TY - JOUR

T1 - Логический и геометрический атомизм от Лейбница до Воеводского

AU - Rodin, Andrei V.

N1 - Funding Information: * Статья подготовлена по материалам выступления на Круглом Столе, организованном В. Г. Лысенко в рамках проекта РГНФ N 13 - 03 - 00547 - "Атомизм и мировая культура". The paper is based on my communikation af the Round Table, organized by Victoria Lysenko in the frame of the project supported by RFH, grant No 13 - 03 - 00547, "Atomism and World Culture". Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Geometrical atomism

KW - Geometrical characteristics

KW - Logical atomism

UR - http://www.scopus.com/inward/record.url?scp=85029908087&partnerID=8YFLogxK

M3 - Обзорная статья

AN - SCOPUS:85029908087

SP - 134

EP - 142

JO - ВОПРОСЫ ФИЛОСОФИИ

JF - ВОПРОСЫ ФИЛОСОФИИ

SN - 0042-8744

IS - 6

ER -