This is a known transformation in logic, and is called conversion by contraposition, or negative conversion. But it is far from exhausting the solution we have obtained. Logicians have overlooked the fact, that when we convert the proposition All
s are (some)
s into All not-
s are (some) not-
s there is a relation between the two (somes), understood in the predicates. The equation (18) shews that whatever may be that condition which limits the