Note 138 — Chapter IV

The following is from Mansel’s Aldrich, p. 61,—“Conversion by contraposition, which is not employed by Aristotle, is given by Boethius in his first book, De Syllogismo Categorico. He is followed by Petrus Hispanus. It should be observed, that the old logicians, following Boethius, maintain that in conversion by contraposition, as well as in the others, the quality should remain unchanged. Consequently the converse of ‘All A is B’ is ‘All not-B is not-A,’ and of ‘Some A is not B,’ ‘Some not-B is not not-A.’ It is simpler, however, to convert A into E, and O into I, (‘No not-B is A,’ ‘Some not-B is A’), as is done by Wallis and Archbishop Whately; and before Boethius by Apuleius and Capella, who notice the conversion, but do not give it a name. The principle of this conversion may be found in Aristotle, Top. II. 8. 1, though he does not employ it for logical purposes.”