David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Thought: A Journal of Philosophy 1 (1):36-40 (2012)
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.
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Hartry H. Field (2008). Saving Truth From Paradox. Oxford University Press.
Saul A. Kripke (1975). Outline of a Theory of Truth. Journal of Philosophy 72 (19):690-716.
Richard Heck (2007). Self-Reference and the Languages of Arithmetic. Philosophia Mathematica 15 (1):1-29.
Richard Heck (2005). Truth and Disquotation. Synthese 142 (3):317--352.
Vann Mcgee (1994). Truth, Vagueness, and Paradox: An Essay in the Logic of Truth. Philosophical Review 103 (1):142-144.
Citations of this work BETA
Richard Heck (2012). More on 'A Liar Paradox'. Thought: A Journal of Philosophy 1 (4):270-280.
Julien Murzi (2012). On Heck's New Liar. Thought: A Journal of Philosophy 1 (2):258-269.
Elia Zardini (2012). It Is Not the Case That [P and 'It Is Not the Case That P' Is True] nor Is It the Case That [P and 'P' Is Not True]. Thought: A Journal of Philosophy 1 (4):309-319.
David Ripley (2013). Response to Heck. Thought: A Journal of Philosophy 5 (2).
Similar books and articles
Paolo Crivelli (2004). Aristotle on the Liar. Topoi 23 (1):61-70.
Kevin Scharp (2010). Truth's Saviour? [REVIEW] Philosophical Quarterly 60 (238):183 - 188.
Jeff Snapper (2012). The Liar Paradox in New Clothes. Analysis 72 (2):319-322.
Bradley Dowden, Liar Paradox. Internet Encyclopedia of Philosophy.
Shahid Rahman, Tero Tulenheimo & Emmanuel Genot (eds.) (2008). Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox. Springer.
Ahmed Alwishah & David Sanson (2009). The Early Arabic Liar: The Liar Paradox in the Islamic World From the Mid-Ninth to the Mid-Thirteenth Centuries Ce. Vivarium (1):97-127.
Richard Kenneth Atkins (2011). This Proposition is Not True: C.S. Peirce and the Liar Paradox. Transactions of the Charles S. Peirce Society 47 (4):421-444.
Keith Simmons (1993). Universality and the Liar: An Essay on Truth and the Diagonal Argument. Cambridge University Press.
J. C. Beall (ed.) (2007). Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
Added to index2009-01-28
Total downloads212 ( #12,786 of 1,801,598 )
Recent downloads (6 months)46 ( #19,270 of 1,801,598 )
How can I increase my downloads?