I must have been sleeptyping too, in my earlier comment about the lack of a past tense form with "must", since "must" is already a past tense form (of the obsolete "mote").

It's interesting that "I have got to" and "I must" both use past tense forms for a present tense meaning. At first, I wondered whether this was because the use of "must"/"have got to" implies an obligation that has already been imposed; but that doesn't necessarily explain e.g.

1. You must go directly to the headmaster's study...

where the obligation is imposed at the moment of utterance. But then, perhaps such an obligation would have to be based on some previous requirement, e.g. school rules.

"You have to go directly" does seem the weaker form; and it may well imply a subjective requirement on the speaker's part, rather than an objective requirement – though the latter is also possible; but then, we have the use of "had to" for both in the oblique form.

Though on reflection (and again rebutting my earlier post) this is also possible, if less common:

2. He said I must go directly... 

It's a murky little modal.

MrP

CalifJim wrote:

The conflation of two modals. Why don't you just get rid of one of them? This is not the conflation of two modals.  It is a distinction in usage based on a different parameter from the one you may be used to.  That is, the distinction is made on the basis of whether the meaning is epistemic or deontic, not whether it is subjective or objective.  Since a distinction still exists, I don't think we can say that the two are conflated. CJ

Note: epistemic modality is subjective and deontic modality is objective.

CalifJim wrote:

epistemic modality is subjective and deontic modality is objective. I disagree completely.  Objectivity has more to do with an external viewpoint, subjectivity with an internal viewpoint.  If there is any possible and slight correlation between the subjective/objective polarity and the epistemic/deontic polarity, I would reverse your quote:  Epistemic modality (having to do with cold logic) is objective; deontic modality (having to do with our interpersonal, social interactions, and the excercise of the will) is subjective.  But even this is suspect.  I don't view subjective and objective as exact enough terms to explain the use of modals to students.  They are too subject to a variety of interpretations, which, in my experience, confuse students more than enlighten them. CJ

It gets a bit more complicated than that, I'm afraid. Epistemic modality can have a subjective (more prototypical) and an objective side.

Tell me, which of the following is epistemic, IYO? Which is subjective?

It may rain tomorrow. (Uttered by a weaterman)

It may rain tomorrow. (Uttered by a layman)

milky,

Both of these are epistemic.  Both are objective, and vacuously true:  It is possible that it will rain tomorrow.  No one's subjective feelings need be consulted on this.  The rules of logic alone render the statement true no matter who says it.  (The truth table for It may be the case that X is consistently true for all  X.)
To be deontic, may would have to take on the meaning has permission to, as in:  It has permission to rain tomorrow.  Had you annotated the sentence with (Uttered by a witch-doctor), I might be tempted to consider a deontic reading!  Otherwise, impossible!

_____
I'm surprised you chose may as the example.  must allows many more opportunities for exploring the possibility of a combination of subjectivity with the epistemic usage of modals.

CJ