A Liar Paradox

The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: From ¬(p ∧ p), infer ¬ p. It is, interestingly enough, also essential to the argument that the ‘strong’ form of the diagonal lemma be used: the one that delivers a term λ such that we can prove: λ = ¬ T(⌈λ⌉); rather than just a sentence Λ for which we can prove: Λ ≡ ¬T(⌈Λ⌉). The truth-theoretic principles used to generate the paradox are these: ¬(S ∧ T(⌈¬S⌉); and ¬(¬S ∧ ¬T(⌈¬S⌉). These are classically equivalent to the two directions of the T-scheme, but they are intuitively weaker. The lesson I would like to draw is: There can be no consistent solution to the Liar paradox that does not involve abandoning truth-theoretic principles that should be every bit as dear to our hearts as the T-scheme. So we shall have to learn to live with the Liar, one way or another.
Keywords liar  truth
Categories (categorize this paper)
DOI 10.1002/tht3.5
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,765
Through your library
References found in this work BETA
Saving Truth From Paradox.Hartry H. Field - 2008 - Oxford University Press.
Outline of a Theory of Truth.Saul A. Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Self-Reference and the Languages of Arithmetic.Richard Heck - 2006 - Philosophia Mathematica 15 (1):1-29.
Truth and Disquotation.Richard Heck - 2004 - Synthese 142 (3):317--352.

View all 8 references / Add more references

Citations of this work BETA
More on 'A Liar Paradox'.Richard Heck - 2012 - Thought: A Journal of Philosophy 1 (4):270-280.
On Heck's New Liar.Julien Murzi - 2012 - Thought: A Journal of Philosophy 1 (2):258-269.
Response to Heck.David Ripley - 2013 - Thought: A Journal of Philosophy 5 (4).

Add more citations

Similar books and articles
Added to PP index

Total downloads
379 ( #8,205 of 2,214,489 )

Recent downloads (6 months)
13 ( #29,832 of 2,214,489 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature