A comment by Frank on my "Correcting misinformation" posting:
Whether or not peanuts are nuts or not, the statement "May contain nuts" on the package cannot be rendered untrue. It could just as easily read "May contain chicken feathers" and still be true. They didn't say it did, just that it "may".
The background… Lloyd & Mitchinson had claimed in The Book of General Ignorance:
Peanuts… are not nuts. So the legendary health warning on a packet of peanuts ("may contain nuts") is, strictly speaking, untrue.
and I noted:
Obviously, peanuts must count as nuts for legal purposes (hence the health warning), so botany is not the only source of technical definitions.
Now Frank has taken us away from the question of what nut means to the question of what may means (or, rather, conveys).
We're discussing "possibility may" here (and not the "permission may" of "May I have another helping, please?"). Frank's (implicit) position is that the semantics of possibility may is nothing more than the possibility operator of modal logic, glossable in English roughly as 'it is possible that'. That is, "This package may contain nuts" is semantically equivalent to "It is possible that this package contains nuts".
This is not an unreasonable analysis, and in fact something like it is widely adopted by semanticists. But that can't be the end of the matter: if possibility may is nothing but the possibility operator, then there would not be much point in using it; almost anything is possible — it is possible that the package contains chicken feathers, or a miniature copy of the King James Bible, or helium, or whatever — so what would be the point in asserting one possibility out of zillions?
The thing is, sentences (and larger discourses) convey more than they say, and ordinary people (who aren't logicians or formal semanticists) quite sensibly think of "meaning" mostly in terms of what expressions convey, rather than in terms of truth and falsity alone. Semanticists, too, analyze conveyed meaning, but they separate it from truth conditions. The point is that to insist on truth conditions as the entire account of meaning, as Frank seems to do, is to miss a great deal of what there is to say about meaning.
Back to the specific case of possibility may. What, I asked above, would be the point in asserting one possibility (call it X) out of zillions? Because the possibility of X is relevant to your audience, and because there is some likelihood of X. As a result, it is informative to assert (in this context) the possibility of X. "May contain nuts" is informative on a packet of food; it serves as a warning to those who want to avoid nuts in their diet.
"Contains nuts" would, of course, be even more informative, if true, and this warning is indeed found on packages and containers (and on restaurant menus and so on) — most famously, on cans of nuts, where the warning seems absurd (though, of course, the warning merely satisfies legal requirements).
"May contain nuts" is used for packaging copy that might be used on a number of different products, in a product line that includes some nut-containing items. Yes, it would be more helpful to the users to design packages separately, with more precise information, but it's probably more expensive to do so.
But now we're into matters of commerce and law rather than meaning.