Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Brown, Joshua D. K. and Garson, James W. 2016. A New Semantics for Vagueness. Erkenntnis,

    Meadows, Toby 2016. Sets and supersets. Synthese, Vol. 193, Issue. 6, p. 1875.



  • DOI:
  • Published online: 01 May 2010

Kripke’s theory of truth offered a trivalent semantics for a language which, like English, contains a truth predicate and means of self-reference; but it did so by severely restricting the expressive power of the logic. In Kripke’s analysis, the Liar (e.g., This very sentence is not true) receives the indeterminate truth value, but this fact cannot be expressed in the language; by contrast, it is straightforward to say in English that the Liar is something other than true. Kripke’s theory also fails to handle the Strengthened Liar, which can be expressed in English as: This very sentence is something other than true. We develop a theory which seeks to overcome these difficulties, and is based on a detailed analysis of some of the linguistic means by which the Strengthened Liar can be expressed in English. In particular, we propose to take literally the quantificational form of the negative expression something other than true. Like other quantifiers, it may have different implicit domain restrictions, which give rise to a variety of negations of different strengths (e.g., something other than true among the values {0, 1}, or among {0, 1, 2}, etc). This analysis naturally leads to a logic with as many truth values as there are ordinals—a conclusion reached independently by Cook (2008a). We develop the theory within a generalization of the Strong Kleene Logic, augmented with negations that each have a nonmonotonic semantics. We show that fixed points can be constructed for our logic, and that it enjoys a limited form of ‘expressive completeness’. Finally, we discuss the relation between our theory and various alternatives, including one in which the word true (rather than negation) is semantically ambiguous, and gives rise to a hierarchy of truth predicates of increasing strength.

Corresponding author
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

T. Burge (1979). Semantical paradox. Journal of Philosophy, 76, 169–198.

E. Chemla (2009). Presuppositions of quantified sentences: Experimental data. Natural Language Semantics, 17(4), 299–340.

H. Field (2003a). A revenge-immune solution to the semantic paradoxes. Journal of Philosophical Logic, 32, 139–177.

H. Field (2008). Saving Truth from Paradox. Oxford University Press.

M. Glanzberg (2001). The liar in context. Philosophical Studies, 103, 217–251.

M. Glanzberg (2004). A contextual-hierarchical approach to truth and the liar paradox. Journal of Philosophical Logic, 33, 27–88.

A. Gupta , & R. L Martin . (1984). A fixed point theorem for the weak Kleene valuation scheme. Journal of Philosophical Logic, 13, 131–135.

S. Kripke (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690–716.

H. Leitgeb (2005). What truth depends on. Journal of Philosophical Logic, 34, 155–192.

J. Myhill (1984). Paradoxes. Synthese, 60, 129–143.

P. Schlenker (2004). Conditionals as definite descriptions: A referential analysis. Research on Language and Computation, 2(3), 417–162.

P. Schlenker (2007). The elimination of self-reference: Generalized Yablo-series and the theory of truth. Journal of Philosophical Logic, 36(3), 251–307.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *