Recently, a literature has arisen around a novel semantic paradox, known as the v-Curry. Modeled after Curry’s paradox, we begin with the sentence “the inference from this sentence to absurdity is valid.” We assume that sentence, show that absurdity follows, and thus infer that the sentence is correct. Repeating the reasoning then allows us to prove an absurdity under no assumptions. What makes the v-Curry interesting is that it appears to generate a paradox with no appeal to the usual rules of logic, and so to force us to give up the more fundamental “structural” rules of logic. My project here is to argue that this appearance is misleading, and that the v-Curry is far less concerning than its proponents claim. The first two chapters tackle the initial claim that paradox can be generated without appeal to the usual rules of logic. In fact, the derivation presented to prove this is insufficiently careful with the Diagonal Lemma, and correcting for this mistake yields instances of a “substitution of identicals” step that could be objected to. Indeed, not only could these be objected to, there are respected, established theories (in particular, Contextualist theories) that would be committed to doing so. The third chapter then takes a more philosophical tack, arguing that there is actually nothing new or surprising about the v-Curry. Either it is simply a disguised restatement of Gödel’s Second Incompleteness Theorem, or it is simply packaging all of the most controversial behavior of the material conditional in semantic settings into the “is valid” construction. Either way, any philosophically sophisticated solution to semantic paradoxes will already be committed to saying something that resolves the v-Curry from the start. I conclude, then, that the lesson to be learned from the v-Curry is not that we should revise our logic, but that we should always emphasize keeping our formal resolutions to paradox philosophically grounded.
