'Must' & probability

Question

Sometimes I notice that there is a difference in opinions regarding the use of 'must' relating to probability.

These three sentences look to me correct:

He must be in the library (He and the key to the library are absent)

He must have done the work. (No tools in the room)

He must be lucky. (He won a lottery)

But the use of 'must' in the three examples below looks to me incorrect:

He must be in the library. (Usually he is there at this time)

He must have done his work. (As a rule he finishes at 5 but now is 6)

He must be happy. (He won a lottery)

What is your opinion?

Answer 1

There are actually three four common usages of must.

1. Indicating that something is a necessity, or is compulsory 'You must do your homework'.
2. Indicating that something is very likely or very probable 'He must be in the library (Usually he is there at this time).
3. As a noun (and related to 1.) something that is essential or very important. 'Reading Fowler's Modern English Usage is a must for all English students'.
4. As a noun, it refers to young wine.

Answer 2

The examples that make you uneasy seem to use the modal verb must in its epistemic meaning, expressing the speaker's degree of confidence in the proposition. (Or, in what you refer to as 'probability'.)

Here's a sample paper that discusses the nuances expressed by epistemic must, for reference.

Answer 3

English like most languages are imbued with idiomatic and sarcastic usage.

We know that the following phrases are meant to be courteous polite phrases

• Please
• Could you please
• I would

However when used in many contexts, those phrases actually mean to say "Well, I am being as polite and gentle as possible to tell you knuckle-head to do what I think is best."

• Please sit down !
• Could you please shut up ?
• I would not tell my children to walk alone in the night like you did.

Must is a word that connotes mandatory.

• It must be there but it isn't.
• For the fish to survive, you must clean the tank, but you didn't.

Usually, must is used in cohortative subjunctive or imperative subjunctive situations. But what happens when you use the word must in a propositional subjunctive situation?

Reference: Use of subjunctive form

Subjunctive situations have been categorized/quantized by linguists into various pigeon-holes, but in reality is a continuum. Just as real and imaginary numbers are a continuum of combinations, frequently a sentence is formed to describe a situation with a mix of real and subjunctive moods.

Like when real numbers are applied to the imaginary axis, when normal tenses and moods are applied to the imaginary realm, they take a turn in their directions. The varying and diverse combination of real and imaginary, influences the how the direction changes.

• Imperative: You must have $10 to buy the ticket.
• Cohortative: You must win the game for us.

Propositional disguised as imperative to imbue intensity of belief:

• My credit card must be in the house, or else I'm doomed.
• He must be in the library, but I am not sure.
• He must be lucky. (I know he is not that good. It is just luck)

A mix of propositional and imperative

• He must be lucky. He must have been lucky to have won the race. I really need him to have been lucky. Otherwise, there is no hope for me to win the next race against him.