Reduction, Interpretation and Invariance

Abstract

This paper sketches a way of describing reduction relations among theories as a special case of a more general view of the logical structure of related empirical theories. The key concepts in this view are “model element” (Sec. 1) and “inter- theoretical link” (Sec. 2). Model elements provide a formal characterization of the conceptual apparatus of individual theories. Intertheoretical links provide a unified treatment of particular, well-known intertheoretical relations such as reduction, specialization and theoritization and include, as well, other types of relations among empirical theories. The global structure of empirical science is represented as a net of linked theories (Sec. b). Central to the understanding of empirical science are interpreting links. These links provide a kind of “empirical semantics” for the mathematical apparatus associated with individual theories. Interpreting links are characterized and distinguished from reducing links (Sec. 3). The concept of an interpreting links provides us with a formal characterization of the distinction between theoretical and non-theoretical concepts, relative to a given theory and the net in which it lives (Sec. 5), as well as a formal characterization of the intended applications of a theory in a net (Sec. 7). The role of invariance principles in relation to interpreting links is described (Sec. 6). Finally, these ideas are exploited to provide an account of the way interpreting and reducing links work together (Sec. 8).