Holton (2017) observed that languages seem to lack ‘contrafactive’ attitudes which
presuppose that their complement proposition is false. This gap is surprising given the existence of factive predicates (know, regret), which presuppose the truth of their complement, and anti- veridical predicates (be wrong, be incorrect) which entail the falsity of their complement.

We propose that the absence of contrafactives is an instance of a more general phenomenon: the impossibility of predicates which denote false belief (FB; Bp ∧ ¬p). We argue that this generalization follows from a constraint on internal lexical coherence, namely that a lexical item’s backgrounded content must ‘support’ its at-issue content, either as an ontological precondition (Roberts & Simons 2022) or initiator of a causal chain (q.v. Goldman 1967). In our view, false belief is unlexicalizable because doxastic content of attitudes is always at-issue (Anand & Hacquard 2014), but a backgrounded ¬p cannot support the belief that p. We also show that many predicates that look like FB predicates on the surface, including be wrong, are not in fact bona fide examples of FB, and moreover do not violate our lexical constraint.

We then consider and reject plausible alternative proposals that the FB gap arises
because such meanings are not communicatively useful, either because they are systematically producible with scalar implicatures (cf. Horn 1989) or too uninformative (cf. Enguehard & Spector 2021).We conclude by suggesting that our constraint on the lexicon may help us understand why FB predicates are difficult to learn (Maldonado et al. 2022, Strohmaier & Wimmer 2022).