Double modals are a feature of certain dialects of American English. For a long time I thought this construction was limited to the South, but I have since learned that there are other areas of the country featuring double modals, including Michigan. Some of the more common examples of double modals include "might could", as in "I might could do it" for "I might be able to do it", or "used to could", as in "I used to could do it" for "I used to be able to do it". Because these constructions are stigmatized in prescriptivist grammar (and perhaps because they don't occur in the Northeast or California), they haven't gotten a lot of attention in the linguistic literature. Given that current syntactic theory places modals in the T node, it's unclear how we should represent something like "might could".
One idea that non-speakers of the relevant dialects have is that double modals are redundant or unnecessary (in addition to of course being incorrect). However, to speakers of these dialects phrases like "might could" and "might be able to" are not in complementary distribution. In an example like "might should", the double modal indicates a very different information state than "should". A better translation would be "It might be the case that I should", expressing perhaps an irrealis deontic mood. A good example of non-speaker confusion can be found in one of the COCA hits for "might should", referring to a Southerner saying "he might should go" rather than "he might go". Of course, any person that speaks a double modal dialect knows that these two are not at all equivalent semantically or truth-conditionally. My point here is not to poke fun at those who don't know how to use double modals (although I might should poke fun at those who poke fun at those who use double modals). My point is simply that double modals enrich the English language, sometimes creating a shorter way to indicate an information state ("I might could" versus "I might be able to"), and sometimes conveying information that can't easily be conveyed any other way. It fills a niche in the same way that y'all or youse fills the want for a contrastive second person plural pronoun.
Jerome Stueart interview (pt. 3)
5 months ago