ABSTRACT
Propositions whose contradictories are self-contradictory have sometimes been called 'necessary truths', sometimes 'a priori propositions', sometimes tautologies. It is sometimes held that the sense in which such propositions can be certain, and therefore also the sense in which they can be 'known to be true', must be different from the sense in which contingent propositions are sometimes 'certain' and 'known to be true'. Some philosophers have in fact suggested that no contingent proposition is ever, as a matter of fact, known to be true. It might be said that some people have had dream-images which were exactly like sensory experiences which they had when they were awake. And then it may be said: If it is logically possible for some dream-images to be exactly like sensory experiences which are not dream-images, surely it must be logically possible for all the dream-images occurring in a dream at a given time to be exactly like sensory experiences which are not dream-images.
