Francez Colloquium

November 1
Cobb 201
University of Chicago
Scope and predicational structure in summative existentials

Existential sentences like (1) can be called summative, since they involve what Gendler-Szabo (2010) calls summative readings.

(1) There could be (only) three winners in the race (at this point).

On a prominent reading of (1), it is true iff there are (only) three people who might (at this point) win the race. This reading is summative in that it requires summing up the number of individuals who satisfy a condition (in this case, roughly, wins the race) across different possible worlds. This reading is straightforwardly captured by the logical form in (2):


However, no existing theory of existentials can produce this logical form from the syntactic structure it posits for the construction.

This talk describes why all existing theories fail to capture summative readings, and why they cannot be made to capture them using recently proposed mechanisms of scope-splitting (e.g. Abels and Marti 2010). It then proposes an analysis that does. The leading intuition of this analysis is that in summative existentials, pivots denote neither quantifiers (contra e.g. Barwise and Cooper 1981, Keenan 1987, Francez 2010) nor properties (contra McNally 1992), but rather are interpreted as individual concepts.