In this paper, we expose the idea that the meaning of linguistic units is not given before the utterance but it emerges from the interaction of the units with the context. We then reject the traditional approaches promoting the view that the meanings of words are listed in dictionaries. Consequently we assume that meaning, and more generaly linguistic categories are continuous as they emerge from multidimentional interactions in context. Now the question is: what is the nature of this continuity (continuum)? More specifically, what are the relations between this continuum / continuity and a multidimensional analysis ? Should a continuum be considered as a view on a phenomenom actually depending on a multiplicity of dimensions? We explore the notion of continuity focussing on linguistisc phenomenons like : (1) the nature of postverbs in English (e.g. ‘over’, ‘on’,…) and the question of the distinction between adverb, preposition, verb particle (Col and Poibeau 2013) and (2) the nature of complements and the arguments / adjuncts distinction in French and Japanese (Marchal et al 2013).