The topic of this paper seems perhaps over-ambitious, touching as it does on several questions which have become serious theoretical issues over the last decades and some of them over several centuries. The controversy on the nature of grammatical categories has marked Philosophy and Linguistics throughout the twentieth century; the more modest controversy on aspect and its relationship to the disputed category Aktionsart, as well as its relationship to tense, has been dealt with in a vast amount of literature.
This short paper cannot provide a definitive answer; it has the more modest aim of showing
     a) that Greek aspect and Aktionsart form a continuum
     b) that the two categories remain nevertheless distinct
and thus hopefully contribute to the broader discussion on gradience, in particular intersective gradience, as defined by Aarts (2007).