I argue that in Bertrand Russell’s An Essay on the Foundations of Geometry (1897), his forms of externality serve the same fundamental role in grounding the possibility of geometry that Immanuel Kant’s forms of intuition serve in grounding geometry in his critical philosophy. Specifically, both provide knowledge of bare numerical difference, where we have no concept of this difference. Because geometry deals with such conceptually homogeneous magnitudes and their composition on both accounts, forms of intuition or externality (respectively) are at its foundation.

中文翻译：

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还不完全是神秘的朦胧边缘：罗素《几何学基础论文》中的直觉


我认为，在伯特兰·罗素（Bertrand Russell）的《论几何学基础》（An Essay on the Foundations of Geometry，1897）中，他的外部性形式在为几何学的可能性奠定基础方面发挥着相同的基本作用，就像伊曼纽尔·康德（Immanuel Kant）的直觉形式在他的批判哲学中为几何学奠定基础所起的作用一样。具体来说，两者都提供了裸数值差异的知识，而我们没有这种差异的概念。因为几何学在两个方面都处理了这种概念上齐次的大小及其组成，所以直觉或外部性的形式（分别）是其基础。