Using "may not" when something is not sometimes true

Question

When we want to say something is sometimes true or happens sometimes, we use "can":

A vegetarian diet can provide enough calories for a child's normal growth.

What modal would you use if you wanted to say something is not sometimes true or doesn't happen sometimes? Would you use "may not"?

A vegetarian diet may not provide enough calories for a child's normal growth.

I think we wouldn't use "can't" there. Am I right?

John Lawler · Accepted Answer

The problem is that

Modals, like may, and
Negatives, like not,

are both Operators (along with Quantifiers, like every).
All operators have Scope; that is, they are meaningful only within some part of the sentence, and not outside it. And when there are two operators in a sentence -- a negative with a modal, as here, or a negative with a quantifier, or a quantifier with a modal, or two modals, etc. -- there are two scopes covering parts of the same sentence, and one is usually inside another. This makes for differences and confusions.
In the case of Modal + Negative, consider

"Cinderella may not attend the ball", said her stepmother.
"This may not be the right place", said the driver.

First, note that may not refers to permission and prohibition in (1), but only to possibility or probability in (2). This is the distinction between Deontic Modals and Epistemic Modals; (1) is deontic and (2) is epistemic.

In what follows, Possible stands for both epistemic and deontic modality -- may is a Possible modal, not a Necessary modal like must.

Second, note that the scope of the negative in (1) includes the scope of deontic may. That is, (1) means that permission (may) is negated (not); logically,

It is not true that "Cinderella may attend the ball".
symbolically, Not (Possible (Attend (Cinderella, ball)))

Third, note that the scope of the epistemic may in (2) includes the scope of the negative not. That is, (2) means that negation ("this is not correct) is possible; logically,

It may be that "this is not the correct place".
symbolically, Possible (Not (Correct (This place)))

So that's the way it is with may not -- it has two meanings, and they're different in how they work.
Getting back to the original question, let me note that sometimes is a quantifier, and has its own scope, which helps complicate matters. And the phrase not sometimes true is, as noted in the comments, already unclear, so let's just say that modals and negatives and quantifiers are very complex and not given to easy explanations.

Using "may not" when something is not sometimes true

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