By understanding laws of nature as geometrical rather than linguistic entities, this paper addresses how to describe theory structures and how to evaluate their continuity. Relying on conceptual spaces as a modelling tool, we focus on the conceptual framework an empirical theory presupposes, thus obtain a geometrical representation of a theory’s structure. We stress the relevance of measurement procedures in separating conceptual from empirical structures. This lets our understanding of scientific laws come closer to scientific practice, and avoids a widely (...) recognised deficit in current philosophy of science accounts, namely to risk a collapse of the physical into the mathematical. (shrink)

According to a seminal paper by Barsalou , frames are attribute-value-matrices for representing exemplars or concepts. Frames have been used as a tool for reconstructing scientific concepts as well as conceptual change within scientific revolutions . In the frame-based representations of scientific concepts developed so far the semantic content of concepts is determined by a set of attribute-specific values. This way of representing semantic content works best for prototype concepts and defined concepts of a conceptual taxonomy satisfying the no-overlap principle. (...) In addition to the semantic content of prototype concepts and defined concepts, frames can also contain empirical knowledge that is represented as constraints between the values of the frame. Beside prototype concepts and defined concepts, theoretical concepts that are multiply operationalized play an important role in science. However, so far no frame-based representation of theoretical concepts has been proposed. In this paper, it will be shown that theoretical concepts can be represented by frames and that frame-based representations of prototype concepts and defined concepts have another structure than frame-based representations of theoretical concepts. In order to explicate this difference, we will develop a frame-based method for representing all three kinds of concepts by means of mathematical graph-theory. One important consequence will be that the constraints of a frame representing a theoretical concept are entailed by the structure of the frame, as opposed to a frame representing defined or prototype concepts. (shrink)