Asymmetric Negation

I came across a very interesting paper by Fraenkel and Schul on how negative phrases are constructed. It was a delighting moment when I realized that “these things are so true but I haven’t been noticing”. There were several daily intuitions that were formalized in an elegant way.

The axiom of the paper is that negation, despite its name, when applying on an adjective is not equivalent to using the adjective’s antonym. Rather, the resultant phrase is a mitigated version of the antonym. For example, one may say “not hot” to refer to a condition that is neither not but not quite cold.

The paper then conjectures 2 factors that can possibly control the degree of this mitigation effect.

The first one whether is an adjective and its antonym is a contrary or contradictory pair. What is the difference? Contrary pairs cannot both be true but can both be false (e.g. hot-cold), whereas contradictories do not have an intermediate degree (e.g. open-close). It is reasonable to hypothesize that mitigation occurs with contraries more than contradictories. With contraries, there is intuitively room to vary between the two poles.

The second factor is whether the adjective is the marked or unmarked member in a pair of antonyms. The marked member is “the one which carries a distinctive features that distinguishes it from the other member, …, is typically the usual, the normal, the positive, the common, and the neutral or less specific, compared to the marked member”. For example, in the good-bad pair, good is the unmarked member. The paper postulates that mitigation is stronger when negating on a marked member. To imagine this claim more clearly, let’s look at this visualization:

Untitled drawing (6)

According to the paper, “not good” should resemble “bad” more than “not bad” resembles “good”. This actually makes sense (to me). When you say something is “not good”, you are more or less making a criticism. Often, “not good” is a polite alternative to “bad”. However, the reverse direction is not true. “Not bad” is not a complement; there is a long way go to from “not bad” to “good”. I also try with other antonym pairs such as strong-weak, beautiful-ugly and see the same effect. This even works for Vietnamese! “không tốt” (not good) is closer to “tệ” (bad) than “không tệ” (not bad) to “tốt” (good).