Learnability and Linguistic Theory

220 Pages·1989·5.693 MB·English

by  Robert J. Matthews (auth.), Robert J. Matthews, William Demopoulos (eds.)

LEARN ABILITY AND LINGUISTIC THEORY
STUDIES IN THEORETICAL PSYCHOLINGUISTICS
Managing Editors:
Tom Roeper, Dept. of Linguistics, University of Massachusetts at Amherst
Kenneth Wexler, Dept. of Brain and Cognitive Science, MIT, Cambridge, Mass.
Editorial Board:
Robert Berwick, Artificial Intelligence Laboratory, MIT, Cambridge, Mass.
Manfred Bierwisch, Zentralinst. flir SprachwissenschaJt,
Akademie der WissenschaJten der DDR
Merrill Garrett, University ofA rizona,'Tucson
Lila Gleitman, School of Education, University of Pennsylvania
Mary-Louise Kean, University of California at Irvine
Howard Lasnik, University of Connecticut at Storrs
John Marshall, Neuropsychology Unit, Radcliffe Injirmwy, Oxford
Daniel Osherson, MIT, Cambridge, Mass.
Yukio Otsu, Tokyo Gakugei University, Tokyo
Edwin Williams, Princeton University
VOLUME 9
LEARNABILITY
AND
LINGUISTIC THEORY
Edited by
ROBERTI. MATTHEWS
Rutgers University, New Brunswick, N.J., U.S.A.
and
WILLIAM DEMOPOULOS
University of Western Ontario, London, Ontario, Canada
KLUWER ACADEMIC PUBLISHERS
DORDRECHT I BOSTON I LONDON
Library of Congress Cataloging-in-Publication Data
Learnab11ity and linguistic theory I edited by Robert J. Matthews and
William Demopoulos.
p. cm. -- (Studies in theoretical psycholinguistics>
Inc 1u des index.
ISBN -13:978-0-7923-0558-3 e-ISBN-13: 978-94-009-0955-7
DOl: 10.1007/978-94-009-0955-7
1. Language acquisition. 2. Learning ability. 3. Grammar,
Comparative and general. 4. Psycholinguistics. I. Matthews,
Robert J., 1943- II. Demopoulos, William. III. Series.
P118.L3898 1989
401 •• 93--dc20 89-2556
Published by Kluwer Academic Publishers,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
Kluwer Academic Publishers incorporates the publishing programmes of
D. Reidel, Martinus Nijhoff, Dr. W. Junk, and MTP Press.
Sold and Distributed in the U.S.A. and Canada
by Kluwer Academic Publishers,
101 Philip Drive, Norwell, MA 02061, U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
All Rights Reserved
© 1989 Kluwer Academic Publishers, Dordrecht, The Netherlands
Softcover reprint of the hardcover 1st edition 1989
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner
TABLE OF CONTENTS
PREFACE vii
ROBERT J. MATTHEWS I Introduction: Learnability and
Linguistic Theory 1
DANIEL N. OSHERSON, MICHAEL STOB, and SCOTT
WEINSTEIN I Learning Theory and Natural Language 19
ROBERT J. MATTHEWS I The Plausibility of Rationalism 51
WILLIAM DEMOPOULOS IOn Applying Learnability Theory
to the Rationalism-Empiricism Controversy 77
HOWARD LASNIK IOn Certain Substitutes for Negative Data 89
STEVEN PINKER I Markedness and Language Development 107
JANET DEAN FODOR I Learning the Periphery 129
JOHN TRUSCOTT and KENNETH WEXLER I Some Prob-
lems in the Parametric Analysis of Learnability 155
DAN FINER and THOMAS ROEPER I From Cognition to
Thematic Roles: The Projection Principle as an Acquisition
Mechanism 177
LIST OF CONTRIBUTORS 211
INDEX OF NAMES 213
INDEX OF SUBJECTS 215
v
PREFACE
The impetus for this volume developed from the 1982 University of
Western Ontario Learnability Workshop, which was organized by the
editors and sponsored by that University's Department of Philosophy
and the Centre for Cognitive Science. The volume e~plores the import
of learnability theory for contemporary linguistic theory, focusing on
foundational learning-theoretic issues associated with the parametrized
Government-Binding (G-B) framework. Written by prominent re
searchers in the field, all but two of the eight contributions are pre
viously unpublished. The editor's introduction provides an overview that
interrelates the separate papers and elucidates the foundational issues
addressed by the volume.
Osherson, Stob, and Weinstein's "Learning Theory and Natural
Language" first appeared in Cognition (1984); Matthews's "The Plausi
bility of Rationalism" was published in the Journal of Philosophy
(1984). The editors would like to thank the publishers for permission to
reprint these papers. Mr. Marin Marinov assisted with the preparation of
the indices for the volume.
VB
ROBERT 1. MATTHEWS
INTRODUCTION: LEARNABILITY AND LINGUISTIC
THEORY
1. INTRODUCTION
Formal learning theory, as the name suggests, studies the learnability
of different classes of formal objects (languages, grammars, theories,
etc.) under different formal models of learning. The specification of
such a model, which specifies (a) a learning environment, (b) a learn
ing strategy, and (c) a criterion for successful learning, determines (d)
a class of formal objects, namely, the class that can be acquired to the
level of the specified success criterion by a learner implementing the
specified strategy in the specified enviroment.
jormal model oj learning:
----------(-;a", /b, c', )-d. ......... -..... --
--- ,,/,'. -. ..... ....-
,"
learning learning success class of formal objects
environment strategy criterion (that can be acquired,
in the sense of c, by bon
in a)
that tHe; IC;a.l11C;l 1 c;a.llL.C;~ d lc;:allll11e, lUlI\...-UUll tHdt 111ap~ un::; Ival1ung
environment into these formal objects. Specifically, it is assumed that
both the environment and acquired objects can be coded by the nat
ural numbers, so that the learner can be construed as realizing a
function on the natural numbers. Formal learning theory makes no
general assumptions as to whether the learning function is, for ex
ample, recursive or non-recursive, partial or total, computable or non
computable, though, of course, the particular models of investigated
by formal learning theorists will make such assumptions in the course
of specifying the learning strategy employed in the models.
Work in formal learning theory began in the mid-1960's, with papers
by Solomonoff (1964), Gold (1967), Feldman (1972), Blum and Blum
(1975), and others. Especially influential was Gold's paper "Language
Identification in the Limit," which proved a number of important
Robert f. Matthews and William Demopoulos (eds.). Leamability and Linguistic lheory.
1-17.
© 1989 Kluwer Academic Publishers.
2 ROBERTJ.MATTHEWS
formal results regarding a restricted class of learning models which has
come to be known as the "Gold paradigm." Much of the subsequent
work in formal learning theory, most notably that of Osherson et al.
(1982, 1984, 1986) and Osherson and Weinstein (1982, 1983), has
concerned itself with extensions and generalizations of this paradigm.
The intellectual interest of formal learning theory lies in the possibi
lity that it may contribute significantly to an explanation of how it is
that we are able to come to know what we know on the basis of limited
experience (what Chomsky [1986] has dubbed "Plato's problem").
Presumably formal learning theory would do this by specifying the
class of learning functions that human learners realize and in virtue of
which they are able to map a course of experience into knowledge.
Some hope that formal learning theory will enable us to recast the
much-discussed debate between rationalists and empiricists in terms of
competing claims regarding the learning functions realized by human
learners. Such a reformulation of the debate might enable us to see
what empirical evidence, if any, would decide the issues in that debate
one way or another.
Formal learning theorists have emphasized the import of their re
sults for linguistics. Specifically, they claim that formal learning theory
can provide non-trivial conditions of explanatory adequacy on theories
of natural language.1 Osherson and Weinstein (1983, p. 37) put the
claim this way:
For a class of languages to be the natural languages, the class must be learnable by
children on the basis of the kind of linguistic exposure typically afforded the young. Call
this the leamability condition on the class of natural languages. Formal learning theory is
an attempt to deploy precise versions of the learnability condition in the evaluation of
theories of natural language. In the present context, such a theory will specify (a) the
kind of linguistic input available to children, (b) the process by which children convert
that experience into successive hypotheses about the input language, and (c) the criteria
for "internalization of a language" to which children ultimately conform. From (a)-(c) it
should be possible to deduce (d) the class of languages that can be internalized in the
sense of (c) by the learning mechanism specified in (b) operating on linguistic input of
the kind characterized in (a). Such a theory is correct only if (d) contains exactly the
natural languages.
Linguists agree that linguistic theories must satisfy a learnability
condition, namely, that the set of grammars made available by an
adequate linguistic theory must be such that any member of this set
could be acquired by child-learners on the basis of the kind of linguistic
experience typically afforded them for learning language. (This is just
Chomsky's condition of explanatory adequacy.) Yet many linguists
INTRODUCTION 3
tend to dismiss the claim of formal learning theorists to be able to
provide non-trivial adequacy conditions on linguistic theories. More
over, they assume (and indeed claim) that the fact that recently pro
posed linguistic theories make available only a finite number of
grammars for natural languages insures that these theories satisfy the
learn ability condition. As one well-known linguist put it, "there's no
theory of leamability if there's only a fInite number of core grammars."
Both claims deserve careful scrutiny.
2. LEARNING-THEORETIC ADEQUACY CONDITIONS ON
LINGUISTIC THEORY
The reason that many linguists have thought it unlikely that formal
learning theory can provide non-trivial adequacy conditions on ling
uistic theory is presuIl)ably this: a set of conditIons are adequacy
conditions on any explanatorily adequate linguistic theory only if they
can be justified without recourse to any existing linguistic theory.
Otherwise these conditions would simply affirm without independent
argument a preference for the theoretical assumptions of a particular
theory or class of theories. It is just this meta-requirement on ade
quacy conditions that formal learning theorists would appear unable to
meet. Adequacy conditions on linguistic theory are necessary con
ditions for a linguistic theory's being true; such conditions are justified
by demonstrating that they are (would be) satisfied by a true theory.
The claim of formal learning theorists to be able to provide such
conditions rests on the presumption that formal learning-theoretic re
sults can provide the required justification for proposed conditions.
But this, many linguists believe, is highly unlikely given that it does not
seem possible even to formulate a correct (or even approximately
correct) learning model for natural language using the recursive
theoretic vocabulary in which formal learning-theoretic results are
couched. If a reasonable approximation of the correct model cannot be
formulated in the vocabulary of formal learning theory, then it is
unclear how the learning-theoretic justification of proposed adequacy
conditions would proceed: how could one demonstrate that these con
ditions would be satisfied by a true theory?
In order to appreciate formal learning theory'S inability to formulate
even a reasonable approximation of the correct learning model for
natural language, consider, for example, the empirically plausible sug
gestion that the criterion of successful acquisition incorporated in the
correct model of language learning permits the language acquired by a
4 ROBERTJ.MATTHEWS
successful learner to differ in certain precise ways from the language to
which he is exposed. It would be extremely implausible to suppose that
the correct criterion is captured by any of the finite-difference criteria
investigated by Osherson and Weinstein (1982). (Such criteria count
the learner successful in acquiring a language L just in case he con
verges on some language L' such that the symmetric difference be
tween these two languages is finite.) The problem with these criteria is
not simply that they would count as having s.uccessfully acquired English
the learner who acquired a language differing from English in that all
strings of length n or less (say, n = 2,000 words) were sentences of a
different language (e.g., French), though this, of course, is a problem.
Rather the problem is that these criteria focus on the number of
differences permitted by the success criterion, rather than on the sort
of differences permitted. Available empiricaI-evidence regarding idio
lectal variation suggests that successful acquisition of a natural langu
age requires that the learner acquire a core of a linguistic constructions
shared by all speakers of the language, while permitting idiolectal
variation in certain peripheral constructions. Thus, for example, suc
cessful acquisition of English would seem to require that the learner
master the aspects of bounding, government, thematic-role assign
ment, binding, case, and control that are peculiar to English, while at
the same time permitting idiolectal variation in such peripheral con
structions as the optional contraction of I want to stay to I wanna stay.
Of course, if as seems certain the idiolectal variation permitted by the
success criterion must be stated in terms of grammatical rules or
principles, then this variation will be non-finitary, since the differences
in rules will be projected over the non-finitary fragment of the lan
guage generated by means of derivations that employ the rules in
question. (The symmetric difference between two languages that differ
only in whether they permit wanna-contraction, for example, will be
non-finitary. )
The point here is not that these finite difference criteria are not
plausible candidates for the correct success criterion for natural lan
guage learning; no one, including formal learning theorists such as
Osherson and Weinstein, thinks that they are. Rather the point is that
it seems extremely implausible to suppose that the correct criterion can
be stated independently of the theoretical resources made available by
the correct linguistic theory. Similar remarks could be made regarding
the correct specification of the learning environment and the learning