According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess an exact quantity of the elements in a collection without counting them), or on the ability to approximate quantities (i.e., to assess an approximate quantity of the elements in a collection without counting them), or both, fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm. In the final section, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics.

根据解释自然数概念含义的最强大范式之一，自然数从核心认知能力中获得了很大一部分概念内容。Carey的自举提供了一个模型，用于建立成熟的数学概念时核心认知的作用。在本文中，我对本范式中的各种理论进行了概念分析，得出结论认为，这些理论基于对子元素进行替换的能力（即，在不计算元素的情况下评估集合中元素的确切数量）或基于近似的能力。数量（即评估一个近似值集合中元素的数量而不计算它们），或两者都不为自举精确的自然数的概念提供概念基础。特别是，我认为现有理论都无法解释自然数结构的关键特征之一：自然数级数连续元素之间的等距。我建议这种规律性可以基于另一种先天的认知能力，即对节奏规律性的敏感性。在最后一节中，我从数学哲学中的结构主义立场出发，提出了在核心认知范式中的新立场。