“Can you pass the salt?”
“Yes, I can.”
And then of course he doesn’t.
This is an easy example of violating the hidden rules of conversation as described by philosopher Paul Grice. The rules are commonly known as the Gricean Maxims (“commonly” in certain circles, that is). A good way to be introduced to this topic is to watch Tom Scott’s short video, which packs quite a bit of information into an entertaining five minutes. Needless to say, it just barely skims the surface of a topic that’s easily worth a masters thesis or two — and I’m sure that it has been the material for exactly that. I first learned about Grice’s maxims (in great detail) when I was a Special Graduate Student at MIT for one semester in 1978. (Those were the days when well-financed school systems, such as Lincoln-Sudbury, would grant teachers a sabbatical, which means either a semester off at full pay or a year off at half pay. The only requirements were that you had to have been there for more than seven years, you had to have a plan that was at least loosely related to what you were teaching, and you had to return. If you were taking courses, the school system paid the tuition. As I say, “those were the days”; sabbaticals wouldn’t fly in public schools today. So I took the semester and studied linguistics, logic, and AI at MIT.)
Anyway, the key mathematical and linguistic distinction here is between what is literally said and what is implied; I’m using the colloquial, natural English sense of the word “imply,” not the mathematical sense of an “if…then.” As philosophers use the latter sense, Grice had to invent a new word: implicature. So the conversation at the top of this post involves implicature, as the first speaker clearly is asking the second one to pass the salt, even though she doesn’t actually say so. An empirical question is when and how people learn these unstated rules, a fertile ground for psycholinguistic studies. If you want to read a typical research paper on that matter, check one out here.
You may want to know who are the two speakers in my fictional conversation above. I won’t tell you. All I’ll say (as my pronouns suggest) is that the first one is female, the second one is male; also the first is neurotypical, and the second is either on the spectrum or else a mathematician or computer scientist. Don’t tell me that there’s a redundancy there.