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<p>Galileo’s <i>reductio ad absurdum</i> refutation of Aristotle’s view on free fall through a thought experiment stands as a profoundly influential event in the history of scientific thought. From a purely logical perspective, formalizing the reasoning structure of Galileo’s thought experiment reveals its underlying assumptions with greater clarity. Building on this, the study employs a critical hypothetical premise, namely the velocity composition formula <b>G</b>, to circumvent the <i>reductio ad absurdum</i> approach against Aristotle’s view. It then directly demonstrates that any two freely falling objects fall to the ground simultaneously. Furthermore, it is proven that three distinct velocity composition formulas correspond to three different perspectives on free fall: the Aristotelian, the Galilean, and a third alternative view. Each remains internally self-consistent, reflecting the laws of motion within three distinct cosmological paradigms. Through a meta-methodological analysis, this study clarifies long-standing misconceptions surrounding Galileo’s thought experiment.</p><p>Aristotle’s view on free fall exerted a profound and long-lasting influence on Western thought until it was ultimately refuted by Galileo through both thought experiments and free-fall experiments. Galileo’s thought experiment, employing a <i>reductio ad absurdum</i> strategy, aimed to demonstrate the fallacy of Aristotle’s claim that heavier objects fall faster than lighter ones. This has led to a widespread misconception that Aristotle’s view on free fall contains an internal contradiction. This paper conducts a logical analysis to clarify the basic clues and key premises of the fundamental reasoning underlying Galileo’s thought experiment. It argues that Aristotle’s view on free fall is not internally inconsistent and that Galileo’s refutation, strictly speaking, does not constitute a definitive rebuttal. In doing so, this study seeks to dispel several seemingly plausible yet misleading interpretations surrounding this issue.</p>

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A logical examination of Aristotle and Galileo’s “two iron balls” problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • Xiaoliu Du,
  • Feifei Yang,
  • Guoping Du

摘要

Galileo’s reductio ad absurdum refutation of Aristotle’s view on free fall through a thought experiment stands as a profoundly influential event in the history of scientific thought. From a purely logical perspective, formalizing the reasoning structure of Galileo’s thought experiment reveals its underlying assumptions with greater clarity. Building on this, the study employs a critical hypothetical premise, namely the velocity composition formula G, to circumvent the reductio ad absurdum approach against Aristotle’s view. It then directly demonstrates that any two freely falling objects fall to the ground simultaneously. Furthermore, it is proven that three distinct velocity composition formulas correspond to three different perspectives on free fall: the Aristotelian, the Galilean, and a third alternative view. Each remains internally self-consistent, reflecting the laws of motion within three distinct cosmological paradigms. Through a meta-methodological analysis, this study clarifies long-standing misconceptions surrounding Galileo’s thought experiment.

Aristotle’s view on free fall exerted a profound and long-lasting influence on Western thought until it was ultimately refuted by Galileo through both thought experiments and free-fall experiments. Galileo’s thought experiment, employing a reductio ad absurdum strategy, aimed to demonstrate the fallacy of Aristotle’s claim that heavier objects fall faster than lighter ones. This has led to a widespread misconception that Aristotle’s view on free fall contains an internal contradiction. This paper conducts a logical analysis to clarify the basic clues and key premises of the fundamental reasoning underlying Galileo’s thought experiment. It argues that Aristotle’s view on free fall is not internally inconsistent and that Galileo’s refutation, strictly speaking, does not constitute a definitive rebuttal. In doing so, this study seeks to dispel several seemingly plausible yet misleading interpretations surrounding this issue.