SQuaRed-EX: Scientific Quantitativeness Reduced and Explained

Physical quantities - things like length, mass, charge, and volume-are commonly represented in science and everyday practice with mathematical entities, like numbers and vectors. We explain why I cannot reach the iced coffee 105cm away from me on the table by citing the fact that my arm is 72cm long and 72 < 105. However, we don't think that the arithmetical '<' relation between the numbers 72 and 105 is directly explaining anything about my arm or the coffee. Rather, these mathematical terms explain indirectly by representing some directly explanatory physical feature of the system itself. A complete account of the physical world should give us an understanding of the underlying "quantitative structure" in virtue of which these mathematical representations are successful. This is the Problem of Quantity. Although researchers in the metaphysics of science and philosophy of physics recognize that the quantitative structure of the world cries out for explanation, attempts to resolve the problem have hitherto relied on taking some quantitative structure to be fundamental, "unexplained primitives" (using these primitives to explain the rest of that quantity's structure). I reject this approach, which I call "quantitative primitivism", and propose a groundbreaking and ambitious approach that allows me to give fully reductive and complete explanations a quantity's structure. The project, "Scientific Quantities: Reductively Explained" or "SQuaRed- EX" aims to 1) develop complete reductive accounts of quantitative structure that use fundamental physical quantities' role in the physical world to explain why they can be so well represented by mathematics, 2) develop extensions of the reductive-explanatory approach to quantities outside of fundamental physics, including quantities in thermodynamics and chemistry, and 3) disseminate these results and the reductive-explanatory approach used to produce them, guiding future research in the field in a more fruitful direction.