<OT> New Posting: ROA-624

[roa at ruccs.rutgers.edu]

ROA 624-1003

Just How Many Languages Are There?

Andries W Coetzee <awc at linguist.umass.edu>

Direct link: http://roa.rutgers.edu/view.php3?roa=624


Abstract:
Optimality Theory assumes the candidate set generated for
any given input is of infinite cardinality. If all of the
candidates in the candidate set were potential winners (optimal
candidates under some ranking), then OT would have predicted
an infinite typology—there would be infinitely many possible
languages. However, Samek-Lodovici and Prince (1999) have
shown that in standard OT (with only markedness and IO Correspond
ence constraints), only a finite number of candidates from
the infinite candidate set can actually be winners—the (infinite)
majority of the candidates in the candidate set is harmonically
bounded, and will therefore never be selected as winners
under any ranking.

Their argument for the finite cardinality of the set of
potential winners rests on the assumption that cardinality
of CON is finite. If every possible ranking between the
n constraints in CON were to select a unique winner, then
there can be maximally n! different winners for any given input.

The addition of non-IO Correspondence constraints to CON
threatens this general result. Both OO Correspondence constraints
and Sympathy constraints can result in an otherwise harmonically
bounded candidate being selected as winner. Non-IO Correspondence
constraints therefore decrease the size of the set of harmonicall
y bounded candidates and increase the size the set of potential
winners. A question that therefore needs answering: Is the
set of potential winners still of finite cardinality in
an OT grammar with Sympathy constraints and OO Correspondence
constraints? If this question can be answered in the affirmative,
then OT predicts a finite typology even with non-IO Correspondenc
e constraints added to CON. However, if the addition of
non-IO Correspondence constraints increases the set of potential
winners to an infinite size, then an OT grammar with these
constraints added to CON will predict an infinite typology.

In this paper I argue that under reasonable assumptions
it can be shown that the cardinality of the set of potential
winners is finite even with the addition of Sympathy and
OO Correspondence constraints. I argue that each of Sympathy
Theory OO Correspondence Theory adds only finitely many
constraints to CON. I then use the same argument that Samek-Lodov
ici and Prince use for standard OT. There are only finitely
many rankings (n!) between finitely many constraints (n).
Even if each of these rankings were to select a unique winner,
only a finite number of winners can be selected.

Comments: This also appeared in: Kadowaki, Makoto and Kawahara, Shigeto (eds.)  2003.   NELS 33: Proceedings of the North East Linguistic Society 33.   Amherst: GLSA.   p.103-114.
Keywords: size of the candidate set, OO Correspondence, Sympathy Theory
Areas: Phonology,Formal Analysis
Type: Manuscript

Direct link: http://roa.rutgers.edu/view.php3?roa=624