paradigms

[Andrew Carstairs-McCarthy]

Hi everyone

Dan Everett certainly set something off!  As I am one of the people
who think that paradigms deserve a central place in the theory of
inflectional morphology, let me try to respond to some of the points
made.

I agree that it's not sensible to have a preconceived opinion about
whether any particular notion belongs in a good theory of morphology,
including the notion 'paradigm'.  A good theory, I take it, is one
that (a) is economical, (b) is sufficiently powerful, i.e. is
consistent with what does happen (pretty much: some inconsistencies
may count as problems for future research rather than fatal
counterevidence, though deciding which is which may be
controversial), and (c) is not excessively powerful, i.e. is
inconsistent with as much as possible of what doesn't happen.  A
theory such as DM that doesn't use the notion 'paradigm' is more
economical than one that does, so to that extent it would be nice if
DM were correct.  But DM practitioners need to check whether their
compliance with criterion (a) in this respect is compatible with
satisfying criteria (b) and (c).

I approach the paradigm issue from the following angle.  It's
puzzling that languages tolerate complex inflection class systems,
with a variety of ways of expressing e.g. 'genitive plural' or '2nd
person singular' that don't correlate neatly with any independent
syntactic or semantic or even phonological factors.  No creator of an
artificial auxiliary language (such as Esperanto) has ever saddled it
with an inflection class system, and if all languages lacked them (as
many do), no linguists would puzzle their heads about why this was
so.  It could be (as has traditionally been thought) that inflection
class systems are just one kind of messy residue that phonological
change leaves in its wake, and what allows this residue to perpetuate
itself down the generations is the human brain's phenomenal capacity
to remember arbitrary linguistic facts.  If that is correct, then we
can be satisfied with a theory of morphology that essentially imposes
no constraint on the array of inflectional resources that a language
can have (the number of distinct '2nd person singular' suffixes, for
example), nor on how these can be organised and distributed among
inflection classes.  So, if that is correct, there will be no problem
about fulfilling criterion (c) in relation to inflection class
behaviour: no theory could ever be too powerful.  It seems to me that
at least some DM practitioners reject the paradigm as a theoretical
notion because they take precisely this view (usually implicitly
rather than explicitly) of inflection class systems: 'paradigms' as
arrays of forms are useful in pedagogical grammars, perhaps, but they
are not linked to any constraint on what can or cannot happen in
languages.

So: are inflection class systems such a free-for-all, or not?  That's
where I part company with the DM view, and am somewhat disappointed
by DMers' lack of interest in the question.  It seems to me that,
over the years, quite a body of evidence has accumulated that
inflection class systems are not a free-for-all, and that the
inflectional resources of a language are distributed (broadly
speaking) 'economically', so as to yield a total of inflection
classes that is at or near the minimum that is mathematically
possible, given those resources.

Dave Barner asks for some examples, so here is one (taken, slightly
adapted, from Carstairs-McCarthy 1994).  Standard German has a
considerable array of inflectional resources for nouns, some of which
is arbitrary in that the choice that any given noun makes from within
the array is not predictable on the basis of gender (masculine,
feminine or neuter) or anything else.  Of the eight case-number cells
for which German masculine nouns inflect, the two that are most
lavishly endowed with inflectional resources are the genitive
singular and the plural (syncretised for all cases except the dative):
Gen Sg:  -s, -en, -ens
Plural:  -e, -en, -er, -s
(I ignore here some phonologically conditioned e/Ø alternations.)
The inflectional resources of German are thus compatible with the
existence of as many as 12 inflection classes, which is what we would
observe if each noun's choice of Gen Sg suffix implied nothing about
its choice of Plural suffix, and vice versa.  At the other end of the
scale, the minimum number of inflection classes is four, because all
four Plural suffixes need work (so to speak).  So what is the actual
total of masculine inflection classes in German?  The answer is six:
                          I            II           III          IV
V              VI
Gen Sg               -s           -s             -s           -en
-s            -ens
Plural                 -e           -er           -s           -en
-en           -en
What are we to make of this from the point of view of morphological
theory?  Conceivably, nothing.  It could be just how various
historical residues panned out.  But one thing is noticeable about
this distribution of inflectional resources: there is precisely one
'elsewhere' suffix for each of the two cells Gen Sg and Plural, i.e.
precisely one suffix that appears in more than one inflection class,
namely -s for Gen Sg, and -en for Plural.  All the other suffixes are
found in one inflection class only.  That's far from inevitable:
there are innumerable ways in which one could redistribute the German
resources among six inflection classes such that that observation
would not hold.

Again, what are we to make of this?  Again, perhaps nothing: it could
be an accident.  But it seems at least worth exploring the
possibility that it is not an accident.  We could explore, in other
words, the possibility that, in any language, given an array of
competing inflectional resources, each item must either (a) identify
its inflection class or (b) be the sole 'elsewhere' item, used in
those inflection classes that lack an exponent of their own for the
cell in question.  Well, explorations of that kind have begun, and
the results seem promising (I give references at the end, in response
to Dave Barner's request).  For present purposes, though, what's
important (it seems to me) is that conducting such explorations
relies on according to the notion 'inflection class' a central place
in morphological theory -- in other words, in making theoretical use
of the notion 'paradigm', in one of its senses.

If one still wishes to do without 'paradigm' as a theoretical notion,
there are two choices: either (i) to produce reasons for thinking
that the German state of affairs and similar states of affairs in
other languages really are accidental (showing, perhaps, that there
are many languages where the inflectional resources can't be
parcelled out neatly into the two categories 'class-identifying' and
'elsewhere'), or (ii) to show that I am wrong in thinking that the
notion 'paradigm' (in some sense) is needed in order to accommodate
this observation in a morphological theory that satisfies criterion
(c), i.e. a theory that is sufficiently restrictive.  I know that
Jonathan Bobaljik has said he has given his reasons for not liking
the paradigm notion; nevertheless, I am not aware that anyone has yet
done either of (i) or (ii).  If I've missed something in the
literature on this, please tell me!

I've gone on long enough.  I'll close by saying three things.  First,
I've given one kind of reason for the theoretical centrality of the
paradigm.  Other people, such as Greg Stump, Andy Spencer and Kersti
Börjars, have argued for the paradigm on grounds that are
substantially independent of mine, and I don't want to comment here
on those other reasons.  Secondly, I feel sheepish in that all the
references I cite below are by me.  It looks like naked
self-promotion.  But, by way of excuse, I seem to be about the only
person conducting this particular line of inquiry.  (The references
from before 1994 assume a now superseded version of the 'paradigm
economy' idea, but the data should still be of interest and perhaps
even some of the discussion.)  Thirdly -- yes, I did say earlier that
it would be nice, in the interests of criterion (a) (economy), to
dispense with the notion 'paradigm' if we can.  But there is also
criterion (c) to consider -- a criterion that no one forgets about
when doing syntax, but which for some reason doesn't seem to be so
generally borne in mind by people doing morphology.

Carstairs, Andrew.  1983.  Paradigm economy.  Journal of Linguistics
19: 115-25.
Carstairs, Andrew.  1984.  Paradigm economy in the Latin third
declension.  Transactions of the Philological Society 117-37.
Carstairs, Andrew.  1987.  Allomorphy in Inflexion.  London: Croom Helm.
Carstairs, Andrew.  1988.  Nonconcatenative inflection and paradigm
economy.  In: Theoretical Morphology: Approaches in Modern
Linguistics, ed. by Michael Hammond and Michael Noonan, 71-7.  San
Diego: Academic Press.
Carstairs-McCarthy, Andrew.  1994.  Inflection classes, gender and
the Principle of Contrast.  Language 70: 737-88.
Carstairs-McCarthy, Andrew.  1998.  How lexical semantics constrains
inflectional allomorphy.  Yearbook of Morphology 1997, 1-24.
Cameron-Faulkner, Thea and Carstairs-McCarthy, Andrew.  2000.  Stem
alternants as morphological signata: evidence from blur avoidance in
Polish nouns.  NLLT 18: 813-35
Carstairs-McCarthy, Andrew.  2001.  Grammatically conditioned
allomorphy, paradigmatic structure, and the Ancestry Constraint.
Transactions of the Philological Society 99: 223-45.  [Discusses
Bobaljik 'The ins and outs of contextual allomorphy'.]
Carstairs-McCarthy, Andrew.  2002.  Directionality and locality in
allomorphy: a response to Adger, Béjar and Harbour.  Transactions of
the Philological Society 101: 117-24.  [A reply to a DM-based
critique of C-McC 2001.]

Any comments on all this?  Apologies again for the length.

Andrew
--
Andrew Carstairs-McCarthy
Professor, Department of Linguistics,
School of Classics and Linguistics.
University of Canterbury, Private Bag 4800, Christchurch, New Zealand
phone (work) +64-3-364 2211; (home) +64-3-355 5108
fax +64-3-364 2969
e-mail andrew.carstairs-mccarthy at canterbury.ac.nz
http://www.ling.canterbury.ac.nz/adc-m.html