Logics of Objects as a Framework for the Non-Formal Sciences

This paper proposes a particular kind of logics as a formal framework for the non-formal sciences. Such logics of objects turn out to be quite different from recent mathematical logic, but they can be seen as updated versions of the classic conception of logic that is due to Frege, Russell, and the early Carnap. Though obsolete, from the point of view of pure mathematics, logics of this kind may turn out to be of interest for situations beyond the field of pure mathematics, because the task of logic, in such situations, appears to be quite different.—After pointing out the principal difference between logics for the formal and the non-formal sciences (section 1), we consider the fundamental features of a framework for the latter as rigidity, hyper modality and typed relational flexibility (section 2), and we discuss the formal specification of a logic of objects that implements these features (section 3). 1 Internal versus external ontologies The approach to formal logic that was developed and became canonical in the first half of the twentieth century specifies a logic as an uninterpreted language plus a class of semantic interpretations that allows to define truth of a formula of the language. Mathematicians use logics, in this sense, for the characterization of forms of realities. They are not concerned with questions like which formal reality provides the best characterization of the actual world, or what are the actual properties of these and those objects. Instead, the mathematicians are only concerned with internal characterizations of realities. For example, they ask for a formula that characterizes a particular semantic interpretation of an uninterpreted language up to isomorphism, i. e. describes the whole formal structure of this reality. If a semantic interpretation is characterized by a formula, in this sense, we may say that a language allows to express the internal ontology of it. Mathematicians obviously investigate mainly internal ontologies, in this sense.