Restrictions on the Meaning of Determiners: Typological Generalisations and Learnability

It is standardly assumed that a close relationship holds bet ween (i) the learnability of languages with some property P, and (ii) the existence of languages with prop- erty P as revealed by typological studies. If it is not possible for a human to acquire a language with P, then clearly no speakers will be found of any language with P. The inverse, though not logically necessary, is often also i mplicitly thought to be true: that if no natural language exists with P, then languages with P are unlearn- able. This is not without reason, of course. Since the questi on of how children manage to acquire their native languages as quickly as they do is still largely unan- swered, linguists are interested in discovering possible c onstraints on the learner's hypothesis space, for which typological generalisations would seem to make good candidates.1 Assuming that we would like the formalisms used to describe natural language semantics to have the ability to express all and only the languages that human beings can naturally acquire, discoveries about constraints on the learner's hypothesis space in turn dictate which formalisms are too powerful and which are too weak. In this paper we examine the relationship between learnability and typology in the area of determiner meanings. We begin with two generalisations about the meanings that determiners of the world's languages are foun d to have, and inves- tigate the learnability of fictional determiners with unatt ested meanings. If partici- pants in our experiments fail to learn such determiners, then this would suggest that they are unattested because they are unlearnable. If, on the other hand, participants are able to learn the determiners in question, then some other explanation for their absence in the languages of the world is necessary. Specifically, the generalisations we consider are (i) that a ll natural language determiners are conservative, and (ii) that no natural lang uage has a determiner analogous to most that expresses "less than half" rather than "more than half". The standard formal tools used to describe determiner meanings are powerful enough to express both kinds of unattested determiner meanings. This is undesirable if they are indeed unlearnable. We find that learnability correlate s with (i), whereas it does not with (ii). Thus the lack of nonconservative determiners in the world's languages