Part II, Chapter 18: Of the Conversion of Affirmative Propositions
WE call the conversion of a proposition the changing of the subject into the attribute, and of the attribute into the subject, without affecting the truth of the proposition, or rather, so that it necessarily follows from the conversion that it is true, supposing that it was so before.
Now, by what we have just said, it will be easily understood how this conversion must be effected, for as it is impossible that one thing can be joined to another, without that other thing being also joined to the first, and that it follows very clearly that if A is joined to B, B is joined to A, it is clearly impossible that two things can be conceived as identified, which is the most perfect of all unions, unless that union be reciprocal,—that is to say, that we be able mutually to affirm the two united terms, in the manner in which they are united, which is called conversion.
Thus, as in particular affirmative propositions, e. g., when we say some man is just, the subject and the attribute are both particular—the subject, man, being particular by the mark of particularity which is added to it—and the attribute, just, being so also, inasmuch as its extension being restricted by that of the subject, signifies only the justice which is in some man, it is evident that if some man is identified with some just, some just is also identified with some man, and that thus we need only change the attribute into the subject, preserving the same particularity, in order to convert such propositions.
The same thing cannot be said of universal affirmative propositions, because in these propositions the subject alone is universal, that is to say, taken according to its whole extension. The attribute, on the contrary, being limited and restrained, and consequently, when we make it the subject by conversion, it must preserve the same restriction, and have added to it a mark which determines it, that it may not be taken generally. Thus, when I say that man is an animal, I unite the idea of man with that of animal, restraining and confining it to men alone. Therefore, when I wish to look at that union under another aspect, beginning with animal, and then affirming man, it is necessary to preserve to this term the same restriction, and in order that no mistake may be made, add to it some mark of determination.
So that, since universal affirmative propositions can only be converted into particular affirmatives, we ought not to conclude that they are converted less properly than the others, whereas they are made up of a general subject and a restricted attribute, it is clear that when they are converted by changing the attribute into the subject, they ought to have a subject restricted and confined, that is to say, particular: whence we obtain these two rules.
Rule 1
The universal affirmative propositions may be converted by adding a mark of particularity to the attribute when changed into the subject.
Rule 2
Particular affirmative propositions are to be converted without any additional change, that is to say, by retaining for the attribute, when changed into the subject, the mark of particularity which belonged to the first subject. But it is easily perceived that these two rules may be reduced to one, which includes them both.
The attribute being restrained by the subject in all affirmative propositions, if we wish to change it to the subject, we must preserve that restriction and give it a mark of particularity, whether the first subject were universal or particular.
Nevertheless, it often happens that universal affirmative propositions may be converted into other universals. But this happens exclusively, when the attribute is not in itself of wider extension than the subject, as when we affirm the difference, or the property of the species, or the definition of the thing defined; for, then, the attribute not being restricted, may be taken as generally in conversion as the subject was—all man is rational; all rational is man.
But these conversions, being true only under particular circumstances, are not reckoned true conversions, which ought to be certain and infallible, by the simple transposition of the terms.