用不一致的数学表示世界,The British Journal for the Philosophy of Science

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用不一致的数学表示世界
The British Journal for the Philosophy of Science ( IF 3.2 ) Pub Date : 2020-12-01 , DOI: 10.1093/bjps/axz001
Colin McCullough-Benner ₁

Affiliation

根据物理现象的数学表示的标准解释，在物理目标系统和数学理论挑选的结构之间建立结构保持映射对于这种表示是必不可少的。在本文中，我认为这些说明未能对利用不一致数学理论的科学表述给出令人满意的解释，并提出了一种替代的、强有力的数学表述的推论说明，它不仅对不一致数学的应用提供了更好的解释，而且也是对一般物理现象的数学表示的令人信服的解释。1. 数学不一致和表示问题2。3.早期微积分映射帐户和早期微积分3.1。部分结构3.2。不一致的结构3.3。相关的总一致结构4。应用 4.1 中早期微积分的有力推论说明。数学表示的稳健推理概念 4.2．强大的推理概念和不一致的数学4.3。强大的推理概念和映射帐户5。超越不一致的数学不一致的数学和表示问题早期微积分映射说明和早期微积分部分结构不一致结构相关的完全一致结构早期微积分在应用中的强推论说明数学表示的强推论概念强推论概念和不一致数学强大的推理概念和映射帐户超越不一致的数学

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Representing the World with Inconsistent Mathematics

According to standard accounts of mathematical representations of physical phenomena, positing structure-preserving mappings between a physical target system and the structure(s) picked out by a mathematical theory is essential to such representations. In this paper, I argue that these accounts fail to give a satisfactory explanation of scientific representations that make use of inconsistent mathematical theories and present an alternative, robustly inferential account of mathematical representation that provides not just a better explanation of applications of inconsistent mathematics, but also a compelling explanation of mathematical representations of physical phenomena in general. 1. Inconsistent Mathematics and the Problem of Representation2. The Early Calculus3. Mapping Accounts and the Early Calculus3.1. Partial structures3.2. Inconsistent structures3.3. Related total consistent structures4. A Robustly Inferential Account of the Early Calculus in Applications 4.1. The robustly inferential conception of mathematical representation4.2. The robustly inferential conception and inconsistent mathematics4.3. The robustly inferential conception and mapping accounts5. Beyond Inconsistent Mathematics Inconsistent Mathematics and the Problem of Representation The Early Calculus Mapping Accounts and the Early Calculus Partial structures Inconsistent structures Related total consistent structures A Robustly Inferential Account of the Early Calculus in Applications The robustly inferential conception of mathematical representation The robustly inferential conception and inconsistent mathematics The robustly inferential conception and mapping accounts Beyond Inconsistent Mathematics

更新日期：2020-12-01

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