Realism and Empirical Equivalence

The main purpose of this paper is to investigate various notions of empirical equivalence in relation to the two main arguments for realism in the philosophy of science, namely the no-miracles argument and the indispensability argument. According to realism, one should believe in the existence of the theoretical entities (such as numbers and electrons) postulated by empirically adequate theories. According to the no-miracles argument, one should do so because truth is the the best explanation of empirical adequacy. According to the indispensability argument, one should do so because the theoretical terms employed in the formulation of an empirically adequate theory are practically indispensable for the formulation of its empirical content. The no-miracles argument might be refuted if one can establish an underdetermination thesis to the effect that every theory has empirically equivalent rivals that are incompatible with each other. Insofar as truth cannot explain the empirical adequacy of two incompatible theories, there is an obvious conflict between the underdetermination thesis and the no-miracles argument. I show that, under certain assumptions, some but not all notions of empirical equivalence support the underdetermination thesis. The indispensability argument might be refuted if one can establish a dispensability thesis to the effect that, for any theory with a practical formulation (e.g. for any axiomatizable theory), there is an empirically equivalent theory with a practical formulation in purely empirical terms. I show that (using axiomatizability as the measure of practicality) some but not all notions of empirical equivalence support this thesis