 An argument establishing that a particular formal theory is trivial will pose a problem if either of the following is the case: (i) we wish to use the formal theory in our inquiries, as we use set theory when doing mathematics, or (ii) we wish to use the formal theory in order to model features of language or thought, in particular the claims to which some speakers or thinkers are committed. Either way, the target theory’s triviality would show that it is inadequate for its intended purpose. So this is a second challenge posed by Curry’s paradox.