Leibovich et al. argue that the processing of continuous magnitudes is more automatic than the processing of (discrete) number. Such a claim is in line with some of our recent studies in which we repeatedly observed that decisions on discrete number are inevitably influenced by continuous magnitudes (e.g., Gebuis & Reynvoet Reference Gebuis and Reynvoet2012b; Smets et al. Reference Smets, Sasanguie, Szücs and Reynvoet2015). Despite describing slightly different mechanisms of how number can be inferred from continuous magnitudes – that is, either through “the mediation of inhibition” as proposed in the current review (Leibovich et al.) or through “sensory integration of continuous magnitudes” (Gebuis et al. Reference Gebuis, Cohen Kadosh and Gevers2016) – both reviews basically put forward the same conclusion. The take-home message of both is that the ability to extract discrete number originates from the ability to process continuous magnitudes, a finding that consequently seriously questions the existence of an approximate number system (ANS) as an evolutionary ancient system.

Besides the consequences of this conclusion for numerosity processing being addressed in the review of Leibovich et al., such a proposition also has serious implications for symbolic number (e.g., verbal number words, digits, etc.) processing. In particular, the symbol grounding problem (i.e., how symbols acquire their numerical meaning) needs to be revisited in light of these new arguments (Reynvoet & Sasanguie Reference Reynvoet and Sasanguie2016). The presumed idea of the existence of the ANS has resulted in the proposal that when children are confronted with symbolic numbers for the first time, they acquire the numerical meaning of these symbols by mapping them onto this ANS (e.g., Dehaene Reference Dehaene2001; Halberda et al. Reference Halberda, Mazzocco and Feigenson2008). In turn, because these symbols are crucial for learning formal mathematics (e.g., calculation), the assumption of symbol–ANS mapping has inspired researchers to hypothesize and observe that the performance on a numerosity discrimination task (which is assumed to index the ANS) is related to individual differences on a (symbolic) mathematics achievement test. In other words, following this assumption, the ANS would thus serve as the basis of symbolic numbers and also later symbolic arithmetic. Leibovich et al. (abstract), however, suggest that “continuous magnitudes are more automatic and basic than numerosities,” and that we need to derive discrete number from these continuous magnitudes (see also Gebuis et al. Reference Gebuis, Cohen Kadosh and Gevers2016). If this is the case – which we believe it is – then the assumption that we learn symbolic numbers by mapping them on such a magnitude system seems very unlikely.

The present review suggests in particular that to derive discrete number from visual sets, we must apply cognitive control. It is well known that cognitive control develops through childhood (Anderson Reference Anderson2002). The continuing development of cognitive control functions like inhibition is also manifested in the performance of young children on a numerosity discrimination task. For example, when examining the performance on incongruent trials (i.e., continuous magnitudes correlate negatively with number) in 7-year-old children, Szücs et al. (Reference Szücs, Nobes, Devine, Gabriel and Gebuis2013) observed a performance at chance. Defever et al. (Reference Defever, Reynvoet and Gebuis2013) demonstrated that the congruency effect (i.e., the performance difference between congruent and incongruent trials) in children ranging from 6 to 11 years old decreased with increasing age. These studies demonstrate that the ability to infer number from continuous magnitudes, just like cognitive control functions, develops during elementary school. In contrast, children's knowledge and understanding of numerical symbols (i.e., digits) is completed earlier. For example, Sasanguie et al. (Reference Sasanguie, De Smedt, Defever and Reynvoet2012) demonstrated that 5-year-old kindergartners are able to compare digits with an accuracy far above chance. By the time children finish second grade, not only are they almost perfect in symbolic number discrimination (Sasanguie et al. Reference Sasanguie, De Smedt, Defever and Reynvoet2012), but also they master several symbolic calculation skills (e.g., multiplications), whereas they still encounter problems deriving number from visual sets (e.g., Szücs et al. Reference Szücs, Nobes, Devine, Gabriel and Gebuis2013). In sum, when symbolic numbers are learned, the ability to infer number from the magnitude system has not reached its full potential yet – because of its dependence on the development of cognitive control functions. More specifically, children still struggle with inhibiting continuous magnitudes (Leibovich et al.) or integrating this sensory information (Gebuis et al. Reference Gebuis, Cohen Kadosh and Gevers2016), resulting in inaccurate judgements of number on stimuli where continuous information negatively correlates with number. As a consequence, it unlikely that such a magnitude system is the ground for learning symbolic numbers.

In our recent paper (Reynvoet & Sasanguie Reference Reynvoet and Sasanguie2016), we evaluated a promising alternative for symbol grounding. In a first step, numerical symbols are mapped on the object tracking system, a system that allows us to keep track of up to four items (see also Carey Reference Carey2009). In a second phase, knowledge about the counting list may be used to infer critical principles of the symbolic number system, such as the principle that numbers later in the counting list are larger (Davidson et al. Reference Davidson, Eng and Barner2012). As a result, gradually, symbolic numbers are primarily represented through (order) associations with other symbolic numbers in a separate semantic network of symbolic numbers (Sasanguie et al. Reference Sasanguie, De Smedt and Reynvoet2017). Very recently, it was demonstrated through computational modeling that classic effects in numerical cognition, like the distance and the size effect, can be accounted for by such a network (Krajcsi et al. Reference Krajcsi, Lengyel and Kojouharova2016).

In sum, the current review rightly identifies some serious challenges for the idea that we have an innate sense of numbers. An issue that has been overlooked, however, concerns the fact that this re-evaluation of the ANS into an “approximate magnitude system” (AMS) has important implications for symbolic number processing: It is impossible that symbols are learned by associating them with a magnitude system that, at the time of symbol acquisition, is not able to compute discrete number.