According to the common conception of argument, the virtues of arguments turn, in part, on the virtues of assertion of their premises. I suggest that, on plausible Gricean assumptions about cooperative conversation, the common conception yields the claim that it is never appropriate to advance arguments in cooperative conversations. But that claim is absurd! Holding on to the Gricean assumptions, I reject the common conception of argument in favour of an alternative conception, on which all that matters, as far as premises go, for the virtue of arguments, is whether those premises belong to the arguments’ targets: interlocutors’ beliefs, theories, etc.