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The Yablo ParadoxAn Essay on Circularity$
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Roy T Cook

Print publication date: 2014

Print ISBN-13: 9780199669608

Published to Oxford Scholarship Online: September 2014

DOI: 10.1093/acprof:oso/9780199669608.001.0001

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Origins and Mathematics

Origins and Mathematics

Chapter:
(p.11) 1 Origins and Mathematics
Source:
The Yablo Paradox
Author(s):

Roy T Cook

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199669608.003.0002

This chapter presents the origin, history, and mathematics of the Yablo paradox. Careful formulations of the paradox within both arithmetic and a pointer semantics-based language are presented, as well as a number of formal results and philosophical observations that will be critical in the chapters to follow (e.g. the fact that the Yablo paradox, formulated in Peano arithmetic with a truth predicate, is not inconsistent, but merely ω-inconsistent). This chapter also provides a partial solution to the Characterization Problem (for the pointer semantics language) and shows how this problem is equivalent to an outstanding problem in the theory of directed graphs— that of determining whether a directed graph has a kernel.

Keywords:   Yablo paradox, arithmetic, pointer semantics, truth, directed graphs

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