Glen on legalistic reading and Venn diagram problems

In an earlier post, I asked why the sentence "Thirty students take geometry, and 25 students take Spanish" seems, to me, an acceptable -- and typical -- way of saying: "Thirty students take geometry, and another set of 25 students take Spanish."

I think Glen has explains it:

Out of context, there is an implicit contrast: "Two students do X, and three students do Y" is a common sentence pattern in English, which implies that you are talking about five students and how they divide up. If X and Y aren't obviously alternatives, this form implies that they are. "Two students take Spanish and three take French" would be natural English if talking about five students. If talking about four students, it would be odd. "Two students take Chinese, and three students are hispanic" might prompt an exasperated, "What, hispanic students can't take Chinese?", because it does seem to contrast X, taking Chinese, with Y, being hispanic.

If you didn't mean to contrast one group of students from another, you would probably say it differently. For example, "The geometry class has 30 students, the Spanish class has 25, and some students could be in both classes."

But in the context of a math problem, all of that changes. Math problems written in natural language still require you to make disambiguating assumptions--it is still natural language, after all--but they want to you put more weight on what is literally said and less on other factors ("bayesian priors").

In such a context, you are trained to interpret "Two students do X, and three students do Y," without assuming two disjoint groups. You learn to be literal and legalistic in a math problem context, which is a context-based re-weighting of the factors involved in interpretation of language.

I'm glad Glen has used the term "legalistic": that's exactly what I was thinking.

I'm not a legal reader by any means, but when I do read legal documents -- or, more to the point, when I read a legally vetted explanation of a state of affairs to which I object -- I instantly switch to a literal-minded, 'legalistic' mode. I take it as a given that legally vetted statements count on readers to make inferences that aren't in fact true, and to be mollified by those inferences to boot.

In short, legally vetted public relations statements, which is what I'm talking about, practice a particular form of lying by omission, which is lying via exploitation of the conventions of natural language. (I'll have to be on the look-out for examples...)


Further:

I have an email from Katharine asking whether I'm thinking of the Gricean maxims (pdf file). I hadn't been, because I'd never heard of the Gricean maxims, but I think she's right.