Making Sense of Numbers Without a Number Sense

The idea that the number-sensitive behavior of young infants is best explained by ascribing (innate) conceptual knowledge of numbers and numerical operations to them is widespread in both philosophy and psychology. Furthermore, such knowledge is deemed necessary as a basis to acquire more sophisticated arithmetical knowledge. We will argue that, despite its initial plausibility, ascription of innate conceptual knowledge fails to account for the observed behavior. In particular, we will argue that the key assumption—viz., that the behavior is to be explained as a product of knowledge deployment—is not only unwarranted but also that the postulation of the required knowledge raises unsolved problems. We argue that these problems can be avoided if one adopts a socio-historical view of the ontogenesis of arithmetical knowledge. On this account, knowledge acquisition requires a community of already accomplished knowers. To substantiate our claims, we will sketch an account, inspired by Wittgensteinian models of language acquisition, of how a child could acquire numerical knowledge within a community of already accomplished reckoners on the basis of universally shared non-epistemic behaviors.