The Structure and Content of a Physical Theory

Abstract

In analyzing a physical theory we may distinguish at least four aspects of it: the background, the form, the content, and the evidence-if any. By the background of a theory we mean the set of its presupposi-tions. By the form or structure, the logico-mathematical formalism quite apart from its reference to physical objects or its empirical support. By the content or meaning, that to which the theory is supposed to refer, quite apart from either its form or the way the theory is put to the test. And the evidence a theory enjoys is of course the set of its empirical and theoretical supporters. In this chapter an analysis of the internal structure and the external reference of a physical theory will be sketched. To avoid talking in a vacuum we shall take a particular theory as our object of analysis. And, to make our work more interesting and easier, we shall build the theory from scratch-i.e. with the sole help of generic (logical and mathematical) ideas. We shall proceed in the following way. We shall start with a very simple idea which shall subsequently be expanded into a self-sufficient mathematical formalism Po. We shall find it impossible to assign a physical interpretation to all the basic concepts of Po in order to turn this calculus into a physically interpreted calculus. Whereupon we shall expand this narrow formalism into a more comprehensive structure 1\. Next we shall transform this mathematical theory into a physical theory PI by the adjunction of appropriate interpretation assumptions. Then we shall perform a further generalization, yielding a theory P2 which will turn out to be the well known two component theory of the neutrino. In the process we shall see the self-propelling virtue of mathematics, we shall realize how the mathematical structure limits the possible meanings of the key symbols, and how these meanings are suggested as the theory is worked out rather than being assigned at the outset.