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In this chapter we examine aspects of Leibniz’s changing views on infinitesimals prior to his invention of the differential algorithm in October 1675, and in the period immediately afterwards. We show how he moved from regarding infinitesimals as actual elements of the continuum, to a point of view where the bounded infinite and the infinitely small were treated as mathematical fictions, and the question of their existence was postponed. When Leibniz resumes the latter question in the early to mid-1676, he comes to reject their existence; they may still be used as fictions, but they are not possible objects.

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The Question of the Existence of Infinitesimals (1669–1676)

  • 章节

  • 发表日期：

    2025年

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  • Richard T. W. Arthur,
  • David Rabouin

摘要

In this chapter we examine aspects of Leibniz’s changing views on infinitesimals prior to his invention of the differential algorithm in October 1675, and in the period immediately afterwards. We show how he moved from regarding infinitesimals as actual elements of the continuum, to a point of view where the bounded infinite and the infinitely small were treated as mathematical fictions, and the question of their existence was postponed. When Leibniz resumes the latter question in the early to mid-1676, he comes to reject their existence; they may still be used as fictions, but they are not possible objects.