The self-contradictory and the inconceivable
THE law of contradiction, like any other logical law, may be interpreted in various ways. (1) It may be held that the relation of contradiction holds between objects; one object (or event or process) contradicts another object (event or process). The law of contradiction then states that nothing, physical or mental, is self-contradictory. On this interpretation the law of contradiction is stated thus: A cannot be both B and not-B at the same time (where 'A' and 'B' stand for any real thing, mental or physical). (2) Or, we may hold that the law of contradiction is a law of thought, not a law of things. On this interpretation, it is stated thus: A cannot be thought to be both B and not-B at the same time (where 'A' and 'B' stand for any real thing, mental or physical). (3) Or ,we may hold that the relation of contradiction holds neither between things nor between thoughts, but between sentences or propositions. It is only a sentence or proposition that can contradict another sentence or proposition. On this interpretation the law of contradiction is stated thus: NKpNp (where 'p' stands for a sentence or proposition). (4) Or, we may hold that the relation of contradiction holds neither between things, nor between thoughts, nor even between sentences or propositions. It is we who contradict ourselves. The law of contradiction, like any other logical law, is really a rule, an imperative, binding only on rational beings who want to think logically. The laws of logic thus "apply" only to performers who either obey or violate them.