[FOM] expressive power of natural languages
meskew at math.uci.edu
Wed Nov 30 18:59:44 EST 2011
It seems to me that English cannot be classified as any type of formal language.
First, how would many-sorted first order logic be enough to capture things like tenses, subjunctive moods, commands and exclamations, gerunds, prepositions, adverbs, reference to English itself, etc. in a way that at all resembles the actual structure of spoken English?
Second, the rules of English grammar are somewhat fluid and the language changes over time. Without well-defined syntax, how could it be formal?
Third, unique readability fails. Bob said Joe saw his friend.
Fourth it is often vague.
Fifth, what rules of grammar or semantics prevent the Berry paradox in English? Nothing; the paradox makes us realize that the intuitive semantics don't work.
On Nov 30, 2011, at 11:36 AM, "americanmcgeesfr at gmx.net" <americanmcgeesfr at gmx.net> wrote:
> Hello FOMers,
> I was wondering if there is any (at least semi-)conclusive view about the expressive power of a natural language like english resulting in a statement like "whatever it is, it is a language of at least 2nd order". Of course, I know of TarskiÂ´s comment suspecting natural languages to be somehow (semantically) universal. But what IÂ´m interested in is a hint pointing me in a direction what to look for, i.e. is the fact that one quantifies over classes in a natural language enough to label it higher order? Can there be anything wrong to take it to be at least a many-sorted first-order language?
> Alex Nowak
> FOM mailing list
> FOM at cs.nyu.edu
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