Rules vs. Lists

[Rob Freeman]

On Sat, Jul 5, 2008 at 9:13 PM, A. Katz <amnfn at well.com> wrote:
>
> MORE rules implicit than examples? That's a stretch, as a list of unitary
> items has at most as many rules as examples.

Thanks. I wanted you to see that. It is something different from what
we have considered before. Not impossible, just not something which
has been considered, to my knowledge.

> However, I suppose the English derivational system might provide something
> like that. If English lexemes are listed one at a time, and most English
> speakers are unaware that they have subparts (and I've done research on
> this -- monolingual English speakers are amazingly imperceptive about
> derivations that are obvious to the rest of us), and if you then add the
> derivational rules that might account for some of these words, then you
> have a system where each item is a rule in itself, and also some rules for
> deriving the items, so there are more rules than examples. But... this is
> only so if you try to conflate the derivational insensitivity of the
> average English speaker with the patterns implicit in the words.
>
> ...
>
> It's kind of a cheat, because we are listing from the point of view of
> more than one speaker, so that two systems overlap. But because the
> knowledge of speakers can evolve over time, such an overlap is not
> psychologically improbable.

Yes, if you regard each example as a rule in itself, and yet have
productive rules over them, then almost trivially you will have more
rules than examples.

I don't think we need conflate speakers to do this. Most of us will
accept that there is something unique about almost every utterance,
while finding productive regularities over them.

But it is not hard to find an argument that even the number of
productive rules might be greater than the number of examples.

As David pointed out in an earlier message:

"...if you have examples A, B, C and D and extract a schema or rule
capturing what is common to each pair, you have 6 potential rules,
(AB, AC, AD, BC, BD, and CD), so sure, in theory you could have more
rules than subcases. Add in levels of schemas (rules capturing what's
common to AB-CD, AB-AC, ...) and you can get plenty of rules."

The question is do we?

-Rob