Part II, Chapter 20: Of the Conversion of Negative Propositions
SINCE it is impossible totally to separate two things, except the separation be mutual and reciprocal, it is clear that if I say, No man is a stone, I can say also that no stone is a man: for if any stone were a man, that man would be a stone; and, consequently, it would not be true that no man was a stone. And thus,
Negative universal propositions may be converted, by simply changing the attribute into the subject, and preserving to the attribute, when it has become the subject, the same universality which the first subject had; for the attribute, in negative universal propositions, is always taken universally, since it is denied according to the whole of its extension, as we have already shown above.
But for this very reason we cannot convert particular negative propositions;—we cannot say, for example, that some physician is not a man, because we said that some man is not a physician. This arises, as I said, from the very nature of the negation which we have just explained, which is, that in negative propositions the attribute is always taken universally, and according to the whole of its extension; so that, when a particular subject becomes the attribute, by conversion, in a particular negative proposition, it becomes universal, and changes its nature contrary to the rules of true conversion, which ought not to change the extension or limitation of the terms. Thus, in this proposition, Some man is not a physician, the term, man, is taken particularly; but in this false conversion, Some physician is not a man, the word man is taken universally. Now, because the quality of physician is separated from some man in this proposition, Some man is not a physician, and because the idea of triangle is separated from that of some figure in the other proposition, Some figure is not a triangle,—it by no means follows that there are physicians which are not men, and triangles which are not figures.