Theory-Elements

Abstract

In this chapter we discuss the simplest kind of set-theoretic structure that may be identified with, or serve as a logical reconstruction of an empirical theory. We call these structures ‘theory-elements’. Theory-elements consist of two parts — a purely formal, mathematical structure K which we call a ‘theory-core’ and a class of ‘intended applications’. Roughly, the formal core K is used to “say something” about the intended applications I. This distinction is introduced in Sec. II.1 and the remainder of the chapter is devoted to discussing different components of the theory-core (Secs. II.2–II.4), the intended applications (Sec. II.6) and the form of the claim made with the core about the intended applications (Secs. II.5 and II.7). Theory-elements are elementary empirical theories in two senses. First, they are the smallest set-theoretical entities that may have empirical claims associated with them. Second, more complex, non-elementary, “molecular” empirical theories are all built from theory-elements that are linked in specific ways (Ch. IV). Paradigm examples of theory-elements in our sense are “fragments” of theories associated with specific laws — for example, the theory of elastic forces, the classical theory of gravitational forces and the theory of van der Waals’ gases.