Author(s)

Peter Eldridge-Smith

Philosophy, Research School of the Social Sciences, Australian National University, Canberra, Australia.

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.

Liar paradox, Hypodox, Truth, T-Schema, Substitution of Identicals

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.