Alexander was born at 436 George Street, in what is now the commercial heart of Sydney, Australia. He was the third son of Samuel Alexander, a prosperous saddler, and Eliza née Sloman. Both parents were Jewish. His father died just before he was born, and Eliza moved to Victoria in 1863 or 1864. They went to live at St Kilda, and Alexander was placed at a private school kept by a Mr Atkinson.

In 1871, he was sent to Wesley College, Melbourne, then under the headmastership of Professor Irving and was always grateful for the efficiency and comprehensiveness of his schooling. He matriculated at the University of Melbourne on 22 March 1875 to do arts. He was placed in the first class in both his first and second years, was awarded the classical and mathematical exhibitions (top of year) in his first year. In his second year won the exhibitions in Greek, Latin and English, mathematics and natural philosophy; and natural science.

England

In May 1877, Alexander left for England in an attempt to win a scholarship, arriving at the end of August. Undecided whether to go to Oxford or Cambridge he chose Oxford and sat for a scholarship at Balliol College. Among the competition were George Curzon and J. W. Mackail. Though his tutor thought little of his chances Alexander achieved second place after Mackail and gained a scholarship.

At Oxford, he obtained a first class in Classical and Mathematical Moderations, a rare achievement, and a first class in Greats, his final examination for the degree of B.A., in 1881. Two of his tutors were Thomas Hill Green and Henry Nettleship, who exercised a great influence on his early work.

After taking his degree, Alexander was made a Fellow of Lincoln College, where he remained as philosophy tutor from 1882 to 1893. It was during this period that he developed his interest in psychology, then a neglected subject. In 1887, he won the Green moral philosophy prize with an essay on the subject "In what direction does Moral Philosophy seem to you to admit or require advance?" This was the basis of his volume Moral Order and Progress, which was published in 1889 and went into its third edition in 1899.

By 1912, however, Alexander had altered his views to some extent and considered that the book had served its purpose, had become dated, and should be allowed to die. During the period of his fellowship at Lincoln, he had also contributed articles on philosophical subjects to Mind, the Proceedings of the Aristotelian Society, and the International Journal of Ethics. He did some travelling on the continent, and in the winter of 1890-1 was in Germany working at the psychological laboratory of Professor Hugo Münsterberg at Freiburg. Among his colleagues at Lincoln was Walter Baldwin Spencer.

For some time, Alexander had wanted to obtain a professorship. He made three unsuccessful attempts before he was appointed at the University of Manchester in 1893, remaining there for the rest of his life. There, he quickly became a leading figure in the University. Unconventional in his attire and his manner of conducting his classes, there was something in him that drew students and colleagues alike to him. He wrote little, and his growing deafness made it difficult for him to get much out of philosophical discussions, though he could manage conversation.

An important change in his home life occurred in 1902 when the whole of his family — his mother, an aunt, two elder brothers and his sister came from Australia to live with him. This in some families would have been a dangerous experiment, but it worked well in Alexander's case. His sister became a most efficient hostess and on Wednesday evenings fellow members of the staff, former pupils, a few advanced students and others would drop in and spend a memorable evening. His home at that time was at 6 Mauldeth Road West in Withington (from 1904 in the City of Manchester).

He was given the Hon. LL.D. of St Andrews in 1905, and in later years he received Hon. Litt. D. degrees from Durham, Liverpool, Oxford and Cambridge. In 1908, he published Locke, a short but excellent study, which was included in the Philosophies Ancient and Modern Series. He was president of the Aristotelian Society from 1908—1911 and from 1936—1937. In 1913, was made a fellow of the British Academy. He was appointed Gifford lecturer at Glasgow in 1915, and delivered his lectures in the winters of 1917 and 1918. These he developed into his great work Space, Time, and Deity, published in two volumes in 1920, which his biographer has called the "boldest adventure in detailed speculative metaphysics attempted in so grand a manner by any English writer between 1655 and 1920." That its conclusions should be universally accepted was scarcely to be expected, but it was widely and well reviewed, and made a great impression on philosophic thinkers at the time and for many years after. His Arthur Davis Memorial Lecture on Spinoza and Time was published in 1921, and in 1924 Alexander retired from his chair.

Semi-retirement

Before he retired, Alexander had longed for leisure, but it was impossible for him to be idle. He continued to give short courses and single lectures in connection with the extramural department, he graded examinations for higher degrees and also did some reviewing. He retained until 1930 the office of presenter for honorary degrees. His short orations when presenting were models of grace and skill. He remained on many committees, always ready to give them the benefit of his help and wisdom. Alexander kept up his interest in the British Academy and the British Institute of Philosophy, as well as in Jewish communities in England and Palestine.

Honours

In 1925, he was honoured by the presentation of his bust by Epstein to the university of Manchester, where it was placed in the centre of the hall of the arts building, which is named after him. He was Herbert Spencer lecturer at Oxford in 1927, and in 1930, amid congratulations from all over the country, the Order of Merit was conferred on him, the first to an Australian-born.

In 1933, he published Beauty and other Forms of Value, mainly an essay in aesthetics, which incorporated passages from papers that had appeared in the previous 10 years. Some of the earlier parts of the book were deliberately meant to be provocative, and Alexander had hoped that artists of distinction in various mediums might be tempted to say how they worked. He had, however, not reckoned with the difficulty most artists find in explaining their methods of work and the response was comparatively meagre.

Death and legacy

He was greatly troubled by the sufferings of the Jews in Europe and gave much of his time and money in helping to alleviate them. Early in 1938, he realized that his end was approaching and he died on 13 September 1938. He was unmarried and his ashes lie in Manchester Southern cemetery (British Jewish Reform Congregation section).

His will was proved at about £16,000 of which £1,000 went to the university of Jerusalem and the bulk of the remainder to the university of Manchester. In 1939, his Philosophical and Literary Pieces was published with a memoir by his literary executor, Professor John Laird. This volume included papers on literary subjects, as well as philosophical lectures, several of which had been published separately.

When lecturing, Alexander could be quite informal, at times dropping into a kind of conversation with his class, and would follow a side track if it looked promising. He did not always give the impression that he was much interested in teaching, yet he was a great teacher whose influence was widespread. He was one of the greatest speculative thinkers of his time.

A theatre at Monash University, Melbourne, is named for him and a cast of his bust by Epstein stands in its foyer.

The building formerly known as 'Humanities Lime Grove' at the University of Manchester was renamed the 'Samuel Alexander Building' in 2007. It was given Grade II listed building status by English Heritage on 12 Feb 2010. As in Melbourne, a cast of his bust by Epstein stands in its foyer.

Two key concepts for Alexander are those of an "emergent quality" and the idea of emergent evolution:

His task, as in any metaphysical theory, was to account for every aspect of existing reality in the simplest and most economical basis. Alexander's idea was to start with space and time, each of which he regarded as inconceivable without the other, in fact mutually equivalent. Out of this, pure spacetime emerges, through a process Alexander describes simply as "motion", the stuff and matter that make up our material world:

Alexander absolutizes spacetime, and even speaks of it as a "stuff" of which things are made. At the same time he also says that spacetime can be called "Motions" — not motion in the singular, but complexes of motions with kaleidoscopic changes within a continuum. So one might say that for Alexander motion is primitive, and space and time are defined through relations between motions.

Alexander asked the question:

The question went largely unanswered and his work is mostly ignored (or, at best, little known) these days.

Alexander was a contemporary of Alfred North Whitehead, whom he influenced, and mentored others who went on to become major figures in 20th century British philosophy.