Re: Universal grammar

Hans Aberg wrote:
In article <1161246509.794397.244600@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, "Rob
Freeman" <groups@xxxxxxxxxxxxxxxxxxx> wrote:

... Is it
always possible to find a consistent set of rules which completely
describes all the patterns in a distribution?

This is somewhat too diffuse to be possible to be pinned down in
mathematics...

Well, thanks for trying.

Personally I am not convinced it has nothing to do with Goedel's
theorem:

Is it possible to reduce all of mathematics to logic?/Is it possible to
reduce all patterns to logic?

Apparently Goedel himself interpreted his proof as a demonstration of
philosophical idealism. If mathematical "truth" could not be reduced to
logic, then it must have some independent existence... He used this to
contrast himself with the logical positivists (who felt a theory only
needed to be consistent with the evidence?)

If nothing else, as an interpretation of evidence, the parallel with
Chomsky is amusing.

Independently of any connection with Goedel's proof, I think the
question is interesting. Perhaps you are right and it is beyond
mathematics to prove either way whether all distributions can be
described in terms of rules.

I would like to know though. My hunch is there are many which cannot.

-Rob

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