Abstract

This chapter proposes an alternative, a posteriori approach to the ontological inquiry into numbers, grounded in the view that the fundamental phenomenon to be explained in an investigation of the metaphysics of mathematics is a class of human experiences. Humans do mathematics and use it to help them solve practical and theoretical problems. When investigating the metaphysics of mathematics, we are looking for a set of entities that can account for the main features displayed by these human experiences. This investigation can follow a “reverse engineering” strategy: starting with the assumption that certain humans have numerical competence, go back to a time when they did not, and observe what happened in the meantime. This involves answering two questions: what does a human being experience during cognitive development so as to acquire numerical competence, and what, in the history of the human species, enabled us to acquire it? Hopefully, data about our experiences as individuals and as a species will suggest a hypothesis about what entities underlie our number concepts.