1. The data for this paper were supplied by my colleagues of the Summer Institute of Linguistics in Mexico: Kenneth S. Hilton (Tarahumara); Ethel Wallis (Mezquital Otomi); Georgia Hunter and Betty Stoudt (San Pedro Molinos Mixtec); John and Elaine Beekman, Wilbur Aulie, and Viola Warkentin (Ch’ol). Wilbur Aulie kindly checked the Ch’ol material with eleven informants during the writing of the paper. Cf. also Harold Harwood Hess, The Syntactic Structure of Mezquital Otomi, unpubl. doctoral dissertation, University of Michigan, and John Paul Daly, Generative Syntax of Mixteco, unpubl. doctoral dissertation, Indiana University, for alternate analyses of two of the systems. Thanks are due to John Crawford, Ilah Fleming, and Sarah Gudschinsky for helpful comments.
2. A. Van Katwijk, in his ‘A Grammar of Dutch Number Names’ (Foundations of Language 1, 1965, 51–8), side-steps this problem in his description of Dutch number names by the use of ‘etcetera’ in rule 1.6 of his grammar. This open-ended rule introduces primitives with values above 100, of which he lists eight. Presumably more could have been listed, but it is fairly certain that sooner or later the addition of more primitives would begin to require on-the-spot coining.
3. Noam Chomsky, Aspects of the Theory of Grammar, The M.I.T. Press, Cambridge, Mass., 1965, p. 5.
4. Personal communication.
5. read ‘/’: ‘in the environment’; ‘ $$\mathop \# \limits^ \sim$$ ’: ‘not word boundary’.