Abstract

“Curry’s paradox”, as the term is used by philosophers today, refers to a wide variety of paradoxes of self-reference or circularity that trace their modern ancestry to Curry (1942b) and Löb (1955). The common characteristic of these so-called Curry paradoxes is the way they exploit a notion of implication, entailment or consequence, either in the form of a connective or in the form of a predicate. Curry’s paradox arises in a number of different domains. Like Russell’s paradox, it can take the form of a paradox of set theory or the theory of properties. But it can also take the form of a semantic paradox, closely akin to the Liar paradox. Curry’s paradox differs from both Russell’s paradox and the Liar paradox in that it doesn’t essentially involve the notion of negation. Common truth-theoretic versions involve a sentence that says of itself that if it is true then an arbitrarily chosen claim is true, or—to use a more sinister instance—says of itself that if it is true then every falsity is true. The paradox is that the existence of such a sentence appears to imply the truth of the arbitrarily chosen claim, or—in the more sinister instance—of every falsity. In this entry, we show how the various Curry paradoxes can be constructed, examine the space of available solutions, and explain some ways Curry’s paradox is significant and poses distinctive challenges.