It is worth emphasizing that to claim that “2+2=4 in Peano Arithmetic independent of observation” is not to claim that our knowledge of this fact about Peano Arithmetic is independent of observation. (The former claim is about our map of the territory; the latter is about our map of our map of the territory.)
Could you elaborate? It sounds to me like the former claim is about the territory, and the latter is just hard for me to parse.
Could you elaborate? It sounds to me like the former claim is about the territory, and the latter is just hard for me to parse.