The answer to this question, and the question quoted in this question, is the same, really.
Put as an aphorism, it's simple enough:
- Every Modal Auxiliary Verb In English Is Unique.
Every one of the 9 auxiliary verbs has some partial resemblance and partial parallelism to other modals -- but none of them are completely parallel, all participate in different idioms, all have different meanings when combined with negations and quantifications, none of them are paradigmatic in any useful way. Each one is unique, in other words.
Modal auxiliary verbs are basically on the road to becoming new inflections, the way the verb forms of Latin habere became the paradigmatic person markers of Romance future tenses. They've been stripped of all their inflections (except the -d/-t in the 5 modals formed from preterite roots, which adds a syllable in negative contractions), so their paradigms are no longer available (thou mayst or thou mayeth?), and their monosyllabic structure slips through the contractions to show up as a consonant here and a nasalization there in ordinary speech.
Can is a good example of just how weird (another word for unique, really) modal auxiliaries can be. First, there are several categories for modals.
A modal auxiliary is either a Necessary modal, like must, or a Possible modal, like may. Necessary modals include must, shall, will, should, would, and Possible modals include can, could, may, might. Necessary is also called "Square" and "Possible" is also called "Diamond", because of the logical symbols used for them. Every language has both types of modal, though they aren't always auxiliary verbs as in English.
A modal auxiliary verb can contract, and usually does, with other auxiliary verbs, negative morphemes, prepositions, complementizers, and other components of the verb phrase. This can get quite complicated. In some American dialects, affirmative can is pronounced with a higher lax vowel /kɛn/, instead of /kæn/. The negative can't, however, is pronounced /kæn/, with the final /t/ suppressed. Or the /kn/ sequence (especially with a syllabic /n/) might get used by itself:
- /ˌknɛnibəɾi'siyəm/ Can anybody see him?
Every modal auxiliary has at least two senses, with various names, of which the two most common are the Deontic, or "Social" sense, like the deontic must of
- Cinderella must be home by midnight.
Deontic senses have to do with authority, permission, obligation, and control of behavior. They often stem from social prohibitions and prejudices, rather than logic or planning.
and the Epistemic, or "Logical" sense, like the epistemic must of
- Cinderella must have gone to the wrong party
Epistemic senses represent conclusions affirmed by the speaker, generally after consideration of circumstances, times, past behavior, and motives, of what seems to be most or least likely situation.
Note that can does not normally use an epistemic sense in the affirmative:
- *This can be the right place
does not mean
- This might be the right place.
It means, if anything, that if enough work were done to transform it, that it could be made into the right place, rather than that there is a possibility we've arrived.
Provided it's in a negative environment, however, we can (deontic) use an epistemic can, because epistemic can is a Negative Polarity Item.
- This can't be the right place.
Can has another sense beside its epistemic and deontic senses, however; it has to do with personal ability. Indeed, be able to is the usual periphrastic equivalent of ability can
- He can/is able to leap tall buildings at a single bound.
This doesn't mean he just did it, or does it often, or in fact has ever been seen to do it -- just that he has the capacity, according to the speaker. This entails the possibility, of course, but it's a different sort of possibility.
And that's what one finds every time when investigating modals -- they're sui generis to a fault. Every single one has dozens of special functions and constructions and interpretations that are welded or glued or stapled or soldered into or onto or underneath some part of the Big Machine, and they all work. More or less. But there really aren't many useful generalizations except the one I put in boldface above.
