And in fact it seems the binary logic is the only type of logic there is. The law of excluded middle is absolute - the simplest question possible is a yes or no question.
Yet, is this actually so?
Like all the questions pertaining to the laws of logic, it's literally the most difficult question possible, because you generally can't use logic
For instance, what would a world where A = !A or A != A look like? I can imagine it, (chaotically changing things) but when I try to conceive it logically, it all falls apart.
The law of the excluded middle might be easier since you can use identity and contradiction to analyze it, unlike the example.
Still, this is an unexamined assumption of all human endeavors; that the law of excluded middle holds everywhere. On the other hand, I cannot even guarantee if it is true.
The reason this is important is that the binary nature of logic is the reason for the NIP. Binary logic cannot describe a continuous universe.
"General relativity, for instance, has successfully predicted many things that we can observe, such as gravitational lensing, so we also take seriously its predictions for things we cannot, like the internal structure of black holes."
Except that the internal structure of black holes is a singularity, and impossible to describe with bits. Most physicists acknowledge that this means GR is inherently incomplete - the problem isn't physical infinities, but physics theories that have infinities.