ABSTRACT Robert Hooke’s development of the theory of matter-as-vibration provides coherence to a career in natural philosophy which is commonly perceived as scattered and haphazard. It also highlights aspects of his work for which he is rarely credited: besides the creative speculative imagination and practical-instrumental ingenuity for which he is known, it displays lucid and consistent theoretical thought and mathematical skills. Most generally and importantly, however, Hooke’s ‘Principles … of Congruity and Incongruity of bodies’ represent a uniquely powerful approach to the most pressing challenge of the New Science: legitimizing the application of mathematics to the study of nature. This challenge required reshaping the mathematical practices and procedures; an epistemological framework supporting these practices; and a metaphysics which could make sense of this epistemology. Hooke’s ‘Uniform Geometrical or Mechanical Method’ was a bold attempt to answer the three challenges together, by interweaving mathematics through physics into metaphysics and epistemology. Mathematics, in his rendition, was neither an abstract and ideal structure (as it was for Kepler), nor a wholly-flexible, artificial human tool (as it was for Newton). It drew its power from being contingent on the particularities of the material world.

中文翻译：

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开普勒与牛顿之间：胡克的“一致与不一致原则”与数学的自然化

摘要 罗伯特·胡克 (Robert Hooke) 对物质振动理论的发展为通常被认为是分散和随意的自然哲学事业提供了连贯性。它还突出了他工作中很少有人称赞的方面：除了他众所周知的创造性思辨想象力和实用工具的独创性之外，它还展示了清晰而一致的理论思想和数学技能。然而，最普遍和最重要的是，胡克的“物体的一致性和不一致性原理”代表了一种独特而有力的方法来应对新科学最紧迫的挑战：使数学在自然研究中的应用合法化。这一挑战需要重塑数学实践和程序；支持这些做法的认识论框架；以及可以理解这种认识论的形而上学。胡克的“统一几何或机械方法”是通过将数学与物理学交织成形而上学和认识论来共同应对这三个挑战的大胆尝试。在他看来，数学既不是抽象的理想结构（就像开普勒那样），也不是完全灵活的人造人类工具（就像牛顿那样）。它的力量来自取决于物质世界的特殊性。人造人类工具（就像牛顿一样）。它的力量来自取决于物质世界的特殊性。人造人类工具（就像牛顿一样）。它的力量来自取决于物质世界的特殊性。