Holger Andreas

This paper aims to set forth Carnapian structuralism, i.e., a syntactic view of the structuralist approach which is deeply inspired by Carnap’s dual level conception of scientific theories. At its core is the axiomatisation of a metatheoretical concept AE(T) which characterises those extensions of an intended application that are admissible in the sense of being models of the theory-element T and that satisfy all links, constraints and specialisations. The union of axiom systems of AE(T) (where T is an element of the theory-net N) will allow us to present scientific theories in an axiomatic fashion so that deductive reasoning in science can be formalised. Thereupon defeasible and paraconsistent means of reasoning will be introduced. The logical study of scientific reasoning is the key motivation of Carnapian structuralism. A further motivation is to help overcome the syntactic-semantic split in the philosophy of science.

Some scientific theories are inconsistent, yet non-trivial and meaningful. How is that possible? The present paper aims to show that we can analyse the inferential use of such theories in terms of consistent compositions of the applications of universal axioms. This technique will be represented by a preferred models semantics, which allows us to accept the instances of universal axioms selectively. For such a semantics to be developed, the framework of partial structures by da Costa and French will be extended by a few elements of the Sneed formalism, also known as the structuralist approach to science.

In this paper, a new account of empirical claims in structuralism is developed. Its novelty derives from the use that is made of the linguistic approach to scientific theories despite the presumed incompatibility of structuralism with that approach. It is shown how the linguistic approach can be applied to the framework of structuralism if the semantic foundations of that approach are refined to do justice to the doctrine of indirect interpretation of theoretical terms. This doctrine goes back to Carnap but has been advanced until the present day without a proper semantic explanation.

This article concerns the split between syntactic and semantic approaches to scientific theories. It aims at showing that an axiomatic representation of a scientific theory is a precondition of comprehending if the models of contain infinite entities. This result is established on the basis of the proposition that the human mind—which is finitely bounded for all we know—is not capable of directly grasping infinite entities. In view of this cognitive limitation, an indirect and finite representation of possibly infinite components of the models of a scientific theory proves to be indispensable. Sets of axioms and sets of axiom schemes provide such a representation. These considerations will be cast into an argument for an axiomatic conception of scientific theories. The article concludes with a case study of the ideal gas model.

A simple explanation of theoreticity says that a term is theoretical if and only if it refers to nonobservational entities. Paradigmatic examples of such entities are electrons, neutrinos, gravitational forces, genes etc. There is yet another explanation of theoreticity: a theoretical term is one whose meaning becomes determined through the axioms of a scientific theory. The meaning of the term ‘force’, for example, is seen to be determined by Newton’s laws of motion and further laws about special forces, such as the law of gravitation. Theoreticity is a property that is commonly applied to both expressions in the language of science, and referents and concepts of such expressions. Objects, relations and functions as well as concepts thereof may thus qualify as theoretical in a derived sense.

Als Wissenschaftslogik bezeichnet Carnap jene Disziplin, welche die Nachfolge der traditionellen Philosophie im 20. Jahrhundert antreten sollte. Den zentralen Bezugspunkt von Carnaps wissenschaftslogischen Arbeiten bildet die von Frege und Russell entwickelte mathematische Logik. Dies gilt auch für die Zweistufenkonzeption, mit der Carnap ein allgemeines Schema zur Analyse der Bedeutung von Begriffen nichtmathematischer Theorien entwirft. Dabei wird die Abhängigkeit der begrifflichen Bedeutung von den Aussagen der jeweiligen Theorie explizit anerkannt, was eine Überwindung der Dogmen des Empirismus innerhalb des Logischen Empirismus einschlieβt. Allerdings geht Carnap in seinen Arbeiten zur Semantik formaler Sprachen auf die spezifischen Eigenschaften von theoretischen Termen nicht ein, so daβ die Überwindung der Dogmen des Empirismus unvollständig bleibt. Darauf gründet sich die wesentliche Aufgabe der vorliegenden Untersuchung, welche darin besteht, die Deutung von theoretischen Termen durch Postulate im Rahmen der mathematischen Logik exakt zu beschreiben.

The concept of measurement is fundamental to a whole range of different disciplines, including not only the natural and engineering sciences, but also laboratory medicine and certain branches of the social sciences. This being the case, the concept of measurement has a particular relevance to the development of top-level ontologies in the area of knowledge engineering. For this reason, the present paper is concerned with ontological aspects of measurement. We are searching for a list of concepts that are apt to characterize measurement methods in a general manner. To establish such means of characterization, we will primarily deal with the semantics of measurement values.

Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the theoretical terms once these terms are introduced through the axioms of a theory.