Two visits to Germany in 1817 and 1820 led to William's taking up the study of German and later on that of contemporary German philosophy, which was almost entirely neglected in British universities. In 1820 he was a candidate for the chair of moral philosophy in the University of Edinburgh, which had fallen vacant on the death of Thomas Brown, colleague of Dugald Stewart, and Stewart's consequent resignation, but was defeated on political grounds by John Wilson, (1785-1854), the "Christopher North" of Blackwood's Magazine. Soon afterwards (1821) he was appointed professor of civil history, and as such delivered several courses of lectures on the history of modern Europe and the history of literature. The salary was £100 a year, derived from a local beer tax, and was discontinued after a time. No pupils were compelled to attend, the class dwindled, and Hamilton gave it up when the salary ceased. In January 1827 his mother, to whom he had been devoted, died. In March 1828 he married his cousin, Janet Marshall.
In 1829 his career of authorship began with the appearance of the well-known essay on the "Philosophy of the Unconditioned" (a critique of Auguste Comte's Cours de philosophie)--the first of a series of articles contributed by him to the Edinburgh Review. He was elected in 1836 to the Edinburgh chair of logic and metaphysics, and from this time dates the influence which, during the next twenty years, he exerted over the thought of the younger generation in Scotland. Much about the same time he began the preparation of an annotated edition of Thomas Reid's works, intending to annex to it a number of dissertations. Before, however, this design had been carried out, he was struck (1844) with paralysis of the right side, which seriously crippled his bodily powers, though it left his mind wholly unimpaired.
The edition of Reid appeared in 1846, but with only seven of the intended dissertations, one unfinished. At his death he had still not completed the work; notes on the subjects to be discussed were found among his manuscripts. Considerably earlier, he had formed his theory of logic, the leading principles of which were indicated in the prospectus of "an essay on a new analytic of logical forms" prefixed to his edition of Reid. But the elaboration of the scheme in its details and applications continued during the next few years to occupy much of his leisure. Out of this arose a sharp controversy with Augustus de Morgan. The essay did not appear, but the results of the labour gone through are contained in the appendices to his Lectures on Logic.
Hamilton also prepared extensive materials for a publication which he designed on the personal history, influence and opinions of Martin Luther. Here he advanced so far as to have planned and partly carried out the arrangement of the work; but it did not go further, and still remains in manuscript. In 1852-1853 appeared the first and second editions of his Discussions in Philosophy, Literature and Education, a reprint, with large additions, of his contributions to the Edinburgh Review. Soon after, his general health began to fail. Assisted by his devoted wife, he persevered in literary labour; and during 1854-1855 he brought out nine volumes of a new edition of Stewart's works. The only remaining volume was to have contained a memoir of Stewart, but this he did not live to write. He taught his class for the last time in the winter of 1855-1856. Shortly after the close of the session he was taken ill, and died in Edinburgh.
Hamilton's positive contribution to the progress of thought is comparatively slight, but he stimulated a spirit of criticism in his pupils, by insisting on the great importance of psychology as opposed to the older metaphysical method, and by his recognition of the importance of German philosophy, especially that of Immanuel Kant. By far his most important work was "Philosophy of the Unconditioned," the development of the principle that for the human finite mind there can be no knowledge of the Infinite. The basis of his argument is the thesis, "To think is to condition." Deeply impressed with Kant's antithesis between subject and object, the knowing and the known, Hamilton laid down the principle that every object is known only in virtue of its relations to other objects. From this it follows limitless time, space, power and so forth are humanly speaking inconceivable. The fact, however, that all thought seems to demand the idea of the infinite or absolute provides a sphere for faith, which is thus the specific faculty of theology. It is a weakness characteristic of the human mind that it cannot conceive any phenomenon without a beginning: hence the conception of the causal relation, according to which every phenomenon has its cause in preceding phenomena, and its effect in subsequent phenomena. The causal concept is, therefore, only one of the ordinary necessary forms of the cognitive consciousness limited, as we have seen, by being confined to that which is relative or conditioned.
As regards the problem of the nature of objectivity, Hamilton simply accepts the evidence of consciousness as to the separate existence of the object: "the root of our nature cannot be a lie." In virtue of this assumption Hamilton's philosophy becomes a "natural realism." In fact his whole position is a strange compound of Kant and Reid. Its chief practical corollary is the denial of philosophy as a method of attaining absolute knowledge and its relegation to the academic sphere of mental training. The transition from philosophy to theology, i.e. to the sphere of faith, is presented by Hamilton under the analogous relation between the mind and the body. As the mind is to the body, so is the unconditioned Absolute or God to the world of the conditioned. Consciousness, itself a conditioned phenomenon, must derive from or depend on some different thing prior to or behind material phenomena. Curiously enough, however, Hamilton does not explain how it comes about that God, who in the terms of the analogy bears to the conditioned mind the relation which the conditioned mind bears to its objects, can Himself be unconditioned. He can be regarded only as related to consciousness, and insofar is, therefore, not absolute or unconditioned. Thus the very principles of Hamilton's philosophy are apparently violated in his theological argument.
Hamilton regarded logic as a purely formal science; it seemed to him an unscientific mixing together of heterogeneous elements to treat as parts of the same science the formal and the material conditions of knowledge. He was quite ready to allow that on this view logic cannot be used as a means of discovering or guaranteeing facts, even the most general, and expressly asserted that it has to do, not with the objective validity, but only with the mutual relations, of judgments. He further held that induction and deduction are correlative processes of formal logic, each resting on the necessities of thought and deriving thence its several laws. The only logical laws which he recognized were the three axioms of identity, noncontradiction, and excluded middle, which he regarded as severally phases of one general condition of the possibility of existence and, therefore, of thought. The law of reason and consequent he considered not as different, but merely as expressing metaphysically what these express logically. He added as a postulate--which in his theory was of importance--"that logic be allowed to state explicitly what is thought implicitly." in logic, Hamilton is known chiefly as the inventor of the doctrine of the "quantification of the predicate," i.e. that the judgment "All A is B " should really mean "All A is all B," whereas the ordinary universal proposition should be stated "All A is some B." This view, which was supported by Stanley Jevons, is fundamentally at fault since it implies that the predicate is thought of in its extension; in point of fact when a judgment is made, e.g. about men, that they are mortal ("All men are mortal"), the intention is to attribute a quality (i.e. the predicate is used in connotation). In other words, we are not considering the question "what kind are men among the various things which must die?" (as is implied in the form "all men are some mortals") but "what is the fact about men?" We are not stating a mere identity (see further, e.g., H. W. B. Joseph, Introduction to Logic, 1906, pp. 198 foll.).
The philosopher to whom above all others Hamilton professed allegiance was Aristotle. His works were the object of his profound and constant study, and supplied in fact the mould in which his whole philosophy was cast. With the commentators on the Aristotelian writings, ancient, medieval and modern, he was also familiar; and the scholastic philosophy he studied with care and appreciation at a time when it had hardly yet begun to attract attention in his country. His wide reading enabled him to trace many a doctrine to the writings of forgotten thinkers; and nothing gave him greater pleasure than to draw forth such from their obscurity, and to give due acknowledgment, even if it chanced to be of the prior possession of a view or argument that he had thought out for himself. Of modern German philosophy he was a diligent, if not always a sympathetic, student. How profoundly his thinking was modified by that of Kant is evident from the tenor of his speculations; nor was this less the case because, on fundamental points, he came to widely different conclusions.
Hamilton was more than a philosopher; his knowledge and interests embraced all subjects related to that of the human mind. He studied anatomy and physiology. He was also well-read in ancient and modern literature, being particularly interested in the 16th and 17th centuries. Among his literary projects were editions of the works of George Buchanan and Julius Caesar Scaliger. His general scholarship found expression in his library, which became part of the library of the University of Glasgow.
He also may have had influence upon subsequent philosophy in a somewhat negative way, as the inspiration for a critique by John Stuart Mill which resulted in perhaps the clearest statements ever of the idea of matter as the permanent possibility of sensation.
His chief practical interest was in education--an interest which he manifested alike as a teacher and as a writer, and which had led him long before he was either to a study of the subject both theoretical and historical. He thence adopted views as to the ends and methods of education that, when afterwards carried out or advocated by him, met with general recognition; but he also expressed in one of his articles an unfavourable view of the study of mathematics as a mental gymnastic, which excited much opposition, but which he never saw reason to alter. As a teacher, he was zealous and successful, and his writings on university organization and reform had, at the time of their appearance, a decisive practical effect, and contain much that is of permanent value.
His posthumous works are his Lectures on Metaphysics and Logic, 4 vols., edited by HL Mansel, Oxford, and John Veitch (Metaphysics; Logic); and Additional Notes to Reid's Works, from Sir W. Hamilton's Manuscripts., under the editorship of HL Mansel, D.D. (1862). A Memoir of Sir W. Hamilton, by Veitch, appeared in 1869.