Arithmetic, Culture, and Attention

Abstract

AbstractThe study of numerical cognition has undergone tremendous progress in recent years, accumulating scores of data on cognitive systems that could be involved in the uniquely human ability to practice formal arithmetic. Among the important questions tackled by this burgeoning domain of research is what happens to the limited cognitive systems that we share with many animal species to allow us to develop arithmetically-viable numerical content. While answers to this question have varied, most have attributed a constitutive role to culturally-inherited extracranial cognitive support in their explanation of how numerical content emerges from our innate cognitive machinery. The idea here is that we need to look at our interaction with external support for cognition like fingers, numerals, and number words, to explain what allows us to go beyond the size and precision limitations of the cognitive systems we are born with. In this paper, I challenge this externalist answer to the origins of our arithmetical skills and argue for an internalist approach to the development of formal arithmetical skills. I argue that culture-independent learning trajectories involved in learning the meaning of number words as well as individual differences in arithmetical abilities against fixed cultural backgrounds suggest adopting a pluralist approach to our formal numerical abilities, where externalism only holds beyond an initial segment of the natural numbers. In Sect. 1, I discuss the appeal of adopting cognitive externalism with respect to numerical cognition. Then, in Sect. 2, I discuss culture-invariant aspects of the learning trajectory we follow when learning the meaning of number words. Section 3 contains an introduction to research into Spontaneous Focusing on Numerosity (SFON), in order to illustrate how individual differences in arithmetical abilities could be explained by referring only to things going on inside the head. I close in Sect. 4 by offering a few remarks on why paying attention to numerical aspects of the world, as framed by SFON research, may be a good place to build an internalist explanation of how we learn to manipulate numbers.