Fair enough 😉 I can appreciate the "shades of grey" stance. For practical purposes, a tolerance for "shades of grey" is generally the more flexible approach, and more in line with "common sense" and real life practices, etc... as it seems we can rarely ever make a clear distinction about real world affairs that we might then attempt to model. I guess the question there though would be: Is it because there is no distinction, or is it because we just can't see it?

For the sake of debate (which I love) let me play devil's advocate and posit these notions and see how far down the rabbit hole we can go:

- Anything outside and/or BOTTOM/TOP of the domain of "true or false" is either inapplicable to true or false or unknown/unknowable as true or false and therefore cannot be evaluated as such. In this example, the other values outside true and false, or the grey, is akin to the mind filling in the blanks of an incomplete picture, and not actually an implication that a BOTTOM or TOP actually exists or that there is actually anything outside that domain. The grey here is only an approximation on the unknown, unknowable, or the seemingly inapplicable. Once known, knowable, or applicable though... it becomes either true or false. That is a limitation on "the knower", not true/false.

- As for any known "value" that is seemingly "grey", seemingly not quite true or false - as opposed to chalking this up to a multi-valued system of logic, one could instead attribute this to a layer of complexity (contrived or otherwise) on top of a fundamental true/false framework, but still essentially a subset of that framework. That's not to say there's anything wrong with going for complexity. The world can be a pretty complex place, so having a complex system of logic can help with understanding interactions at higher orders of magnitude, without the need to evaluate each element individually (i.e. - When counting on your fingers, the finger is only ever up or down, either there is/true/up or there is not/false/down, but since we only have a limited number of fingers to work with... decimal system).

- Any known value perceived to be somewhere either in between true and false or other than, and not one or the other, is actually not one value (simple/atomic), but only represented as one value as a result of higher levels of complexity on top of the fundamental. At it's core though, it is a collection of true and false values, which if decomposed would yield only the two values, regardless of how infinitely or infinitesimally true or false they might be.

I'm sure I have violated one or more mathematical principles somewhere along the way, so feel free to school me 😉 I'm more of a philosopher than a mathematician any way 😎

This is what happens when I can't sleep... :hehe: