No subject

[A. Katz]

Jon Aske <Jon.Aske at SALEM.MASS.EDU> on Tue, 23 Jun 1998 19:23:36 -0400
wrote:

>I think nobody would disagree with the claim that we all learned in
>Linguistics 101 that the number of possible sentences in a language
>is infinite.

I didn't respond immediately, because I wanted to see if anyone else
would disagree or have any comments on this point.

The number of possible sentences in a language is infinite, only if
we assume the following:

      a) that there is no upper bound on the length of a possible
         sentence

      and

      b) that there isn't a rate of historical change associated with
repeated use that would eventually lead to the evolution of a form of
the language that is not intelligible to the speakers of the earlier
sentences.

  The second issue is very complicated and would require too lengthy a
discussion. But the first issue is pretty simple.  Assuming that we
are not dealing with a mathematical construct, but are talking about
language as it is used by human beings, there are physical limitations
to our processing abilities in real time. Give a speaker too long and
complicated a sentence, and he will not be able to understand it.
While the exact limit may vary from individual to individual, I think
that we could establish a factual upper bound that would hold true for
the species as a whole.

Writing allows for longer sentences, because it permits us more time
in which to process and requires less of our storage capacity. But
even in writing, there is an upper bound past which no one --
not even a well-educated German :-> -- is able to retain in short term
memory the variables at the start of a sentence in order to properly
appreciate their logical effect on input toward the end of the
sentence.

So long as there is an upper bound to the length of a possible
sentence, then the number of possible sentences in a language is not
infinite. (It may be very large, allowing for an immense number of
novel sentences to be uttered in one lifetime, but -- even given an
immortal speaker -- generating an infinite number of sentences in an
unchanging language would eventually lead to repetition.)

I'm pretty sure that I am not the first to have thought of this. Can
anybody provide me with citations to existing texts in which this
argument is made? I would be most grateful.

                         --Aya Katz

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