Philosophical Studies

, Volume 174, Issue 1, pp 79–103 | Cite as

Lie-toe-tease: double negatives and unexcluded middles



Litotes, “a figure of speech in which an affirmative is expressed by the negative of the contrary” (OED) has had some tough reviews. For Pope and Swift (“Scriblerus” 1727), litotes—stock examples include “no mean feat”, “no small problem”, and “not bad at all”—is “the peculiar talent of Ladies, Whisperers, and Backbiters”; for Orwell (1946), it is a means to affect “an appearance of profundity” that we can deport from English “by memorizing this sentence: A not unblack dog was chasing a not unsmall rabbit across a not ungreen field.” But such ridicule is not without equivocation, given that litotes, or “logical” (non-concordial) double negation, may or may not be semantically redundant. When the negation of a logical contrary yields an unexcluded middle, it contributes to expressive power: someone who is not unhappy may not be happy either, and an occurrence may not be infrequent without being frequent. But if something is not possible, what can it be but possible? Why does Crashaw’s “not impossible she” survive rhetorically while Orwell’s “not unsmall rabbit” is doomed? How is Robbie being “not not friends” with Mary on 7th Heaven distinct from being friends with her, if not not-p reduces to p? The key is recognizing in litotes a corollary of MaxContrary, the tendency for contradictory (wide-scope) sentential negation ¬p to strengthen (at least) pragmatically to a contrary ©p, as when the formal contradictory Fr. “Il ne faut pas partir” (lit. ‘It is not necessary to leave’) is reinterpreted as expressing a contrary (‘one must not-leave’). Just as the Law of Excluded Middle can apply where it “shouldn’t”, resulting in pragmatically presupposed disjunctions between semantic contraries, so that “p v ©p” amounts to an instance of “p v ¬p”, the Law of Double Negation can fail to apply where it “should”. When not not-p conveys ¬©p, the negation of a virtual contrary, the middle between p and not-p is no longer excluded, rendering the Fregean dictum that “Wrapping up a thought in double negation does not alter its truth value” not unproblematic.


Affixal negation Contrariety (contrary opposition) Disjunctive syllogisum Double negation Excluded middle Implicature Litotes Square of opposition 



Some of this material was presented in other forms at other forums, including the first World Congress on the Square of Opposition in Montreux (June 2007), LNAT (Logic Now and Then) in Brussels (November 2008), ESSLLI in Ljubljana (August 2011), SCLP in Santa Cruz (November 2011), CRISSP in Brussels (December 2011), the LOT Summer School in Driebergen (July 2012), AMPRA 1 in Charlotte (October 2012), the CIL Logical Words workshop in Geneva (July 2013), and of course Go Figure in London (June 2013). I am grateful to commenters at those occasions and to Barbara Abbott, Donka Farkas, Dany Jaspers, Mark Liberman, Jacques Moeschler, Laura Neuhaus, and Mihaela Popa for helpful interactions.


  1. Aristotle. Prior Analytics, H. Tredennick, trans. Cambridge: Harvard University Press, 1938.Google Scholar
  2. Aristotle. Categories and De Interpretatione, J. L. Ackrill, trans. Oxford: Clarendon, 1963.Google Scholar
  3. Aristotle. Metaphysics, H. Apostle, trans. Bloomington: Indiana U. Press, 1966.Google Scholar
  4. Aristotle. On Rhetoric, G. A. Kennedy, trans. New York: Oxford University Press, 1991.Google Scholar
  5. Arlen, H., & Mercer, J. (1944). Ac-cent-tchu-ate the positive. Song from musical film “Here Come the Waves”.Google Scholar
  6. Bolinger, D. (1972). Degree words. The Hague: Mouton.CrossRefGoogle Scholar
  7. Bosanquet, B. (1888). Logic (Vol. 1). Oxford: Clarendon.Google Scholar
  8. Brown, P., & Levinson, S. (1987). Politeness. Cambridge: Cambridge U. Press.Google Scholar
  9. Caffi, C. (1999). On mitigation. Journal of Pragmatics, 31, 881–909.CrossRefGoogle Scholar
  10. Collins, C., & Postal, P. (2014). Classical NEG raising: an essay in the syntax of negation. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
  11. Colston, H., & Gibbs, R. (2012). Interpreting figurative meaning. Cambridge: Cambridge U. Press.Google Scholar
  12. Ducrot, O. (1973). La preuve et le dire. Paris: Maison Mame.Google Scholar
  13. Eliot, T.S. (1942) Little Gidding, in Four quartets. Reprinted London: Faber & Faber, 1960.Google Scholar
  14. Erasmus, D. (1517). Colloquia, C. R. Thompson, trans. Chicago: University of Chicago Press, 1965.Google Scholar
  15. Fowler, H. W. (1926). A dictionary of modern English usage. New York: Oxford University Press.Google Scholar
  16. Frege, G. (1919). Negation. In M. Beaney (Ed.), The Frege reader (pp. 346–361). Oxford: Blackwell.Google Scholar
  17. Geach, P. T. (1972). Logic matters (p. 1980). Reprinted Berkeley: University of California Press.Google Scholar
  18. Grice, H. P. (1989). Studies in the way of words. Cambridge: Harvard University Press.Google Scholar
  19. Harbach, C. (2011). The art of fielding. New York: Little, Brown.Google Scholar
  20. Heyting, A. (1956). Intuitionism: an introduction. Amsterdam: North-Holland.Google Scholar
  21. Hoffmann, M. (1987). Negatio contrarii: A study of Latin litotes. Assen: Van Gorcum.Google Scholar
  22. Horn, L. (1984). Toward a new taxonomy for pragmatic inference: Q-based and R-based implicature. In D. Schiffrin (Ed.), Meaning, form, and use in context (pp. 11–42). Washington: Georgetown University Press.Google Scholar
  23. Horn, L. (1989). A natural history of negation. Chicago: University of Chicago Press. Reissue edition, Stanford: CSLI, 2001.Google Scholar
  24. Horn, L. (1991). Duplex negatio affirmat…: The economy of double negation. In Papers from the parasession on negation, CLS 27 (pp. 78–106). Chicago: Chicago Linguistic Society.Google Scholar
  25. Horn, L. (2002a). The logic of logical double negation. Proceedings of the Sophia symposium on negation (pp. 79–111). Tokyo: Sophia University.Google Scholar
  26. Horn, L. (2002b). Uncovering the un-word: A study in lexical pragmatics. Sophia Linguistica, 49, 1–64.Google Scholar
  27. Horn, L. (2005). An un-paper for the unsyntactician. In S. Mufwene, et al. (Eds.), Polymorphous linguistics: Jim McCawley’s legacy (pp. 329–365). Cambridge, MA: MIT Press.Google Scholar
  28. Horn, L. (2010). Multiple negation in English and other languages. In L. Horn (Ed.), The expression of negation (pp. 111–148). Berlin: de Gruyter Mouton.CrossRefGoogle Scholar
  29. Horn, L. (2014). The singular square: Contrariety and double negation from Aristotle to Homer. In J. Blochowiak et al. (Eds.), Collection of papers dedicated to Jacques Moeschler.
  30. Horn, L. & Wansing, H. (2015). Negation. In E. Zalta (Ed.), Stanford encyclopedia of philosophy.
  31. Jespersen, O. (1917). Negation in English and other languages. Copenhagen: Høst.Google Scholar
  32. Jespersen, O. (1924). The philosophy of grammar. London: Allen & Unwin.Google Scholar
  33. Krifka, M. (2007). Negated antonyms: Creating and filling the gap. In U. Sauerland & P. Stateva (Eds.), Presupposition and implicature in compositional semantics (pp. 163–177). Houndmills: Palgrave Macmillan.Google Scholar
  34. Lausberg, H. (1960). Handbuch der literarischen Rhetorik. München: M. Hueber. (Translated as Handbook of literary rhetoric. Leiden: Brill, 1998).Google Scholar
  35. Levinson, S. C. (2000). Presumptive meanings: The theory of generalized conversational implicature. Cambridge, MA: MIT Press.Google Scholar
  36. Liberman, M. (2012). Double lie toe tease. Language Log post, March 12, 2012.
  37. Miller, H. (1956). Big Sur and the oranges of Hieronymus Bosch. New York: New Directions.Google Scholar
  38. Neuhaus, L. (to appear). Four potential meanings of double negation: The pragmatics of nicht un- constructions. International Review of Pragmatics.Google Scholar
  39. Orwell, G. (1946). Politics and the English language. Reprinted in Collected essays (pp. 353–367). London: Secker & Warburg, 1961.Google Scholar
  40. Parsons, T. (2012). The traditional square of opposition. In E. Zalta (Ed.), Stanford encyclopedia of philosophy.
  41. Peacham, H. (1593). The garden of eloquence. London: H. Iackson.Google Scholar
  42. Puttenham, G. & Puttenham, R. (1589). The arte of English poesie. London: Field.Google Scholar
  43. Quintilian, M. F. Institutio oratoria. H.E. Butler, trans. Loeb Classical Library. London: William Heinemann, 1920–1921.Google Scholar
  44. Richter, F. K. (1944). Hitler and words. Etc, 1, 256–258.Google Scholar
  45. Sapir, E. (1944). Grading: A study in semantics. Reprinted in P. Swiggers et al. (Eds.), The collected works of Edward Sapir, I (pp. 447–70). Berlin: de Gruyter, 2008.Google Scholar
  46. Scriblerus, M. (1727). The Art of Sinking. Pseudonymous publication by A. Pope, J. Swift and J. Arbuthnot, appearing in first edition of the Swift-Pope Miscellany. Reproduced under editorship of E. L. Steeves. New York: King’s Crown Press, 1952.Google Scholar
  47. Seright, O. (1966). Double negatives in Standard American English. American Speech, 41, 123–126.CrossRefGoogle Scholar
  48. Sigwart, C. (1885). Logic, vol. I., H. Dendy, trans. New York: Macmillan, 1895.Google Scholar
  49. Tammet, D. (2006). Born on a blue day. New York: Free Press.Google Scholar
  50. van der Wouden, T. (1996). Litotes and downward monotonicity. In H. Wansing (Ed.), Negation: A notion in focus (pp. 145–167). Berlin: de Gruyter.Google Scholar
  51. Ward, G., & Hirschberg, J. (1991). A pragmatic analysis of tautological utterances. Journal of Pragmatics, 15, 507–520.CrossRefGoogle Scholar
  52. Zaefferer, D. (1991). Conditionals and unconditionals: Cross-linguistic and logical aspects. In D. Zaefferer (Ed.), Semantic universals and universal semantics (pp. 210–236). Berlin: Foris.Google Scholar

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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Linguistics and PhilosophyYale UniversityNew HavenUSA

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