 Expanding on parts of Grice’s celebrated argument (Grice 1989: 44–46), suppose one would propose to analyze or in such a way that not only (25a) would logically follow from  (25)  but also (25b) and/or (25c). A major problem for such a strong analysis of or is that it would fail to account for the fact that both the exclusive and the ignorance inferences are easily cancellable. One can say Mary invited John or Bill or both (cancellation of exclusive inference), or The prize is either in the attic or in the garden. I know that because I know where I put it, but I am not going to tell you (cancellation of ignorance-modal inference, from Grice 1989: 45). A strong theorist could then respond that there are two senses of or, a strong one and a weak (truth-functional) one, with the latter employed in the previous cases of cancelation. But as Grice replied, 