Universa Philosophia

Conversion is a necessary consequence of one proposition to another from the transposition of terms, that is, by changing the subject into the predicate and the predicate into the subject; and it occurs in three ways. First, simply, by the mere transposition of terms, with the same quality and quantity preserved: thus the universal negative and the particular affirmative are converted, as nullus homo est lapis, therefore nullus lapis est homo. Likewise aliquis homo est albus, therefore aliquod album est homo. The reason a priori, because the terms thus converted are altogether really the same in both propositions, and from one term to another really the same the consequence holds, as if some man is white, then some white thing is a man, because a white man is some white thing.

Secondly, conversion occurs per accidens in a universal negative and a universal affirmative, when the extremes are changed while the quality remains, but the quantity is changed, as omnis homo est animal, therefore aliquod animal est homo. Likewise nullus homo est albus: therefore aliquod album non est homo, because if no man is white, then no white thing is a man, otherwise some man would be white; but if no white thing is a man, then some white thing is not a man. The reason is that, the identity of man with white being denied, the identity of white with man is denied, because it is the same; but if it is denied of every white thing, the same is denied of some white thing, indeed contained under every one.

Thirdly, it occurs by contraposition in a universal affirmative and a particular negative, by the addition of certain negations, as omnis homo est animal, therefore omne non animal est non homo, because if it is not an animal, it is not a man, who is an animal, and it cannot be an animal and a non-animal. Likewise it is converted by this: therefore aliquod animal non est non homo, which is equivalent to this, aliquod animal est homo. Likewise aliquis homo non est lapis, therefore aliquod non lapis non est homo. Here the word non is taken infinitantly, signifying something which is not a man. Likewise note that in this third conversion constancy must be added, that is, the existence of the thing must be posited; for example, omnis homo est ens, if it is converted by this, therefore omne non ens est non homo, is false: because a non-being, although it is not a man, is nevertheless not a non-man, because to be a non-man says to be something which is not a man; but a non-being is not something, taking is and something properly. But in the negative there ought to be constancy in the subject of the converted proposition, as if you say Antichristus non est bonus, if it is converted by this, therefore aliquod non bonum est non Antichristus, this is false, because at present there are some non-good things which nevertheless are not Antichrist; but if the word Antichristus had the constancy of existing, the proposition would be true: for then some non-good thing, namely Antichrist himself, would not be non-Antichrist, that is, would be Antichrist himself. Finally, the identity of the terms of the converted proposition and of the converting one must be attended to; for which it will be worthwhile to know equipollence, whence a proposition cannot be converted by another which has terms really distinct from its own, because the consequence is not from one thing to a distinct thing, but to the same, as from man to rational is a consequence, but not to non-man. But there are many trifles of boys here; but the force of negations must be attended to.

The whole of conversion is closed by these verses.

Asserit A, negat E, sunt universaliter ambae.
Asserit I, negat O, sunt particulariter ambae.

That is, the letter A signifies a universal affirmative proposition, E a universal negative, I a particular affirmative, O a particular negative; take therefore the two verses.

Simpliciter feci, convertitur Eva per acci.
Asto per contra, sic fit conversio tota.

That is, simply are converted the universal negative and the particular affirmative signified by this word feci. Per accidens are converted the universal negative and the universal affirmative signified by this word Eva; by contraposition, however, the universal affirmative and the particular negative signified by this word asto.

The definition is converted simply with the defined, as animal rationale with man, and this animal rationale with this man. Likewise a proposition with a singular subject and predicate, as Petrus est hoc album, ergo hoc album est Petrus. You ask, how is this Petrus est homo converted? For it seems to be converted per accidens, as ergo aliquis homo est Petrus, where the quantity of the proposition is changed. Someone will answer that every proposition in which a universal is affirmed of its inferior is converted simply, because the universal is then predicated confusedly: for this Petrus est homo is equivalent to this, Petrus est aliquis homo, because homo is said confusedly of Peter: which proposition is of the same quantity as this, Petrus est homo. On the contrary, because this proposition omnis homo est animal is converted per accidens thus, aliquod animal est homo, therefore similarly the proposition of the argument, because omnis homo est animal is equivalent to this, est aliquod animal. The reason is that the quantity of a proposition is taken from the subject, but the subject of this, Petrus est homo, is of a different quantity from this aliquis homo est Petrus, because the one is singular, the other particular confused; whence that proposition is converted per accidens.