ABSTRACT
This chapter provides a modification of the theory fit for the methodology of empirical disciplines, since, in contradistinction to F. A. Muller’s version, it makes room for urelements. Mathematical logic is introduced in textbooks in such a way that they induce the beginners to imagine that the formalized languages descend from heaven seeking to incarnate in some earthly interpretation. Formalized languages were created originally in order to express propositions about certain mathematical domains, mainly the domain of arithmetic. The problem of choosing an appropriate numerical system must be solved adopting only ‘natural’ systems, like the real number system, that have the desirable computational properties. Models of first-order logic quickly become insufficient and inadequate for mathematics and the empirical sciences. For instance, probability spaces cannot be seen as such models, since the universe of the structure must be the sample space, in order for the language to be able to talk about elementary events.
