$$

$$

Every proposition is either true or false. This famous tautology is called the *law of excluded middle*. As the words “tautology” and “law” suggest, the law of excluded middle is often taken to be obviously true and attempts to deny it as bizarre and esoteric. But it is easy enough to imagine everyday situations that challenge the obviousness of this principle. Suppose I loiter in the doorway of your office, with one foot in the room and the other in the hallway. Am I in your office, or not? The law of excluded middle says that we must regard exactly one of the two propositions as true, but the choice of which seems arbitrary. Such conundrums are typical of the “logic of space.”

This is a companion discussion topic for the original entry at https://blog.algebraicjulia.org/post/2021/09/cset-graphs-4/