One of the first things that bothers me is that Mr. Thompson never seems to tell us what modality itself is, conceptually. Perhaps he believes that we all should know, since his article is written for EFL/ESL teachers. I guess I am a laggard, though, because I must confess I don’t have a really clear idea of this, and I’m convinced that students will not either. Somehow, if we’re going to teach them about modals at all, we have to find a way to get this idea across—if not perfectly clearly, then at least well enough so that they can grasp what it is we’re talking about. To simply start by talking about the forms of modality, and it’s various subdivisions looks to me like heading for trouble.We ask our students to learn a lot when we ask them to learn modal auxiliaries and modal equivalents. [] There are, first of all, the myriad forms taken by the various modals, some of which have subtle distinctions. Students need to become comfortable with the fact that can does not take the auxiliary do in a question (no *do you can speak Spanish?) while have to does (no *Have you to go to Rome?).
More important is that modals are distinguished from other auxiliaries by the fact that they have meaning. Students, therefore, need to become comfortable not only with the grammatical properties of modals, but their semantic properties as well. This is complicated by the fact that there is more than one category of meaning and the same modals are often used in more than one.
The first category -- called "deontic modality" -- is used to perform speech acts, such as offering, requesting, granting permission, commanding, etc.. When I tell my son, "You must be home by 10 o'clock." I am using deontic modality.
The second category -- epistemic modality -- is used to express the speaker's opinion about the truth of a proposition. When I say, "You must be Rachel Thorne. You look just like your sister." I am saying that I am certain that the proposition "you are Rachel Thorne" is true.
A third category of modality is a bit more elusive. One characteristic of both deontic and epistemic modality is that the modals are connected with the speaker, not just the subject. With deontic modality, the modal refers to what the speaker is doing with the sentence. With epistemic modality, the modal refers to how the speaker sees the proposition. The third category -- sometimes called "dynamic modality" -- is more subject-oriented. "Rosa can run a mile in under five minutes." refers to one of Rosa's abilities; it does not give information about the speaker.
A third hurdle for English-language students is that not all languages prefer to use modals to express these ideas. Modality is often expressed with other forms of speech. "You are obliged to be home by 10 o'clock", "I am certain that you are Rachel Thorne. You look just like your sister.", and "Rosa is capable of running a mile in under five minutes." all express the ideas explored, and if they sound stilted it is only because English has a preference for modal verbs rather than modal adjectives.
His distinction of modals from other auxiliaries by the fact that modals have semantic meaning while other auxiliaries (in their auxiliary uses) do not is a gem. Although I know instinctively and immediately that it is true, I have never before voiced the distinction, and so this seems brilliant to me.
The three expressed categories of modals (he uses the term to mean both modal auxiliaries and modal equivalents, which he defines as auxiliaries which may express modality, but which do not behave like members of the closed class of modal auxiliaries—can, could, will, would, etc.) may be useful to linguists, as I’ve said before, but I cannot seem to get my teacher’s mind around it. That is, I can’t see where this will help teachers working with students to develop their expertise in understanding and using modal auxiliaries and/or modal equivalents. I say again, it is enough to explain that modality allows a speaker to express his judgment about the proposition of a sentence. So called “dynamic modality”—Rosa can run a mile in under five minutes—, for example, can clearly be seen in this way. The speaker’s use of can before run creates the meaning that he believes that the proposition Rosa runs a mile in under five minutes is possible. The sentence (with can) is therefore surely about Rosa, but it also is about the speaker of the sentence in a perhaps indirect but nonetheless powerful way. In fact, in a direct comparison of the two sentences,
Rosa can run a mile in under five minutes.
Rosa runs a mile in under five minutes.
I believe the second one is a simple statement of fact (as the speaker sees fact), but the first is the speaker asserting his attitude, at precisely the moment of speaking, about Rosa running a mile in under five minutes. It is grounded in the present moment, whereas the second sentence is a truth expressed without reference to time. (Not, of course, that it is true for all time, but rather that time is irrelevant for the speaker on this subject now). The point of all this is to argue against Thompson’s assertion that this particular use of can points at the subject of the sentence and “does not give information about the speaker”. I don’t buy it. All modality, if I understand modality correctly, is precisely for the purpose of giving information about the speaker’s attitude at the present moment, and not for pointing at any syntactic element of the sentence.
So I return to my original question: For teachers, what is the point of subdividing modality? It appears to me to confuse rather than clarify.
On the other hand, the points he makes in his last paragraph above are excellent. We teachers must help our students to understand that modality, or something like it, can be expressed without necessarily using modal auxiliaries. (Now, of course, we'll have to answer their questions about when to use them and when to use something else.

Larry Latham