Holger Andreas

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.

Concepts and methods coming from the formal logic of science have played only a very subordinated role in the philosophical analysis of thought experiments so far. The present article, therefore, takes a look at thought experimenting from the perspective of the logic of science in a Carnapian spirit. To this end, the widely discussed refutation of Aristotle′s theory of free falling bodies by Galilei will be investigated. Further, two prominent approaches to thought experimenting are subjected to a closer investigation: first, the empiricist interpretation by John D. Norton, and second, the use of mental models by Nancy J. Nersessian. The existence of creative abductions, which introduce theoretical concepts, will be found to pose a seemingly insurmountable problem for the empiricist approach. The use of mental models, by contrast, proves to exhibit very interesting connections to the semantics of theoretical concepts. Such models can be shown to determine, in part, the meaning of theoretical concepts in cases where the understanding of such concepts is not entirely founded on explicit axioms.

The distinction between the syntactic and the semantic approach to scientific theories emerged in formal philosophy of science. The semantic approach is commonly considered more advanced and more successful than the syntactic one, but the transition from the one approach to the other was not brought about without any loss. In essence, it is the formal analysis of atomic propositions and the analysis of deductive reasoning that dropped out of consideration in at least some of the elaborated versions of the semantic approach. In structuralist theory of science, as founded by Sneed and Stegmüller, the focus is on global propositions concerning the question of whether or not certain empirical systems satisfy a set-theoretic predicate that encodes the axioms of a scientific theory. Hence, an analysis of deductive reasoning from atomic premisses with the help of a given theory is missing. The objective of the present paper is to develop a deductive system on the basis of the structuralist framework. This system comes with a novel formulation of empirical propositions in structuralism.