De Morgan Augustus (1806–71), prolific British mathematician, logician, and philosopher of mathematics and logic. He is remembered chiefly for several lasting contributions to logic and philosophy of logic, including discovery and deployment of the concept of universe of discourse, the cofounding of relational logic, adaptation of what are now known as De Morgan’s laws, and several terminological innovations including the expression ‘mathematical induction’. His main logical works, the monograph Formal Logic (1847) and the series of articles ‘On the Syllogism’ (1846–62), demonstrate wide historical and philosophical learning, synoptic vision, penetrating originality, and disarming objectivity. His relational logic treated a wide variety of inferences involving propositions whose logical forms were significantly more complex than those treated in the traditional framework stemming from Aristotle, e.g. ‘If every doctor is a teacher, then every ancestor of a doctor is an ancestor of a teacher’. De Morgan’s conception of the infinite variety of logical forms of propositions vastly widens that of his predecessors and even that of his able contemporaries such as Boole, Hamilton, Mill, and Whately. De Morgan did as much as any of his contemporaries toward the creation of modern mathematical logic. See also DE MOR- GAN ‘ S LAWS , LOGICAL FORM , RELATIONAL LOGIC , UNIVERSE OF DISCOURS. J.Cor.