Hostname: page-component-7dd5485656-pnlb5 Total loading time: 0.001 Render date: 2025-10-29T10:09:35.635Z Has data issue: false hasContentIssue false
  • English
  • Français

EMBRACING THE TECHNICALITIES: EXPRESSIVE COMPLETENESS AND REVENGE

Published online by Cambridge University Press:  11 April 2016

NICHOLAS TOURVILLE  and
ROY T COOK
Get access Rights & Permissions [Opens in a new window]

Abstract

The Revenge Problem threatens every approach to the semantic paradoxes that proceeds by introducing nonclassical semantic values. Given any such collection Δ of additional semantic values, one can construct a Revenge sentence:

This sentence is either false or has a value in Δ.

The Embracing Revenge view, developed independently by Roy T. Cook and Phlippe Schlenker, addresses this problem by suggesting that the class of nonclassical semantic values is indefinitely extensible, with each successive Revenge sentence introducing a new ‘pathological’ semantic value into the discourse. The view is explicitly motivated in terms of the idea that every notion that seems to be expressible (e.g., “has a value in Δ”, for any definite collection of semantic values Δ) should, if at all possible, be expressible. Extant work on the Embracing Revenge view has failed to live up to this promise, since the formal languages developed within such work are expressively impoverished. We rectify this here by developing a much richer formal language, and semantics for that language, and we then prove an extremely powerful expressive completeness result for the system in question.

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 325 - 358
Copyright
Copyright © Association for Symbolic Logic 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

BIBLIOGRAPHY

Beall, J. (2006). True, false, and paranormal. Analysis, 66(2), 2–14.Google Scholar
Beall, J. (2008). Revenge of the Liar: New Essays on the Paradox. Oxford: Oxford University Press.Google Scholar
Cook, R. (2008). Embracing Revenge: On the Indefinite Extensibility of Language, in (Beall 2008), pp. 31–52.Google Scholar
Cook, R. (2009). What is a truth value, and how many are there? Studia Logica, 92, 183–201.CrossRefGoogle Scholar
Cook, R. (2013). Key Concepts in Philosophy: Paradoxes. Cambridge, UK: Polity Press.Google Scholar
Dummett, M. (1993). The Seas of Language. Oxford: Oxford University Press.Google Scholar
Field, H. (2008). Saving Truth from Paradox. Oxford: Oxford University Press.CrossRefGoogle Scholar
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690–716.CrossRefGoogle Scholar
Linnebo, Ø., & Rayo, A. (2012). Heirarchies ontological and idealogical. Mind, 121, 269–308.CrossRefGoogle Scholar
Priest, G. (1990). Boolean negation and all that. Journal of Philosophical Logic, 19(2), 201–215.CrossRefGoogle Scholar
Rayo, A. (2007). Beyond Plurals, in (Rayo & Uzquiano 2007), pp. 220–254.Google Scholar
Rayo, A., & Uzquiano, G. (2007). Absolute Generality. Oxford: Oxford University Press.Google Scholar
Rosenblatt, L., & Szmuc, D. (2014). On pathological truths, this Review, 7(4), 601–617.CrossRefGoogle Scholar
Russell, B. (1906). On Some Difficulties in the Theory of Transfinite Numbers and Order Types, in (Russell 1973), pp. 135–164.Google Scholar
Russell, B. (1973). Bertrand Russell, Essays in Analysis. New York: Braziller.Google Scholar
Schlenker, P. (2010). Super-liars, this Review, 3(3), 374–414.CrossRefGoogle Scholar
Tarski, A. (1933). The Concept of Truth in the Languages of the Deductive Sciences, in (Tarski 1983), pp. 252–278.Google Scholar
Tarski, A. (1983). In Corcoran, J., editor. Logic, Semantics, Metamathematics: Papers from 1923 to 1938. Indianapolis: Hackett Publishing.Google Scholar
Williamson, T. (1998). Indefinite extensibility. Grazer Philosophische Studien, 55, 1–24.CrossRefGoogle Scholar