After a short residence at Heidelberg (1871), where he began his study of German philosophy, he returned to Edinburgh as assistant first to Henry Calderwood and later to A. Campbell Fraser; he joined the staff of the Encyclopædia Britannica (9th edition) (1874) and studied widely in the Advocates' Library.

In 1876 he came to England as successor to W. S. Jevons in the chair of logic and philosophy, at Owens College, Manchester. In 1883 he received the honorary degree of LL.D. In 1893 he went to the University of Aberdeen, and finally in 1895 to the chair of logic at the University of Glasgow, which he held till his death.

His wife, Margaret Duncan, the daughter of a Manchester merchant, was a woman of kindred tastes, and their union was entirely happy.

It is matter for regret to the student that Adamson's active labors in the lecture room precluded him from systematic production. His writings consisted of short articles, of which many appeared in the Encyclopaedia and in Mind, a volume on Kant and another on Fichte. At the time of his death he was writing a History of Psychology, and had promised a work on Kant and the Modern Naturalists. Both in his life and in his writings he was remarkable for impartiality. It was his peculiar virtue that he could quote his opponents without warping their meaning. From this point of view he would have been perhaps the first historian of philosophy of his time, had his professional labors been less exacting.

Except during the first few years at Manchester, he delivered his lectures without manuscripts. In 1903, under the title The Development of Modern Philosophy and Other Essays, his more important lectures were published with a short biographical introduction by W. R. Sorley of Cambridge University (see Mind, xiii. 1904, p. 73 foil.). Most of the matter is taken verbatim from the note-book of one of his students. Under the same editorship there appeared, three years later, his Development of Greek Philosophy.

In addition to his professional work, he did much administrative work for Victoria University and the university of Glasgow. In the organization of Victoria University he took a foremost part, and, as chairman of the Board of Studies at Owens College, he presided over the general academical board of the Victoria University. At Glasgow he was soon elected one of the representatives on the court, and to him were due in large measure the extension of the academical session and the improved equipment of the university.

Throughout his lectures, Adamson pursued the critical and historical method without formulating a constructive theory of his own. He felt that any philosophical advance must be based on the Kantian methods. It was his habit to make straight for the ultimate issue, disregarding half-truths and declining compromise. He left a hypothesis to be worked out by others; this done, he would criticize with all the rigour of logic, and with a profound distrust of imagination, metaphor and the attitude known as the will-to-believe.

As he grew older his metaphysical optimism waned. He felt that the increase of knowledge must come in the domains of physical science. But this empirical tendency as regards science never modified his metaphysical outlook. He has been called Kantian and Neo-Kantian, Realist and Idealist (by himself, for he held that appearance and reality are co-extensive and coincident).

At the same time, in his criticism of other views he was almost typical of Hegelian idealism. All processes of reasoning or judgment (i.e. all units of thought) are (i) analysable only by abstraction, and (2) are compound of deduction and induction, i.e. rational and empirical. An illustration of his empirical tendency is found in his attitude to the Absolute and the Self. The " Absolute " doctrines he regarded as a mere disguise of failure, a dishonest attempt to clothe ignorance in the pretentious garb of mystery. The Self as a primary, determining entity, he would not therefore admit. He represented an empiricism which, so far from refuting, was actually based on, idealism, and yet was alert to expose the fallacies of a particular idealist construction (see his essay in Ethical Democracy, edited by Stanton Coit).

Described in the Cambridge History of Modern Literature (XIV,48) as "the most learned of contemporary philosophers." He was an outspoken \Agnostic and a Utilitarian in ethics. In the symposium Ethical Democracy (1900) he says that even the most pretentious proofs of the existence of God are "intellectually unrepresentable" and that "the world conquered Christianity" instead of the other way about.