First-Order Mereotopology
First-Order Mereotopology
复制标题
一阶分体拓扑学
DOI：
10.1007/978-1-4020-5587-4_2
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Ian Pratt
中科院分区：
文献类型：
--
作者：
Ian Pratt
坐标几何的众多成就之一是对几何实体的性质提供了一个概念上优美而统一的解释。根据这种解释，一个原始的空间实体是点，点的一个原始几何性质是坐标位置。所有其他几何实体--直线、曲线、曲面和物体--都不过是点的集合;涉及这些实体的所有性质和关系都可以根据组成它们的点的相对位置来定义。这种归约的成功和力量是如此之大，以至于空间区域与它们所包含的点集的识别似乎已经变得几乎是不言自明的了，然而，多年来，许多作者对这种概念制度表示了不安。这种不安的主要来源是这样一种信念，即我们的空间理论应该只使用那些系统化空间经验数据所绝对必要的资源。因为点与我们日常交往的对象是如此遥远的抽象，并且坐标位置与我们直接感知的空间属性和关系是如此遥远的亲戚，因此出现了这样一个问题，即是否不可能有替代的空间数学模型-特别是，原始空间实体不是点的模型，而是区域，其中，原始的空间属性和关系是定性的，而不是定量的。
One of the many achievements of coordinate geometry has been to provide a conceptually elegant and unifying account of the nature of geometrical entities. According to this account, the one primitive spatial entity is the point, and the one primitive geometrical property of points is coordinate position. All other geometrical entities—lines, curves, surfaces and bodies—are nothing but collections of points; and all properties and relations involving these entities may be defined in terms of the relative positions of the points which make them up. The success and power of this reduction is so great that the identification of spatial regions with the sets of points they contain has come to seem virtually axiomatic.Over the years, however, various authors have expressed disquiet with this conceptual régime. The primary source of the disquiet is the conviction that our theory of space should use only those resources absolutely necessary to systematize the data of spatial experience. For points are such remote abstractions from the objects with which we daily interact, and coordinate position such a distant relative of the spatial properties and relations which we directly perceive, that the question arises as to whether alternative mathematical models of space are not possible—in particular, models in which the primitive spatial entities are not points, but regions, and in which the primitive spatial properties and relations are qualitative rather than quantitative.