Asymptotic Reasoning: Explanation, Reduction, and Emergence

99-83696—Robert W. Batterman（俄亥俄州立大学）“渐近推理：解释，还原和出现”一种涉及数学渐近的推理形式在科学研究的许多不同背景中被采用。本项目研究应用数学家和物理学家使用的“渐近推理”。在许多情况下，对渐近状态方程的数学研究，涉及一种物理动机的简化，可以产生描述感兴趣现象的显著和主要特征的公式。该项目旨在阐明这种渐近“简化”的本质，并理解为什么它通常非常富有成效。该项目还认为，这种特殊类型的简化导致了对感兴趣的现象的显著特征的深刻理解和解释，这是其他方法无法做到的。有人认为，现存的解释和理解的哲学理论忽视了这种广泛的推理形式。这项研究将对科学理解、解释和涌现的本质产生新的见解。它建立在过去对理论间渐近极限关系的性质和重要性的研究之上。早期的工作集中于这样一个事实，即在理论之间的某些渐近状态（例如，“介于”量子力学和经典力学之间的半经典状态）中，显著结构出现，发挥着至关重要的解释作用。当前项目的重点是为什么以及如何这种渐近推理是卓有成效的问题。

99-83696 -- Robert W. Batterman (Ohio State University) "Asymptotic Reasoning: Explanation, Reduction, and Emergence"A form of reasoning involving mathematical asymptotics is employed in many different contexts in scientific investigations. This project examines "asymptotic reasoning" as applied mathematicians and physicists use it. In many instances, the mathematical investigation of equations in an asymptotic regime, which involves a kind of physically motivated simplification, can yield formulas describing the salient and dominant features of the phenomenon of interest. The project aims to illuminate the nature of this asymptotic "simplification" and to understand why it is often very fruitful. The project also argues that this special type of simplification results in a deep understanding and explanation, unavailable by other means, of the salient features of the phenomenon of interest. It is argued that the extant philosophical theories of explanation and understanding overlook this widespread form of reasoning. The research will result in new insights about the nature of scientific understanding, explanation, and emergence. It builds upon past investigations into the nature and importance of asymptotic limiting relations between theories. That earlier work focused on the fact that in certain asymptotic regimes between theories (for instance, the semiclassical regime "between" quantum and classical mechanics) salient structures emerge which play crucial explanatory roles. The current project focuses on the questions of why and how this asymptotic reasoning is as fruitful as it is.