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Kant and Newton on the a priori necessity of geometry

机译：康德和牛顿论几何的先验必要性

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In the Transcendental Aesthetic, Kant explicitly rejects Newton's absolutist position that space is an actually existing thing; however, Kant also concedes that the absolutist successfully preserves the a priori necessity that characterizes our geometrical knowledge of space. My goal in this paper is to explore why the absolutist can explain the a priori necessity of geometry by turning to Newton's De Gravitatione, an unpublished text in which Newton addresses the essential features associated with our representation of space and the relationship between our geometrical investigation of space and our knowledge of the form of space that is a part of the natural order. Attention to Newton's account of space in De Gravitatione offers insight into the sense in which absolutist space is a priori and reveals why, in the Aesthetic, Kant could concede a priori geometrical knowledge to his absolutist opponent. What I highlight in particular is that, by Kant's standards, Newton employs the very constructive method of mathematics that secures the a priori necessity of geometry, even though, as an absolutist, and as emphasized in the arguments of the Aesthetic, Newton fails to provide a metaphysics of space that explains the success of his mathematical method.
机译：在先验美学中，康德明确拒绝了牛顿的绝对主义立场，即空间实际上是存在的东西。然而，康德也承认，专制主义者成功地保留了表征我们的空间几何知识的先验必要性。我在本文中的目的是探索绝对主义者为什么可以通过转向牛顿的《引力论》来解释几何学的先验必要性，这是一部未发表的文章，其中牛顿论述了与我们的空间表示和我们的几何学研究之间的关系有关的基本特征。空间以及我们对作为自然秩序一部分的空间形式的了解。牛顿在《引力场》中对空间的描述提供了洞察力，即绝对主义空间是先验的，并揭示了为什么康德可以在美学上让他的绝对主义对手承认先验几何知识。我特别要强调的是，按照康德的标准，牛顿采用了非常有建设性的数学方法来确保先验几何的必要性，尽管作为绝对主义者，并且正如美学论点所强调的那样，牛顿未能提供空间的形而上学解释了他的数学方法的成功。

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