ABSTRACT
This chapter describes the traditional oppositions by an unsymmetrical figure, since the symmetry of a square is ill-adapted to represent unsymmetrical relations. One proposition is incompatible with another if they cannot be true together, but propositions may be compatible without being so related that it is possible either to infer the one from the other, or to infer from the truth or falsity of the one that the other is true or false. Since the traditional Logicians confined their attention to the fourfold schedule, they were content to recognize only four relations and they failed accordingly to distinguish between superimplication and subimplication. Singular propositions of the form Socrates is wise cannot properly be regarded as falling under the figure of opposition. Since the obverse gives a proposition with the contradictory of the original predicate, contraposition is obtained by converting the obvert of the original. The universal propositions deny existence; the particular propositions affirm existence.
