Gleanings in Dialectics

...and this is so whether it is taken in the matter of existence or in necessary matter. Whether in the possible, you will always find this: that the universal negative and the particular affirmative are simply converted with themselves—that is, the universal with the universal and the particular with the particular—and that which is of the transposed order corresponds in truth and falsity to that which is of the direct order. However, the universal affirmative or the particular negative do not have this in every matter, so that those which are of the direct order and the transposed order correspond to each other in truth and falsity. For example, if I say "Every man is an animal," it does not respond in truth to "Every animal is a man," which is why it is said that the affirmative universal is not simply converted with itself. In the same way, the particular negative is not found to be conformable in the transposed and direct order in truth and falsity; for if you say "Some man is not a grammarian," you will speak the truth, as is clear in this direct order, but not simply in the transposed order, "Some grammarian is not a man," since this is false. But only in two matters are these said to be simply converted with themselves, namely the universal affirmative and the particular negative: that is, in convertible matter and in entirely impossible matter. The universal, indeed, in convertible matter, so that it is simply true by converting: "Every man is a risible being," "Every risible being is a man," both are simply true. This simple conversion is thus, from the definition placed above; it is evident that the aforementioned universal is simply converted with itself. But the particular negative is simply converted with itself in this matter, so that it is similarly false, both that which is of the direct order and that which is of the transposed: "Some man is not a risible being" is false; in the same way, "Some risible being is not a man" is false. They have the opposite manner in respect to impossible matter, for the universal affirmative is simply converted with itself so that it is false in both orders, as "Every man is an ass," "Every ass is a man," both are false. But in the particular negative, both are similarly true: "Some man is not an ass," "Some ass is not a man." From this, it is clear how the opposites behave in these two matters, and both the universal affirmative and the particular negative in simply converting. From which the error of Paulus Venetus Paul of Venice (1369–1429), Italian philosopher and logician is manifest, who thought that the universal affirmative...