bebboe wrote:davidbackslashse wrote: Natural languages (the kind we speak) are recursive and are capable of generating sentences of infinite length (in practical terms, though, we're really only capable of processing up to about three embedded clauses). Formal languages, as in the quote, are defined over the set of strings in full that make them up.
This is a common misunderstanding. There is no such thing as a sentence of infinite length, at least not in natural languages. The length of sentences in natural languages is unbounded, but not infinite. There is no upper bound to the length of sentences, that is, given any sentence, you can always construct a sentence that is longer than it, but this is NOT the same as saying that there are sentences of infinite length (though it follows from this that the cardinality of the set of English sentences is infinite). Not that this really matters in this discussion, but since even some of the most educated people I know tend to claim that Chomsky claimed that there were sentences of infinite length, I felt like clearing this up.
You're right, I phrased that badly. Thanks!