Conceptual obstacles to the existence of an innate sense of number in the brain

Abstract

Lorenzi et al. (2025) argue for the innateness of the “number sense” by presenting behavioral and neural evidence. They cite research demonstrating that various species can distinguish numerosities early in development and that their brains contain specialized regions or neurons (“number neurons”) dedicated to this ability. Based on these findings, they conclude that an innate sense of number exists in the brain.

While their evidence supports the existence of such a cerebral mechanism, much of the debate on this topic does not question the existence or innateness of the mechanism itself, but rather its numerical nature. As Visibelli, Porru, Lucangeli, Butterworth, and Benavides-Varela (2024, p. 2) note: “A clear consensus concerning the existence of the number sense, however, is yet to be reached … it remains open to debate whether sensitivity to numerical information really indicates a number-specific capacity.” The issue may be more conceptual than experimental: “[s]ome disagreements [about the existence of the number sense] may ultimately be a result of the varying ways that researchers define number, numerosity, quantity, and so on” (Wilkey and Ansari 2020, p. 82). Lorenzi, Kobylkov, and Vallortigara fail to address this conceptual aspect of the discussion.

The expression “sense of number” suggests that numbers are perceptual properties. Frege (1960) argued persuasively against this idea. Consider, for example, a pair of dolls. It cannot be taken as an instance of two without further qualification; the same pair could also exemplify four doll arms, eight limbs, or even one pair. Unlike surface area, number is not an inherent property of the pair that could be perceived through the senses. The attribution of number to stimuli requires the adoption of a criterion for what counts as a unit.

It could be said that the ANS divides stimuli into units and “counts” them, potentially involving “number neurons.” Indeed, neurons responsive to numerosity have been identified experimentally, as Lorenzi, Kobylkov, and Vallortigara note. However, this does not imply that numerosity-perceiving species have numbers in their brains. Sensitivity to what we regard as numerical stimuli can arise through non-numerical methods (dos Santos 2023). A simple example can illustrate this point.

Suppose an innumerate person wants to know whether the numerosity of people in a room is equal to the numerosity of chairs in that room. Instead of counting, she can ask each person to sit in a single chair. If no one remains standing and no chair is empty, she can immediately conclude that both sets have the same size. If someone remains standing, there are more people than chairs; conversely, if any chair remains empty, there are more chairs than people. No number is involved in this procedure. Some arguments against the existence of the number sense attempt to explain the observed behavior in terms of non-numerical processes such as this one. For example, Simon (1997) contends that the capacity to distinguish small numerosities in infants and nonhuman animals is non-numerical because the discrimination of small numerosities demands nothing more than establishing one-to-one mappings and making same/different discriminations.

Furthermore, numbers are better understood as cultural artifacts than innate concepts. Núñez (2017) highlights that numbers require symbolic reference, a cultural and conventional feature unique to humans, placing numbers “in a qualitatively separate realm from the quantity-related phenomena observed in nonhuman animals” (Núñez 2017, p. 418). He argues that the belief in innate numerical abilities may arise from terminological confusion. Terminological ambiguity is evident in Lorenzi, Kobylkov and Vallortigara’s text, where the terms “number,” “numerosity,” and “quantity” are used interchangeably. While common in the field, this practice deviates from the original intent behind the term “numerosity.” This term was originally introduced to make a distinction between the magnitude (numerosity) and the scale that measures it (numbers). Numbers are the culturally developed scale we, numerate humans, use to measure numerosity (dos Santos 2022).

The attribution of arithmetical skills to nonhuman animals and infants seems to be a case of anthropomorphic bias—the tendency to understand the minds of nonhuman animals by analogy with our own (Dacey 2017). Numerate humans typically determine numerosity by counting, a practice so ingrained that we often overlook the existence of non-numerical methods for evaluating numerosities. However, the fact that counting and calculating are almost always associated with numerosity for numerate humans does not imply that this is the case for other species or even for children. Humans are not born with the ability to do arithmetic, and many children face significant challenges when learning it in school. How, then, can we credibly attribute innate abilities to perform arithmetic to non-human animals or infants?

The experimental findings presented by Lorenzi, Kobylkov and Vallortigara show, at best, that the sense of numerosity is innate. Without evidence that numbers are involved in how nonhuman animals and infants assess numerosity, there is no basis for claiming the existence of a sense of number in the brain.

Funding

No funds, grants, or other support was received.

Conflict of interest statement: The author declares that he has no competing interests associated with this commentary.

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