Having graduated MA in 1917, he lectured at the University College of South Wales and Monmouthshire (Cardiff) (1917-19), the University of Glasgow (1919-20) and at the University of Edinburgh (1920-26).
but, by about 1932 he began to realise, perhaps before most of his contemporaries, that communism under Stalin in the Soviet Union was a dictatorship with no room for workers' control or participation. He then became aligned with the Trotskyist movement for a period of time.Anderson later abandoned authoritarian forms of socialism and became what would today be called a libertarian and pluralist--an opponent of all forms of authoritarianism. Sometimes he described himself as an anarchist but, after the 1930s, he gave up his earlier political utopianism.
Anderson was censured by the Sydney University Senate in 1931 after criticising the role of war memorials in sanctifying war. In 1943 he was censured by the Parliament of New South Wales after arguing that religion has no place in schools. He founded the Sydney University Freethought Society which ran from 1931 to 1951. He was president of the society throughout that period.
It is legendary that the university's Senate, accepting that it could not realise its desire to sack the controversial Challis Professor, sought to reduce Anderson's stature and influence by creating a new chair of "Moral and Political Philosophy" to which Alan K. Stout was appointed. This tactic misfired when Stout immediately recognised Anderson's genius, became one of his steadiest admirers and declined to undercut his prestige in any way. The result was that Sydney gained a second prestigious and personable philosopher.
He is, arguably, the most important philosopher who has worked in Australia. Certainly he was the most important in both the breadth and depth of influence. Among the philosophers who got their original intellectual formation from Anderson are John Passmore, John Mackie, A.J. (‘Jim’) Baker, David Stove and myself. There are lots more. But for every student who became a philosopher there were far, far, more in the law, in medicine, in journalism, in other academic disciplines, that were profoundly influenced by him. I am inclined to think that, especially in the thirties and forties of the last century, Anderson was the person who set the agenda, and set the tone, for intellectual discussion in Sydney. - David Armstrong (2005)
As a committed empiricist, Anderson argued that there is only one realm of "being" and it can be best understood through science and naturalistic philosophy. He asserted that there is no supernatural god and that there are no non-natural realms along the lines of Platonic ideals. He rejected all notions that knowledge could be obtained by means other than descriptions of facts and any belief that revelation or mysticism could be sources for obtaining truth. He was arguing that traditional christian concepts of good and evil were only meant for slaves and that, in actuality, the idea of morality was empty. For Anderson, the term "good" was valid when applied objectively to human activities which were free, critical and creative but the more common subjective applications were to be avoided or exposed as deceptive. not surprisingly, Anderson's influence was both extensive and controversial as he constantly examined and fearlessly criticized hallowed beliefs and institutions.
In the latter years of his career, the 1950s, Anderson exhibited more conservative views, although A.J. Baker generously interprets his 1950s stage not so much as "a definite change in his overall thinking than ... an alteration of emphasis and interest. To many, though, it seemed that Anderson was departing from his pluralism. During the 1949 coal miners' strike, for instance, he supported the government's action in using troops as strikebreakers. At a Freethought Society meeting in August 1950 he refused to oppose conscription for the war in Korea. In 1951 he refused to allow students to use the Freethought Society to canvass the 'No' case for Menzies' attempt to ban the Communist Party in the referendum of that year. This was the last straw for many Freethinkers; Anderson's apparent authoritarianism caused most to abandon the Freethought Society and to establish the Libertarian Society. The Freethought Society held its last meeting in 1951, while the Libertarian Society functioned from 1952 to 1969.
Anderson broke off contact with the former disciples who formed the Libertarian Society and never associated with "Push" people who routinely sang his praises along with the bawdy songs he had imported to his new country . However, even after retirement in 1958 and to the brink of his death in 1962, he was seen daily in his study, continuing his work and reviewing earlier work. Among his last publications were Classicism (1960), Empiricism and Logic (1962) and Relational Arguments (1962)
(ISBN 9781920898625) 
(ISBN 1920898174)