LINGUIST List 2.747

Sat 02 Nov 1991

Disc: Are languages infinite?

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1. Michael Kac, Are languages infinite?

A quick response to Henry Kucera's comments on my posting in
regard to Hockett's football analogy:
Yes of course, games are played by people just as languages are
spoken by people. Indeed, rule-governed behavior (of which game
playing and language use are two examples) appear to be
distinctively human or close to it. But there is a crucial difference
between (a) what a system of rules allows as a matter of principle
and (b) what kinds of behaviors are possible in the mundane,
workaday world because of limitations on humans and the
physical universe they inhabit. That it's physically impossible for
a team of human football players to score a million points in the
confines of an hour of play is a fact, but it isn't because the rules
of football either state or imply that this should be so. It's
necessary to advert to principles which are, or are closely related
to, the ones which also have among their consequences that it isn't
possible for a single cat to catch a million mice in the space of an
hour or for an airplane to travel a million miles in an hour. All
these things are true, but as matters of natural law, not of the
conventions which govern the playing of games or the use of
language.
Having said that, I should go on to say that I don't in point of fact
think that it's especially productive to debate whether languages
are infinite. If you accept certain other assumptions then to
suppose they are serves a useful simplificatory
function. But one needn't necessarily accept those
assumptions: in a book to make its appearance shortly, I argue for
a view of what a grammar of a language is on the basis of which
the question of whether languages are infinite or not can be left
open. I personally incline away from thinking that trying to find
length laws (in the terminology of Langendoen and Postal) is a
good way to spend your time -- even if there are such laws, it's
not clear that recognizing them advances our understanding much.
Why then have I entered the debate at all? The answer is that
I've done so only for purposes of providing what I think is needed
clarification where I perceive conceptual confusion. To compare
doing so to practicing medieval theology seems to me to be at the
very least an inapt analogy from a historical point of view: Plato is
a better model than St. Thomas in this context.
Michael Kac