Does every proposition have a unique contradictory?
Maxwell J. Cresswell · Analysis · 2008
If you think that a proposition can have more than one contradictory, or can have none, then you need read no further. What I will show is that if ... ... It is not obvious that this must be so. If p1 and p2 are distinct but logically equivalent, it might appear that their contradictories, q1 and q2, should also be distinct though logically equivalent. ... In traditional logic, a pair of propositions which satisfy (3)(i) alone are called contraries, and a pair which satisfy (3)(ii) alone are called sub-contraries.2 The relation of contradictoriness defined by (3) is clearly symmetrical: ... Let p1 and p2 be two propositions which are logically equivalent, and assume (1). Then p1 has a contradictory, q. We first show that ... ... ...