The “dematerialization” of units: from measurement sciences to the metaphysics of quantities – UNITS

The UNITS project explores one of the most fundamental yet unresolved questions in the philosophy of science: the nature of quantities. Since Galileo’s assertion that the “great book of nature is written in mathematical language” (Il Saggiatore), the quantification of physical reality has been a cornerstone of scientific progress. However, the underlying nature of quantities—what makes a property genuinely quantitative—remains a subject of philosophical debate. UNITS aims to address this gap by demonstrating that, despite the constructive aspects of measurement practices, certain properties in the physical world are intrinsically quantitative. What drives the project is the recent “dematerialization” of measurement units, which provides a unique opportunity to rethink the nature of quantities and their role in scientific practices. To achieve this, the project is structured around three interconnected research axes:

1. Establishing a Criterion for Quantitativeness
The first objective is to develop a rigorous criterion for what makes a property genuinely quantitative. Traditional approaches to measurement—such as representational theories and the practical turn in philosophy of science—tend to blur the distinction between quantities and mere qualitative properties. For instance, while psychological pain or the hardness of a material can be measured numerically, these properties lack the essential features of quantities like mass or time. UNITS proposes that the defining feature of quantities lies in their dimensional relationships, as reflected in the recent redefinition of measurement units based on fundamental constants. This criterion will not only clarify the nature of quantities but also have far-reaching implications for the philosophy of measurement across various scientific disciplines.

2. Bridging Metrology and the Metaphysics of Quantities
The second research axis connects the ongoing debate about the ontological status of quantities with the latest developments in metrology. A central metaphysical question is whether quantities are absolute properties of objects (e.g., does an object possess its mass intrinsically?) or whether they are relational (e.g., is mass merely a comparison between objects?). The project argues that the recent "dematerialization" of SI units—where fundamental quantities are now defined through physical constants rather than physical artifacts—supports an absolutist interpretation of quantities. By analyzing the role of “intrinsic standards” in modern metrology, UNITS seeks to provide empirical support for the claim that quantities are fundamental aspects of reality, rather than merely relational constructs.

3. Developing a New Theory of Quantities
The third axis of the project builds on recent advances in metaphysical theories of quantities. Traditionally, the leading approach—Mixed Absolutism—attempts to reconcile the absolute and relational aspects of quantities but faces significant theoretical challenges. Instead, UNITS proposes an alternative framework: the state-space theory of quantities. This emerging approach conceptualizes quantities as positions within structured mathematical spaces, capturing both their absolute and relational dimensions. By developing this theory in collaboration with Jo Wolff (University of Edinburgh), the project aims to offer a more coherent and innovative model for understanding the metaphysics of quantities.

Scientific Impact and Future Directions
The implications of UNITS extend beyond metaphysics and measurement theory. The project’s findings will influence fields ranging from climate science (through the study of quantitative indicators) to fundamental physics (in the interpretation of space-time and natural laws). By establishing a solid foundation for the nature of quantities, UNITS lays the groundwork for future large-scale projects (ANR, ERC) and fosters interdisciplinary collaboration between philosophy, physics, and metrology.