That point of view has far-reaching implications that make me uncomfortable. Consider two physical theories that are equivalent in every respect, except they use different definitions of real numbers. So they have a common part C, and theory A is the conjunction of C with “real numbers are Dedekind cuts”, while theory B is the conjunction of C with “real numbers are infinite binary expansions”. According to your and Eliezer’s point of view as I understand it right now, at most one of the two theories can be “true”. So if C (the common part) is “true”, then ordinary logic tells us that at most one definition of the real numbers can be “true”. Are you really, really sure you want to go there?
That point of view has far-reaching implications that make me uncomfortable. Consider two physical theories that are equivalent in every respect, except they use different definitions of real numbers. So they have a common part C, and theory A is the conjunction of C with “real numbers are Dedekind cuts”, while theory B is the conjunction of C with “real numbers are infinite binary expansions”. According to your and Eliezer’s point of view as I understand it right now, at most one of the two theories can be “true”. So if C (the common part) is “true”, then ordinary logic tells us that at most one definition of the real numbers can be “true”. Are you really, really sure you want to go there?