In this article I give an overview of some recent work in philosophy of science dedicated to analysing the scientific process in terms of (conceptual) mathematical models of theories and the various semantic relations between such models, scientific theories, and aspects of reality. In current philosophy of science, the most interesting questions centre around the ways in which writers distinguish between theories and the mathematical structures that interpret them and in which they are true, i.e. between scientific theories as linguistic (...) systems and their non-linguistic models. In philosophy of science literature there are two main approaches to the structure of scientific theories, the statement or syntactic approach -- advocated by Carnap, Hempel and Nagel -- and the non- statement or semantic approach --advocated, among others, by Suppes, the structuralists, Beth, Van Fraassen, Giere, Wojcicki. In conclusion, I briefly review some of the usual realist inspired questions about the possibility and character of relations between scientific theories and reality as implied by the various approaches I discuss in the course of the article. The models of a scientific theory should indeed be adequate to the phenomena, but if the theory is 'adequate' to (true in) its conceptual (mathematical) models as well, we have a model-theoretic realism that addresses the possible meaning and reference of 'theoretical entities' without relapsing into the metaphysics typical of the usual scientific realist approaches. (shrink)

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field. Our approach was inspired by the work of Whitehead, though our (...) philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

The paper, as Part I of a two-part series, argues for a hybrid formulation of the semantic view of scientific theories. For stage-setting, it first reviews the elements of the model theory in mathematical logic (on whose foundation the semantic view rests), the syntactic and the semantic view, and the different notions of models used in the practice of science. The paper then argues for an integration of the notions into the semantic view, and thereby offers a hybrid semantic view, (...) which at once secures the view's logical foundations and enhances its applicability. The dilemma of either losing touch with the practice of science or yielding up the benefits of the model theory is thus avoided. (shrink)

This paper is the second of a two-part series on models and theories, the first of which appeared in International Studies in the Philosophy of Science, Vol. 11, No. 2, 1997. It further explores some of themes of the first paper and examines applications, including: the relations between “similarity” and “isomorphism”, and between “model” and “interpretation”, and the notion of structural explanation.