首页> 外文期刊>Journal for general philosophy of science >Urbild und Abbild. Leibniz, Kant und Hausdorff iiber das Raumproblem The Original and the Copy. Leibniz, Kant and Hausdorff on the Problem of Space
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Urbild und Abbild. Leibniz, Kant und Hausdorff iiber das Raumproblem The Original and the Copy. Leibniz, Kant and Hausdorff on the Problem of Space

机译:原型和图像。莱布尼兹(Leibniz),康德(Kant)和豪斯多夫(Hausdorff)关于空间“原件”和“复制件”的问题。莱布尼兹,康德和豪斯多夫论空间问题

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The article attempts to reconsider the relationship between Leibniz's and Kant's philosophy of geometry on the one hand and the nineteenth century debate on the foundation of geometry on the other. The author argues that the examples used by Leibniz and Kant to explain the peculiarity of the geometrical way of thinking are actually special cases of what the Jewish-German mathematician Felix Hausdorff called "transformation principle", the very same principle that thinkers such as Helmholtz or Poincare applied in a more general form in their celebrated philosophical writings about geometry. The first two parts of the article try to show that Leibniz's and Kant's philosophies of geometry, despite their differences, appear to be preoccupied with the common problem of the impossibility to grasp conceptually the intuitive difference between two figures (such as a figure and its scaled, displaced or mirrored copy). In the third part, it is argued that from the perspective of Hausdorff s philosophical-geometrical reflections, this very same problem seems to find a more radical application in Helmholtz's or Poincare's thought experiments on the impossibility of distinguishing distorted copies of our universe from the original one. I draw the conclusion that in Hausdorff's philosophical work, which has received scholarly attention only recently, one can find not only an original attempt to frame these classical arguments from a set-theoretical point of view, but also the possibility of considering the history of philosophy of geometry from an uncommon perspective, where especially the significance of Kant's infamous appeal to "intuition" can be judged by more appropriate standards.
机译:本文试图一方面重新考虑莱布尼兹和康德的几何哲学之间的关系,另一方面又重新考虑19世纪关于几何学基础的辩论。作者认为,莱布尼兹和康德用来解释几何思维方式的特殊性的例子实际上是犹太德国数学家费利克斯·豪斯多夫(Felix Hausdorff)所谓的“变换原理”的特例,该原理与诸如亥姆霍兹或庞加莱在其关于几何的著名哲学著作中以更一般的形式应用。本文的前两部分试图表明,莱布尼兹和康德的几何哲学尽管有所不同,但似乎都被普遍的问题困扰,即不可能从概念上把握两个人物之间的直观差异(例如人物及其比例尺)。 ,替换或镜像副本)。在第三部分中,有人认为,从豪斯多夫的哲学-几何学反思的角度来看,这个同样的问题似乎在亥姆霍兹或庞加莱的思想实验中找到了更根本的应用,因为它不可能将我们扭曲的宇宙副本与原始宇宙区分开来。一。我得出的结论是,在最近才受到学者关注的Hausdorff的哲学著作中,不仅可以发现从集合论的角度来构架这些古典论点的原始尝试,而且可以发现考虑哲学史的可能性。从不寻常的角度看几何学,特别是可以用更合适的标准来判断康德臭名昭著的“直觉”的重要性。

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