Grelling’s Paradox

Abstract

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.

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References

  1. J. Cargile (2002) ‘Logical Paradoxes’ D. Jacquette (Eds) A Companion to Philosophical Logic Blackwell Publishers Oxford 105–114

    Google Scholar 

  2. A. Church (1960) ‘Paradoxes, Logical’ D. Runes (Eds) Dictionary of Philosophy Littlefield Adams Totowa NJ 224–225

    Google Scholar 

  3. P. Geach (1961) ArticleTitle‘Ryle on Namely Riders’ Analysis 21 64–67

    Google Scholar 

  4. K. Gödel (1951) ‘Russell’s Mathematical Logic’ P.A. Schilpp (Eds) The Philosophy of Bertrand Russell EditionNumber3 Tudor Publishing Company New York 125–153

    Google Scholar 

  5. L. Goldstein (2003) ArticleTitle‘Farewell to Grelling’ Analysis 63 31–32 Occurrence Handle10.1111/j.0003-2638.2003.00390.x

    Article  Google Scholar 

  6. K. Grelling L. Nelson (1908) ArticleTitle‘Bemerkungen zu den Paradoxieen von Russell und Burali-Forti’ Abhandlungen der Fries’schen Schule, neue Folge 2 301–334

    Google Scholar 

  7. K. Grelling (1936) ArticleTitle‘The Logical Paradoxes’ Mind 45 481–486

    Google Scholar 

  8. D. Kaplan (1989a) ‘Afterthoughts’ J. Almog J. Perry H. Wettstein (Eds) Themes from Kaplan Oxford University Press New York 565–614

    Google Scholar 

  9. D. Kaplan (1989b) ‘Demonstratives’ J. Almog J. Perry H. Wettstein (Eds) Themes from Kaplan Oxford University Press New York 481–563

    Google Scholar 

  10. S. Kripke (1975) ArticleTitle‘Outline of a Theory of Truth’ Journal of Philosophy 72 690–716

    Google Scholar 

  11. N. Lawrence (1950) ArticleTitle‘Heterology and Hierarchy’ Analysis 16 77–84

    Google Scholar 

  12. R. Martin (1968) ArticleTitle‘On Grelling’s Paradox’ Philosophical Review 77 321–331

    Google Scholar 

  13. G.E. Moore (1903) Principia Ethica Cambridge University Press Cambridge

    Google Scholar 

  14. W.V. Quine (1970) Philosophy of Logic Prentice-Hall, Inc. Englewood Cliffs, NJ

    Google Scholar 

  15. W.V. Quine (1987) Quiddities Harvard University Press Cambridge MA

    Google Scholar 

  16. W.V. Quine (1990) The Pursuit of Truth Harvard University Press Cambridge MA

    Google Scholar 

  17. W.V. Quine (1995) From Stimulus to Science Harvard University Press Cambridge MA

    Google Scholar 

  18. F.P. Ramsey (1925) ArticleTitle‘The Foundations of Mathematics’ Proceedings of the London Mathematical Society 25 338–384

    Google Scholar 

  19. B. Russell (1940) An Inquiry into Meaning and Truth George Allen and Unwin Ltd London

    Google Scholar 

  20. G. Ryle (1952) ArticleTitle‘Heterologicality’ Analysis 11 61–69

    Google Scholar 

  21. U. Saarnio (1974) ArticleTitle‘Die Grellingsche Paradoxie und ihre exakte Lösung’ Dialectica 28 243–261

    Google Scholar 

  22. N. Salmon (1998) ArticleTitle‘Nonexistence’ Nous 32 277–319 Occurrence Handle10.1111/0029-4624.00101

    Article  Google Scholar 

  23. B.H. Slater (1973) ArticleTitle‘ ȁ8Is ‘Heterological’ Heterological’ Mind 82 439–440

    Google Scholar 

  24. P. Sullivan (2003) ArticleTitle‘A note on incompleteness and heterologicality’ Analysis 63 32–38 Occurrence Handle10.1111/j.0003-2638.2003.00391.x Occurrence HandleMR1952881

    Article  MathSciNet  Google 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.

  26. J.E. Wiredu (1976) ArticleTitle‘Paradoxes’ Second Order 5 3–26

    Google Scholar 

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Correspondence to Jay Newhard.

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Newhard, J. Grelling’s Paradox. Philos Stud 126, 1–27 (2005). https://doi.org/10.1007/s11098-004-7808-z

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Keywords

  • Precise Formulation
  • Semantic Content
  • Philosophical Debate
  • Semantic Context
  • Indexical Expression