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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数字意义代表（有理数）数字。

从现在的正统观点来看，人类和许多其他动物拥有“数感”或近似数字系统（ANS），它代表数字。最近，这种正统的观点受到了许多批评，这些批评质疑ANS是否真正代表数字。我们将批判的三行区分为：同余论，混杂论和不精确论证，并表明没有成功。然后，我们提供了积极的理由，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奇异替代品，例如“数字”或“量子”。这样做，我们提出了一个被忽略的问题：什么样的数字？支持正统观点的人在这个问题上非常反对。但这是不令人满意的，因为对正统观点的预测 包括预期ANS成功或失败的情况，请打开所代表的数字的种类。作为回应，我们建议ANS不仅代表自然数（例如7），而且还代表非自然有理数（例如3.5）。但是，它不表示无理数（例如√2），因此不能更一般地表示实数。这使我们的建议脱离了现有的猜想，加深了我们对ANS的理解，并为将来的研究铺平了道路。因此无法更一般地表示实数。这使我们的建议脱离了现有的猜想，加深了我们对ANS的理解，并为将来的研究铺平了道路。因此无法更一般地表示实数。这使我们的建议脱离了现有的猜想，加深了我们对ANS的理解，并为将来的研究铺平了道路。