Clarke Sam, Beck Jacob
Department of Philosophy & Centre for Vision Research, York University, Toronto, ONM3J 1P3, Canada.
Behav Brain Sci. 2021 Apr 12;44:e178. doi: 10.1017/S0140525X21000571.
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.
按照目前的正统观点，人类和许多其他动物拥有一种“数字感”，即近似数字系统（ANS），它能够表征数字。最近，这种正统观点受到了众多批评，这些批评质疑ANS是否真的能表征数字。我们区分了三条批评路线——来自一致性、混淆因素和不精确性的论证——并表明这些论证都没有成功。然后，我们给出了正面理由，来支持ANS确实能表征数字这一观点，而不仅仅是表征非数字的混淆因素或数字的奇特替代物，比如批评者所提出的“数量”或“数量词”。在此过程中，我们提出了一个被忽视的问题：是哪种数字？正统观点的支持者在这个问题上一直相当含糊。但这并不令人满意，因为正统观点的预测，包括ANS有望成功或失败的情况，都取决于所表征的数字类型。作为回应，我们提出ANS不仅能表征自然数（如7），还能表征非自然数有理数（如3.5）。然而，它不能表征无理数（如√2），因此更普遍地说，它不能表征实数。这使我们的提议有别于现有的猜想，完善了我们对ANS的理解，并为未来的研究铺平了道路。
