The Poznań school methodology of idealization and concretization from the point of view of a revised structuralist theory conception

Abstract

My thesis is that some methodological ideas of the Poznań school, i.e., the principles of idealization and concretization (factualization), and the correspondence principle can be represented rather successfully using the relations of theoretization and specialization of revised structuralism.

Let <n(i), t(j)> (i=1,...m, j=1,...k) denote the conceptual apparatus of a theory T, and a class M={<D, n(i), t(j)>} (i=1,...m, j=1,...k) the models of T. The n-components refer to the values of dependent variables and t-components to the values of independent variables of the theory. The n- and t-components in turn represent appropriate concepts. Consider T ^* as a conceptual enrichment of T with concepts <n(i ^*), t(j ^*)> (i<i ^* or j<j ^*) and models M ^*={<D ^*, n(i ^*), t(j ^*)>}. If the classes M and M ^* are suitably related, then the situation illustrates both the case of the theoretization-relation of (revised) structuralism and of the factualization-principle of the Poznań school.

Assume now that the concepts n(i′), t(j′) of T for some i′, j′ are operationalized using some special assumptions generating appropriate empirical values n and t for these concepts. Let M′ denote the class {<D,...n,...t,...>} which is formed by substituting n and t for values of concepts n(i′), t(j′) in the elements of M. If the classes M and M′ are related in a suitable way then the situation is an example of both the specialization-relation of (revised) structuralism and the concretization-principle of the Poznań school. The correspondence principle in turn can be represented as a limiting case of the theoretization-relation of (revised) structuralism.