几何图形与几何物体相似吗?

Axel Arturo Barceló Aspeitia
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引用次数: 0

摘要

几何图形部分地通过视觉上的相似性来表现它们的主题。我为这个假设辩护,反对Panza的批评,他认为历史证据表明欧几里得几何的对象至少从欧几里得图中获得了一些空间特征。然而,人们普遍认为,基于相似性的描绘再现了其主题的视觉特征。因此,根据Panza,欧几里得图不可能是基于相似的。我认为这种普遍的直觉是错误的。只要描绘和主题在视觉上相似,哪个先出现并不重要。因此,对于基于相似性的欧几里得图来说,只要它们彼此相似,它们是否再现几何物体的视觉特征是无关紧要的,反之亦然。为了支持我的论点,我将概述一种基于相似性的描述,这种描述并不假设描述的视觉外观来源于其主题的视觉外观。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Do geometrical diagrams resemble geometrical objects?

Geometrical diagrams represent their subjects partially through visual resemblance. I defend this hypothesis against a critique by Panza, who argues that historical evidence indicates that the objects of Euclidean Geometry derive at least some of their spatial features from Euclidean diagrams. However, it is a widespread intuition that resemblance-based depictions reproduce the visual features of their subjects. Therefore, according to Panza, Euclidean diagrams cannot be resemblance-based. I will argue that this common intuition is misguided. As long as the depiction and its subject resemble each other visually, it does not matter which one comes first. Thus, for Euclidean diagrams to be resemblance-based, it is irrelevant whether they reproduce the visual features of geometrical objects, or vice versa, as long as they resemble each other. To support my argument, I will outline a resemblance-based account of depiction that does not assume that the visual appearance of depictions is derived from the visual appearance of their subjects.

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