good news from generative grammarians

[Mohanan, Karuvannur P]

Whether or not HPSG and Chomsky's Binding Theories are "theories" (or are
frameworks) depends upon what we mean by the word "theory" (or framework),
and what type of theory we have in mind. I thought the following
distinctions might be useful to  minimize talking at cross purposes when
exploring the questions. (Please note that what I am trying to do is
articulate my personal position, so when I make statements like "A theory is
a set of connected propositions" what I mean is "As I see it, a theory is a
set of connected propositions.")
Mohanan

What is a "theory"?

A theory is a set of connected propositions. A formal theory (or formalism)
(e.g., set theory, graph theory, and number theory in mathematics) is a set
of connected axioms, and the theorems that can be deduced from the axioms. A
substantive theory of a phenomenon (e.g., quantum theory, theory of
relativity, Darwin's evolutionary theory, theories of knowledge, truth and
morality in philosophy, Aristotle's theory of tragedy, and T.S. Elliot's
theory of the objective correlative in literature) is a set of connected
propositions that claim to reveal the nature of the phenomenon. (Note: I am
using the term "substantive" very broadly here to mean "justified on the
basis of experience.") As special cases of substantive theories, scientific
theories seek to understand phenomena by gathering observable information
and providing explanations for them, philosophical theories seek to
understand phenomena by reflecting upon what is taken for granted as true
premises about phenomena (without engaging in gathering new information),
and aesthetic theories seek to understand phenomena by articulating
intuitive perceptions or reflecting upon such perceptions. So our question
about HPSG and P&P is:  in what sense can we affirm or deny that they are
theories? (For our discussion, philosophical and aesthetic theories are not
crucial, but it is useful to keep them in the background to have a sense of
what kinds of animals we are dealing with in this territory.)

The claims of a formal theory are justified through proof, i.e., the
demonstration that the claims (alleged theorems) follow deductively from its
axioms. For instance, take Pythagoras' theorem (the proposition that the
square of the hypotenuse is equal to the sum of the squares of the sides):
the theorem is validated by demonstrating that it follows deductively from
the axioms of Euclidean geometry. In contrast, the claims of a scientific
theory are justified through evidence and reasoning. For instance, take the
hypothesis that electrons are negatively charged: we justify it by
demonstrating that, together with the other hypotheses in the theory, it
provides the best explanation for the widest range of explanations. (Formal
claims are not validated by appealing to (experiential) evidence:  we do not
justify Pythagoras' theorem by showing that in all the observed triangles,
the square of the hypotenuse is equal to the sum of the squares of the
sides.) In other words, while formal theories are validated through
deductive reasoning, scientific theories are validated through observations
and speculative-deductive reasoning.

The claims of philosophical  theories are justified by showing that they
follow rationally (but not necessarily deductively) from the premises that
we are committed to or take to be true. Thus, in a theory of ethics, the
claim that telling lies is immoral is justified by showing that it follows
from the axiom that causing unhappiness is immoral, an axiom that we accept
without justification. The claims of a theory in philosophy of science (such
as Kuhn's theory) are justified by showing that they follow rationally from
what we take to be true in scientific knowledge and the history of science.

As for claims of aesthetic theories, they are typically accepted as "true"
by the academic community if they make intuitive sense, i.e. if the claims
create an intuitive resonance based on subjective experience in the
individuals of the community, or if they can be rationally justified on the
basis of intuitive perceptions. The truth (verisimilitude) of a Rembrandt
paining is judged intuitively, not through evidence and/or reasoning. This
also applies to the assessment of the credibility of Aristotle's theory of
poetics and Derrida's theory of deconstruction.

Prototypical theories in the physical sciences such as the theory of
gravitation and quantum theory of the subatomic phenomena have five
distinguishing characteristics:
(a) they contain a set of propositions called laws,
(b) most propositions of the theory are expressed in mathematical
formalisms,
(c) the observations against which the theories are tested are
	i)  typically quantitative,
	ii) experimental, and
	iii) replicable.

Not all scientific theories exhibit all of these characteristics.
(a) The Big Bang theory of cosmology and the theory of continental drift in
geography, for instance, do not include any laws of their own. Instead of
seeking to formulate laws (law = the statement of a systematic relation
between observable or theoretical variables), these theories provide a
"model" of the phenomena they seek to understand.
(b) While Newton's theory of gravitation employs Euclid's geometry  and
Einstein's theory of gravitation employs a non-Euclidean geometry, Darwin's
evolutionary theory does not use any mathematical formalisms.
(c) While the observations of Newton's theory are quantitative measurements,
those of learning theories and syntactic theories are not.
(d) While physics, chemistry, and syntax are largely experimental, very
little experimentation is possible in astronomy.
(e) Finally, while the observations on the functioning of the normal brain
are replicable in neuroscience, those of brain impaired human subjects in
clinical neuroscience are hard to replicate.

HPSG and Chomskian theories

Is Chomsky's Binding theory in LGB a theory? If we use the term "theory" to
mean "scientific theory", yes, it is a theory: it consists of a set of
connected propositions that explain (=predict) observations on
cross-linguistic phenomena.  The theory was rejected because its predictions
happened to be wrong. If we demand that every scientific theory be expressed
in terms of a mathematical formalism, then Binding theory is not a theory.
However, by this token, Darwin's theory of evolution is not a theory either.
So the expression of theoretical propositions in mathematical formalisms
cannot be taken as a defining feature of scientific theories.

Is HPSG a theory? If we use the term "theory" to mean "scientific theory",
the answer would depend upon whether  HPSG makes testable predictions of
cross-linguistic phenomena. If it can be shown that it does, then it is a
scientific theory. If not, it is at best a formal theory that is useful in
the expression of scientific theories. (I doubt if HPSG is a formal theory,
though. If it is a formal theory, it should minimally have a set of axioms
and a set of theorems proved on the basis of the axioms. Does HPSG offer any
theorems deduced from HPSG axioms?)

Theories vs. Frameworks and Models

If we restrict our attention to scientific theories (and not include such
things as feminist theories and postcolonial theories), we may say that
frameworks and models are underspecified theories. That is to say, we cannot
draw out testable predictions from them until we supplement them with
additional theoretical propositions (In this sense, frameworks and models
are part of what Lakatos calls the "core" of a scientific theory, testable
only when the "peripheral belt" is added.)

A framework is a set of logically or conceptually related concepts. A
distinctive feature framework, for instance, contains such concepts as
voice, sonorant, consonantal, back, and labial, while the IPA framework
contains such concepts as voice, plosive, fricative, velar, and mid. A
framework of grammatical categories contains such concepts as noun, verb,
preposition, noun phrase and prepositional phrase. A framework of
grammatical functions contains such concepts as subject, object and
predicate. Newton's framework for his theory of gravity and motion contains
concepts such as time, space, motion, distance, velocity, acceleration,
mass,  and force. Most of these concepts are found in  Einstein's framework
for his theory of motion and gravity, but it replaces "force" with "field",
absolute motion with relative motion, and noninteracting space and time with
interacting space and time. A framework becomes a theory when it is
supplemented with the statements of laws (the counterpart of what linguists
call universal principles/ constraints/ conditions.) such that we can infer
predictions from them. In the absence of universal laws, the empirical
content of a framework is the claim that the framework provides the best
basis for the construction of a theory for the phenomenon in question (e.g.
the distinctive feature in question yields the best descriptions of
phonological phenomena), "best' being a matter of correctness of
predictions, generality (scope), simplicity, etc.

A model is a physical or abstract object, an entity around which we can
construct our laws (e.g. the heliocentric and geocentric models of the solar
system, Rutherford's model of the atom). Like frameworks, models are also
underspecified (i.e., they need to be supplemented with the statement of
laws) In this sense, neither Syntactic Structures nor Aspects give us
theories, though they give models and frameworks. To my knowledge, the
attempt to construct a theory in generative grammar began with A-over-A,
subsequently followed by Island Constraints, and later by the universal laws
in Relational Grammar. This aspect of theory received sufficient attention
in Chomskian syntax only with the advent of LGB (e.g. the universal laws of
binding theory, subjacency etc.) Phonologists continue to develop models and
frameworks, without seriously attempting to construct theories (e.g. lexical
phonology is a model, not a theory (contrary to the title of Mohanan's book
"A Theory of Lexical Phonology, as far as I know, Optimality Theory is a
framework, not a theory, because it hasn't made a non-negotiable commitment
to a set of universal laws/constraints.)

It is clear that HPSG yields a framework. It also provides a model that
restricts itself to a single dimension of representation, contrasting with
the dual dimension (dual planes?) of PF and LF in minimalism, and the
multidimensional representations in LFG. Does HPSG yield a theory? Depends
upon whether it contains universal laws which are distinct from those of LFG
and minimalism. (My guess is that the different schools of syntax have
started borrowing freely from one another's collections of laws/constraints,
so it is not easy to tell them apart as theories.)

On the concept of "generative"

A word of clarification on "generative" vs. HPSG which implies that HPSG is
not a generative theory.

There are two distinct meanings associated with the term generative:
Meaning A: A generative theory is  an explicit characterization.
Meaning B: A generative theory is a theory of the mental linguistic systems
of human beings (the language faculty.)

Under meaning A, "to generate X" means "to explicitly characterize X". For
instance, the formula 2n+1 generates (explicitly characterizes) all and only
the set of odd numbers. In this sense, all mathematical and scientific
theories (including set theory and theory of gravity) are generative. This
was one of the meanings of generative in early generative grammar.

Meaning A, however, can be implemented either declaratively (as a set of
explicit propositions) or procedurally (as a set of explicit instructions).

Meaning A1: explicit propositions (declarative)
Meaning A2: explicit instructions, as part of a production algorithm
(procedural)

Most people associate 'generative" with A2.

Meaning A2 is concerned with the form of the theory, while meaning B is
concerned with its substance.  Chomsky's Syntactic Structure (1957) is
generative under meaning A2, but not under meaning B, because in 1957, the
object of inquiry was "language" as an infinite set of sentences. The object
of inquiry at this time was an external entity, not the mental linguistic
system of human beings. The first appearance of generative grammar under
meaning B was in Aspects (1965) whose full implications were worked out in
the eighties as I-grammar. Like P&P, LFG is a generative grammar under
meaning B; it is not generative under meaning A2. In my opinion (which I
will not defend here) OT is a generative theory under meaning A2, but not
under meaning B.

It is clear that HPSG is not generative under meaning A2. It is unclear
whether or not HPSG is generative under meaning B. Its proponents do not
seem to have a strong commitment to the acceptance or rejection of the
object of inquiry in generative grammar (probably because they are worried
about people like Katz who have asserted that linguistics is a formal
discipline, not an empirical one.)

Whatever the conclusion, the intended contrast between HPSG and "generative
grammars" in this discussion must be made clear. Is the contrast between
declarative and procedural formalisms? Or is it in the view of language as a
mental linguistic system?

Mohanan
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K.P.Mohanan
Professor, Dept. of English Language and Literature,
National University of Singapore, Singapore 119260
Tel: (65) - 874 - 6042
Homepage: http://courses.nus.edu.sg/course/ellkpmoh
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