|Title:||From Intensional Properties to Universal Support|
|Authors:||Birgit Alber, Natalie DelBusso, Alan Prince|
|Comment:||To appear in Language: Phonological Analysis|
|Abstract:||A factorial typology is a set of grammars. We are not given the grammars directly, but must deduce them from the way that the posited constraints deal with the posited structures. How do we know that we have examined enough candidate sets to discriminate all the grammars that are allowed by our assumptions? This is the problem of finding a universal support for a typology. Without a universal support, we don't have the typology, and without the typology, many types of systematic claims about it must languish unjustified.
Here we show how the universal status of a proposed support may be established when we have exact descriptions of the types of optima allowed in the grammars. If a typology is factored into (intensional) ranking properties in the sense of Alber & Prince (in prep.), and if the property values are associated with (extensional) traits carried by optima, then a grammar as a combination of values is associated with a description of its optima as a conjunction of the traits associated with the values. If the descriptions thereby obtained uniquely denote single candidates, then the grammars cannot be further refined, and the support that produced the grammars must be universal.
This method of associating extensional characteristics with ranking patterns answers a much more general question: what do the languages of a typology look like? Since a typology is generated from a finite sample of candidate sets, we cannot in general be satisfied with remarking about the distribution of traits in the sample. We must use the grammars to project over the entire set of optima. The grammatical structure relevant to this enterprise is encoded in the ranking properties that combine to give the grammars.