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The Liar Hypodox: A Truth-Teller’s Guide to Defusing Proofs of the Liar Paradox

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DOI: 10.4236/ojpp.2019.92011    240 Downloads   567 Views Citations

ABSTRACT

It seems that the Truth-teller is either true or false, but there is no accepted principle determining which it is. From this point of view, the Truth-teller is a hypodox. A hypodox is a conundrum like a paradox, but consistent. Sometimes, accepting an additional principle will convert a hypodox into a paradox. Conversely, in some cases, retracting or restricting a principle will convert a paradox to a hypodox. This last point suggests a new method of avoiding inconsistency. This article provides a significant example. The Liar paradox can be defused to a hypodox by relatively minimally restricting three principles: the T-schema, substitution of identicals and universal instantiation. These restrictions are not arbitrary. For each, I identify the source of a contradiction given some presumptions. Then I propose each restriction as a reasonable way to deal with that source of contradiction.

Cite this paper

Eldridge-Smith, P. (2019) The Liar Hypodox: A Truth-Teller’s Guide to Defusing Proofs of the Liar Paradox. Open Journal of Philosophy, 9, 152-171. doi: 10.4236/ojpp.2019.92011.

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