In English, to express strong obligation we can use either must or have (got) to. Grammars remind us that must is often used to express internal (personal) obligation, deduction (likelihood), and exhortation.
- The insulin shots for your pet must be given at twelve-hour intervals. (deontic)
- We must be late, there's no one in the foyer. (epistemic)
- If he wants to be healthier he must exercise. (deontic)
However, they tell us that have to tends to convey the rules and laws of an external authority which we have no choice but to follow and/or obey. The longer construction have got to is normally classified as being informal, and idiomatic in speech.
- I'm sorry but we have to leave early. (deontic)
- (a) You've got to believe me. (informal)
(b) You gotta believe me. (very informal)
In my experience, this distinction between internal and external authority is very hazy and subjective, with the exception of sentence 2 where no obligation is expressed, native speakers use must and have (got) to more or less interchangeably.
In order to prove my point, consider how English expresses obligation in the past, the form had to is used whereas must is used with the perfect infinitive, i.e. must + have + past participle, to make speculations about the past and to convey certainty.
- The insulin shots had to be given at twelve-hour intervals.
- We must have been late, there was no one in the foyer
- If he wanted to be healthier he had to exercise
- We apologised and said we had to leave early.
- You had to believe me.
In the sentences with had to, the distinction between internal and external obligation is completely lost, greater context is required to know who the person or entity of authority is. In other words, HAD TO functions as the past for both HAVE TO and MUST. If this distinction, which many grammar sites (see below) explain is relevant, why does it disappear in the past?
- How and when did have to express the sense of obligation? What void did it fill?
- If deductions (epistemic) in the past can be expressed with must + have + PP what happened to deontic must in the past? Is there an etymological explanation?
- What happened to the distinction between internal (subjective) and external (objective) obligation when we speak about the past? Did it ever exist?
Modals (1) Obligation
What's the difference between must and have to?
must / have to / have got to
Modals to express obligation: MUST, HAVE (GOT) TO
English modal verbs
Categorization principles of modal meaning categories