Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv University, Israel.
Stud Hist Philos Sci. 2021 Apr;86:84-92. doi: 10.1016/j.shpsa.2021.01.004. Epub 2021 Mar 2.
Structuralists typically appeal to some variant of the widely popular 'mapping' account of mathematical representation to suggest that mathematics is applied in modern science to represent the world's physical structure. However, in this paper, I argue that this realist interpretation of the 'mapping' account presupposes that physical systems possess an 'assumed structure' that is at odds with modern physical theory. Through two detailed case studies concerning the use of the differential and variational calculus in modern dynamics, I show that the formal structure that we need to assume in order to apply the mapping account is inconsistent with the way in which mathematics is applied in modern physics. The problem is that a realist interpretation of the 'mapping' account imposes too severe of a constraint on the conformity that must exist between mathematics and nature in order for mathematics to represent the structure of a physical system.
结构主义者通常诉诸于广受欢迎的“映射”解释来表明数学在现代科学中被应用于代表世界的物理结构。然而，在本文中，我认为这种对“映射”解释的现实主义解释预先假定物理系统具有与现代物理理论不一致的“假定结构”。通过两个关于微分和变分微积分在现代动力学中应用的详细案例研究，我表明，为了应用映射解释，我们需要假设的形式结构与数学在现代物理学中的应用方式不一致。问题在于，对“映射”解释的现实主义解释对数学和自然之间必须存在的一致性施加了过于严格的限制，以使数学能够代表物理系统的结构。
