TITLE:
The Liar Hypodox: A Truth-Teller’s Guide to Defusing Proofs of the Liar Paradox
AUTHORS:
Peter Eldridge-Smith
KEYWORDS:
Liar paradox, Hypodox, Truth, T-Schema, Substitution of Identicals
JOURNAL NAME:
Open Journal of Philosophy,
Vol.9 No.2,
May
8,
2019
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.