笔记：自然语言的定义
最近讨论问题，我曾提出一个想法：自然语言能表达任何形式语言表达的东西。显然有人不同意这个命题。我没有继续讨论，因为察觉到，必须明确地界定“自然语言”——这里，常识的印象似乎隐藏着问题，甚至某种悖论。
在网络上搜索"natural languages"，阅读了一些比较好的来源。有许多一般性的解释，和常识或直觉的理解差不多：解释为“人类的语言”（列举实例说明），同时指明是相对于“形式语言”、“人工语言”的概念。这不算是定义。
从英文维基百科的条目看到了一个比较好的定义（附后）。这基本上算是一个生成式的界定吧，比较符合我的想法。但强调”人类“其实是不必要的。如果有火星人，他们也会有自己的自然语言。我想，应当上升到”智能交流“的层面。整理我的理解要点如下：
1）智能群体交流信息的过程（“语言游戏”）中自然形成的语言，非预先设计；
2）形成的过程就是认知的过程。
3）认知的无限性，决定了自然语言的无限性（开放、无边界、不确定）
第二点很重要。非常重要。回顾之前讨论时的想法，更坚定了：
1）自然语言能够表达任何形式语言所表达的东西（是“能不能”，不是“好不好”）
2）逻辑上看，一个智能群体中产生的任何形式语言、所谓领域专用语言之类，都是其自然语言的子集。
3）“人工语言”与“自然语言”概念区别的要点：“人工”是为“有目的地设计的”，自然语言是自然发生的。这里其实隐藏着悖论（跳出三界之外，智能的所有行为都是自然过程），把自然语言看作“人工语言”的超集，这个悖论也就自然消解了。
附：网络上读到的代表性的解释，摘抄如下
http://grammar.about.com/od/mo/g/natlangterm.htm
Definition:
A human language, such as English or Standard Mandarin, as opposed to constructed language, artificial language, machine language, or the language of formal logic.
The theory of universal grammar proposes that all natural languages have certain underlying rules that shape and limit the structure of the specific grammar for any given language.
Observations:
"The term 'natural language' is used in opposition to the terms 'formal language' and 'artificial language,' but the important difference is that natural languages are not actually constructed as artificial languages and they do not actually appear as formal languages. But they are considered and studied as though they were formal languages 'in principle.' Behind the complex and the seemingly chaotic surface of natural languages there are--according to this way of thinking--rules and principles that determine their constitution and functions. . . ."
(Sören Stenlund, Language and Philosophical Problems. Routledge, 1990)
"Natural language is the embodiment of human cognition and human intelligence. It is very evident that natural language includes an abundance of vague and indefinite phrases and statements that correspond to imprecision in the underlying cognitive concepts. Terms such as 'tall,' 'short,' 'hot,' and 'well' are extremely difficult to translate into knowledge representation, as required for the reasoning systems under discussion. Without such precision, symbolic manipulation within the computer is bleak, to say the least. However, without the richness of meaning inherent in such phrases, human communication would be severely limited, and it is therefore incumbent on us (to attempt) to include such facility within reasoning systems . . .."
(Jay Friedenberg and Gordon Silverman, Cognitive Science: An Introduction to the Study of Mind. SAGE, 2006)
http://en.wikipedia.org/wiki/Natural_language
In the philosophy of language, a natural language (or ordinary language) is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect.
在语言哲学中，自然语言（或普通语言）是指人类智慧所处理的语言，它们是人类固有的语言能力的结果，以非蓄意的方式出现。（译得有些生硬，请多多指教）
----时间分界线----
“自然语言能表达任何形式语言表达的东西”可以说是我的一种直觉。这个观点在Tarski的经典论文中，有非常明确的支持：
A characteristic feature colloquial language (in contrast to various scientific languages) is its universality. It would not be in harmony with the spirit of this language if in some other language a word occurred which could not be translated into it; it could be claimed that ‘if we can speak meaningfully about anything at all, we can also speak about it in colloquial language’. (A. Tarski 1983/1935, p. 164)
塔斯基文中的 colloquial language (or, everyday language), 与我思考中的所谓“自然语言”是一致的，应该说，用“日常语言”也许更确切。这段论述的基本观点就是，任何一个专门语言（例如数学语言）所能表达的东西，也可以用日常语言说明。
从某种角度看，这也许就是一个最平凡的断言，但一旦试图证明它，就会触碰到逻辑学里最深刻的话题。
2015.2.27补记
在网络上搜索"natural languages"，阅读了一些比较好的来源。有许多一般性的解释，和常识或直觉的理解差不多：解释为“人类的语言”（列举实例说明），同时指明是相对于“形式语言”、“人工语言”的概念。这不算是定义。
从英文维基百科的条目看到了一个比较好的定义（附后）。这基本上算是一个生成式的界定吧，比较符合我的想法。但强调”人类“其实是不必要的。如果有火星人，他们也会有自己的自然语言。我想，应当上升到”智能交流“的层面。整理我的理解要点如下：
1）智能群体交流信息的过程（“语言游戏”）中自然形成的语言，非预先设计；
2）形成的过程就是认知的过程。
3）认知的无限性，决定了自然语言的无限性（开放、无边界、不确定）
第二点很重要。非常重要。回顾之前讨论时的想法，更坚定了：
1）自然语言能够表达任何形式语言所表达的东西（是“能不能”，不是“好不好”）
2）逻辑上看，一个智能群体中产生的任何形式语言、所谓领域专用语言之类，都是其自然语言的子集。
3）“人工语言”与“自然语言”概念区别的要点：“人工”是为“有目的地设计的”，自然语言是自然发生的。这里其实隐藏着悖论（跳出三界之外，智能的所有行为都是自然过程），把自然语言看作“人工语言”的超集，这个悖论也就自然消解了。
附：网络上读到的代表性的解释，摘抄如下
http://grammar.about.com/od/mo/g/natlangterm.htm
Definition:
A human language, such as English or Standard Mandarin, as opposed to constructed language, artificial language, machine language, or the language of formal logic.
The theory of universal grammar proposes that all natural languages have certain underlying rules that shape and limit the structure of the specific grammar for any given language.
Observations:
"The term 'natural language' is used in opposition to the terms 'formal language' and 'artificial language,' but the important difference is that natural languages are not actually constructed as artificial languages and they do not actually appear as formal languages. But they are considered and studied as though they were formal languages 'in principle.' Behind the complex and the seemingly chaotic surface of natural languages there are--according to this way of thinking--rules and principles that determine their constitution and functions. . . ."
(Sören Stenlund, Language and Philosophical Problems. Routledge, 1990)
"Natural language is the embodiment of human cognition and human intelligence. It is very evident that natural language includes an abundance of vague and indefinite phrases and statements that correspond to imprecision in the underlying cognitive concepts. Terms such as 'tall,' 'short,' 'hot,' and 'well' are extremely difficult to translate into knowledge representation, as required for the reasoning systems under discussion. Without such precision, symbolic manipulation within the computer is bleak, to say the least. However, without the richness of meaning inherent in such phrases, human communication would be severely limited, and it is therefore incumbent on us (to attempt) to include such facility within reasoning systems . . .."
(Jay Friedenberg and Gordon Silverman, Cognitive Science: An Introduction to the Study of Mind. SAGE, 2006)
http://en.wikipedia.org/wiki/Natural_language
In the philosophy of language, a natural language (or ordinary language) is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect.
在语言哲学中，自然语言（或普通语言）是指人类智慧所处理的语言，它们是人类固有的语言能力的结果，以非蓄意的方式出现。（译得有些生硬，请多多指教）
----时间分界线----
“自然语言能表达任何形式语言表达的东西”可以说是我的一种直觉。这个观点在Tarski的经典论文中，有非常明确的支持：
A characteristic feature colloquial language (in contrast to various scientific languages) is its universality. It would not be in harmony with the spirit of this language if in some other language a word occurred which could not be translated into it; it could be claimed that ‘if we can speak meaningfully about anything at all, we can also speak about it in colloquial language’. (A. Tarski 1983/1935, p. 164)
塔斯基文中的 colloquial language (or, everyday language), 与我思考中的所谓“自然语言”是一致的，应该说，用“日常语言”也许更确切。这段论述的基本观点就是，任何一个专门语言（例如数学语言）所能表达的东西，也可以用日常语言说明。
从某种角度看，这也许就是一个最平凡的断言，但一旦试图证明它，就会触碰到逻辑学里最深刻的话题。
2015.2.27补记
