One of the legal tests for causation turns on whether an intervening act was "abnormal." In my criminal law class last week, I pointed out that if the act was abnormal, the result would be X, but if the act was not abnormal, then it would be Y. I also flagged for students that "not abnormal," clumsy as the phrase is, isn't quite the same as "normal." But there was a bit of confusion about how "not abnormal" can indeed be different from "normal."
I thought the issue — the difference between opposites and negations (is there a better term than "negation," by the way?) — was worth briefly explaining to my first-semester law students, so that's what I plan to do this afternoon. Here's what I plan to say:
1. Many adjectives have both an antonym and a negation. The antonym of "tall," for instance, is "short" — it's at the other extreme of the height spectrum from "tall." But the negative of "tall" is not "short." Many people, after all, are neither short nor tall; the negative of tall includes both the short and the ones in the middle. Thus, "not tall," clunky as it is, means something different from "short."
2. The English negative prefixes — "non-," "un-," "in-," and the like — sometimes mean opposite and sometimes mean negative (and sometimes something altogether different). "Illegal" pretty much means "not legal." "Abnormal," on the other hand, doesn't quite mean "not normal" — there are things in between normal and abnormal (say, the relatively rare but not very rare) that would qualify as "not abnormal." Likewise, "not unhappy" is not the same as "happy" (even setting aside cases where "not unhappy" is used for some rhetorical effect).
As a general matter, when some quality is either present or not (e.g., legal or illegal), the antonym is the same as the opposite. But if there's a spectrum (e.g., short to tall), the antonyms often differ from the opposites.
a. What's the negation (not antonym) of "positive number"?
b. (Borrowed from Lewis Carroll:) What's the negation (not antonym) of "once there was a princess"?
c. What's the negation of "lean and mean"? (This is a good way of also introducing DeMorgan's Law.)
Any suggestions about this? Is it so obvious that first-semester law students are sure to already know all about this? Are there some better examples I can use, or some easier ways of explaining it?
Of course, I realize that this isn't quite teaching law; but I think this is important for lawyers to know, and in my experience throwing in a few minutes of general knowledge every so often makes class more fun.