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Books > Science & Mathematics > Mathematics > Philosophy of mathematics
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The Yablo Paradox - An Essay on Circularity (Hardcover)
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The Yablo Paradox - An Essay on Circularity (Hardcover)
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Roy T Cook 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 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 we have the Characterization
Problem, which asks 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 draw interesting connections
between philosophical problems and purely mathematical ones. Next
is the Circularity Question, which addresses whether or not the
Yablo paradox is 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 circular 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, Cook turns his attention to 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? Cook argues that although
there are general constructions-unwindings-that transform circular
constructions into Yablo-like sequences, it turns out that these
sorts of constructions are not 'well-behaved' when transferred from
semantic puzzles to puzzles of other sorts. He concludes with a
short discussion of the connections between the Yablo paradox and
the Curry paradox.
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