Basic Categories Common to the Sciences and Music Theory: Number, Function, and Set

The foundational scientific categories of number, function, and set are often assumed to possess axiomatic precision and to serve as many-faceted yet rigorous models of physical reality. However, historical and philosophical studies of science reveal that this presumed clarity does not hold. Music theory, which incorporates these categories into its conceptual and analytical framework, only amplifies the epistemological difficulties, demonstrating that the notions of number, set, and function are far from being settled. The present three-part, fourteen-chapter collection brings together a wide range of perspectives on how these categories have been reinterpreted and developed as they were borrowed from mathematics and the natural sciences into music theory. Our aim has been to represent scholars across the globe, spanning early-career researchers to well-established figures working within music theory and its interdisciplinary contexts. At this stage, our intention is to open the field to further, more detailed, and more focused discussion.