|Humboldt, Wilhelm von|
He believed that language
is a rule-governed system.
(1767 — 1835) Purportedly, he was the first European to posit that human language is a rule-governed system. Noam Chomsky acknowledges him as an intellectual predecessor, and often quotes Humboldt's definition of language as a system which "makes infinite use of finite means" (from Über den Dualis 1827), meaning that an infinite number of sentences can be generated by a finite set of grammatical rules.
I beg to differ: Unlike in mathematics, where there ARE techniques for proving that the set of all numbers is infinite. Linguistics has no technique for proving that the set of all sentences is infinite.
For example, in mathematics you can create a proof along the lines of:
(1) The set of numbers is finite
(2) Because of (1), there must be a number that is the greatest number in this set of all numbers. Call that number X.
(3) But according to the rules of mathematics, there must be a number X+1.
(4) This contradicts (1); hence the set of all numbers must be infinite. QED.
But this technique doesn't work in linguistics, because sentences aren't numbers. They have an additional requirement: they must be meaningful to be called sentences. So when we start to generate the set of all sentences, there will come a point when the sentences contain so many words that they cease to be meaningful. Thus, the simple technique in the above proof, which works very well for numbers, falls apart if you try to apply it to language.
For this reason, I believe that the statement "an infinite number of sentences can be generated from a finite set of rules" is unprovable, unless you remove the requirement that they be meaningful. But if you do that, the statement has no value at all. It reduces to something like "if we keep doing it, it will continue being done."