Philosophical Studies Pub Date : 2021-04-16 , DOI: 10.1007/s11098-021-01639-8 Trevor Teitel
Formal criteria of theoretical equivalence are mathematical mappings between specific sorts of mathematical objects, notably including those objects used in mathematical physics. Proponents of formal criteria claim that results involving these criteria have implications that extend beyond pure mathematics. For instance, they claim that formal criteria bear on the project of using our best mathematical physics as a guide to what the world is like, and also have deflationary implications for various debates in the metaphysics of physics. In this paper, I investigate whether there is a defensible view according to which formal criteria have significant non-mathematical implications, of these sorts or any other, reaching a chiefly negative verdict. Along the way, I discuss various foundational issues concerning how we use mathematical objects to describe the world when doing physics, and how this practice should inform metaphysics. I diagnose the prominence of formal criteria as stemming from contentious views on these foundational issues, and endeavor to motivate some alternative views in their stead.
中文翻译:
理论上的对等不可能
理论等效性的形式标准是特定种类的数学对象之间的数学映射,特别是包括数学物理学中使用的那些对象。支持正式标准的人声称,涉及这些标准的结果所具有的含义超出了纯粹的数学范围。例如,他们声称形式标准取决于使用我们最好的数学物理学作为世界模样的指南,并且对物理学的形而上学的各种辩论都具有通缩的含义。在本文中,我研究了是否存在可辩驳的观点,根据这种观点,正式标准具有重要的非数学意义(无论是此类意义还是其他意义),都达到了主要的负面结论。一路上,我讨论了各种基本问题,这些问题涉及我们在进行物理学时如何使用数学对象来描述世界,以及这种实践如何为形而上学提供信息。我认为形式标准的突出是源于对这些基本问题的有争议的观点,并努力激发一些替代观点来代替它们。