[FOM] expressive power of natural languages
Robert Black
mongre at gmx.de
Wed Nov 30 18:36:02 EST 2011
Am 30.11.11 20:36, schrieb americanmcgeesfr at gmx.net:
> 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?
Well, there are reasonably natural and provably non-first-orderizable
sentences like 'Some critics admire only one another' (taking this to
mean that there are some critics such that anyone admired by one of them
is another one of them) or, even more famously, 'Napoleon is not one of
my ancestors' (assuming that our only access to the concept of ancestor
is via the concept of parent). The classic reference on these matters is
George Boolos's 'To Be is to Be a Value of a Variable (or to Be Some
Values of Some Variables)', J.Phil. 1984.
Robert Black
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