I don’t know if naturalness ratings distinguish presuppositions from nonpresuppositions: Did Mandelkern et al. 2020 discover that they do?

Presuppositions have long been taken to be a well-defined class of content that is characterized by typically projecting and by being conventionally associated with particular lexical items or constructions (e.g., Beaver et al., 2024; Heim, 1983; Mandelkern et al., 2020; van der Sandt, 1992). While the strength of the projection inference is often taken to distinguish presuppositions from nonpresuppositions, experimental investigations that used inference tasks suggested that the strength of the projection inference does not distinguish the two (e.g., de Marneffe et al., 2019; Degen & Tonhauser, 2022; Tonhauser et al., 2018; White & Rawlins, 2018). Mandelkern et al. (2020) proposed that a different measure, namely comparison of naturalness ratings in explicit ignorance and support contexts, distinguishes presuppositions from nonpresuppositions. This paper presents the results of an experiment designed to investigate Mandelkern et al.’s (2020) proposal in the domain of factive and nonfactive clause-embedding predicates. The results do not support Mandelkern et al.’s (2020) proposal, which means that the question of whether presuppositional projection inferences can be distinguished from nonpresuppositional ones is still open.