Learn English – Can “must not” be used alternately to “can’t” in AE to say that sth is logically impossible

american-englishcolloquialismsusage

Does American English allow the use of "must not" instead of "can't" to say that something is believed to be logically impossible?

Please consider the following examples:

It must not be true!

How can you say such a thing? You must not be serious! (-you gotta be kidding!)

A: Joe wants something to eat.
B: But he just had lunch. He must not be hungry already.
(-it's impossible that he is hungry because he just had lunch)

I just bought a box of cereal yesterday. It must not be empty already.

You just started filling out your tax forms 10 minutes ago. You must not be finished with them already?

If A is bigger than B, and B is bigger than C, then C must not be bigger than A.

Best Answer

What you're asking about is called the Epistemic sense of a modal.

Every modal auxiliary verb that's still used in English has at least two senses:

  1. The Epistemic sense, which has to do with logic and perceived probability
    This may/might be the place ~ This must/should be the place ~ This could be the place.

  2. The Deontic sense, which has to do with permission and obligation
    You may/might kiss his ring now ~ You must/should kiss his ring now.

In addition, there is an Alethic sense, which has to do with personal ability, and shows up only with can. E.g, He can bench-press 150 kg means 'He is able to bench-press 150 kg', which obviously entails that it is logically possible but attributes this possibility to the subject rather than to logic.

That's general. Specifically, modals are irregular as hell, and must and can are more so than usual. In addition, all modals interact with negatives, but not in the same ways. Again, they're different.

In American English (UK Englishes vary), epistemic can occurs only in a negative environment.
This can't be the place ~ This can't be true, but not *This can be the place ~ *This can be true.
I.e, epistemic can is a Negative Polarity Item (NPI). In American English, at least.

Can, outside negative environments, usually takes an Alethic sense instead of an Epistemic one,
but it's equally common as equivalent to Epistemic may 'permitted to'.
You can/may leave 'You are permitted to leave'.

Epistemic must is not an NPI, but it has a specific meaning with not.
You must not go to the ball means 'You are obliged not to go to the ball'.
It does not mean 'You are not obliged to go to the ball'.
Logically, that's Not (Possible (Go (You, Ball))).

On the other hand, the periphrastic modal have to, which means must in the affirmative,
(You have to leave now = You must leave now 'You are obliged to leave now'),
means 'You are not obliged to leave now' in the negative,
and not 'You are obliged not to leave now'.
Logically, that's Possible (Not (Go (You, Ball))).

So, to answer the original question, Yes. I.e, since they're both negative, can't and must not both negate possibility (i.e, Not (Possible (P)) instead of Possible (Not (P))) in their epistemic senses, so they're equivalent.

Of course, the differences among logical possibility, personal ability, and official permissions can be very complex and hard to distinguish, so there are -- Surprise! -- exceptions. Just like everything else about modals, negatives, and quantifiers (these are logically Operators, which have logical superpowers of binding foci).