This is certainly a strange divergence of intuitions. I think the story of how I came to know 2+2=4 goes like this: Someone taught me that 2 meant -oo- and 4 meant -oooo-. Then someone probably be told me that 2+2=4 but I don't think they would have needed to. I think I could easily have come to the conclusion myself since given -oo- and -oo- I can count four dots. If pushing four objects together meant one of the objects disappeared I would probably just stop pushing objects together and count in my head. If counting the objects made one of them disappear I would be pretty damn frustrated but I'm pretty confident I could realize that reality was changing as a result of a mental operation and not that I was counting wrong. Aside from being tortured with rats or Cardassian pain sticks I don't see what would make me think that 2+2 didn't =4.
I'm not sure how to explain my thinking any better except to say that it is the same thinking that lead generations of philosophers and mathematicians to conclude that mathematical knowledge was a different kind of knowledge than knowledge of our surrounding and the natural world. My reason is the reason Kant distinguished the analytic from the synthetic- a sense that a rational mind could figure these things out without sensory input.
Saying that 2+2=4 is a tautology in a certain axiomatic system defined with '+' means that you couldn't have anything but 2+2=4 in that system. It's simply mandatory, and a rational person could not wake up one day and be convinced that 2+2=3 within a self-consistent system that deduces 2+2=4.
While tautological truth is independent of observation (let's call it mathematical truth), it is dependent upon context (i.e., a self-consistent axiomatic system). Some mathematical truths in one axiomatic system are false in another. When we talk about whether a a m...
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."