A few weeks ago I caught myself saying "might didn't". When it came out I was confused, and assumed, like my cohorts, that it was a speech error. But the next day I did a bit of google searching, and realized that in fact "might didn't" is a construction associated with the use of double modals, and that perhaps I was successfully integrating double modals into my grammar.
One example: "Great Tools For YouTube And Online Music Streaming You Might Didn't Know Of"
In standard English this would be "Great Tools...You Might Not Have Known Of", or hypercorrect "...Of Which You Might Not Have Known". The "might didn't" construction indicates to me that syntacticians are missing the boat if they claim double modals are merely lexicalied constructions inserted whole into T. "Did" isn't a modal, and there are clear syntactic parallels between "might could" and "might did". What we need is a theory of grammar for double modal dialects that correctly accounts for the pattern of usage, not a theory that best fits standard dialects and half-heartedly accounts for certain superficial aspects of double modal grammars. Personally, I'm interested in a proper syntactic account of double modals because I'm all for accurate description of minority languages and dialects, but I have a feeling that such dialects could also reveal important things about what might could be a part of Universal Grammar.
Jerome Stueart interview (pt. 3)
4 years ago