"loss of generality"

[Sydney Lamb]

On Tue, 29 Jun 2004, Rob Freeman wrote:

> ...
> Yes, that could be where we are at cross-purposes. I'm talking about
> subjectivity from utterance to utterance not just from language to language,
> or even individual to individual. I believe that not only does each
> individual form a slightly different representation of linguistic structure,
> but that same individual forms a different representation of linguistic
> structure (to an extent limited by the functional contrasts required by the
> message only) from utterance to utterance.

Why call this sujectivity?

> That means you can explain non-linearity as a redefinition of each phoneme
> (e.g. voiced or un-voiced) by the same individual from context to context.

No. That would be RETAINING linearity. The whole point of
rejecting a linearity requirement is to make it unnecessary to
do this.

> Does my equation of non-linearity with subjectivity make more sense if you
> think of a phoneme as subjective on its context within an utterance?

No.

Lamb:
> > But all this has nothing to do (as far as I can see) with
> > whether or not we recognize non-linear features in phonology.
> > One could have either subjective or (hypothetically)
> > across-the-board objective representations of phonological
> > structure with some non-linear features.
>
> Well, we _could_ have objective phonological structure with non-linear
> combination, but how would we implement it?
>
> Even if we entertain the possibility, consider the complexity. The value
> associated with every element in a combination of phonemes would have to have
> an extra +x (not only adding, but swapping values completely, as from voiced
> to voiceless) from every other phoneme in the combination. Who could tell
> ...

No. That is the problem you would get if you RETAIN linearity.

> In fact I really don't think you can keep non-linear combination of
> _objective_ phonemes (as opposed to combinations which are non-linear because
> the phonemes are subjective) and keep biuniqueness as a fundamental defining
> principle of structure, Syd. If you want to propose there is something
> objective under all those +x's you have to accept you can never learn it.
> Biuniqueness will only give you the sum of a particular non-linear
> combination operation.

Not at all.

>
> We are slipping into the abyss. Isn't it much better to accept that the
> idealized, objective, phoneme does not exist at all (for it to need to
> change),

Change? Are we now suddenly adding diachronic considerations?

> Perhaps that's not a proof, but can you think of another mechanism which would
> produce non-linear combinations of phonemes? In particular one which
> maintains biuniqueness as a fundamental parameter?

There is really no problem. Your mention of production prompts
me to bring up an additional consideration that is usually
neglected (and was neglected during the whole period of
classical phonemics, as well as during the period of
Chomsky-Halle phonology: we have to distinguish production
phonology from receptive phonology -- their structures are not
the same. They are even processed in entirely different (though
interconnected) parts of the cortex. From the point of view of
production phonology, the linearity condition is actually
retained w.r.t. voicing of obstruent clusters. At the beginning
of the cluster the voice is turned off or on (as the case may
be), and it just remains that way -- no add'l voicing operation
needed -- till the end of the cluster.

> ...
> Our vocal tract is telling us we want to produce the least contrast we have
> to, but what is the smallest contrast the system allows us? If the system
> were a linear concatenation of objective phonemes then the option of
> producing voiceless versions would not be available, not from the point of
> view of the system itself.
>

I don't see this at all.

> We could take the "hard" non-linear case and have each phoneme in a
> combination of multiple "objective" phonemes.

Nor this.

> Or we could take Chomsky's view. We could try to explain the omission of the
> voiced/voiceless contrast as a performance limitation acting on a
> structurally invariant ideal.

This is NOT what Chomsky proposed.

(Your additional discussion is not repeated here, as it depends
on the same misunderstanding of what is meant by relaxing the
linearity requirement. If we can straighten out the above
points, then it will be unnecessary to dwell further on the
rest.)


> > > ...
> > > What was the subsequent theoretical and practical impact of your
> > > observation that there was a need for "relaxing the linearity
> > > requirement" over combinations of phonemes? Has this been taken on board
> > > by people trying to model phonemes for speech recognition, for example?
> >
> > What happened was weird. Chomsky responded to my published
> > account (e.g. Prolegomena to a theory of phonology, Language
> > 1966) by saying that (approx quote) "Lamb's attempt at
> > refutation amounts to accepting my solution in toto with
> > a change of notation". (!!) This despite that fact that
> > Chomsky's solution retains linearity while rejecting
> > biuniqueness (contrastive function), while mine rejects
> > linearity while preserving biuniqueness.
>
> Well, I don't find it too surprising... I guess Chomsky found non-linear rules
> to be quite as untenable as a rules which exhibited a "loss of generality".

I think the problem was not this; rather that the possibility of
abandoning the linearity requirement didn't even occur to him.
(Although once one considers it a little, it becomes obvious
that it is just a troublesome excrescence handed down from
tradition, influenced by alphabetic writing.)

> ...
> It's a pity. I think this observation, whether you characterize it as "loss of
> generality" or "relaxing the linearity condition",

No -- these are two quite different things. What I had shown was
that by relaxing the linearity condition we can handle the
obstruent clusters without loss of generality.

 - Syd


Sydney M. Lamb			http://www.ruf.rice.edu/~lamb/
Linguistics and Cognitive Sciences
Rice University, Houston, TX