The map is not the territory. There’s no little XML tag attached to helium atoms with the wave equation written on it. Math was created by humans to describe our observations—we didn’t arrive at it by pure thought. The reason 2 + 3 = 5 is a theorem of Peano arithmetic and moving three large, distinct objects next to two large, distinct objects makes a group of five large, distinct objects is the correspondence of the Peano axioms and inference rules to reality.
So I think Eliezer’s error here was a fallacy of compression. “2 + 3 = 5” refers to two distinct propositions—that “2 + 3 = 5″ is a theorem of Peano arithmetic, and that moving a group of 3 apples (or one of many other types of large, distinct objects) next to a group of 2 apples will result in a group of 5 apples.
The map is not the territory. There’s no little XML tag attached to helium atoms with the wave equation written on it. Math was created by humans to describe our observations—we didn’t arrive at it by pure thought. The reason 2 + 3 = 5 is a theorem of Peano arithmetic and moving three large, distinct objects next to two large, distinct objects makes a group of five large, distinct objects is the correspondence of the Peano axioms and inference rules to reality.
So I think Eliezer’s error here was a fallacy of compression. “2 + 3 = 5” refers to two distinct propositions—that “2 + 3 = 5″ is a theorem of Peano arithmetic, and that moving a group of 3 apples (or one of many other types of large, distinct objects) next to a group of 2 apples will result in a group of 5 apples.