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.

中文翻译：

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自然语言和自然数的集合论概念

本文提出了一种新的单纯形数字理论，该理论结合了对Chomsky（2008）的自然数集理论的轻微修改，它假设自然数的概念是先天的。新理论使人们有可能考虑数字在计数中的行为，以及儿童学习数字时所经历的发展阶段。关键思想是，与自然数概念相对应的集合论对象要经受将句法对象转换为语音形式时适用的操作。这些操作提供了至关重要的链接，可将数字的含义与包含数字的计数列表相连接。所提出的分析的一个显着特征是，基本原则是通过招募语言计算得出的，因此不再规定。