That 2+2=4 is a fact about a mathematical system that exists independently of the physical universe, including us humans that decided to use those symbols to express that fact. That fact is in the territory. But, in order to interact with the physical universe, it has to be discovered by some physical system that explores logical conclusions, such as our brains. This exploration builds our map of the territory. Our uncertainty about the tautological statement does not reflect some vagueness in the territory of logic, but our uncertainty about the workings of our physical brains, and their ability to build maps that reflect the territory.
Problems of logic have 100% correct answers, but our physical brains cannot become 100% entangled with those correct answers. It is observation, which can be abstract observations of our own logical reasoning, which give us increasing entanglement which approaches, but never reaches, 100%.
This is really helpful and I think I agree with all of it. I've just never understood "observation" to include my logical reasoning. If your position is that we know 2+2=4 by virtue of observing our own reasoning and not by virtue of any sensory data (information about the outside world) then I don't think that position is any different from the one I already hold. But is this Eliezer's position? His OB post made it sound like he could be swayed to think 2+2=3 as a result of external events mediated by his sensory perception of those events. That is what I objected to.
David Stove's "What Is Wrong With Our Thoughts" is a critique of philosophy that I can only call epic.
The astute reader will of course find themselves objecting to Stove's notion that we should be catologuing every possible way to do philosophy wrong. It's not like there's some originally pure mode of thought, being tainted by only a small library of poisons. It's just that there are exponentially more possible crazy thoughts than sane thoughts, c.f. entropy.
But Stove's list of 39 different classic crazinesses applied to the number three is absolute pure epic gold. (Scroll down about halfway through if you want to jump there directly.)
I especially like #8: "There is an integer between two and four, but it is not three, and its true name and nature are not to be revealed."