthened the campaign that ended such tests in the Universities Tests Act of 1871. By his own account, the struggle over assenting to the Articles led him back to philosophy, and much of the thinking later set out in the Methods was done while he wrestled with it.
The book's method came from the same scruple. Sidgwick took the rules ordinary decent people live by — tell the truth, keep promises, be just — and examined them one at a time. Wherever they turned vague or contradicted each other, he found, people settled the case by asking what would do the most good. Two schools had been treated as enemies: the intuitionists, who held that conscience simply sees what is right, and the utilitarians who followed Jeremy Bentham and John Stuart Mill. On his showing, careful intuition leads to utilitarianism. Only the case for self-interest refused to be absorbed. In a late chapter he went further: a utilitarian might rightly do in private what it would be wrong to advocate in public, and even this permission might best be kept from the many. Plain moral sense, he conceded, rejects the very idea of such a private morality.
He looked outside the study for what would make duty and self-interest coincide. Eleanor Balfour, whom he married in 1876, did scientific work with her brother-in-law, the physicist Lord Rayleigh; with her he helped found the Society for Psychical Research in 1882, and he was twice its president. The Sidgwicks hoped to find evidence that a person survives death, which they took to be an essential support of morality. The evidence never came, and near the end of his life he judged the work largely a waste of time, though he allowed that it had yielded some positive results. His other public cause was the education of women. In 1871 he rented a house, at his own risk, for women attending lectures in Cambridge, and that house was the beginning of Newnham College.
F. H. Bradley, the Oxford idealist, attacked the book's main argument in a pamphlet in 1877. Sidgwick became Knightbridge Professor of Moral Philosophy at Cambridge in 1883 and was re-elected to his Trinity fellowship in 1885. He died of cancer on 28 August 1900. In 1930 the Cambridge philosopher C. D. Broad judged the Methods the best treatise on moral theory ever written. John Rawls, the Harvard political philosopher, introduced its 1981 reprint as the clearest statement of classical utilitarianism, and in 2014 the utilitarian philosophers Katarzyna de Lazari-Radek and Peter Singer took one of its phrases as the title of The Point of View of the Universe, a book arguing that the deadlock between the two answers can be broken in utilitarianism's favour. Whether it can is still disputed.