We investigate whether the factive presuppositions associated with some clause-embedding predicates are fundamentally discrete in nature—as classically assumed—or fundamentally gradient—consistent with recent proposals that projection is gradient in general (e.g., the Gradient Projection Principle of Tonhauser et al. (Journal of Semantics 35(3):495–542, 2018)). To carry out this investigation, we develop statistical models of presupposition projection that implement these two hypotheses, fit these models to existing inference judgment data aimed at measuring projection (Degen and Tonhauser (Open Mind 5:59–70, 2021)), and compare the models’ fits to the data using standard statistical model comparison metrics. We find that models implementing the hypothesis that presupposition projection is fundamentally discrete fit the data better than models implementing the hypothesis that it is fundamentally gradient. To evaluate the robustness of this finding, we collect three additional datasets: a replication of the original dataset, as well as two datasets that modify the methodology of the original. Across the three datasets, we again find that models implementing the hypothesis that presuppositions are discrete fit the data better than models implementing the hypothesis that they are gradient. We argue that these results favor an account according to which factive presuppositions are fundamentally discrete in nature, and we discuss how this discreteness might be understood within classical semantic accounts of factive predicates, as well as accounts of presupposition projection that tie it to the question under discussion (QUD).
