Under certain conditions, existential sentences have readings that are not predicted and cannot be modeled, given common assumptions about the construction. For example, the sentence There could be three outcomes to this election is normally taken to express that three things could be the outcome of the election, not that it is possible that the election will have three outcomes. This article proposes the first analysis of such “summative” readings of existentials, premised on a novel semantics for cardinal determiners as counting the values of an individual concept across indices. The analysis is shown to predict the observed descriptive generalizations about summative existentials, including the highly restricted circumstances that give rise to them. The unorthodox semantics proposed for cardinals is argued to be independently motivated.