Group in Logic and the Methodology of Science

Guided by a desire to eliminate language that refers to unobservable structure from mechanics, Ernst Mach proposed a definition of mass in terms of more directly observable data. A great deal of literature surrounds the question of whether this proposed definition accomplishes its stated goal, or even whether it constitutes a definition. In this talk we aim to bring clarity to this debate by using methods from model theory and from modal logic to classify, reconstruct, and evaluate these arguments. In particular, we exhibit a general construction of first-order modal frames for appropriately presented scientific theories with epistemic constraints. These frames allow us to characterize which properties are “modally definable” in the sense of Bressan.