There are but two ways in which the proposition, No Xs are Ys, can be understood. 1st, In the sense of All Xs are not-Y. 2nd, In the sense of It is not true that any Xs are Ys, i.e. the proposition ``Some Xs are Ys'' is false. The former of these is a single categorical proposition. The latter is an assertion respecting a proposition, and its expression belongs to a distinct part of the elective system. It appears to me that it is the latter sense, which is really adopted by those who refer the negative, not, to the copula. To refer it to the predicate is not a useless refinement, but a necessary step, in order to make the proposition truly a relation between classes. I believe it will be found that this step is really taken in the attempts to demonstrate the Aristotelian rules of distribution.

The transposition of the negative is a very common feature of language. Habit renders us almost insensible to it in our own language, but when in another language the same principle is differently exhibited, as in the Greek,   for , it claims attention.