**Disclaimer.** The question below is necessarily vague. I understand neither the subject matter *topos theory* nor the object about which my question is (the construction of a fractional / non-binary / elastic notion of truth). Thanks in advance for your patience.

I've often heard whispers of vague statements like: "*topos theory* can be used to give continuous, subtle, and perhaps a much more interesting notion of *truth* (not just **True** or **False**, **Right** or **Wrong**, **Correct** or **Incorrect**)". For lack of better terminology, let us refer to this mysterious phenomenon / concept as *fractional truth*.

Question.What is a minimal construction which already displays this phenomenon?

I have essentially no knowledge of topos theory (but a decent handle on set theory, group theory, and topology, etc., and I'm naively assuming that this should be sufficient to understand the would-be construction, which I'm also assuming can be made so simple).

9more comments