P.S. the Western tradition leans towards the law of the excluded middle, which can lead to binary thinking, rooting for the right team. Other traditions hold to true, false, neither true nor false, or both true and false. Or could have a little slidy scale instead of a toggle and then a UI library that you need to link against and fastcgi support and
/blog/2023/08/28/history-of-the-world-part-iii.gmi
So this turned into a little rabbit hole of digressionary research. At least the logic part, not any UI library or linking. So one thing that Aristotle is said to have said is that every claim must be either true or false with no other options. This tidbit got hard boiled into Western logic for a long while. (This may have been assisted by a particular belief in only good versus only evil and no other option.)
Another thing that Aristotle is said to have said is that there are statements that are neither true, nor false. Whoops, is that a third choice? An example would be "the first cat born in the 22nd century will be named Socrates" which is (at this time) indeterminate, neither true nor false. Worse, you can have statements that are both true and false. Various paradoxes such as the old "this statement is false" apply here.
Apparently logicians now argue whether traditional Aristotelian logic remains shipworthy or has transcended, like the Moskva, to submarine service. Maybe within the system it is okay, but not if you step outside, or invite Gödel in? Douglas Hofstadter also talks about the need to maybe step outside a system to understand it.
So above we had four options (true, false, neither, both) which were reportedly in active use around the time of the Buddha. Apparently the Buddha went beyond these four choices, adding another option, "other" or as some call it, the ineffable. Part of this is pragmatism, unrelated to logic: if a fool invades, you want to beat him and worry about other things—is the invader balding?—or, how Orthodox is the Church he belongs to?—only later, or never. The logical aspect involves questions that do not make sense or where an answer cannot be given within the framework.
Nonsensical questions run along the lines of "when the fire went out, which direction did it go?"—if the fire had been a cat, then the question would be reasonable. This gets into metalinguistic territory: "when did you stop beating your wife?", "5 is not blue", and so forth. Some of these fall into the "neither true nor false" (if one has never had a wife) and may be difficult to tell apart from something that is ineffable.
Philosophers in the Western tradition have touched on the ineffable, as have mathematicians dabbling with plurivalent logic. How can you talk about something that you can't talk about, anyways? The mathematical version involving ordinals in one of the links below seems pretty legible. Beyond that, it's often a zen master overflowing your teacup. This implies that one should use a language with overflow protection, or at least to stay away from zen masters armed with teapots.
https://aeon.co/essays/the-logic-of-buddhist-philosophy-goes-beyond-simple-truth
tags #philosophy