Although he was now the Professor of Mathematics at Edinburgh, his interests were firmly in philosophy and he also taught moral philosophy at Edinburgh during session 1778-79 while Adam Ferguson was in America. Stewart taught mathematics at Edinburgh for 13 years until Adam Ferguson resigned in 1785 when he was appointed to the philosophy chair and resigned from the chair of mathematics.
Kahit na siya ay ngayon ang Propesor ng Matematika sa Edinburgh, Matatag ang kanyang interes sa pilosopiya at siya rin nagtuturo moral pilosopiya at Edinburgh sa panahon ng session 1778-79 habang Adam Ferguson ay sa America. Stewart tinuturuan matematika at Edinburgh para sa 13 taon hanggang Adam Ferguson-ayon sa 1785 kapag siya ay hihirangin upang angkinin ang pilosopiya silya at kalooban mula sa silya ng matematika.