may or may not

so a few posts ago, there was a discussion of the semantics/pragmatics of “whether or not” constructions. to sum up: “whether p” constructions (and yes/no questions) demonstrate strong exhausitivity–the idea that knowing the answer to the question is to know the true complete answer (as opposed to just a true answer). lance does a nice job of expositing this in the comment to the “whether” post, so go check that out. so the question is: if to know “whether p” is the same as to know “whether not p”, why do people ever say “whether or not p” (e.g. “john knows whether or not sara likes funk music”)

anyway, tangentially, it occurred to me that there’s a similar puzzle with the disjunction of “may”. the following example comes from an online personality quiz:

“This may or may not describe you: An ‘individual’, i.e. a person who does not conform to society’s beliefs that all people should follow trends and do what their peers do.”