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<p>In this study we examine Hegel’s understanding of the infinitesimal in the early form of the calculus by focusing on his concept of quality, and argue that Hegel could provide a coherent explanation for Newton’s concept of vanishing quantities. We begin by reviewing research on the relevant issues, noting that research from the perspective of quality has been emphasized. Second, we briefly introduce the situation of the concept of the infinitesimal in the calculus and Hegel’s related evaluations. Third, we trace Newton’s idea. In his <i>Principia</i>, he proposes the notion of vanishing quantities to explain the infinitesimal. Newton’s work can be seen as a step forward, but it is still not clear enough. Finally, through conceptual analysis, we explore how the concepts of quality and limit are embedded in the concept of quantity in Hegel’s philosophy.</p>

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Hegel’s Philosophical Interpretation of Newton’s Vanishing Quantities

  • 期刊论文

  • 发表日期：

    2025年7月26日

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  • Haiyang Jiang,
  • Zhijun Fan,
  • Yuechen Zhou

摘要

In this study we examine Hegel’s understanding of the infinitesimal in the early form of the calculus by focusing on his concept of quality, and argue that Hegel could provide a coherent explanation for Newton’s concept of vanishing quantities. We begin by reviewing research on the relevant issues, noting that research from the perspective of quality has been emphasized. Second, we briefly introduce the situation of the concept of the infinitesimal in the calculus and Hegel’s related evaluations. Third, we trace Newton’s idea. In his Principia, he proposes the notion of vanishing quantities to explain the infinitesimal. Newton’s work can be seen as a step forward, but it is still not clear enough. Finally, through conceptual analysis, we explore how the concepts of quality and limit are embedded in the concept of quantity in Hegel’s philosophy.