"loss of generality"

Rob Freeman rjfreeman at email.com
Tue Jun 29 11:32:15 UTC 2004


On Tuesday 29 June 2004 00:24, Sydney Lamb wrote:
> On Mon, 28 Jun 2004, Rob Freeman wrote:
> > > >  ... Rather it
> > > > looks to me to be evidence that a focus on the "centrality of the
> > > > contrastive function of linguistic elements" (which is also the
> > > > foundation of Functionalism) implies structural subjectivity in
> > > > language.
> > >
> > > I'm sorry to say that I don't see this connection. I'm not
> > > disagreeing (necessarily) -- just don't get the implication.
> > > What am I missing?
> >
> > One way of seeing the connection is to equate "relaxing the linearity
> > requirement" with structural subjectivity. This seems natural to me. They
> > both imply you need to look at the whole utterance to know the elements.
> > ...
>
> It could be that the problem I am (still) having is related to
> your definition of subjectivity. To me, subjectivity implies
> that each individual forms and uses his/her own individual
> representation of linguistic structure. This surely has to be
> so, imho.

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.

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.

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?

> 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
what the "real" phoneme might be under all that. No wonder Chomsky thought a
true (universal?) representation could not be learned.

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.

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), that the idea of an idealized phoneme is just an average of
contrasts (subjective, because the contrasts needed differ from word to word)
needed to make meaningful distinctions (only those consistent with getting
the message across) each time.

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? Producing the phoneme anew
each time as an average of only the necessary contrasts would do it.

> > ...
> > Another way of looking at it -- if you allow combinations of linguistic
> > elements to be non-linear, your results will be indistinguishable from
> > strings formed by "linear" combinations of subjective elements.
>
> I don't follow this at all. Are you sure you want to say this?

I'll stick with it. If subjective elements are thought of as subjective on the
context of an utterance I think it is true.

Can you think of anything which might distinguish the them?

> > I think "relaxing the linearity condition" and "subjective elements" are
> > saying very much the same thing. Unless we can think of some other
> > mechanism explaining how non-linear combination might occur.
>
> The mechanism can be explained on an objective basis in terms of
> ease of articulation...

Well that's a motivation, but what about a mechanism?

In real life practical constraints push us to do all kinds of things, but what
actually happens is limited by what the system will allow.

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.

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

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.

But in either case there is no way of knowing what the real system is, because
there is no way of knowing what the objective phonemes are like! We are back
searching for Universal Grammar. Biuniqueness only tells us what the
observables are. It is no longer a fundamental principle.

> > ...
> > What is the evidence? Is it that language has a single, universal
> > structure, or that structure is generalized, subjectively, on the spot,
> > parameterized only by meaningful contrasts?
>
> I go with the latter view, although there are universal
> properties, because of shared biological and environmental
> features.

Yes, I don't think the universal nature of language exists much beyond a
mechanism for identifying and associating (contrasting) repeated segments in
sequences.

That combined with the common functional motivation of the "real" world.

A system to produce language must have these common (and common biological)
capabilities, which, as I'm sure you know, all indications (e.g. speed of
parallel search, flexibility, robustness...) tell us would be supremely
suited to some kind of network implementation.

I don't mind if someone wants to call that Universal Grammar.

> > ...
> > 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 do see them as rather the same thing -- subjective combinations of elements
(or combinations of subjective elements, or both).

What it comes down to in the end is whether you accept the subjective
(non-linear, non-general) combinations, or if you reject the biuniqueness
which produces them.

Chomsky was probably happy you agreed with the basic observation that a
phoneme consistent with a definition in terms of biuniqueness is not
consistent in combination, but didn't see a non-linear rule as a credible
solution (not as system, anyway). So he felt we were forced to return to his
solution -- that the contrastive patterns we see in the data are not the true
patterns at all (competence) but only corruptions of those patterns
(performance).

> How did others (besides Chomsky) react? As far as I can tell, by
> simply ignoring these published refutations of mine, with their
> alternative solutions. It came to be generally accepted that the
> notion of a contrastive phoneme (Chomsky's "biuniqueness") had
> been thrown out by Chomsky. The phoneme was dead for the next
> two or three decades. Nobody (other than my students) was even
> aware of my refutation of his argument.

It's a pity. I think this observation, whether you characterize it as "loss of
generality" or "relaxing the linearity condition", is nice evidence that
language strings are produced by top down, ad-hoc, generalization according
to minimum contrasts. Accepting the implications of non-linearity as a
positive statement about the nature of phonemes ("loss of
generality"/non-linearity/subjectivity), rather than a negative statement
about the significance of functional contrast (biuniqueness), could have
forced us to seek ways to systematically generate non-linear sequences of
phonemes, viz. constant subjective generalization of phonemes within each
utterance parameterized only by the functional contrasts demanded by the
context.

How did Functionalism treat this? Surely Functionalism did not reject a
fundamental role for functional contrast? Or did Functionalists stop thinking
about structure altogether?

-Rob



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