 To spell out the sense in which Curry’s paradox constrains theories we need to say what a Curry sentence is. Informally, a Curry sentence is a sentence that is equivalent, by the lights of some theory, to a conditional with itself as antecedent. For example, one might think of the argument of  section 1.1  as appealing to an informal theory of truth. Then the sentence “\(k\) is true” serves as a Curry sentence for that theory. That is because, given what our informal theory tells us about what \(k\)’s truth involves, “\(k\) is true” should be equivalent to “If \(k\) is true, then time is infinite” (since this conditional is \(k\) itself).