H. P. Grice, "Pragmatic contradiction as a contradictio in terminis"

pragmatic contradiction, a contradiction that is generated by pragmatic rather than logical implication. A logically implies B if it is impossible for B to be false if A is true, whereas A pragmatically implies B if in most (but not necessarily all) contexts, saying ‘A’ can reasonably be taken as indicating that B is true. Thus, if I say, “It’s raining,” what I say does not logically imply that I believe that it is raining, since it is possible for it to be raining without my believing it is. Nor does my saying that it is raining logically imply that I believe that it is, since it is possible for me to say this without believing it. But my saying this does pragmatically imply that I believe that it is raining, since normally my saying this can reasonably be taken to indicate that I believe it. Accordingly, if I were to say, “It’s raining but I don’t believe that it’s raining,” the result would be a pragmatic contradiction. The first part (“It’s raining”) does not logically imply the negation of the second part (“I don’t believe that it’s raining”) but my saying the first part does pragmatically imply the negation of the second part.