  Curry-completeness responses to Curry’s paradox hold that there are theories that are Curry-complete yet nontrivial; such a theory must violate one or more of the logical principles assumed in the Curry-Paradox Lemma. Since the rule Id has generally been left unquestioned (but see French 2016 and Nicolai &amp; Rossi forthcoming), this has meant denying that the conditional \({\rightarrow}\) of a nontrivial Curry-complete theory satisfies both MP and Cont. Accordingly, responses have fallen into two categories.