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Can Natural Language Express Any Thing that Formal Language Can

Recently, I have talked about the idea that is, everything that can be expressed in formal language is also able to be expressed in natural language. Someone don’t agree this proposition. I think, to discuss this, an important prerequisite should be the definition of natural languages.
I have read some of definitions on Internet. There are many general explanations, which are in some common sense or intuitive understanding, typically like this one:

“A human language, such as English or Standard Mandarin, as opposed to constructed language, artificial language, machine language, or the language of formal logic.”

(About.com, http://grammar.about.com/od/mo/g/natlangterm.htm)
but these are not the well definition I want. A better definition got from Wikipedia (English):

“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. ”

These are my understandings:

  • A natural language is generated in the process of the communication among intelligent individuals’ community, naturally and gradually.
  • The progress of evolution of the natural language is the progress of cognition (like as Wittgenstein‘s language-game).
  • The evolvability of cognition dominates the evolvability of a natural language.
  • The differences between artificial language and natural language are: the artificial is purposefully designed but natural language is naturally occurring.
  • In fact, the evolution of a natural language is ever made by human but has no explicit planning or objectives, as a whole.
  • And actually, to emphasis on ‘human being’ is unnecessary.

Based upon these understandings, I made a little improvement to the proposition at the beginning:

A natural language will be able to express any thing that can be expressed by any formal languages, while the formal language(s) is designed by the people who thinking in the natural language.

The question is about ‘able’ but not ‘suitable’, although it seems not the same of many people’s intuition.
At last, Zhang3 has mentioned to me that natural languages maybe corresponding to Chomsky hierarchy type-0. I agree but not sure, because I do not know more about that discipline. What is your comment?


About TY

interested in models & modeling, software, information systems, applications & engineering for enterprises


6 thoughts on “Can Natural Language Express Any Thing that Formal Language Can

  1. I think the answer is yes… But this would lead to very long phrases!
    In fact, formal languages are a way to explicit, by definition, word’s meaning. Telling in natural language the same thing as with a formal language would imply that, as anybody should be able to understand, we explain in natural language all the meaning hold by the word we would use.

    Posted by vhanniet | July 19, 2011, 00:31
    • Yes, that is, why I said that it’s about ‘able’ but not ‘suitable’.
      By the way, do you think, a natural language and a formal language, which level of abstraction is higher?

      Posted by TY | July 19, 2011, 17:15
  2. They seem equal in abstraction-ability… But I would say that the natural language has even more abstraction power as applying on a much larger domain. For example, how would you qualify the abstraction level of the word “freedom”?

    Posted by vhanniet | July 20, 2011, 16:28
    • Well, basically agree. I tend to think of a natural language as the *superset* of certain formal languages. The questions about ‘abstraction’ seems to be a trap ;-)
      I have been thinking about it for these days, it appears that can be found some more practical clues…

      Posted by TY | July 20, 2011, 17:06
  3. Do you think of a meta-formal language which would “reverse-meta-model” a set of formal languages?
    Is this a kind of example for a “expressing business rules” goal: http://nrl.sourceforge.net/? (probably not, but it helps to precise your goal ;D)

    Posted by vhanniet | July 22, 2011, 19:42
    • I’m not very understanding you question.

      Have a look at the NRL. I like its nature style, but, to such the DSLs, I’ve been having some questions…this is a quite long topic. I prefer that focus on ontologies, rather then DSLs.

      Posted by TY | July 22, 2011, 20:32

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