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Expressive power

Mathematics can communicate a range of meanings that is as wide as (although different from) that of a natural language.

这段话向我们传达了这样的含义：不同的语言所能够描述的meaning的范围是不同的。下面我们使用集合的观点来描述这个含义：如果我们将语言“所能够描述的meaning”放到一个集合中，把这个集合称为 meaning set，那么不同语言的meaning set的大小是不同的。使用我们的自然语言来描述就是：有的语言能够描述的范围更大、有的语言无法描述另外一个语言所表达的。这就是本节标题中的“expressive power”的含义。

关于expressive power，参见：

维基百科Expressive power
维基百科Combinatory categorial grammar （其中提及了expressive power）

Chomsky hierarchy

关于expressive power的另外一个非常经典的案例是: Chomsky hierarchy，参见 Formal-language 章节。