Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics.†

Sébastien Gandon*

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Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics.†

机译：走向特定主题的逻辑主义？罗素的数学原理中的几何理论。†

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Russell's philosophy is rightly described as a programme of reduction of mathematics to logic. Now the theory of geometry developed in 1903 does not fit this picture well, since it is deeply rooted in the purely synthetic projective approach, which conflicts with all the endeavours to reduce geometry to analytical geometry. The first goal of this paper is to present an overview of this conception. The second aim is more far-reaching. The fact that such a theory of geometry was sustained by Russell compels us to question the meaning of logicism: how is it possible to reconcile Russell's global reductionist standpoint with his local defence of the specificities of geometry?

机译：罗素的哲学被正确地描述为将数学还原为逻辑的程序。现在，1903年发展起来的几何学理论已经不能很好地适应这种情况，因为它深深植根于纯粹的合成投影方法，该方法与将几何学简化为解析几何学的所有努力相矛盾。本文的首要目标是概述这一概念。第二个目标是更深远的。罗素坚持这种几何学理论的事实迫使我们质疑逻辑主义的含义：怎样才能使罗素的全球还原论立场与他对几何学特性的局部辩护相协调？

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《Philosophia Mathematica》 |2009年第1期|p.35-72|共38页
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Sébastien Gandon*;
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†PHIER, Université Clermont-Ferrand II, 4 rue Ledru, 63000 Clermont-Ferrand, France. sebastien.gandon{at}univ-bpclermont.fr;

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1. Which Arithmetization for Which Logicism? Russell on Relations and Quantities in The Principles of Mathematics [J] . Sbastien Gandon History and Philosophy of Logic . 2008,第1期

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2. Logic as a Science and Logic as a Theory: Remarks on Frege, Russell and the Logocentric Predicament [J] . Anssi Korhonen Logica Universalis . 2012,第3a4期

机译：逻辑作为科学和逻辑作为理论：关于弗雷格，罗素和标志中心困境的评论
3. Logic as a science and logic as a theory: Remarks on Frege, Russell and the Logocentric Predicament [J] . Korhonen A. Logica universalis . 2012,第3a4期

机译：逻辑科学与逻辑理论：关于弗雷格，罗素和标志中心困境的评论
4. From Geometry to Algebra and Vice Versa: Realistic Mathematics Education Principles for Analyzing Geometry Tasks [C] . Al Jupri International Conference on Mathematical Sciences . 2017

机译：从几何到代数，反之亦然：逼真的数学教育原则，分析几何任务
5. MR. F. H. BRADLEY'S THEORY OF LOGIC: AN ESSAY ON THE 'PRINCIPLES OF LOGIC.'. [D] . OSCANYAN, FREDERICK STONE. 1969

机译：先生。 F. H. BRADLEY的逻辑理论：关于“逻辑原理”的论述。
6. A New Set of Independent Postulates for the Algebra of Logic with Special Reference to Whitehead and Russells Principia Mathematica [O] . Edward V. Huntington 1932

机译：逻辑代数的一组新的独立假设特别参考怀特海和罗素的数学原理
7. Toward a topic-specific logicism? Russell’s theory of geometry in the Principles of Mathematics. [O] . Sébastien Gandon 2013

机译：走向特定主题的逻辑主义？罗素在数学原理中的几何理论。
8. On Dual Extremum Principles in Applied Mathematics. [R] . noble, b. sewell, m. j. 1971

机译：论应用数学中的双极性原则。

Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics.†

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