Recent research in semantics and pragmatics has revived the debate about whether there are two cognitively distinct categories of conversational implicatures: generalised and particularised. Generalised conversational implicatures are so-called because they seem to arise more or less independently of contextual support. Particularised implicatures are more context-bound. The Default view is that generalised implicatures are default inferences and that their computation is relatively autonomous--being computed by some default mechanism and only being open to cancellation at a second stage when contextual assumptions are taken into consideration (Chierchia, 2004; Horn, 1984; Levinson, 2000 i.a.). It is at that second stage where contextual assumptions are considered that "particularised" implications are computed. By contrast, Context-Driven theorists claim that both generalised and particularised implicatures are generated by the same process and only where there is contextual support (Carston, 1998; Sperber & Wilson, 1986 i.a.). In this paper, we present three on-line studies of the prototypical cases of generalised implicatures: the "scalar implicatures" "some of the Fs" greater than "not all the Fs" and "X or Y" greater than "either X or Y but not both." These studies were designed to test the context-dependence and autonomy of the implicatures. Our results suggest that these scalar implicatures are dependent on the conversational context and that they show none of the autonomy predicted by the Default view. We conclude with a discussion of the degree to which such implicatures are purely context-driven and whether an interactionist default position may also be plausible.