In this paper, I argue that that polysemy is a two-sided phenomenon. It can be reduced neither to pragmatic modulation nor to ambiguity, for it is a mixture of both. The senses of a polysemous expression result from pragmatic modulation but they are stored in memory, as the senses of an ambiguous expression are. The difference with straightforward ambiguity is that the modulation relations between the senses are transparent to the language users: the senses are felt as related – they form a family of senses. In other words, whereas two homonymous expressions are different expressions, with the same phonological realization but distinct meanings, a polyseme is a single expression, i.e. a semantic as well as a phonological unit. It has one meaning, which should not be confused with the separate senses which it contributes in context. Different ways of thinking of that unitary meaning will be discussed, and consequences drawn for the debate between more or less radical versions of Contextualism.