Restricting the T‐schema to Solve the Liar

Philosophy and Phenomenological Research (forthcoming)
  Copy   BIBTEX


If we want to retain classical logic and standard syntax in light of the liar, we are forced to restrict the T-schema. The traditional philosophical justification for this is sentential – liar sentences somehow malfunction. But the standard formal way of implementing this is conditional, our T-sentences tell us that if “p” does not malfunction, then “p” is true if and only if p. Recently Bacon and others have pointed out that conditional T-restrictions like this flirt with incoherence. If we want to keep the “malfunction” motivation, our only other option is to non-conditionally restrict the T-schema, but Field and others have given powerful philosophical and technical arguments against this kind of approach. Here I argue that if we really take the philosophical motivation for restricting T-sentences seriously, we can explain why conditional restrictions fail, answer Field's argument, and reason in a coherent way about truth using a non-conditional restriction strategy. This cracks the door open for a fully classical response to the liar and related paradoxes. In closing, I argue that, when properly understood, this kind of “restriction” is not really a restriction at all. If this is right, then the holy grail of liar studies (classical logic, naïve truth, and standard syntax) may yet be attainable. (Note for readers: when this paper was first put online, the typesetters had changed some instances of corners to brackets, leading to confusion. The paper has now been corrected online by PPR, so please make sure you have the corrected version before reading or citing.)



    Upload a copy of this work     Papers currently archived: 80,001

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Denying The Liar.Dale Jacquette - 2007 - Polish Journal of Philosophy 1 (2):91-98.
Curry, Yablo and duality.Roy T. Cook - 2009 - Analysis 69 (4):612-620.
Equiparadoxicality of Yablo’s Paradox and the Liar.Ming Hsiung - 2013 - Journal of Logic, Language and Information 22 (1):23-31.
An Update of Tarski: Two Usages of the Word “True”.Zhen Zhao - 2022 - Journal of Logic, Language and Information 31 (3):505-523.
Classical Logic and the Liar.Yannis Stephanou - forthcoming - Logic and Logical Philosophy:1.
Literary Self-Reference: Five Types of Liar's Paradox.David Lehner - 2020 - Philosophy and Literature 44 (2):476-485.
Liar-type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
Liar paradox.Bradley Dowden - 2001 - Internet Encyclopedia of Philosophy.
Can deflationists be dialetheists?Bradley Armour-Garb & J. C. Beall - 2001 - Journal of Philosophical Logic 30 (6):593-608.
Buddhist Epistemology and the Liar Paradox.Szymon Bogacz - forthcoming - Australasian Journal of Philosophy:1-17.


Added to PP

125 (#108,915)

6 months
125 (#9,221)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Jared Warren
Stanford University

Citations of this work

No citations found.

Add more citations

References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Can the Classical Logician Avoid the Revenge Paradoxes?Andrew Bacon - 2015 - Philosophical Review 124 (3):299-352.
On a family of paradoxes.Arthur Prior - 1960 - Notre Dame Journal of Formal Logic 2 (1):16-32.
Paradoxes of grounding in semantics.Hans G. Herzberger - 1970 - Journal of Philosophy 67 (6):145-167.

View all 27 references / Add more references