Holger Andreas

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.