Following a brief preface, the second section of this paper discusses Mill's early reflections on the problem of how deductive inference can be illuminating. In the third section it is suggested that in his Logic Mill misconstrued the feature that the premises of a logically valid argument contain the conclusion as the ground of a charge that deductive proof is question-begging. The fourth section discusses the nature of the traditional petitio objection to syllogism, and the fifth shows that Mill had (...) a theory capable of answering it. The final section cites the confusion described in section 3 to explain why Mill nevertheless continued to think that syllogistic proofs beg the question. (shrink)