On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g., 7), but also non-natural rational numbers (e.g., 3.5). It does not represent irrational numbers (e.g., √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.

中文翻译：

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数感代表（有理）数

从现在的正统观点来看，人类和许多其他动物都具有“数感”或近似数系 (ANS)，它代表数字。最近，这种正统观点受到了许多质疑，质疑 ANS 是否真正代表数字。我们区分了三行批评——来自的论点一致性,混淆， 和不精确——并表明没有一个成功。然后，我们提供积极的理由来认为 ANS 真正代表了数字，而不仅仅是批评者提出的非数字混淆或数字的外来替代品，例如“numerosities”或“quanticals”。在这样做的过程中，我们提出了一个被忽视的问题：什么样的数字？正统观点的支持者在这个问题上非常腼腆。但这并不令人满意，因为正统观点的预测，包括预期 ANS 成功或失败的情况，都取决于所表示的数字类型。作为回应，我们建议 ANS 不仅代表自然数（例如，7），还代表非自然有理数（例如，3.5）。然而，它不代表无理数（例如，√2），因此不能更普遍地代表实数。