Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Conversion is “a change of the extremes of a proposition, from subject to predicate and from predicate to subject, with quality and truth preserved,” that is, the copula remains affirmative or negative in both propositions, and each proposition is true.¹ One must always attend carefully to what is truly the subject and truly the predicate in propositions, so that these, and no others, are transposed. For example, if you say, “A head a man has,” “head” is not the subject but “man,” since it supplies the subject to the verb; therefore it should be converted as follows: “Therefore, one who has a head is a man.” And if you say, “A horse is required for riding,” it converts into “What is required for riding is a horse,” since “is required” is the predicate.

There are three kinds of conversion: simple or mutual; per accidens or non-mutual; and by contraposition, which is also mutual, but with respect to finite and infinite extremes. Simple conversion is that in which the predicate is changed into the subject while the same quantity is retained, as in “No man is a stone,” therefore “No stone is a man”; and “Some man is white,” therefore “Something white is a man.” Conversion per accidens, or to a particular, occurs when the predicate is changed into the subject without retaining the same quantity. Thus, “Every man is an animal” cannot be converted as “Therefore every animal is a man,” but as “Therefore some animal is a man.” Note that propositions which convert simply, if they are universal, can all the more be converted per accidens, since the particular is contained under the universal. Conversion by contraposition is a change of predicate into subject with the terms varied as finite and infinite. Thus, from “Every man is an animal,” it rightly follows, “Therefore every non-animal is a non-man”; and from “Some man is not white,” “Therefore what is non-white is not a non-man.” This conversion was devised to supply mutual conversion in cases that cannot be converted mutually in themselves. Strictly speaking, it is not a conversion of terms, because the same terms or extremes do not remain; rather, it is conversion according to sense, with terms changed from finite to infinite.

The rules of conversion are these. First: A universal negative proposition converts simply. Second: A particular affirmative proposition converts simply. Third: A universal affirmative proposition converts per accidens. A universal negative can also convert per accidens. Fourth: A universal affirmative and a particular negative convert by contraposition. We shall treat the foundation and proofs of these conversions in question 7, article 3.

To remember these rules, the four vowels A, E, I, O are used to signify these four propositions. A signifies a universal affirmative, E a universal negative, I a particular affirmative, and O a particular negative. A verse is formed that includes all the conversions:

FECI converts simply, EVA per accidens, ASTO by contraposition; thus the whole conversion is formed.

Here Feci indicates that a universal negative and a particular affirmative convert simply. Eva signifies that a universal negative can also convert per accidens, while a universal affirmative always converts per accidens. Asto signifies that a universal affirmative and a particular negative can convert by contraposition. Hence this verse for the letters:

A affirms, E denies; both are universal. I affirms, O denies; both are particular.