Leibovich et al. provide a critique of theories that posit an innate number sense. They propose that a “number sense” develops, via, for example, statistical learning, from the correlation between continuous magnitudes and numerosity. The authors argue that although numerosities are learned (through educational and cultural interactions), the perception of continuous magnitudes is innate. Thus, innate skills for the perception of continuous magnitudes set the stage for learning procedures for addressing discrete quantities.

Instead, we suggest that the evidence presented for (and against) the innateness of magnitude perceptions should be considered as addressing contrasts such as “primacy/no primacy” or even “automatic/not automatic” processing, in characterizing human numerical cognition at different phases of its development, rather than directly pertaining to innateness.

If innate means “not acquired” (e.g., Logan Reference Logan and Wyer1997), arguments for innateness and learning are mutually dependent. This is especially true when learning reaches a level wherein performance is “automatic” in the sense that it is fluent, is highly accurate, and exhibits a primacy in processing. Indeed, skilled automatized performance, especially when acquired implicitly, resembles innate processing. That is, both innate processing and automatized processing – perceptual, conceptual, or motor – are fast and may involve the involuntary direction of attention to stimuli and even, in some cases, a lack of conscious awareness (Karni Reference Karni1996; Logan Reference Logan and Wyer1997). Specifically, both implicit learning and explicit learning may result in automatic processing of information that behaviorally is manifested in high levels of fluency. Fluency is reflected in the speed and accuracy of processin, as well as in a subjective experience of ease (Karni & Bertini Reference Karni and Bertini1997; Poldrack & Logan Reference Poldrack and Logan1998). Thus, learning experiences can determine the saliency of a specific cue. Moreover, when a stimulus becomes salient, its salient (as opposed to the non-salient) features will automatically capture attention (Smith et al. Reference Smith, Jones and Landau1996; Treisman & Gelade Reference Treisman and Gelade1980), which in turn will further facilitate the learning process and enhance saliency. Therefore, saliency per se, even in early life or in animal studies, is not sufficient for proving “innateness”; it may simply indicate the end point of a learning process.

In both innate and acquired skills, automatized processing occurs independently of top-down expectancies and thus leads to processing primacy. Consider, for example, the Stroop effect lending primacy to a complex and clearly acquired ability, reading (MacLeod Reference MacLeod1991; Stroop Reference Stroop1935). The Stroop effect reflects the robust primacy of script processing (reading) even over simple color report in skilled readers. In the classic Stroop task, participants are instructed to name the color of the ink in which words denoting colors are printed. The Stroop effect refers to the fact that skilled readers cannot refrain from reading the words and, in fact, from accessing the meaning of the color words. Reading attains such primacy (automatic processing) that it interferes with the naming of (ink) colors. The primacy effect of reading can be found in other sensory domains. A recent study shows that tactile texture discrimination is interfered with by unintentional Braille reading of incongruent texture-denoting words in the blind (Jarjoura & Karni Reference Jarjoura and Karni2016).

There is evidence that automatic Stroop-like interferences develop with practice. For example, in a numerical Stroop-like effect that occurs when participants are presented with two digits that differ in physical size and numerical value and have to compare the digits using one of the dimensions, the interference between these two dimensions changes with practice (Tzelgov et al. Reference Tzelgov, Yehene, Kotler and Alon2000) and schooling (Girelli et al. Reference Girelli, Lucangeli and Butterworth2000; Rubinsten et al. Reference Rubinsten, Henik, Berger and Shahar-Shalev2002). Thus, a numerical Stroop effect does not occur in physical comparisons at the beginning of first grade, but an adult-like pattern of the numerical Stroop effect was found in third grade and on (Girelli et al. Reference Girelli, Lucangeli and Butterworth2000; Rubinsten et al. Reference Rubinsten, Henik, Berger and Shahar-Shalev2002). These data suggest that automatic activation of the numerical values of Arabic numerals develops, and attains primacy in processing, over the first years of schooling.

There is, moreover, ample evidence supporting the notion that very early implicit learning experiences – from visual and motor constrained environments (e.g., Held & Hein Reference Held and Hein1963) to cultural-social exposure (e.g., see review by Kuhl Reference Kuhl2010) – can effectively generate and shape processing primacies. Consider in this light the processing primacy (bias) attained within even a few hours of exposure to a given visual environment, as attested by classical studies on dark-reared kittens (Held & Hein Reference Held and Hein1963). Very early life experience-dependent bias can even eliminate “innate” abilities as manifest in, for example, the finding that babies lose their ability to perceive multiple phonemic cues (sounds used in languages) that are irrelevant to their language experience before they attain 1 year of age (Eimas Reference Eimas1975; Eimas et al. Reference Eimas, Siqueland, Jusczyk and Vigorito1971; Lasky et al. Reference Lasky, Syrdal-Lasky and Klein1975; Werker & Lalonde Reference Werker and Lalonde1988). On the other hand, by 10 months of age, language-specific differences can be discerned in the babbling of infants raised in different countries (de Boysson-Bardies Reference De Boysson-Bardies, De Boysson-Bardies, de Schonen, Jusczyk, MacNeilage and Morton1993). The main question is not of innateness of perception or action, but rather how infants learn and form selective phonemic categories that make a difference in their language so early in life (Kuhl Reference Kuhl2010).

To summarize, most of the evidence reviewed in Leibovich et al.'s article, including the interpretation of brain imaging studies, relates to the automaticity-primacy of processing continuous magnitudes (inferred from measures of fluency). This, we would argue, does not constitute sufficient evidence for determining the status of task performance as “a basic sense” or “innate” because implicit (and explicit) learning experiences in infancy (and later in life) can generate fluency, accuracy, and, importantly, primacy for processing specific cues. There is no a priori reason to suppose that the processing of continuous magnitudes or discrete quantities cannot reflect implicit learning experiences even from very early on in life. Indeed, it has been argued that in some situations constructs such as discrete and countable magnitudes may precede constructs of continuous magnitudes and may affect their development (Starr & Brannon Reference Starr and Brannon2015). We suggest that studies of biology–environment interactions, shaping our repertoire of automaticity, are warranted.