 What happens when a presupposition is false? The textbook proto-history of answers to this question goes as follows. According to Frege (1892), if an expression A suffers from presupposition failure, then any sentence containing A will lack a truth value; Russell (1905) famously denied this, holding that such a sentence will always be true or false; and then Strawson (1950) reaffirmed Frege’s position, more or less. What is less well known, at least insofar as it usually doesn’t make it into introductory classes on philosophy of language, is that in subsequent work, Strawson partly recanted his initial view and came to doubt that presupposition failure invariably entails lack of truth value.