In the OB post tautologies have to be empirically observed somehow, Eliezer writes about waking up one day and discovering all sorts of evidence that 2+2=3. This wouldn't be evidence that 2+2=3 in Peano arithmetic, it would be evidence that Peano arithmetic just doesn't apply for some reason. In my down-voted comment, I was just giving an example of how there can be different kinds of arithmetic if you are willing to be flexible about what arithmetic is. (If you are not willing to be flexible, then you are not willing to allow the observation that 2+2=3 as an observation about arithmetic, because this is not possibly true in standard arithmetic. Well, the observations are possible but you'd have to account for it as some kind of grand delusion.) My point is that 2+2=4 in Peano Arithmetic independent of observation, but observation tells you if Peano arithmetic applies or not.