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- About the most recognized use of Mathematician's Answer is answering "yes" when meaning "both". "Do you prefer it shaken, or unstirred?" "Yes." This is universally understood by more or less everyone on the Internet. Which is what bugs me, since technically, mathematically if you will, such an answer would mean "yeah, one or more of them", which is nearly no answer at all. What is appalling is that no one else seems to notice the incongruity, and the Internet should be smarter than that. Am I wrong? Are they wrong? Is the Internet broken? The uncertainty is tearing me apart.
- To give you an actual answer: This is a semantics issue. Most people never specify that the person has to give them an answer as the first listed choice, the second listed choice, or both. They just say give them an answer. When you ask an either/or question without adding in more specifications, "Yes" is still the correct answer because the question could be interpreted as "Do you like either X or Y?" instead of "Which do you prefer more, X or Y?" In the former, "Yes"/"No" is a suitable answer because I could break it down into two questions (Do you like X? Do you like Y?) that I can choose to answer at the same time with one answer since they were originally in the same question to begin with. With the latter, which is the example you gave, I'm specifically told to give an answer between two given options that I presumably feel a certain way about to some degree in either case. Of course, if someone wanted to be an asshole, they could just respond with part of the question by saying "I could possibly like X or Y more.", but then they just look uncertain.
- "Mathematically" (well, formal-logically -- whatever), most people who say "or" in casual conversation are understood to be using the exclusive or, for which "both" is not a valid answer. But, if you don't specify, you could be (mis)interpreted as using the "regular" or, for with "both" is the correct answer. More generally, it's about people treating it as a logical query ("is X or Y true?") rather than a request for elaboration.
- The Mathematician's Answer is, in that context, supposed to be "yes," meaning "yes, one or more of them." Wait...is that basically what the last guy said?
- Amusingly, that was not a Mathematician's Answer.
- When spending too much time around people too fond of this particular ploy, the quickest way to get a useful answer is to respond to the "Yes" with "Which?"
- Given the Mathematician's Answer's association with the Straw Vulcan and other only-pseudo-logical tropes, it's entirely possible that the authors know "yes" isn't a valid, let alone logical, answer to the question, but the person doing the answering wants to be cryptic and/or a smartass. It's very rare that the answerer doesn't recognize their Mathematician's Answer for what it is.