Asymptotic Reasoning: Explanation, Reduction, and Emergence

渐近推理：解释、归约和涌现

• 批准号: 9983696
• 负责人: Robert Batterman
• 金额: $ 5.63万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-04-01 至 2000-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9983696&HistoricalAwards=false
• 关键词: Asymptotic; Reasoning; Explanation; Reduction; Emergence

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.

99-83696 --罗伯特·W. Batterman（俄亥俄州州立大学）“渐近推理：解释、还原和涌现“一种涉及数学渐近的推理形式在科学研究中的许多不同背景下被采用。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，在渐近状态下对方程的数学研究，涉及一种物理动机的简化，可以产生描述感兴趣现象的显着和主导特征的公式。该项目旨在阐明这种渐近“简化”的性质，并理解为什么它往往是非常富有成效的。该项目还认为，这种特殊类型的简化导致了对兴趣现象的显著特征的深刻理解和解释，这是其他手段无法实现的。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。这项研究将导致对科学理解，解释和出现的性质的新见解。它建立在过去的调查性质和重要性的渐近理论之间的限制关系。早期的工作集中在这样一个事实上，即在理论之间的某些渐近区域（例如，量子力学和经典力学之间的半经典区域），出现了起关键解释作用的突出结构。目前的项目集中在为什么和如何这种渐近推理是富有成效的，因为它是问题。