Innocent implicatures

•I defend the view that some implicatures do not involve maxim violations.•They are inferred when one infers speaker beliefs one doesn’t share.•I clarify Grice and Levinson's views to make room for such implicatures.•This includes a clarification of the maxim of Relation.•It also includes a clarified account of cases where maxims clash.

It seems to be a common and intuitively plausible assumption that conversational implicatures arise only when one of the so-called conversational maxims is violated at the level of what is said. The basic idea behind this thesis is that, unless a maxim is violated at the level of what is said, nothing can trigger the search for an implicature. Thus, non-violating implicatures wouldn’t be calculable. This paper defends the view that some conversational implicatures arise even though no conversational maxim is violated at the level of what is said.