A forgotten lesson ...

Aristotle

Aristotle (Metaphysics XIII) on the reification of the mathematical:

'It is said that the objects of mathematics—i.e. numbers and lines and the like—are substances,' and some say moreover 'that the mathematical substances are the only substances.' But conclusions contrary to the truth follow, 'if one supposes the objects of mathematics to exist thus as separate entities. For if they exist thus they must be prior to sensible spatial magnitudes, but in truth they must be posterior; for the incomplete spatial magnitude is in the order of generation prior, but in the order of substance posterior, as the lifeless is to the living ...'

'Grant that they are prior in formula. Still not all things which are prior in formula are prior in substance. For those things are prior in substance which when separated from other things surpass them in the power of independent existence, but those arc prior in formula out of whose formulae the formulae of other things are compounded; and these two properties are not coextensive. For if attributes, such as "moving" or "white," do not exist apart from their substances, the white is prior to the white man in formula, but not in substance. For it cannot exist separately, but is always along with the concrete thing; and by the concrete thing I mean the white man. Therefore it is plain that neither is the result of abstraction prior nor that which is produced by adding determinants posterior; for it is by adding a determinant to the white that we speak of the white man.'