Gleanings in Dialectics

...negative it is to be said that it is not necessary for it to be converted with itself, since sometimes it is converted, and sometimes not. But nevertheless, both will necessarily be converted per accidens to something that has been previously converted by itself. Now it will be clear how this is. We have said the universal negative is converted simply with itself. Let us also say now that this is converted per accidens to the particular negative from the presupposition that if the universal is true, the particular is also true. Therefore, let us convert this: "No man is a stone," saying "No stone is a man." Because "Some stone is not a man" follows from this, we say the first negation is converted per accidens into this particular in this figure: "No stone is a man," "No man is a stone," "Some man is not a stone." Do you see how conversion is understood here per accidens? Namely, that first a simple conversion is made; but secondly, with the particular subaltern accepted as converting with itself, per accidens conversion follows. However, the particular negative is not said to be converted per accidens in this sense, as if a universal follows from it. For if someone were to propose and say "Convert this: 'Some man is not a grammarian'," we will say, converting, "No grammarian is a man," making a per accidens conversion, or "Some grammarian is not a man," seeking to convert simply. But it is said to be converted per accidens insofar as it necessarily follows from a universal negative in the transposed order, not, however, so that it is the same in truth and falsity as the universal and the particular, such that a false particular negative follows from a false universal negative. As we said above in simple conversion, it is always found that it is not so in those cases. For a true particular negative can necessarily follow from a false universal by per accidens conversion, as is shown most clearly by this example: "No man is an animal," and "Some animal is not a man," where, as we said, the antecedent is false and the consequent is true. And through these, the error of the juniors and of Paulus can be made clear, who say that in per accidens conversion, sometimes the converted is true and the converter is false, and sometimes the opposite, the converter is true and the converted false. This saying can be conceded for the second part, but for the first part, it must be held as erroneous. For we do not say that this, "Some animal is not a man," has this as a per accidens converter: "No man is an animal." For a universal does not follow from a particular. Therefore, to understand this, we say the particular negative is per accidens...