Note 140 — Chapter IV

In most text-books, no definition of contraposition is given at all, and it may be pointed out that, in the attempt to generalise from special examples, Jevons in his Elementary Lessons in Logic involves himself in difficulties. For the contrapositive of A he gives All not-P is not-S ; O he says has no contrapositive (but only a converse by negation, Some not-P is S); and for the contrapositive of E he gives No P is S. It is impossible to discover any definition of contraposition that can yield these results. Assuming that in contraposition the quality of the proposition is to remain unchanged as in Jevons’s contrapositive of A, then the contrapositive of both E and O is Some not-P is not not-S.