Aristóteles y el problema del concepto y la unidad del número

This paper deals with some problems concerning the composition and unity of mathematical entities in Aristotle. My aim is to explain Aristotle’s thesis according to which, if numbers are not bare heaps of many unities, they must include some cause of unity (Metaph. VIII 3, 1044a2-5). In order to accomplish this goal, I develop some Aristotelian considerations about the metaphysical conditions for the unity and identity of substances. Several problems arise from the fact that numbers are not substance, but quantities (Metaph. X 1, 1052b15 ss.). Therefore, they have neither form nor matter strictly and also lack the kind of unity which can be founded by form. In my conclusion I will state that numbers have for Aristotle a quantitative kind of unity linked to the mental operation of counting by unities (Metaph. XIV 1, 1088a5; X 1, 1052b23-24, a34-b1).