Hamilton, Hamiltonian Mechanics, and Causation

IF 0.9 4区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Foundations of Science Pub Date : 2023-11-06 DOI:10.1007/s10699-023-09923-y
Christopher Gregory Weaver
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Abstract

I show how Sir William Rowan Hamilton’s philosophical commitments led him to a causal interpretation of classical mechanics. I argue that Hamilton’s metaphysics of causation was injected into his dynamics by way of a causal interpretation of force. I then detail how forces are indispensable to both Hamilton’s formulation of classical mechanics and what we now call Hamiltonian mechanics (i.e., the modern formulation). On this point, my efforts primarily consist of showing that the contemporary orthodox interpretation of potential energy is the interpretation found in Hamilton’s work. Hamilton called the potential energy function the “force-function” because he believed that it represents forces at work in the world. Various non-historical arguments for this orthodox interpretation of potential energy are provided, and matters are concluded by showing that in classical Hamiltonian mechanics, facts about the potential energies of systems are grounded in facts about forces. Thus, if one can tolerate the view that forces are causes of motion, then Hamilton provides one with a road map for transporting causation into one of the most mathematically sophisticated formulations of classical mechanics, viz., Hamiltonian mechanics.

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哈密尔顿、哈密尔顿力学和因果关系
我展示了威廉·罗温·汉密尔顿爵士的哲学承诺是如何引导他对经典力学进行因果解释的。我认为汉密尔顿的因果关系形而上学是通过对力的因果解释而注入到他的动力学中的。然后,我详细介绍了力是如何对经典力学的汉密尔顿公式和我们现在所说的哈密顿力学(即现代公式)不可或缺的。在这一点上,我的努力主要是表明当代正统的势能解释是汉密尔顿作品中的解释。汉密尔顿将势能函数称为“力函数”,因为他认为势能函数代表了世界上的作用力。为这种对势能的正统解释提供了各种非历史论点,并通过表明在经典哈密顿力学中,关于系统势能的事实是基于关于力的事实来得出结论。因此,如果人们能够容忍力是运动原因的观点,那么汉密尔顿为人们提供了一个路线图,将因果关系转化为经典力学中数学上最复杂的公式之一,即哈密顿力学。
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来源期刊
Foundations of Science
Foundations of Science HISTORY & PHILOSOPHY OF SCIENCE-
CiteScore
2.60
自引率
11.10%
发文量
51
期刊介绍: Foundations of Science focuses on methodological and philosophical topics of foundational significance concerning the structure and the growth of science. It serves as a forum for exchange of views and ideas among working scientists and theorists of science and it seeks to promote interdisciplinary cooperation. Since the various scientific disciplines have become so specialized and inaccessible to workers in different areas of science, one of the goals of the journal is to present the foundational issues of science in a way that is free from unnecessary technicalities yet faithful to the scientific content. The aim of the journal is not simply to identify and highlight foundational issues and problems, but to suggest constructive solutions to the problems. The editors of the journal admit that various sciences have approaches and methods that are peculiar to those individual sciences. However, they hold the view that important truths can be discovered about and by the sciences and that truths transcend cultural and political contexts. Although properly conducted historical and sociological inquiries can explain some aspects of the scientific enterprise, the editors believe that the central foundational questions of contemporary science can be posed and answered without recourse to sociological or historical methods.
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