At the suggestion of @swamidass I’m going to post portions of the book Science and Its Limits here that will hopefully help everyone get on the same page in regards to what I’ve been trying to express in my previous posts. I’m about half way through the book and so far have gleaned some portions that I think will be helpful in this regard. So I’ll start with this post about how to define theory and let others comment as to what they think about it generally and specifically about the two definitions being offered.
Theories and Models
Preceding discussion has touched on scientific theories, but the term theory has not been explicitly defined. As with science there is no universally subscribed definition of theory, although most conceptions of what a theory is cluster together rather closely. For present purposes we will use the term theory to refer to a network of propositions, some of which involve theoretical concepts, which (ideally) provides a systematic, rigorous account of some portion of the natural realm. A theoretical scientific concept we will take to be a concept that has application, if at all, to physical entities, processes or events not directly observable.
One relatively popular view is that a theory consists of a formal calculus (a set of equations), interpretation of the calculus (providing the meanings and the empirical significance of the symbols used in the equations) and a set of empirical laws (the empirical consequences deducible from the equations as interpreted). Competing with that view is one which stipulates that a theory is not complete without a conceptual model that allows us to intuitively visualize the entities, events and processes to which the other components of the theory refer. This visualization is taken to be crucial since it is, on this second view, only through that visualization that we can in any sense be said to understand what the theory describes. That understanding usually involves being able to construe the unseen, theoretical matters in terms of things with which we are already familiar. It is a reduction to the familiar.