### The Volokh Conspiracy

Mostly law professors | Sometimes contrarian | Often libertarian | Always independent

# How "Rights" Are Like Superscript -1

## Legal language, like mathematical language, often gives multiple definitions to similar terms.

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My post about how the word "right" in American legal usage often includes the entitlements of government as well as of individuals drew this comment:

"But as a matter of American legal language…".

There you go again, conflating law with reality. Legal consensus makes governmental 'rights' no more real than it would make defining 'pi' as 'three' be three, even though that could be enforced by the state with further (not unfamiliar) grotesqueries to compensate for its being unreal.

And this led me to think of this example from math: What does x-1 mean to you? Generally speaking, it would mean 1/x. But what does sin-1 x mean to you, if you know your trigonometry? It wouldn't be 1/sin x, but rather arcsin x, which is to say the inverse of the sin function: sin (arcsin x) = x. More broadly, f-1 (x) is the inverse of the function x, so that f (f-1 (x)) = x. And even if you don't feel at a home with trig and with functions, the point is simple: In math, as in law, we sometimes use the equivalent of homonyms— two different (but often related) concepts that are represented using the same symbols.

The same is true, of course, with computer programming language, where the same symbol can mean quite different things depending on context (usually depending on the data types of the items being operated on)—in the same language, + might mean addition when used with numbers but concatenation when used with text, or date addition when used with a date and an integer. (This is sometimes labeled "overloading" the operator, not in a pejorative sense but just in the sense that the operator has multiple meanings.)

Think of "right" the same way. In ordinary English, of course, the word means many different things—correct, the opposite of left, to restore to an upright position, and more. In law, it usually means a legal entitlement, but of course it has different logical properties and rhetorical qualities when used to refer to different kinds of legal entitlements: entitlements of individuals, groups, or governments, entitlements to get things or to be free from things, entitlements that are seen as stemming from moral principles or entitlements that are seen as stemming from positive law, and more. Just like superscript -1 in math, or the addition symbol in many computer programming languages, it is a sort of homonym, the meaning of which usually has to be understood from context.

Now one could certainly argue that language would be better, because less likely to confuse, if it used fewer homonyms. Perhaps we should stop using sin-1 and instead use arcsin, as many people do, and perhaps we should come up with a new symbol fINV to use for the inverse of a function more generally.

At the same time, language is a grown order, developed over centuries, and there are costs to trying to depart from it or to change it. We often use familiar locutions despite their potential ambiguity, precisely because they are familiar. (For instance, the word "homonym" is somewhat ambiguous—it could refer to two words with the same spelling but different meanings, which are sometimes labeled "homographs," or two words with the same pronunciation but different meanings, which are sometimes labeled "homophones," but I use "homonym" because it's more familiar and because I assume you identified the proper meaning from context.) We certainly don't say that sin-1 is "wrong" in the sense of arcsin just because the same symbol is used for something else in some other context.

The same is true for "right," as in asking whether courts have "a right of ultimate jurisdiction," or whether Congress has a "right" "to tempt the navigators of enemy-vessels to bring them into the American ports." It's not the same sort of right as your right of free speech, or for that matter as your right not to be defamed by a fellow citizen, or your right to have the civil case you bring tried by a jury. As a matter of "reality," or more precisely as a matter of legal analysis, each of these "rights" has somewhat different qualities. But if the question is whether it's correct to call these "rights," that is a question of legal American English (which is to say of convention among users of legal American English), not logic—just as the question whether sin-1 sometimes means arcsin is a question of mathematical language and thus of convention among mathematicians.