Stewart was born on 4 May 1878, in Scotland, to Alexander Stewart (died February 1920) and his wife Lillias Stewart (
née McKellar). They moved to Australia in 1852 and operated a farm at
Ballangeich, Victoria, Stewart was employed as trainee teacher at Warrnambool State School, then taught at
Charlton then
Benalla. He entered
Ormond College,
University of Melbourne, where he graduated in philosophy in 1906 with first class honours, winning the
Hastie Scholarship in Logic and Philosophy, in 1920 Stewart was appointed associate professor of philosophy, a post created for him, then in 1922 was offered the
Hughes Professorship in Philosophy on the recommendation of
Professor Mitchell, the outgoing incumbent, and was appointed the following year. He was appointed deputy vice-chancellor in 1943 and vice-chancellor in 1945, maintaining his academic duties, the last person to combine the two roles. He retired as vice-chancellor in 1948, but remained professor of philosophy until his retirement in 1950, and was made
professor emeritus by the University Council. Other positions he held at Adelaide University at various times included chairman of the University Public Examinations Board and chairman of the university joint committee for tutorial classes. He was foundation chairman of the Students' Union (1926). ==Other activities==