Negation is common to all human languages. What explains its universality? Our hypothesis is that the emergence of expressions for denial, such as the word 'not', is an adaptation to existing conditions in the social and informational environment: a specific linguistic form was co-opted to express denial, given a preference for information sharing, the limits of a finite lexicon, and localized social repercussions against synonymy. In support of our hypothesis, we present a costly signalling model of communication. The model formalizes ordinary aspects of Stalnakerian conversations, implements the conditions we isolated for the emergence of denial, and computes their long-term consequences through a widely employed evolutionary dynamics, whose results are calculated by computer simulations. The model shows that, under a reasonable configuration of parameter values, functional pressure derived from conversational constraints favours the emergence of denial by means of a dedicated expression, such as the word 'not'.