Gleanings in Dialectics

It is also clear what was stated, because no syllogistic form is reduced to another by transposing a non-exclusive universal. But for this, simple conversion and per accidens conversion were invented, so that one syllogistic form might be reduced to another. Paulus, however, is forced to concede the aforementioned consequence because of a bad definition. The conversion of an indefinite affirmative proposition is understood to be simple in every matter in the same way as was said of the particular; but the indefinite negative is not simple, but also in the two aforementioned matters. Concerning the singular affirmative or negative, however, I say that among Aristotle in the first book of the Prior Analytics and among Boethius in the aforementioned place, no mention is made of what conversion it is converted by. But we can say that the singular affirmative is not simply converted, as if the determination were always placed on the subject. For if I said "Something is an animal, Socrates," by converting I would not say "Some Socrates is an animal," but "Socrates is something of an animal," as is clear by reducing Dabitis a mnemonic for a type of syllogism to Darii a mnemonic for a type of syllogism with the minor premise accepted as singular. Conversion can be said to be simple in that no part of the terms is cast away, nor the determination itself. But this will have to be seen by us further in the exposition of the first book of the Prior Analytics. A singular negative is also said to be converted simply, since it behaves similarly in every matter, both in the direct order and in the transposed, namely in truth and falsity, as "Socrates is not white," "The white is not Socrates," and similarly in other matters. Why Aristotle omitted this, we shall say in the first book of the Prior Analytics. Let these suffice for the present concerning simple conversion. Now we must speak of the conversion which Boethius calls per accidens, for which it is assumed that which we took from the beginning, namely: if a universal is true, a particular will necessarily be true. Therefore, so that a perfect knowledge of this may be had, one must begin thus. Just as it is necessary that the universal negative is simply converted with itself, and the particular affirmative, as is demonstrated in the first book of the Prior Analytics, so let us say that the universal affirmative is not necessarily converted with itself in terms, because sometimes it is converted, as has been shown, and sometimes not, as has also been shown. Similarly, concerning the particular...