Dear All:
I tried to post the message clipped below at around 2:30
p.m. today, but as far as I can tell, it didn’t make it – It doesn’t
show up on my list and I never got a receipt note. This may simply be a case of
the internet exercising aesthetic judgment, but in case it’s accidental,
I’m trying again.
One addition – I’d like to make it clear that
what I’m kvetching about are three specific *characteristics* of
some model-theoretic frameworks. Many frameworks don’t have full
determinacy or atemporal metrics – but a lot of the ones in linguistics
do, and those are the ones I’m talking about.
__
Bruce,
Science does not, in
fact, depend on that kind of model. Quite a number of scientific theories are
couched in terms of such models, but that’s not why they’re
scientific – rather, it’s because they make predictions that can be
falsified by reference to mutually observable phenomena. Conflating that
kind of model with science itself is precisely the kind of thing I was whinging
about.
We don’t even have to go
far afield to find scientific theories (or at least, theories as, or more
widely recognized as such, than those in linguistics) that don’t use
models with the three characteristics I was discussing. Biology, by and large,
doesn’t use atemporal simplicity metrics. The operation of a
system, in real time, to perform real tasks, is an integral part of biological
models. If a system with fewer rules and fewer primitives nevertheless requires
far more steps to achieve a particular goal than another system, its
inefficiency counts for at least as much against it as its simplicity (in terms
of an atemporal metric) counts for it.
I would also argue that neural
networks do not “use” objects in the sense that a standard
grammatical model uses a symbol like “noun,” although I did not
make enough of a distinction in my original post. You’re certainly right
that people talk about neural networks in terms of objects (nodes) and their
properties (activation thresholds, etc.). However, they’re not talking
about language when they do that. The nodes and thresholds are not
within the domain itself that the network is modeling. In an “objects and
rules” model, the objects are themselves part of the
“content” the system is modeling; for example,
“noun,” or a value like “+N,” in a standard
grammatical model is considered to be part of language itself. In a
neural network model of language, “threshold value” is not considered
to be a linguistic phenomenon being modeled, but rather part of the description
of the system by which a linguistic phenomenon is modeled. So,
you’re entirely right that you can consider neural networks to have
objects, but those are transparently presented as features of the model
not features of language. Saying something about a threshold
value is saying something about the device language is conjectured to be
running on, not saying something about language. While the network can be
described in terms of objects and rules, the network itself is not
manipulating objects when it operates. There’s no sense in which a
neural network model of language has to presuppose objects as part of
language.
Bill Spruiell
Dept. of English
Central Michigan University.
From: Assembly for the
Teaching of English Grammar [mailto:[log in to unmask]] On Behalf Of Bruce
Despain
Sent: Wednesday, October 17, 2007 5:18 PM
To: [log in to unmask]
Subject: Re: Rules ad nauseam
Bill,
Thanks
for the notice, though I was stultified (proved to be of unsound mind?).
The
set of symbols used as primitives and a set of rules, laws, or principles, is
not unique to linguists. In fact science itself consists of this
kind of model. To attack such a model is to attack science, which has a much
longer track record than any linguist or English maven.
The objects to be manipulated by language are sounds. (disputable?)
The
objects to be manipulated by language are meanings. (disputable?)
The
objects to be manipulated by language are signs written down in symbols.
(disputable?)
The
objects to be manipulated by language are combinations of the above.
(disputable?)
1)
What seems to be the nature of neural nets doesn't mean that no objects
don't exist in the model. Indisputable is that fact that there
are potentials, thresholds, charges, etc.
involved. The model-theoretic framework says nothing about the
reality of the objects posited. The model is no more than a
metaphor for what is being modeled. 2) A fully determinate system does
not come to mind when the modeling is of phenomena like the weather.
There are simply too many elements in the determinate version. Even the
particle theory of matter must be abandoned though it is clearly
determinate. The sheer number of particles involved often becomes so
great as to make the model impractical in making predictions of any but
the roughest statistical kind. Certainly the determinate nature of the
phenomena described ought to be paralleled by that of the model that describes
it. The investigator who wants to put the former in doubt, has
no need for a model with full predictive power. 3) The
number of objects and rules has been a condition since the acceptance of
Occam's razor by most scientists. I would think that the simple nature of
these objects and the statement of these rules in the accepted vernacular of
mathematics would be another consideration.
I
think that there is a likely confusion between a mathematical model and a
particular model for linguistic descriptions. The model-theoretic
principles of mathematics are unavoidable to any formalization. Whether a
specific mathematical model actually serves to describe the phenomena it claims
to can always be disputed and refuted with appropriate data. But we don't
thow away the language because of what people can say with it. If the
phenomena we are trying to describe are indeterminate, then it doesn't make
much sense to use a model that requires determinate phenomena. But
the model itself had better use a determinate framework, or it would
hardly be able to explain anything (have any predictive power).
I
would wonder that failures in the operation (?) of the model of language could
ever be made out to be performance issues. The performance of the model
would have to be faultless, in order to support itself. Maybe people
expect it to make predictions of the performance variety? (Present-day
minimalists are often far too broad in their expectations in this
area.) You say, "The problem is not the framework itself, but rather
its hegemonic status." I think that what many linguists call the
model-theoretic framework is their own model for natural language. This
is the area of hegemony, I believe. This then pits one camp against
another based on their own modeling principles established for their own
purposes, not the two elements you gave for a mathematical model in
science. Certain models can in fact be shown to be faulty based on the
way in which the nature of the elements and mathematical relationships posited do
not match in principle the behavior of the objects being modeled. To
do so does require a bit of sophistication, which, sorry to say, I do not
possess. (Cf. John Casti, Reality Rules)
Bruce
Visit ATEG's web site at http://ateg.org/