Gleanings in Dialectics

In the superior figure, by the habit of propositions toward one another, everyone can easily see for themselves which are contrary, which are contradictory, which are sub-contrary, and which are subaltern. The nature of these figures has also been explained by Aristotle in the book Peri Hermeneias On Interpretation. One thing only do I think should be repeated at present, as it seems to contribute sufficiently to our purpose: if a universal is true, the particular will also be true, whether we speak in affirmation or negation. Based on this foundation, we first say of the contradictories that two of them—specifically the universal negative and the particular affirmative—are simply convertible with themselves in terms of in esse in essence/existence and in matters of necessity. However, the other two contradictories, the universal affirmative and the particular negative, are not at all simply convertible with themselves. Yet, through per accidens by accident/incidentally, the universal affirmative will be converted into a particular affirmative, and the particular negative will also be converted into a universal negative per accidens in some way, as will be declared below according to the mind of Boethius. Let us, therefore, first declare in what manner we understand simple conversion according to Boethius, first defining or describing what we understand by this name, which is called simple conversion. Simple conversion is, therefore, the changed order of terms without the determination quantification being changed. For example, if we say "No man is a stone," we make the predicate term the subject and the subject the predicate. In this way: "No stone is a man," with the determination not changed, as we see done here. For "no" is the universal sign, and in both cases, the determination of the subject is made, both when it is said "No man is a stone" and when it is converted "No stone is a man." Propositions are said to be converted simply if they are true or false in both the direct order and the transposed order, as when we say: "No man is a stone," which is true. With the order transposed, we also say what is true: "No stone is a man." In the same way, if you said what is false in the first order, you will not escape it by changing the order. For example, "No man is an animal" is false; also, that which is of the transposed order will be false, "No animal is a man." In a similar way, speak of the particular affirmative and...

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