The Liar

  • Michael Huemer


The liar sentence, “This sentence is false”, presents a paradox: it is true if and only if it is false. The solution is to hold that the sentence fails to express a proposition. Our language contains implicit rules for the interpretation of sentences. These rules are inconsistent as applied to this case, for they require that the liar sentence be interpreted as expressing the proposition that holds if and only if it does not hold. No proposition can satisfy this condition, so no proposition can be the content of the liar sentence. Analogous solutions apply to the Barber Paradox, Curry’s Paradox, Grelling’s Paradox, and Russell’s Paradox.


  1. Beall, J.C. 2009. Spandrels of Truth. Oxford: Oxford University Press.Google Scholar
  2. Beall, J.C. and Michael Glanzberg. 2011. “Liar Paradox”, Stanford Encyclopedia of Philosophy,, accessed April 30, 2017.
  3. Braakuis, H.A.G. 1967. “The Second Tract on Insolubilia Found in Paris, B.N. Lat. 16.617. An Edition of the Text with an Analysis of Its Contents,” Vivarium 5 (1967): 111–45.CrossRefGoogle Scholar
  4. Clark, Michael. 2002. Paradoxes from A to Z. London: Routledge.Google Scholar
  5. Curry, Haskell B. 1942. “The Inconsistency of Certain Formal Logics”, Journal of Symbolic Logic 7: 115–117.CrossRefGoogle Scholar
  6. Eklund, Matti. 2002. “Inconsistent Languages”, Philosophy and Phenomenological Research 64: 251–75.CrossRefGoogle Scholar
  7. Geach, Peter. 1950. “Russell’s Theory of Descriptions”, Analysis 10: 84–8.CrossRefGoogle Scholar
  8. Grelling, Kurt and Leonhard Nelson. 1908. “Bemerkungen zu den Paradoxien von Russell und Burali-Forti” (“Remarks on the Paradoxes of Russell and Burali-Forti”), Abhandlungen der Fries’schen Schule n.s. 2: 301–34.Google Scholar
  9. Herzberger, Hans G. 1967. “The Truth-Conditional Consistency of Natural Language”, Journal of Philosophy 64: 29–35.CrossRefGoogle Scholar
  10. Huemer, Michael. 2016. Approaching Infinity. New York: Palgrave Macmillan.CrossRefGoogle Scholar
  11. Irvine, Andrew David and Harry Deutsch. 2016. “Russell’s Paradox”, The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta,, accessed May 28, 2017.
  12. Littmann, Greg and Keith Simmons. 2004. “A Critique of Dialetheism”, pp. 314–35 in The Law of Non-Contradiction, ed. Graham Priest, J.C. Beall, and Bradley Armour-Garb. Oxford: Oxford University Press.CrossRefGoogle Scholar
  13. Priest, Graham. 2006a. In Contradiction: A Study of the Transconsistent, expanded ed. Oxford: Clarendon.CrossRefGoogle Scholar
  14. Priest, Graham. 2006b. Doubt Truth to Be a Liar. Oxford: Clarendon.Google Scholar
  15. Prior, Arthur N. 1955. “Curry’s Paradox and 3-valued Logic”, Australasian Journal of Philosophy 33: 177–82.CrossRefGoogle Scholar
  16. Quine, Willard van Orman. 1986. Philosophy of Logic, second ed. Cambridge, MA: Harvard University Press.Google Scholar
  17. Rescher, Nicholas. 2001. Paradoxes: Their Roots, Range, and Resolution. Chicago, IL: Open Court.Google Scholar
  18. Russell, Bertrand. 1902. Letter to Frege dated 16 June, 1902, reprinted on pp. 124–5 in Jean van Heijenoort, ed. From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Cambridge, MA: Harvard University Press, 1967.Google Scholar
  19. Russell, Bertrand. 1903. The Principles of Mathematics. Cambridge: Cambridge University Press.Google Scholar
  20. Russell, Bertrand. 1908. “Mathematical Logic as Based on the Theory of Types”, American Journal of Mathematics 30: 222–62.CrossRefGoogle Scholar
  21. Russell, Bertrand. 1972. “The Philosophy of Logical Atomism”, pp. 1–125 in The Philosophy of Logical Atomism. London: Routledge.Google Scholar
  22. Sainsbury, Richard M. 2009. Paradoxes, 3rd ed. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  23. Sloman, Aaron. 1971. “Tarski, Frege and the Liar Paradox”, Philosophy 46: 133–147.CrossRefGoogle Scholar
  24. Spade, Paul Vincent. 1975. The Mediaeval Liar: A Catalogue of the Insolubilia-Literature. Toronto, Canada: Pontifical Institute of Mediaeval Studies.Google Scholar
  25. Strawson, Peter F. 1950. “On Referring”, Mind 59: 320–44.CrossRefGoogle Scholar
  26. Tarski, Alfred. 1944. “The Semantic Conception of Truth: And the Foundations of Semantics”, Philosophy and Phenomenological Research 4: 341–76.CrossRefGoogle Scholar
  27. Tarski, Alfred. 1983. “The Concept of Truth in Formalized Languages”, pp. 152–278 in Logic, Semantics, Metamathematics: Papers from 1923 to 1938, 2nd ed., ed. John Corcoran, tr. Joseph Henry Woodger. Indianapolis: Hackett.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Michael Huemer
    • 1
  1. 1.Philosophy DepartmentUniversity of Colorado BoulderBoulderUSA

Personalised recommendations