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 Discussions:
Infinite language, Is
Language Really Infinite?
 Polls:
Is
Language Infinite?
 Further
Reading: Linguistic Theory
Wilhelm von Humboldt and Noam Chomsky
Wilhelm von Humboldt's phrase that language is 'the infinite use
of finite means' has been cited by Noam Chomsky, who in turn has
frequently referred to the concept of infinite language, a speaker's competence,
which in Chomsky's terminology is their ability to produce a potentially
infinite number of correct sentences. It has also been argued that it
is possible to generate an infinitely long sentence along the lines of
'this is the rat that ate the corn stored in the barn by the house that
Jack built'.
Language can be theoretically infinite both textually and diachronically,
over time. It would probably be more accurate to use a term such as Alan
Turing's 'infinitive state', which he applied to computer memory which
could always be added to, but would, at any point in time, be limited
in actual use. At any given moment, however brief, there are a finite
number of texts in existence, even though we couldn't calculate them and
the number is changing all the time.
Is Language Infinite Synchronically?
What I would like to look at is whether language is infinite synchronically,
at a point in time. To do this, I want to look at an abstracted and theoretical
version of language, one where the entire vocabulary has been recorded,
together with every single rule for the possible combinations of words
that will allow meaningful sentences to be formed. This is our snapshot
of language and it holds true until a new word or meaning is formed. When
that happens, the system will simply be updated. Every name from every
language, every place, etc., are all included; we a have a machine that
contains the entire language in terms of words and rules. All dialects,
all 'questionable' uses are included; everything that would be accepted
and understood by members of the speech community has been codified and
included. We have inputted all of this into a mega-computer capable of
spewing out trillions of sentences in nanoseconds.
If we take a word like 'book' and consider the list of adjectives that
could come before it, we run through our dictionary and produce a list
that eventually includes every possible adjective. No use, no matter how
implausible or eccentric has been excluded; we keep building the list
until no-one can find any more appropriate adjectives. The list runs to
tens or hundreds of thousands, but size is not important; what matters
is that it has an end. These adjectives can in turn be modified by one
or more adverbs, of which there may well be thousands. Nouns can be used
in the same way as adjectives, as can other words. We list them all and
work out every possible permutation.
Our machine, like Bob Newhart's infinite number of monkeys, pours out
trillions of combinations and entire forests are felled to keep the printers
stocked with paper. But eventually the printer stops and someone says
that it's time to make 'book' plural. Then it will be time to move onto
the verbs it goes with, etc. In this sense, it is theoretically possible
to generate the entire output of a language at any given time. The numbers
involved are so astronomical that they may seem infinite, but they are
not; immeasurable and incalculable are not synonymous with infinite. A
single neologism could offer trillions and trillions of new combinations,
but the synchronic view is always finite; a closed system with a limited
number of words that can combine in a limited number of ways cannot produce
infinity. The fact that we couldn't get remotely close to exhausting a
language's potential supply of sentences does not mean that it is not
theoretically possible. Wilhelm von Humboldt seems to me wrong to believe
that the finite can generate infinite variety; it can only be used infinitely
through repetition.
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