The concept of emergence is commonly invoked in modern physics but rarely defined. Building on recent influential work by Jeremy Butterfield, I provide precise definitions of emergence concepts as they pertain to properties represented in models, applying them to some basic examples from space-time and thermostatistical physics. The chief formal innovation I employ, similarity structure, consists in a structured set of similarity relations among those models under analysis—and their properties—and is a generalization of topological structure. Although motivated from physics, this similarity-structure-based account of emergence applies to any science that represents its possibilia with (mathematical) models.

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相似结构和涌现性质

涌现的概念在现代物理学中经常被引用，但很少被定义。在 Jeremy Butterfield 最近有影响力的工作的基础上，我提供了涌现概念的精确定义，因为它们与模型中表示的属性有关，并将它们应用于时空和恒温物理学的一些基本示例。我采用的主要形式创新是相似结构，它包含在分析中的那些模型及其属性之间的一组结构化相似关系，并且是拓扑结构的概括。尽管源于物理学，但这种基于相似性结构的涌现描述适用于任何用（数学）模型表示其可能性的科学。