数学模型与数学结构在不同语境下的含义辨析  

On Meanings of Mathematical Model and Structure in Different Contexts

作　　者：路卫华 LU Wei-hua(Journal Editorial Department,Shandong University of Science and Technology, Qingdao Shandong 266590,China)

机构地区：[1]山东科技大学学报编辑部

出　　处：《科学技术哲学研究》2019年第4期65-69,共5页Studies in Philosophy of Science and Technology

基　　金：中国博士后科学基金资助项目“认知科学中的科学说明模型研究”(2016M591322);国家社科基金重大项目“认知科学对当代哲学的挑战”(11&ZD187)

摘　　要：概括地说,在数理逻辑、数学及科学语境下,“数学结构”概念主要有三种含义,即一般纯数学中所说的纯粹抽象的数学结构,数理逻辑的模型论中所说的作为语义解释的数学结构以及在科学与应用数学的数学建模中所说的数学模型,前两者之间的区别在于所讨论的数学结构概念是否建立在相关的形式语言之上,以及是否定义了将相关形式语言中的非逻辑常项符号映射到布尔巴基意义下的数学结构中的某些特定元素与关系上的解释函数。而“数学模型”概念,则主要有模型论意义上的模型及数学建模意义上的模型,这两种不同含义。Generally speaking,the concept of“mathematical structure”has three distinct meanings in the contexts of logic,mathematics and sciences,i. e. as the pure abstract structure in pure mathematics;as the semantic interpretation structure in the model theory in mathematical logic;and as the model in mathematical modelling in applied mathematics. The differences between pure abstract structure and semantic interpretation structure are that whether it was based on a related formal language,as well as whether it has defined an interpretation function which maps the non - logical constants in the related formal language to certain elements and relations in a Bourbaki’s mathematical structure. Furthermore,the concept of “mathematical model”has two distinct meanings: one is in the context of model theory in mathematical logic,and the other is in the context of mathematical modelling in applied mathematics.

关 键 词：数学模型 数学结构 模型论 数学建模 布尔巴基 

分 类 号：N02[自然科学总论—科学技术哲学]