Holger Andreas

A central topic in the logic of science concerns the proper semantic analysis of theoretical sentences, that is sentences containing theoretical terms. In this paper, we present a novel choice-semantical account of theoretical truth based on the epsilon-term definition of theoretical terms. Specifically, we develop two ways of specifying the truth conditions of theoretical statements in a choice functional semantics, each giving rise to a corresponding logic of such statements. In order to investigate the inferential strength of these logical systems, we provide a translation of each truth definition into a modal definition of theoretical truth. Based on this, we show that the stronger notion of choice-semantical truth captures more adequately our informal semantic understanding of scientific statements.

Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in the language of science is presented here. This approach preserves compositionality to a large extent. *Received September 2009; revised February 2010. †To contact the author, please write to: Seminar for Philosophy, Logic, and Theory of Science, Hauspostfach 49, Ludwig-Maximilians-Universität, Munich 80539, Germany; e-mail: [email protected].

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.