Robert Adamson was born in Edinburgh on 19 January 1852, the son of a solicitor. He was educated at Daniel Stewart's Hospital, Edinburgh, and entered Edinburgh University in November 1866. In 1871 he graduated with first class honours in philosophy and won a scholarship for being best student in his subject. Adamson spent a short time in Heidelberg, and then became assistant to Henry Calderwood, professor of moral philosophy at Edinburgh, and from 1872 to1874 served in the same office to A. Campbell Fraser, professor of logic and metaphysics.
In 1874 he joined the staff of the Encyclopaedia Britannica , to which he contributed a large number of articles on general literature and philosophical topics. In 1876 Adamson was appointed professor of philosophy and political economy at Owens College, Manchester in succession to W.S.Jevons. In 1882 he relinquished his teaching duties in economics to concentrate on philosophy. Adamson was responsible for a great extension of teaching of philosophy, especially after the creation of the Victoria University in 1880, which gave him freedom to plan courses in line with his own views.
Adamson was active in the foundation and running of the Victoria University, acting as temporary registrar, and as secretary, then chairman of the board of studies. He was a strong supporter for the admission of women to the University on equal terms with men, and he also helped establish a department for training teachers at Owens.
In 1893 Adamson was appointed to the chair of logic at Aberdeen, and in 1895 he moved to Glasgow as professor of logic and rhetoric. At various times he acted as examiner to the universities of Edinburgh, Cambridge, London and Wales. Adamson married Margaret Duncan in 1881, the daughter of a Manchester merchant. They had six children. Adamson died of enteric fever on 5 February 1902. In his memory the University of Manchester established the Adamson Lecture. His library was donated to the University in 1904.
Adamson was initially a prolific writer, but his output diminished as the burden of his academic duties grew. His earliest philosophical sympathies were with idealism, but difficulties in devising a coherent interpretation of reality on these lines led to a growing identification with philosophical realism or naturalism. The outlines of Adamson's theory of knowledge were presented in his posthumously published Modern Philosophy , though his theories were not fully worked out at the time of his death. Adamson had a particular interest in the history of philosophy, with which he critically developed his own views on philosophical questions. Adamson was praised for his exact learning, and for the impartiality and clarity of his thinking.
Adamson was the author of several works including: Roger Bacon: the philosophy of science in the middle ages (Manchester 1876); On the Philosophy of Kant , Shaw Fellowship Lectures 1879, (Edinburgh 1879); Fichte , (Edinburgh 1881); The Development of Modern Philosophy, with other lectures and essays ed. by W.S Sorley, 2 volumes, (Edinburgh 1903); The Development of Greek Philosophy ed. by W S Sorley and R P Hardie, (Edinburgh 1908); and A Short History of Logic ed. by W R Sorley, (Edinburgh 1911).