标题： 形状空间作为概念空间 显示英文标题

标题： Shape space as a conceptual space

摘要： 形状空间的概念是在20世纪后半叶引入的，作为一种有用的分析工具来解决与物质系统内在空间构型相关的问题。近年来，形状空间的几何性质被研究并被用来构建物理学（经典、相对论和量子）的完全关系描述。这一关系框架的主要目的是——最初由Julian Barbour和Bruno Bertotti倡导——将物质系统的动力学描述仅以无量纲和尺度不变的方式表达出来。因此，Barbour-Bertotti的动力学方法代表了对空间和时间作为真实实体的现实性这一著名Leibniz式论点的技术实现。然后，在这种背景下提出了关于形状空间本身的地位问题：它是否是一个实际的物理空间，在其中基本的关系动力学展开，或者它只是一个有用的数学构造？本文论证了后一种答案，并在此过程中探讨了形状空间可能是概念空间的一个特殊案例的可能性。 显示英文摘要

摘要： The notion of shape space was introduced in the second half of the 20th Century as a useful analytical tool for tackling problems related to the intrinsic spatial configuration of material systems. In recent years, the geometrical properties of shape spaces have been investigated and exploited to construct a totally relational description of physics (classical, relativistic, and quantum). The main aim of this relational framework - originally championed by Julian Barbour and Bruno Bertotti - is to cast the dynamical description of material systems in dimensionless and scale-invariant terms only. As such, the Barbour-Bertotti approach to dynamics represents the technical implementation of the famous Leibnizian arguments against the reality of space and time as genuine substances. The question then arises about the status of shape space itself in this picture: Is it an actual physical space in which the fundamental relational dynamics unfolds, or is it just a useful mathematical construction? The present paper argues for the latter answer and, in doing so, explores the possibility that shape space is a peculiar case of a conceptual space.