Philosophical Studies

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

Lie-toe-tease: double negatives and unexcluded middles

  • Laurence Horn


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.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Linguistics and PhilosophyYale UniversityNew HavenUSA

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