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

Open Journal of Philosophy 9 (2):152-171 (2019)
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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.

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Peter Eldridge-Smith
Australian National University

Citations of this work

Can a dialetheist stay regular?Peter Eldridge-Smith & Jeremiah Joven Joaquin - 2024 - Journal of Applied Non-Classical Logics 35 (1):1-20.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The semantic conception of truth and the foundations of semantics.Alfred Tarski - 1943 - Philosophy and Phenomenological Research 4 (3):341-376.
The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Paradox without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251-252.
The ways of paradox.W. V. Quine - 1966 - New York,: Random.

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