Projection variation: Is the family of sentences really a family?

Under the ‘family of sentences’ diagnostic for projection, the projection of content is investigated by embedding the expression that contributes the content in the scope of negation, polar questions, epistemic possibility modals, and conditional antecedents. This paper reports on the results of a set of experiments designed to investigate whether there is variation in the projection of content from under these four types of entailment-canceling operators. The contents investigated are the contents of the complements of 20 English clause-embedding predicates. The results of the experiments suggest (i) that the by-operator variation is small when aggregating over the 20 contents, but (ii) that the effect of operator differs between the clause-embedding predicates. The results of these experiments also extend a result of Degen and Tonhauser 2022, that projection ratings in polar questions do not categorically distinguish factive from non-factive predicates, to cases with negation, the epistemic possibility modal 'perhaps', and conditional antecedents. The observed by-predicate and by-operator variation is not captured by existing theoretical accounts of projection (e.g., Heim 1983, van der Sandt 1992, Abrusán 2011, Schlenker 2021). Our results suggest that an empirically adequate projection analysis must consider interactions between predicates and operators.