Arithmetical cognition is the result of enculturation. On a personal level of analysis, enculturation is a process of structured cultural learning that leads to the acquisition of evolutionarily recent, socio-culturally shaped arithmetical practices. On a sub-personal level, enculturation is realized by learning driven plasticity and learning driven bodily adaptability, which leads to the emergence of new neural circuitry and bodily action patterns. While learning driven plasticity in the case of arithmetical practices is not consistent with modularist theories of mental architecture, it can be enriched by the theory of neural reuse. According to neural reuse, cerebral regions are reused to contribute to multiple neural circuits in functionally constrained ways throughout ontogeny. By hypothesis, learning driven plasticity is complemented by learning driven bodily adaptability, which suggests that there is an interesting functional relationship between finger gnosis, finger counting, and arithmetical practices. The emerging perspective on enculturated arithmetical cognition will be complemented by considerations on associated developmental and acquired disorders, namely developmental dyscalculia and acquired acalculia. The upshot is that we need to take the cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturation into account in order to arrive at a better understanding of the phylogenetic and ontogenetic conditions of arithmetical cognition.
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The considerations on the relationship between proto-arithmetical and arithmetical skills seem to bear on the philosophical debate about the innateness of cognitive traits (Colombo 2017; De Cruz and De Smedt 2010; Laurence and Margolis 2007; Samuels 2004). At first glance, it might seem justified to describe quantity approximation and subitizing as innate cognitive traits and counting, numerical cognition, and arithmetic as acquired cognitive traits. However, there are at least three good reasons to reject the descriptive and explanatory adequacy of the concept of ‘innateness’ in this context. The concept of innateness is highly ambiguous and ill-defined (Mameli and Bateson 2011), it enforces a dichotomy between innate and acquired cognitive traits that does not do justice to the complexity of the genesis of cognitive traits (Linquist 2018), and it is likely to be rooted in folkbiology rather than in systematic scientific reasoning (Griffiths 2002). For these reasons, I am an eliminativist about ‘innateness’ and confine myself to describing the relationship between proto-arithmetical capacities and arithmetical practices in terms of a phylogenetic and ontogenetic trajectory that is heavily influenced by developmental and selective cognitive niche construction. I am grateful to an anonymous reviewer for pressing me on this point.
For an empirical and theoretical assessment of the acquisition of the ordinality principle and the cardinality principles during early childhood, see Davidson et al. (2012).
In Merkley and Ansari (2016) terminology, an example of a number word is ‘four’ and an example of a numeral is ‘4’.
I am grateful to an anonymous reviewer for the suggestion to take network science into consideration.
An anonymous reviewer enquires whether Fodor’s (1983) view that central systems are not organized in a modular fashion might actually be consistent with the theory of neural reuse. I assume that this is not the case, given a crucial difference between the modified modularity theory and the neural reuse theory. The neural reuse theory postulates a fundamental neuro-functional principle governing the overall organization of the brain. By contrast, Fodor’s (1983) fundamental distinction between central and peripheral systems postulates that these two types of systems are organized in significantly different ways. This is incompatible with neural reuse.
In the present context, an interesting question further probing Fodor’s (1983) modified modularity theory is whether the AQS would count as a modular input system or as a non-modular central system. This is hard to determine, given that quantity approximation appears to be deeply anchored in phylogenetically old ways to perceive quantifiable objects and animals in the local environment. At the same time, it could be argued that number approximation is at one remove from the basic perception of sensory stimuli and would thus be an ability that is realized by a non-modular central system. This indicates that the initially clear-cut distinction between input systems and central systems does not provide good guidance for the interpretation of empirical data, at least in the present context.
For a methodological critique of this study, which attributes these results to a statistical fallacy, see Fischer (2010). As far as I can tell, even if the results reported by Gracia-Bafalluy and Noël (2008) were invalid because of this fallacy, this would leave the empirical results reported by Noël (2005) unaffected. Therefore, it remains a viable theoretical possibility that there indeed is a robust relationship between finger gnosis and improvements in mathematical cognition.
There are at least three explanations for the finding that improvements in finger gnosis correlate with capacities in subitizing, counting, and arithmetic. First, it could be the case that there is a direct influence of finger gnosis skills on subitizing. Second, it is possible that finger gnosis influences subitizing indirectly by improving skills in counting and arithmetic, which then have a positive direct impact on subitizing. Finally, we cannot rule out the possibility that this correlation is merely coincidental. Currently, it remains a desideratum for future empirical research to explore this particular relationship between finger gnosis and subitizing.
There are several methodological questions concerning the constraints on the identification and interpretation of dissociations. Discussing these questions in detail is beyond the scope of this paper. For thorough considerations on the methodological challenges for cognitive neuropsychology, see Castles et al. (2014).
The low number of participants in the dyscalculia group is in line with the general tendency in cognitive neuropsychology to conduct “single case studies rather than group studies” (Caramazza and Coltheart 2006, p. 5).
In both conditions, participants were asked to verify or falsify equations consisting of two operands and their sum. In the ‘complex’ condition, the first operand was 2, 3, 4, 5, 6, 7, 8 or 9 and the second operand was 2, 3, 4 or 5. In the ‘simple’ condition, one of the operands was always 1 (Ashkenazi et al. 2012).
I am grateful to an anonymous reviewer for pressing me on this point.
Many thanks to an anonymous reviewer for bringing this study to my attention.
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I am greatly indebted to Markus Pantsar for his very constructive feedback on earlier versions of this paper. I would like to thank him and Catarina Dutilh Novaes for their excellent editorial work. I am also grateful to Alexander Gillett, Max Jones, Richard Menary, and Jean-Charles Pelland for many insightful discussions on enculturation and mathematical cognition.
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Fabry, R.E. The cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturated arithmetical cognition. Synthese 197, 3685–3720 (2020). https://doi.org/10.1007/s11229-019-02238-1
- Mathematical cognition
- Neural plasticity
- Embodied cognition
- Cognitive niche construction
- Cultural learning
- Neural reuse
- Developmental dyscalculia
- Acquired acalculia