Is it true that all conversational implicatures are cancellable? In some recent works (Weiner Analysis 66(2):127–130, 2004, followed by Blome-Tillmann Analysis 68(2):156–160, 2008 and, most recently, by Hazlett 2012), the property of cancellability that, according to Grice (1989), conversational implicatures must possess has been called into question. The aim of this article is to show that the cases on which Weiner builds his argument—the Train Case and the Sex Pistols Case— do not really suffice to endanger Grice’s Cancellability Hypothesis. What (...) Weiner has shown with his examples is that a conversational implicature cannot be cancelled if the speaker, whose utterance gives rise to the implicature, does not intend to cancel it. To implicate is an intentional speech act and, therefore, cancelling an implicature must also be intentional and must be performed by the same speaker whose utterance gives rise to the putative implicature. (shrink)