He was awarded Sir Richard Jebb's prize for Greek literature, took first place in the philosophical classes of Professors Veitch and Caird, and won two scholarships.
For two years he was assistant to the professor of moral philosophy, studied in the theological faculty with the intention of entering the ministry, but apparently was not ordained.
In 1888, instead of returning to Scotland as originally intended, he was appointed lecturer in logic and mental philosophy at the University of Sydney, and was the first Challis professor of those subjects from the beginning of 1890.
Mr J. Perry, the minister of public instruction, immediately called a conference of inspectors and principal officers of his department and' in 1902, J. W. Turner and Sir George Handley Knibbs were appointed as commissioners to inquire into educational systems in Europe and America.
Anderson was the inaugural editor of the Australasian Journal of Psychology and Philosophy 1923–1926, and he also took a great deal of interest in the tutorial classes and Workers' Education Association movements.
Eventually two mural panels were painted for it by the artist Norman Carter, one representing Socrates, Plato, and Aristotle, the other Descartes, Bacon, and Spinoza.