SQuaRed-EX: Scientific Quantitativeness Reduced and Explained

物理量——比如长度、质量、电荷和体积——在科学和日常实践中通常用数学实体来表示，比如数字和向量。我们用我的手臂长72厘米且72 < 105厘米来解释为什么我够不到桌上105厘米远的冰咖啡。然而，我们认为数字72和105之间的算术<关系不能直接解释我的手臂或咖啡的任何事情。相反，这些数学术语通过表示系统本身的一些直接解释的物理特征来间接解释。对物理世界的完整描述应该能让我们理解潜在的“定量结构”，正是由于这种结构，这些数学表示才得以成功。这就是数量问题。尽管科学形而上学和物理哲学的研究人员认识到世界的数量结构迫切需要解释，但迄今为止，解决这个问题的尝试依赖于将一些数量结构作为基本的“无法解释的原语”（使用这些原语来解释该数量结构的其余部分）。我反对这种方法，我称之为“数量原始主义”，并提出一种开创性的、雄心勃勃的方法，使我能够给出一个数量结构的完全还原和完整的解释。项目“科学数量：“还原性解释”或“平方- EX”旨在1)发展数量结构的完整还原性描述，利用基本物理量在物理世界中的作用来解释为什么它们可以很好地用数学表示；2)将还原性解释方法扩展到基础物理之外的量，包括热力学和化学中的量；3)传播这些结果和用于产生它们的还原性解释方法。指导今后该领域的研究朝着更富有成效的方向发展。

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.