LINGUIST List 2.784

Tue 12 Nov 1991

Disc: Is Language Finite?

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1. "Bruce E. Nevin", assume a spherical language
2. Michael Kac, Is language infinite?

An analogy that I hope will not be distasteful to anyone: Masters and
Johnson state that the human birth canal is indefinitely extensible.
This clearly does not mean that it is infinitely so.
In an old joke, several scientists, who happen to be in different
fields, are asked how fast a chicken can fly. Says the physicist,
	Assume a spherical chicken . . .
This is the position of those who argue that language is infinite
because of the formal properties of the metalanguage that they use to
describe language.
Eating behavior is infinite. It can be interrupted by any number of
other behaviors, themselves interruptable, and then resumed. With
suitable symbolization, this can be described by formal systems that
generate infinite sets of symbol strings. The system describing "a
meal" (presumably beginning with the symbol M on the left side of an
arrow) can thus generate meals of infinite length. Eaters must have
incorporated or must innately have such a system, since they produce
behaviors of the predicted sorts. Ergo, eating is infinite. QED.
Setting aside the fact that natural language contains its own
metalanguage as a sublanguage, and that formal systems (mathematics,
logic, and grammatical formalisms) depend on the background vernacular
of shared natural language for their metalanguage . . . that's a clearly
related issue, but discussion here would distend this topic beyond
recognition, so that no one would get the point.
For the humor-impaired, the meal cheekily described above is probably
tongue flambe'.
	Bruce Nevin
	bnbbn.com

A recent response from John Joseph to my reply to Henry Kucera calls into
question the distinction I assume between matters of convention and matters
of natural law. I have drafted a reply and sent it to Joseph; since it's
on the long side, I thought that rather than post it to LINGUIST as well
I'd invite those interested to contact me directly at: kaccs.umn.edu.
Michael Kac