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Consider the sentence C: “If this sentence is true, then David Ripley is a purple giraffe”. Suppose the sentence is true. Then the antecedent of the sentence (“this sentence is true”) is true. According to the inference rule *modus ponens*, if an if-then sentence (such as C) is true and its antecedent is true, then its consequent (“David Ripley is a purple giraffe”) must be true. It follows that *if* C is true, then David Ripley is a purple giraffe. But this conclusion *is* C: in other words, by simply *supposing* how things might turn out if C were true, we have proved that C, in fact, *is* true. So C is true, and since C’s antecedent is the claim that C is true, its antecedent is true as well. Now we can use *modus ponens* again to show that C’s consequent must be true. In other words, David Ripley really is a purple giraffe. QED.

This argument is Curry’s paradox. Obviously, the choice of “David Ripley is a purple giraffe” is arbitrary; a sentence of the form of “If this sentence is true, then X” can be used to prove *any* claim X. Now, in actual fact, David Ripley is not a purple giraffe, but a philosopher of language and logic. According to Ripley, solutions to paradoxes like Curry’s (as well as the Liar and the Sorites) fall into two broad categories: those that solve the paradoxes by messing with the meanings of important concepts (such as the meaning of “if-then”, truth, “not”, etc.) and those that solve them by changing the *structural rules* of inference by appeal to *substructural logics*.…