According to several late medieval logicians, the use the universal quantifier ‘omnis’ creates the requirement that the sentence refers to at least three items—the principle of sufficientia appellatorum. The commitment is such that, when the quota is not fulfilled, one has to import the missing items from the realm of the nonexistent. While the central argument for this principle, whose origin is Aristotle’s De Caelo, stems from the contrast between unrestricted universal quantifiers and binary quantifiers, the discussion is often mixed (...) with another issue, concerning the requirement of a plurality of referents for universals. In this paper, we try to distinguish those different issues and map the reactions of xiii th authors to the principle of sufficientia appellatorum. (shrink)