[Corpora-List] ad-hoc generalization and meaning

[Rob Freeman]

In the "complete grammar?" thread...

On 9/12/07, John F. Sowa <sowa at bestweb.net> wrote:
>
>
> The fact that children by the age of 3 use words for the logical
> operators (e.g., 'and', 'not', 'some', and others) indicates that
> logic somehow evolves out of the infant's early one and two-word
> phrases.  And the fact that all mathematicians, logicians, and
> computer programmers use NLs to explain the most abstruse theories
> imaginable indicates that there is no limit to how far the
> expressive power can evolve.


I'm interested in the problem of logic. In short, I don't see a problem with
it. Not from the point of view of grammar generalized ad-hoc, anyway. I
don't know what specific problems Montague grammar had, but my hunch is that
ad-hoc generalization would solve them. Perhaps you can make the issue
clearer for me.

I have argued the problem with formal grammar has been we've have valued the
result of generalization (grammar) over the process of generalization. Then
we've puzzled that no one generalization is adequate.

If we see the patterns of grammar as the results of generalization (which
must be context specific) then can we not have all the power of formal
grammar, and its logical interpretation, without the limitations?

Frankly, and I am going to get stung for this, I don't see why there should
not be a similar explanation in terms of ad-hoc generalizations for the
logical incompleteness of mathematics. Mathematics can be explained fine in
terms of grammars. The only problem is we find too many of them (c.f.
axiomatic set theory.) Just like language. Could this multiplicity of
grammars for mathematics too not be explained in terms of multiple points of
view accessible through ad-hoc generalizations?

Anyway, leaving mathematics aside. What problems caused Montague grammar to
be rejected? Would they not be solved if grammatical patterns were seen as
the result of ad-hoc generalization over a corpus, and not complete in
themselves?

-Rob
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