Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 8
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Cobreros, Pablo Egré, Paul Ripley, David and van Rooij, Robert 2016. Information Processing and Management of Uncertainty in Knowledge-Based Systems.

    Halpern, Joseph Y. and Kets, Willemien 2015. Ambiguous language and common priors. Games and Economic Behavior, Vol. 90, p. 171.

    Makowski, Marcin Piotrowski, Edward and Sładkowski, Jan 2015. Do Transitive Preferences Always Result in Indifferent Divisions?. Entropy, Vol. 17, Issue. 3, p. 968.

    Halpern, Joseph Y. and Kets, Willemien 2014. A logic for reasoning about ambiguity. Artificial Intelligence, Vol. 209, p. 1.

    Makowski, Marcin and Piotrowski, Edward W. 2014. When I cut, you choose method implies intransitivity. Physica A: Statistical Mechanics and its Applications, Vol. 415, p. 189.

    Dietz, Richard 2013. Comparative concepts. Synthese, Vol. 190, Issue. 1, p. 139.

    ALXATIB, SAM and PELLETIER, FRANCIS JEFFRY 2011. The Psychology of Vagueness: Borderline Cases and Contradictions. Mind & Language, Vol. 26, Issue. 3, p. 287.

    Égré, Paul and Klinedinst, Nathan 2011. Vagueness and Language Use.



  • DOI:
  • Published online: 01 December 2008

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox.

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.

R. J Aumann . (1976). Agreeing to disagree. Annals of Statistics, 4(6), 12361239.

M. Black (1937). Vagueness: an exercise in logical analysis. Philosophy of Science, 4, 427455.

M. Dummett (1975). Wang's paradox. Synthese, 30, 301324.

K. Fine (1975). Vagueness, truth, and logic. Synthese, 30, 265300.

N. Friedman , & J. Y Halpern . (1997). Modeling belief in dynamic system. Part I: foundations. Artificial Intelligence 95(2), 257316.

D. Graff (2000). Shifting sands: an interest-relative theory of vagueness. Philsophical Topics, 28(1), 4581.

J. Y Halpern . (1997). On ambiguities in the interpretation of game trees. Games and Economic Behavior, 20, 6696.

J. Y. Halpern , & R Fagin . (1989). Modelling knowledge and action in distributed systems. Distributed Computing, 3(4), 159179.

J. Y. Halpern , & Y Moses . (1992). A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54, 319379.

C. G Hempel . (1939). Vagueness and logic. Philosophy of Science, 6, 163180.

D. Raffman (1994). Vagueness without paradox. The Philosophical Review, 103(1), 4174.

S. Soames (1999). Understanding Truth. New York, NY: Oxford University Press.

B. C van Fraassen . (1968). Presuppositions, implications, and self-reference. Journal of Philosophy, 65, 136152.

L. A Zadeh . (1975). Fuzzy logics and approximate reasoning. Synthese, 30, 407428.

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? *