Leibniz's idea of universal characteristics has been motivating the development of logical symbolic calculi already for several centuries. The atomistic construction of syntax used by Leibniz and his followers has been later interpreted by Russell as a symbolic expression of the metaphysical doctrine of logical atomism. Leibniz's project of geometrical characteristic is closely related to that of universal characteristics but more specific. It played a major role in the history of algebraic geometry and topology but in the 20th century received little attention from the logical community. However, in the beginning of the new 21st century this situation changed with the emergence of Homotopy Type theory and the related project of building new Univalent Foundations of mathematics in works of Vladimir Voevodsky and his collaborators. In this article we briefly survey the history of the idea of geometrical characteristics in works of brothers Grassmann, Peano, and Voedodsky, and then introduce a notion of geometrical atomism, which complements Russell's logical atomism with a constructive content.
|Переведенное название||Logical and geometrical atomism from leibniz to voevodsky|
|Состояние||Опубликовано - 2016|
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