kitchen table math, the sequel: Glen on legalistic reading and Venn diagram problems

## Friday, September 2, 2011

### 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.

Katharine Beals said...

As far as a non-legalistic, natural language settings in which nondisjoint is possible:

Principal: "Do we have enough textbooks?"
Administrative assistant: Well, 30 students are taking geometry, and 25
students are taking French."

In this situation, it's irrelevant whether there's any overlap, and,
precisely because of this, overlap is possible.

Alternatively, if it's known that there are, say, under 40 students, then overlap is not just possible, but entailed.

I think it's specifically in situations where overlap is
1. not entailed
2. not logically impossible
3. relevant (i.e., worth remarking upon)
where many speakers/writers would add a couple of words like "and another" (to exclude overlap) or "including some of the former" (to convey overlap)

Katharine Beals said...

It seems to me that the principle involved is something like: disambiguate when meaning matters!

Catherine Johnson said...

disambiguate when meaning matters

I will mull!

Catherine Johnson said...

Now I wish I knew more about law as a discipline.

Glen said...

When we try to interpret language input, we have to decide which parts are signal, which parts are probably noise, and what background knowledge to supplement the signal portions with to match known patterns we consider plausible.

Legal writing, philosophical writing, debate writing, math writing, and formal academic writing are similar in that they require you to take what is written as literally as possible--assume that it is all signal, no noise--and to minimize the role of your prior beliefs in judging the meaning.

Law differs from math in that law is written defensively, on the assumption that some readers will exploit any ambiguity to intentionally misinterpret the writer's meaning, while math is written to be sufficient for readers who badly want to avoid misinterpretation.

Jen said...

I was just reading the other posting on this.

It turns out that in my head, when I read those sentences, I see them as two separate circles...but as soon as something in the problem asks about the relationship, I can see them either staying separate, or converging a little (only 2 kids take both) or a lot (20 students take both) or even the 25 student circle being fully submerged into the 30 student circle.

Is this a natural language/visual type of skill? It's certainly not a hardcore logic or math skill!