Philosophical Studies

, Volume 126, Issue 1, pp 1–27 | Cite as

Grelling’s Paradox

  • Jay Newhard


Grelling’s Paradox is the paradox which results from considering whether heterologicality, the word-property which a designator has when and only when the designator does not bear the word-property it designates, is had by ‘ ȁ8heterologicality’. Although there has been some philosophical debate over its solution, Grelling’s Paradox is nearly uniformly treated as a variant of either the Liar Paradox or Russell’s Paradox, a paradox which does not present any philosophical challenges not already presented by the two better known paradoxes. The aims of this paper are, first, to offer a precise formulation of Grelling’s Paradox which is clearly distinguished from both the Liar Paradox and Russell’s Paradox; second, to offer a solution to Grelling’s Paradox which both resolves the paradoxical reasoning and accounts for unproblematic predications of heterologicality; and, third, to argue that there are two lessons to be drawn from Grelling’s Paradox which have not yet been drawn from the Liar or Russell’s Paradox. The first lesson is that it is possible for the semantic content of a predicate to be sensitive to the semantic context; i.e., it is possible for a predicate to be an indexical expression. The second lesson is that the semantic content of an indexical predicate, though unproblematic for many cases, can nevertheless be problematic in some cases.


Precise Formulation Semantic Content Philosophical Debate Semantic Context Indexical Expression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cargile, J. 2002‘Logical Paradoxes’Jacquette, D. eds. A Companion to Philosophical LogicBlackwell PublishersOxford105114Google Scholar
  2. Church, A. 1960‘Paradoxes, Logical’Runes, D. eds. Dictionary of PhilosophyLittlefield AdamsTotowa NJ224225Google Scholar
  3. Geach, P. 1961‘Ryle on Namely Riders’Analysis216467Google Scholar
  4. Gödel, K. 1951‘Russell’s Mathematical Logic’Schilpp, P.A. eds. The Philosophy of Bertrand Russell3Tudor Publishing CompanyNew York125153Google Scholar
  5. Goldstein, L. 2003‘Farewell to Grelling’Analysis633132CrossRefGoogle Scholar
  6. Grelling, K., Nelson, L. 1908‘Bemerkungen zu den Paradoxieen von Russell und Burali-Forti’Abhandlungen der Fries’schen Schule, neue Folge2301334Google Scholar
  7. Grelling, K. 1936‘The Logical Paradoxes’Mind45481486Google Scholar
  8. Kaplan, D. 1989a‘Afterthoughts’Almog, J.Perry, J.Wettstein, H. eds. Themes from KaplanOxford University PressNew York565614Google Scholar
  9. Kaplan, D. 1989b‘Demonstratives’Almog, J.Perry, J.Wettstein, H. eds. Themes from KaplanOxford University PressNew York481563Google Scholar
  10. Kripke, S. 1975‘Outline of a Theory of Truth’Journal of Philosophy72690716Google Scholar
  11. Lawrence, N. 1950‘Heterology and Hierarchy’Analysis167784Google Scholar
  12. Martin, R. 1968‘On Grelling’s Paradox’Philosophical Review77321331Google Scholar
  13. Moore, G.E. 1903Principia EthicaCambridge University PressCambridgeGoogle Scholar
  14. Quine, W.V. 1970Philosophy of LogicPrentice-Hall, Inc.Englewood Cliffs, NJGoogle Scholar
  15. Quine, W.V. 1987QuidditiesHarvard University PressCambridge MAGoogle Scholar
  16. Quine, W.V. 1990The Pursuit of TruthHarvard University PressCambridge MAGoogle Scholar
  17. Quine, W.V. 1995From Stimulus to ScienceHarvard University PressCambridge MAGoogle Scholar
  18. Ramsey, F.P. 1925‘The Foundations of Mathematics’Proceedings of the London Mathematical Society25338384Series 2Google Scholar
  19. Russell, B. 1940An Inquiry into Meaning and TruthGeorge Allen and Unwin LtdLondonGoogle Scholar
  20. Ryle, G. 1952‘Heterologicality’Analysis116169Google Scholar
  21. Saarnio, U. 1974‘Die Grellingsche Paradoxie und ihre exakte Lösung’Dialectica28243261Google Scholar
  22. Salmon, N. 1998‘Nonexistence’Nous32277319CrossRefGoogle Scholar
  23. Slater, B.H. 1973‘ ȁ8Is ‘Heterological’ Heterological’Mind82439440Google Scholar
  24. Sullivan, P. 2003‘A note on incompleteness and heterologicality’Analysis633238CrossRefMathSciNetGoogle Scholar
  25. von Wright G. H. (1983): ‘The Heterological Paradox’ in Philosophical Logic: Philosophical Papers, vol. II, Ithaca NY: Cornell University Press, pp. 1–24.Google Scholar
  26. Wiredu, J.E. 1976‘Paradoxes’Second Order5326Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Jay Newhard
    • 1
  1. 1.University of OklahomaNormanUSA

Personalised recommendations