Equivalence

Abstract

What is it for theories to be equivalent? Two extreme accounts are considered. According to the account I defend, equivalent theories are those that say the same thing at the fundamental level. This leads to certain uncomfortable choices: should a theory of time be based on a fundamental relation of earlier-than, or later-than? Should a metaphysics of logic including negation include also conjunction, or disjunction? These are normally regarded as paradigmatically equivalent theories, but my account cannot recognize this. According to the second extreme account, relations of equivalence need not be underwritten by a fundamental account of their common content. We can "quotient out" theoretical differences by simply saying, without explaining, that theories are equivalent. Objections are given to this account. But the more important moral is that the issue of quotienting often lies under the surface, but has profound implications across metaphysics and philosophy of physics, including the discussions of structuralism in earlier chapters.