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.