comments on "what is LFG"

[Tara W Mohanan]

We (KP and Tara) would like to respond briefly to some of the issues raised
in the responses to our note on What is LFG.

FORMALISM

In response to John Paolilo and Avery Andrews, we would like make it clear
that we do not hold the view that formalism is unimportant. Formalism is
the same as mathematics. To say that formalism is unimportant is to say
that mathamatics is unimportant. As Prof. Shaumyan points out, formalisms
help us to achieve rigour and precision, and allow us to make calculations
which go beyond the range of intuitive reasoning. All that we wanted to say
was that in our (M&M's) *personal* list of priorities, formalism comes
lower than substance.

The remarks on the importance of formalism were also probably triggered by
the close association of formal and substantive aspects of frameworks.
Chances are that we were not very clear in separating the two aspects. Let
us see if we can remedy this. Galileo's laws of motion d = 16 t @ (please
read @ as "raised to 2" = squared) contains both substance and formalism.
The substance it contains is expressed in the symbols d (=distance) and t
(=time). The formalism is that of plain number theory. Take, for instance,
the equation x = 17 y $ (please read $ as "raised to 5"). The formalism is
the same, but the formula does not carry any empirical substance: the x
here could be the weight of a person, the density of population in a
country and so on.

Formal logic is formal because it allows us to calculate inferences from
sets of propositions without knowing the content of the propositions. Thus,
we know that if "P -->  Q" and "P" are true, then "Q" is also true,
regardless of what the symbols P and Q stand for. Saying that a
representation is a directed unordered graph is saying something about its
formal aspect. Such a graph could be used to model syntactic structure, air
line routes, or neural connections. Hence it does not contain any substance
specfic to any phenomenon. However, saying that a representation contains
the entities SUBJ, OBJ, OBJ2 and PRED is saying something about the
substance: these concepts do not extend to, say, air line routes. Whether
or not a framework of representations should distinguish between OBJ and
OBJ2 is a substantive issue, but whether or not a framework of
representations should express grammatical functions as labelled nodes (as
in LFG) or labelled arcs (as in RG) is a formal issue.

Formalisms, unlike theories, do not make any direct predictions. Empirical
claims that can be made in terms of a formalism are somewhat indirect, and
are of the form "Formalism X is inappropriate for domain D" or "Formalism X
is better than Y for domain D" (e.g. Chomsky's claim that phrase structure
grammars are inadequate for natural languages). This is analogous to saying
that for constructing a theory of gravity, the formalism of non-Euclidian
geometry is superior to that of Euclidian geometry. This is a claim that
Einstein could have made, but did not actually make. (Physicists, unlike
linguists, do not appear to engage in debates on which formalism is
superior: they simply draw upon (like Einstein) or invent (like Newton)
formalisms they find useful for their theories.)

MODEL/ARCHITECTURE VS. LAW

We may not have been clear about the use of the terms "model" and "law". By
"law", we refer to a statement of a set of regularities/relationships as in
Boyle's law, Galileo's laws of falling bodies on earth, Kepler's laws of
planetary motion, Newton's laws of motion, Einstein's law of gravity,
Mendel's laws etc. By "model", we mean certain relatively abstract
properties which define the space within which the laws operate. Thus, the
laws of Kepler, Newton, and Einstein, all presuppose the same model of the
solar system. Other examples of "model" include  "model of the atom", "the
aspects model", and so on.

For us (M&M),  the word "architecture" in theoretical linguistics means the
same as "model". When we use the term "model"/ "architecture" in
linguistics, we have in mind assumptions on the modules of the grammar,
levels of representation, and the way these levels are related.

The bulk of the enterprise in theoretical sciences is the formulation of
theoretical laws (laws of magnetism, laws of gravity, laws of genetics,
...). When linguistics came of age, the search for laws became a serious
preoccupation: laws governing the relation between anaphors and their
antecedents (binding conditions),  laws governing the relation between
argument structure and grammatical functions (linking), laws governing the
relation between the wh-expression and the gap it corresponds to
(subjacency), laws governing the wellformedness of phrase structure (X-bar
theory), and so on.

We do not see why Avery Andrews thinks that laws are an acknowledgement of
failure. Take for instance the laws of linking in the Lexical Mapping
Theory. These laws presuppose the architecture of LFG but cannot be deduced
from anything in that architecture. We suspect that Avery does not share
the meanings we have for the words model, architecture, and law, but we are
not in a position to spell out what his meanings are.

PARADIGM

Again, we do not see why Avery is negatively disposed towards paradigms.
All research is done within the context of some paradigm or the other.
Before we construct an analysis, we need to know (implicitly or
explicitly), what it is that we are trying to understand by constructing
the analysis (object of inquiry). We need to know what would constitute an
acceptable analysis, how we can choose between competing analyses (criteria
of success). We need to have certain expectations of what kinds of data
would be most revealing. We need to agree on what constitutes a valid
argument. These are all issues that an individual's research program needs
to settle. When such a research program is shared by the members of a
research community, we call it a paradigm, following Kuhn.

Avery's reaction is negative probably because when the assumptions of a
paradigm are covert, paradigms could cause blindness, and differences in
paradigms could cause miscommunication. There could also be contradictory
assumptions internal to a paradigm whose assumptions are not clearly
visible. Take, for instance, the Chomskian paradigm which says that
generative linguistics is concerned only with
               (A) a human individual's internal mental linguistic system
(=I language) and
               (B) the language faculty of the human race (UG).
The ordinary notion of "language" as in "the English languge", "the Malay
language", etc. is not part of Chomskian generative linguistics, because
this is a matter of
                (C) the linguistic system shared by a speech community
(E-language),
and "speech community" is a sociolinguistic notion. For Chomsky, whether or
not two I-languages belong to the same E-language or not is not a relevant
question. It is relevant for Labov.

Now, language change is not change internal to an I-language, nor is it a
change internal to the human language faculty. It is a change in the
linguistic system shared by a speech community across generations of
individuals. Therefore it should follow that language change is not part of
the Chomskian paradigm of generative linguistcs. To include language change
within the Chomskian paradigm would result in an internal contradiction
with respect to the object of inquiry. Would linguists within the Chomskian
tradition accept this consequence? If not, then we have to re-define our
object of inquiry.

It is issues like this that we refer to when we use the word "paradigm".
Once again, our meanings may not coincide with Avery's.

----
Tara W Mohanan, Dept of English & Literature, NUS