Equivalence from a Metaphysical Point of View

Theodore Sider (Rutgers University - New Brunswick)

Abstract

Equivalent' theories represent the very same state of the world; any differences are merely conventional or notational.  According to one view, equivalent theories are those that say the same thing about fundamental reality, understood in a particularly fine-grained way.  According to a second view, which I call "quotienting" (short for "quotienting-out conventional content by hand"), theories may be equivalent even when we cannot state, in an intrinsic or "artifact-free" way, the content that the theories have in common.  In a sense these are the extreme positions on the metaphysics of equivalence.  The first view (which I accept) leads to the uncomfortable conclusion that we must recognize questions such as whether negation and conjunction, as opposed to negation and disjunction, form the metaphysically correct basis for propositional logic as being genuine questions.  The second is dizzying, but sheds light on various otherwise perplexing viewpoints in metaphysics, philosophy of physics, and philosophy of mathematics.