The Yablo Paradox

Abstract

Abstract This book examines the Yablo paradox—a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others later than it in the sequence—with special attention paid to the idea that this paradox provides us with an example of a semantic paradox that involves no circularity. The three main chapters of the book focus, respectively, on three questions that can be (and have been) asked about the Yablo construction. First, the Characterization Problem: What patterns of sentential reference (circular or not) generate semantic paradoxes? Addressing this problem requires an interesting and fruitful detour through the theory of directed graphs, allowing us to make connections between philosophical problems and purely mathematical ones. Next is the Circularity Question: Is the Yablo paradox genuinely non-circular? Answering this question is complicated: although the original formulation of the Yablo paradox is circular, it turns out that it is not so in any sense that can bear the blame for the paradox. Further, formulations of the paradox using infinitary conjunction provide genuinely non-circular constructions. Finally, we have the Generalizability Question: Can the Yabloesque pattern be used to generate genuinely non-circular variants of other paradoxes, such as epistemic and set-theoretic paradoxes? Although there are general constructions—unwindings—that transform circular constructions into Yablo-like sequences, it turns out that these sorts of construction are not “well-behaved” when transferred from semantic puzzles to puzzles of other sorts. The text concludes with a short discussion of the connections between the Yablo paradox and the Curry paradox.