Truth of a Statement in Physics and Mathematics Posted 21 hours ago · Edited 21 hours ago by Boydstun · Report reply SL, the case of contradiction statements, I'd say, needs to be worked into an account in this vicinity. We think of the statement "A is not-A" as referring to nothing (there are no A's that are also not-A's), but always false, and if false, I'd say it must be meaningful. That is, a statement assessable for truth or falsehood could be taken as a sufficient condition for the statement being a meaningful one. Contradiction statements would seem false and meaningful. In fact they are useful, and again that would suggest they have some kind of meaning. By useful, I'm thinking of their use in indirect proof in which we show a premise to be false given that when joined with premises we take for true we deduce a contradiction. Another aspect of contradiction possibly pertinent is that the conjunction between A and Not-A need not be supplied explicitly by the mind holding A true and holding Not-A true. The conjunction can be supplied merely by the fact that a mind holds both those things (and does not realize it, does not bring them together in mind).