The English language is ripe with ambiguity. This note considers improperly scoped comparisons, not just between apples and oranges, but between something in particular and nothing in general. We call this the incomplete comparative.
Although we recognize how misleading newspaper headlines can be, consider as an example the title of an item in the on-line NewsScan Daily, 23 October 2000:
* More African-Americans Using the Web
The ambiguity is illustrated by considering several possible would-be interpretations:
* More African-Americans Using the Web THAN PREVIOUSLY.
* More African-Americans Using the Web THAN TELEPHONES.
* More African-Americans Using the Web THAN White Americans.
* More African-Americans Using the Web THAN ANYONE ELSE.
(Although much more obscure, we might also consider the possibility that the African-Americans mentioned in the original title are disciples of St. Thomas More, in which case the title would then refer specifically to the More African-Americans.) But actually, what the article means is something like this:
* The rate at which African-Americans are increasing their Web usage is greater than the corresponding rate for white Americans.
So, a more accurate but much less terse headline might be something like this:
* Web Use Among African-Americans Rising Faster Than That of White Americans.
Mathematical notation would be somewhat terser, but less understandable to the nontechies: If Usage(x) is the usage by an ethnic group, and Usage'(x) is the rate of change (per unit time) in the sense of the first derivative in calculus, then
Usage'(African-Americans) > Usage'(White-Americans)
[For some reason, this analysis reminds me of a news item I saw in the 1950s that claimed that the increase in Southern Baptists in the U.S. was much greater than the overall population growth. The article concluded that if that this rate of increase continued, by some year in the future (which I do not remember) there would be ``more Southern Baptists than people''!]
The incomplete comparative is a problem that is exacerbated by a lack of the kind of (semi)strong typing such as that which occurs in the German language: German case endings (nominative, genitive, dative, accusative), gender (der-die-das for masculine, feminine, and neuter), and number (der vs. die for masculine nominative, das vs. die for feminine nominative) all are helpful in disambiguation. Russian is even more (semi)strongly typed with respect to its six cases. However, even in German and Russian certain polymorphic forms still permit residual ambiguity.
So, when you use ``more'' or ``less'', add the completion ``than ...'' and put it in the proper place in the sentence, so you don't get horrible anomalies similar to the misplaced ``only'': Only His Only Grammarian Can Only Say Only What Only He Only Means,
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Here is the NewsScan item in its entirety.
More African-Americans Using the Web
A report released yesterday by the Pew Internet & American Life Study project indicates that African-Americans have gone online at almost twice the rate of white Americans in the past two years, with the number of new African-American users growing by 13% vs. 8% for whites. The percentage of the black population using the Internet rose to 36%, compared with a 50% percentage of whites. A ``striking difference'' was seen in how black Americans were using the Internet, with one-third seeing religious and spiritual information, vs. 20% of whites. Black users also tended to use the Web more often for economic advancement or for quality-of-life issues than whites, and were more likely to listen to music, play games or take part in online chat. Sixty-one percent of the new African-American users are women. (Bloomberg/Los Angeles Times 23 Oct 2000) http://www.latimes.com/business/20001023/t000101198.html