 The names ‘Aristotle’s Theses’ and ‘Boethius’ Theses’ are, of course, not arbitrarily chosen. As to AT, it is argued in Aristotle’s Prior Analytics 57b14 that it is impossible that if not-A, then A, see Łukasiewicz 1957, p. 50. Note, however, that Łukasiewicz and Kneale (1957, p. 66) maintain that Aristotle is making a mistake here. Moreover, Boethius has been said to hold in De Syllogismo Hypothetico 843D that ‘if A then not-B’ is the negation of ‘if A, then B’, (“he said that the negative of Si est A, est B was Si est A, non est B,” Kneale and Kneale 1962, p. 191). If we look at De Syllogismo Hypothetico 843C-D, we find: