Abstract

Our epistemic access to mathematical objects, like numbers, is mediated through our external representations of them, like numerals. Nevertheless, the role of formal notations and, in particular, of the internal structure of these notations has not received much attention in philosophy of mathematics and cognitive science. While systems of number words and of numerals are often treated alike, I argue that they have crucial structural differences, and that one has to understand how the external representation works in order to form an advanced conception of numbers. The relation between external representations and mathematical cognition will be discussed by drawing on experimental results from cognitive science and mathematics education, and I argue for the constitutive role of external representations for the development of an advanced conception of numbers.