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[George Lakoff]

To: Pinker and Prince

From: George Lakoff

Re: Represntational adequacy and implementablility

Perhaps it's time to turn the discussion back on P&P
and discuss the adequacy of the alternative they advocate.

Let us distinguish first between learning and representation.

Most generative linguistics involves representation and
says nothing about learning. Representations
there are constructed by linguistics.
However that theory of representation
has some deep problems, a couple of which have come up in the 
the discussion of past tenses. Here are two problems:

1. Generative phonology cannot represent prototype structures
of the sort Bybee and Slobin described, and which arise
naturally -- and hence can be described easily --
in connectionist models.

As for regular cases: If one puts aside learning and
concentrates on representation, there is no reason why
one could not hand-construct representation of regularities in
connectionist networks,
so that general principles are represented by
patterns of weights.

If this is the case, then, on representational grounds, 
connectionist foundations for
linguistics would appear to be more adequate than
generative foundations that use symbol-manipulation
algortihms.

If generative phonologists can represent the irregular
cases, then let's see the representations.

Moreover, it would seem that if such prototype phenomena
cannot be represented generatively, then a Pinker-style
learning device, which learns generative represetations,
should not be able to learn such prototype phenomena,
since a learning device can't learn something it can't represent.

2. P&P blithely assume that generative linguistic representations
could be implemented in the brain's neural networks.
There is reason to doubt this. Generative phonology uses
sequentially operations that generate proof-like `derivations'.
These sequentially-ordered operations do not occur in real time.
(No one claims that they do or should, since that would make
psychologically indefensible claims.) The derivations are thought of as
being like mathematical proofs, which stand outside of time.

Now everything that happens in the brain does happen
in real time. The question is: Can non-temporal operations
like the rules of generative phonology be implemented
in a brain? Can they even be implemented in neural
networks at all? If so, what is the implementation
like, and would it make an assumptions incompatible
with what brains can do? And what happens to the intermediate
stages of derivations in such an implementation?
Such stages are claimed by generative phonologists to
have ``psychological reality'', but if they don't occur
in real time what reality do they have?

For P&P to defend generative phonology as a possible
alternative, they must show, not just assume,
that the nontemporal sequential operations of
generative phonology can be implemented, preserving
generations, in neural networks operating in real time.

I have not heard any evidence coming from P&P on this issue.

Incidentally, I have outlined a phonological theory that
has no atemporal sequential operations and no derivations, that can
state real linguistic generalizations, and that can
be implemented in connectionist networks.
A brief discussion appears in my paper in the Proceedings
of the 1988 Connectionist Summer School, to be
published soon by Morgan Kaufman.

Well? Do Pinker and Prince have a demonstration that
generative phonology can be implemented in neural networks or not?

If the atemporal sequential operations of generative phonology
cannot be implemented in brain's neural networks, that is
a very good reason to give up on generative phonology
as a cognitively-plausible theory.

                   * * *

Incidentally, I agree with Harnard that nothing P&P said
in their paper has any ultimate consequences for the
adequacy of connectionist foundations for linguistics.
I am, in fact, on the basis of what I know about
both existing generative foundations and possible connectionist
foundations, I am much more optimistic about connectionist foundations.