Negation as Maximal Distance in Discourse Space Theory

Abstract

This paper proposes that natural-language negation is best understood as a discourse phenomenon. It is also proposed that discourse can be treated in a geometrical rather than a propositional framework. This perhaps surprising notion is based on the prevalence of metaphorically spatial meanings in language and in the description of language. In this context, standard geometry is a natural tool. In particular, Discourse Space Theory (DST) uses a vector space of three dimensions, one of which is epistemically modal and incorporates counterfactuality as a location distal to the speaker or subject, who is located at the deictic centre, i.e. the origin of the coordinate system. Counterfactual concepts are interpreted in this model as the distal point on a modal scale. It is then shown how this model can efficiently represent and integrate a variety of well known types of negation. An implied affirmative ‘background’ can be included in a simple fashion. Within the sentence, constituent negation is easy to handle in terms of the location of referents in the abstract discourse space. The inaccessibility of anaphoric antecedents in negated clauses is also implicitly accounted for in the geometric approach. Strikingly, the DST geometry can provide an elegant representation of the relationship between negated and non-negated counterfactual sentences. Finally, the capacity of DST to deal with a classic problem concerning presupposition is outlined. It is suggested, in conclusion, that these examples demonstrate the validity and potential of this framework, which applies simple coordinate geometry to the abstract concepts of ‘space’ that underlie many linguistically encoded concepts