关于变量替换时变量取值语义及定义一致性的技术问询

我最近在研读Kenneth O. May的《Elements of Modern Mathematics》，里面关于常量和变量的定义让我有点困惑，想和大家探讨下我的疑问。

首先是书中关于常量的定义：

A symbol that in a particular context is the name of just one specific thing is called a constant. Grammarians call constants proper nouns. The thing that a constant names is called its value. A constant stands for, or names, its value.

接着作者对变量的解释：

A symbol that, in a particular context, is not a constant but for which any one of certain constants may be substituted is called a variable. For example, 'x' is a variable in the context x/1 = x, and 'a chair' is a variable in the context a chair has four legs. The constants that may be substituted for a variable in a particular context are called significant substitutes for it. The value of a significant substitute is called a value of the variable in a particular context. In our examples, '2' is a significant substitute for 'x' and 'the first chair in the first row' is a significant substitute for 'a chair.' The number 2 and the first chair in the first row are the corresponding values.

我大致理解作者的核心意思：如果一个句子里包含变量x，我们可以用常量来替换这个变量，替换后得到的句子就会形成一个关于该常量所指代事物的命题。

但这里我产生了一个疑问：作者提到当我们用常量替换变量时，这个常量的取值就成为了变量的取值。可根据变量的定义，它是“指代未指定事物的符号”（和指代特定事物的常量相对），那我们真的能有意义地说“变量取了某个特定值”吗？

毕竟x在句子中的本质意义就是指代某个未指定的任意事物，就算要讨论变量的“取值”，那也应该是未指定的事物才对。说替换后变量就获得了常量的取值，这难道不与变量的定义相矛盾吗？

有没有大佬能帮我理清这个逻辑？或者需要补充/修正哪些概念？

备注：内容来源于stack exchange，提问作者Harshit Rajput