your mail

[Sergio Meira S.C.O.]

Aya Katz 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.

Someone once made the following comparison: saying the number of possible
sentences in a language is infinite (which I also interpret as implying
the possibility of sentences of infinite length) is like saying that a
baseball or volleyball match could last forever. And, in both cases, it is
true that they actually don't-- neither do sentences of infinite length
occur (just imagine the philosophical/pratical problems involved!--
wouldn't fit in this universe, etc.), nor endless baseball/volleyball
matches. Yet there is a difference between volleyball (which I, being from
Brazil, know better than this arcane game called baseball) and soccer or
basketball, where there is a real time limit that must be respected.

Sentences are never infinite-- but they don't seem to be bounded either.
You can never point to a certain length and say, that's the boundary--
shorter than that is OK, longer than that is impossible. I take this to be
the 'grain of truth' behind the entire infiniteness-of-language
discussion in formalist circles (i.e. how real-world contingencies force
all sentences to end, but as a performance phenomenon rather than as a
competence one).

When functionalists say, 'sentences aren't infinite!', formalists
think they mean that volleyball is like basketball. And when formalists
say, 'sentences are theoretically infinite', functionalists think they
mean real-life volleyball could go on forever. Is it possible that both
sides are exaggerating something? Just a thought...

Sergio Meira
meira at ruf.rice.edu