The critique of logic, as it was taught on the British Isles, intensified at the beginning of the 19th century. A systematic critique of Aristotelian (syllogistic) logic was undertaken from the standpoint of common sense philosophy chiefly by Scottish philosophers, followers of T. Reid. E. Copleston of Oxford came to logic’s defense. His student, R. Whately, later wrote the textbook Elements of Logic (1826), in which he replied to the objections of Scottish philosophers. The textbook correctly explains that systems of deductive logic need not suffer from the petitio principii fallacy. J. S. Mill at first wrote a positive review of the textbook, but later published his System of Logic. In it, he puts forward the contrary view when evaluating the role of Aristotelian (deductive logic), objecting to the supposedly irredeemable fallacy of petitio principii. The fallacy can be avoided, he argues, in an inductive logic proposed by him. Mill’s objection to the Aristotelian syllogism was based on a misunderstanding of the analytic novelty of the knowledge contained in the conclusion of a valid argument. Mill’s explication of logic is contradictory, based on an associative psychologism and sensualism. The objection against deductive logic is simply mistaken. Mill’s logic and his positions were very critically appraised already by S. Jevons and the standard overviews of the history of logic fail to mention it.
Deductive logic, Inductive logic, J. S. Mill, Petitio principii, Syllogism