The metaphysics of quantity

Abstract

A formal theory of quantity (TQ) grounded in a realist, Platonist metaphysics provides a superior alternative to traditional empiricist and nominalist measurement theories. By employing a second-order syntax within a logically elementary framework, TQ characterizes quantification as an assignment of numbers to properties, or magnitudes, rather than to physical objects themselves. This approach eliminates the need for empirically unsupported assumptions common in first-order theories, such as the requirement that any two physical objects must possess an actual physical sum. TQ demonstrates formal adequacy by showing that its second-order structure supports the standard representation of quantities by real numbers through weakly faithful scales. Furthermore, the theory facilitates a naturalistic Platonism where the existence of universals is an empirical matter subject to scientific confirmation. Within this framework, the distinction between laws of nature and accidental generalizations is objectively based on the second-order structure of the world, rather than on modal primitives or subjective criteria. By bridging theoretical magnitudes with observational facts through explicit bridge laws, TQ maintains empirical relevance while avoiding the ontological limitations of strictly nominalist accounts of measurement. – AI-generated abstract.