[gurtwo]

Casual sentences and mathematics/logic don't go very well together, and lead to ambiguities and interpretation if there are no clear rules defined beforehand. This reminds me of those silly problems that circulate on TikTok with a series of additions and multiplications. The "correct" result depends on how you assume the operations precedence. Here, does "being a liar" mean that we have to take as a true statement the negation of "all my hats are green"? If so, is that "NOT all my hats are green"? How does that translate back to the mathematics realm? Is it {total_hats>0, green_hats>=1}, or is it {total_hats>=0, green_hats>=0}?

[jerf]

The correct answer to almost all of these problems that play with the hierarchy levels between English and Math is "undefined". If you want to play in English, you get intrinsically sloppy, provisional, and context-specific answers, and that is effectively by design and a feature, and anyone who insists that there is only one answer is in error. Our languages work that way for good reasons; we see the costs of the occasional misinterpretations, but the benefits of language not requiring endless precise specifications for everything that is obvious in context is taken for granted.

By contrast, if you want to play in Math space, you need to be rigorous, and provide a Math-quality conversion.

If you refuse, what this reveals about the one posing the problem is that they themselves labor under the delusion that you can apply math rules to English, that there is exactly one and only one such mapping, that everyone should know and agree upon that mapping, and that is so true that you are justified in playing "gotcha!" games with people who don't know this nonexistent mapping.

It doesn't paint a terribly flattering picture of such people, in my opinion.

In the meantime, the rest of us should meditate a bit on "The Only Way To Win Is Not To Play The Game", because spiraling down trying to figure out the exact nature of the aforementioned nonexistent mapping is just a waste of time. There isn't one, so arguing it is just a waste of time and emotional energy. Pick a lane up front. They're both fine, but anything that functions by always choosing whichever lane maximizes the "gotcha!" in the moment is not worth spending time on.