Re: THEORY: How many parameters, constraints, or "types" are there?

On 12/29/05, Thomas Hart Chappell <tomhchappell@...> wrote:

>
> In O.T., the number of different "types" of languages
> will be N! ("enn factorial"), where N is the number of constraints.
>
> But 7! = 5040, and 8! = 40320.
>
> That means, with just eight (8) constraints, there would be more "types" of
> languages, than there have ever been (estimated to be) contemporaneously-
> existing languages.
>
Well, not all constraint rankings give different sets of surfacing
candidate -- if we're doing an OT typology, the number of "types"
created by n constraints is usually a lot less than n!.  Quite often
the precise placement of A vs. B has no effect on what candidates win,
especially down towards the "less important" side of things.  (So, if
we're talking phonology here, markedness constraints that are lower
ranked than any faithfulness constraint won't be relevant for the
purposes of ranking.)

(What's more, if two rankings A > B > C > D and A > C > B > D lead to
the same candidates winning, then there is really no difference
between them, for the simple reason that no evidence would ever allow
the learner to choose between them.  They're really just one ranking A
> B | C > D.)
Anyway, it depends on the constraints used and how often they
conflict, but to take an example... take the OT case-and-voice
analysis of Legendre & Smolensky -- I think I mailed you a copy once.
Their 8 constraints produce, iirc, only a 13-fold distinction of
language types, not a 40k-fold one.

---

About the number of constraints: well, if you're looking to
characterize all the difference between languages (for some level of
the language) you're going to need a lot more than eight.  A complete
account of phonology would probably take around 50.  (I get that
number from an opponent of OT, but iirc she says that's not a
controversial number.)

(That, of course, begs the question that we *can* account for the all
the phonological facts of every language with a reasonable set of
universal constraints.  OT phonology works quite well for its core
strengths like stress assignment and syllable structure, but once we
sit down and try to get everything this way it becomes icky.  You end
up positing some arbitrary constraint like "/k/ can't occur
intervocalically", and then you have to either say it's
language-specific and not a part of UG or that it's universal but only
crucially ranked for, like, Turkish.  Neither is particularly
appetizing.)

If we're working on something like morphosyntax, it'll be fewer, 'cuz
there don't seem to be as many types.  If we're playing around with
case and voice, for example, there are only so many logical
possibilities, and only some fraction of these are attested.

--

If we're working with P&P instead... hmm... I'd go with about 50 for
morphosyntax.  No real reason why, but in the great jar-full-of-candy
that is linguistics, I count 50.  Gotta guess something.  Bear in mind
that both of these are for systematic ways languages can differ;
there's no parameter setting/constraint ranking that causes English
"over" to postpose in "the world over", and none that makes English
call a particular animal "dog" and French "chien".

> For that matter, what would you guess the top 10 parameters or the top 5
> constraints are?
>
What in the world do you mean?

--
Patrick Littell

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