Number Names in Four Languages of Mexico

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.Google Scholar

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.Google Scholar

Noam Chomsky, Aspects of the Theory of Grammar, The M.I.T. Press, Cambridge, Mass., 1965, p. 5.Google Scholar

Personal communication.Google Scholar

read ‘/’: ‘in the environment’; ‘\(\mathop \# \limits^ \sim\) ’: ‘not word boundary’.Google Scholar

It is perhaps not strictly legitimate to include ‘Q:’ and ‘H:’ in the context of these rules. In lieu of a complete picture of Mixtec morphophonemics, this can be considered a temporary device which accounts for every occurrence of u before šiko and not after ùsi. The device is required because of ùsiu šiko ‘220’.Google Scholar

59’ is also heard as luhúmp’ehl iyus k’àl yik’ót bolómp’ehl. Aulie (personal communi¬cation) feels that many speakers would prefer luhun k’àl yik’ót hó?p’ehl iča? k’àl for ‘225’, and believes the average speaker would start off with hó? luhun k’al for numbers including ‘300’, adding to that whatever is needed. Thus, the name for ‘385’ would be hó? luhun k’àl yik’ót hó?p’ehl icà? k’al. He feels most speakers would simplify the name for ‘7599’ to something like hó? luhúm báhk’ yik’ót Pús báhk’ yik’ót bolón k’ál Icá? báhk’ yik’ót bolón luhúmp’ehl. I have chosen (perhaps without justification) to eliminate such forms from consideration in this paper since they differ from other names in employing one or another of the classifiers (viz. -p’ehl, k’ál, etc.) two or more times. This strikes me as being what Aulie has suggested - a simplification - and falls rather into the category of adding shorter number names together to simplify a longer one. Though names formed by this kind of ‘addition’ should also be described for Ch’ol, this has not been attempted here.Google Scholar

For descriptions of such classifiers see Wilbur Aulie, ‘High-layered numerals in Choi (Mayan)’, IJAL 23 (1957), 281–3; Kathryn Keller, ‘The Chontal (Mayan) numeral system’, IJAL 21 (1955), 258–75; Brent Berlin and A. Kimball Romney, ‘Descriptive Semantics of Tzeltal numeral classifiers’, in Transcultural Studies in Cognition (ed. by A. Kimball Romney and Roy Goodwin D’Andrade ), AAA 1964, pp. 79–98.Google Scholar

Cf. Robert E. Longacre, Grammar Discovery Procedures, Mouton, The Hague, 1964, p. 25f, for a discussion of the notion ‘Reading of a formula’.Google Scholar