good news from generative grammarians

[Carl Pollard]

Hi Mohanan,

I appreciate your intention to clarify things, but I'm afraid many of
your remarks have had the opposite effect. A few particulars:


>
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.
>>

Usually for a theory to be called formal it has to be expressed in a
formal language. But the things that a formal theory is about do not
have to have to be unempirical. There are formal theories of quantum
mechanics (e.g.  Mackey's), of classical mechanics (say, Hamilton's),
as well as of of natural language (e.g. Stabler's formalization of
GB).


>
The claims of a formal theory are justified through proof, i.e., the
demonstration that the claims (alleged theorems) follow deductively from its
axioms.
>>

No, the THEOREMS are justified by proof. The AXIOMS are justified to the
extent that they (and the theorems that follow from them) are consistent
with the facts.

>
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.
>>

Certainly many people have pointed out false predictions of Chomsky's
binding theory. However, I think it is wishful thinking to say that it
was `rejected' for this reason. Maybe you and I rejected it, but I
still get sent papers to referee that assume it is correct. The
rejection of Chomsky's BT is not a general sociological fact, however
much we might wish it so.

>
If we demand that every scientific theory be expressed
in terms of a mathematical formalism, then Binding theory is not a theory.
>>

It is not hard to formalize Chomsky's binding theory. Anyway, nobody
demands this, only that the theory in principle be CAPABLE of being
formalized. Once its unclarities and ambiguities are removed, there is
no good reason to deny that Chomsky's BT is a scientific theory.


>
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.
>>

It is HPSG THEORIES (= grammars, or grammar fragments) that make
testable predictions, not HPSG itself. HPSG is no different from GB,
LFG, or categorial grammar in this respect.

>
If not, it is at best a formal theory that is useful in
the expression of scientific theories.
>>

You mean `formal framework'. A formal theory is a theory, scientific or
otherwise, expressed in a formal language.

>
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?)
>>

Fully formalized HPSG grammars are written in a formal language (such
as RSRL) with a model-theoretic interpretation and a proof
theory. Your doubts are not justified.

>
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.
>>

This second sentence is false. This point was extensively discussed
already. Features like PHONOLOGY, ARG-ST, CONTENT, CONTEXT,
DAUGHTERS etc. are essentially levels of representation. The fact
that the model treats them as attributes of a single structure is a
stylistic choice and has no empirical content.

>
Does HPSG yield a theory? Depends upon whether it contains universal
laws which are distinct from those of LFG and minimalism.
>>

Why is THAT, of all things, what the answer depends on? I cannot
assign any sensible interpretation to what you say here.

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

If that is what it implies, then it cannot possibly be a clarification
of anything, but rather an obfuscation.


>
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.
>>

See Bob Levine's careful discussion. I would add that weak
generativity, which is concerned with string sets, has to be
distinguished from strong generativity, which has to do with
structural representations. Carefully formulated theories (=
grammars), no matter whether in GB, LFG, of HPSG, generate a set of
structural representations in this respect. Whether they do so
declaratively or procedurally is an implementational side issue.

>
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.
>>

Practicioners of all three of P&P, LFG, and HPSG agree that the subject
matter of their theories is a mentally represented knowledge system. This
has absolutely no bearing (i.e. is completely orthogonal to) whether
they are (weakly or strongly) generative.

>
It is clear that HPSG is not generative under meaning A2.
>>

It is hard to imagine anything LESS clear than what you have just
asserted. However, as a stylistic matter, an HPSG grammar is typically
generative in a declarative way, e.g. Pollard 1999 "Strong generative
capacity in HPSG", in Webelhuth et al. eds.

>
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
>>

I don't know of any essential difference between practicioners of HPSG
and practicioners of P&P and LFG on this question. We all at least
fancy ourselves to be concerned ultimately with mentally rpepresented
knowledge systems. I don't see what purpose is served by tendentious,
divisive, and unfounded assertions to the contrary. There are enough
things already to splinter the field of syntax without inventing new
ones.

>
(probably
because they are worried about people like Katz who have asserted that
linguistics is a formal discipline, not an empirical one.)
>>

Pure speculation, and false. I don't know of a single shred of evidence
that any practioner of HPSG considers linguistics not to be a empirical
discipline, to say nothing of doing so because of something Katz may have
asserted. Where are you getting this stuff from?

>
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?
>>

Well, you have managed to muddy the water quite a bit, but to try to restore
a little clarity:

  1. Carefully formulated grammars in GB, LFG, and HPSG are both
     weakly and strongly generative, though they have different
     notions (models) of what structural representations are like.
     Even categorial grammars are weakly generative, though not
     strongly (unless you consider normalized proofs as as kind of
     structural representation, but I don't think many CGians would).

  2. Practicioners of all three frameworks DO view languages as mental
     systems. This is one idea of Chomksy's (maybe the ONLY one) that
     we all agree on. (Montague, famously, did NOT, but I don't know
     to what extent categorial gramamrians are influenced by his views
     on this question).

  3. The prodedural/declarative debate seems like a late-70's/early-80's
      relic that has no important bearing on any of the other issues under
      discussion here.

Carl