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Updated: Jul 17, 2025

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现实主义和无限点:线的尽头?
Oisín Parkinson-Coombs1, Rafael Núñez1
1Cognitive Science, UCSD, Gilman Drive, La Jolla, CA 92092 USA.
概括
数学现实主义数学现实主义
科学领域:
- 数学的哲学数学的哲学
- 认知语言学 认知语言学
- 数学的历史数学的历史.
背景情况:
- 数学哲学家利用历史的进步来支持数学现实主义.
- 标准账户使用正式语义分析数学变化.
- 后来的概念通常被视为早期更模糊的概念的精细版本.
研究的目的:
- 挑战对数学进步的标准观点.
- 分析投射几何学的历史发展.
- 研究认知语言学在数学哲学中的作用.
主要方法:
- 应用认知语言学工具来分析投影几何学的发展.
- 检查了数学家使用的历史推理结构.
- 使用正式语义和认知语言学的推断结构进行比较.
主要成果:
- 在投影几何学中确定了两个概念上不相容的推理结构.
- 证明没有一个结构是另一个结构的改进.
- 发现正式语义无法区分这些不兼容的结构.
结论:
- 关于进步的标准解释和数学现实主义面临挑战.
- 认知语言学对于理解数学概念发展至关重要.
- 单纯的形式语义不足以分析某些数学概念的变化.
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