Natural language and set-theoretic conception of natural number

Abstract

This article presents a new theory of simplex numerals that incorporates a slight revision of Chomsky's (2008) set-theoretic conception of natural number, which assumes that the notion of natural number is innate. The new theory makes it possible to account for the behavior of numerals in counting as well as the developmental stages that children go through in learning numerals. The key idea is that set-theoretic objects corresponding to natural number notions are subject to operations that apply when a syntactic object is converted to phonological form. These operations provide a crucial link that connects the meaning of a numeral with the count list consisting of numerals. A notable feature of the proposed analysis is that the Cardinal Principle is derived by recruiting linguistic computation and therefore is no longer stipulated as such.