As someone who has always found the “Law of the Excluded Middle” a bit nonsensical, some years ago I tried to find someone who could say a little about “fuzzy logic,” (as opposed to Aristotelian logic) only to be surprised by how few folks (mathematicians, at least) cared to address it (perhaps it falls more into the realm of philosophy, logic, or even computer science). Anyway, happy to see Jim Propp touching upon it (well, scratching the surface) in his latest piece here:
https://mathenchant.wordpress.com/2022/01/17/bad-soup/
The one sentence in the piece though that somewhat made me cringe is an almost offhand, parenthetical remark where Jim says "Well, you don’t always have to be careful, but when things are fuzzy, you’re aware that they’re fuzzy and you value the removal of the fuzz" (bold added). Actually, I think the problem that arises so often is that people DO NOT consciously or fully recognize "the fuzz" which is what allows them to speak so dichotomously (and strongly, but wrongly) about matters that are not so cut-and-dry as presented. Even if at some level there is 'awareness' of the fuzz, if it is not fully acknowledged, then it may tend to be ignored, swept under the mental carpet like so many dust bunnies (instead of genuinely removed). And while 'fuzziness' is a particular problem in the social/behavioral sciences it can also creep stealthily into math, engineering, and their outgrowths.
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