The Problem with *Mathematical* Abstraction

A precisely defined thing is not the same as a definite thing.

Mathematical abstraction does not save us from the cost of precision.

In fact, it exacerbates the problem.

A precisely defined thing is not the same as a definite thing.

People tend to reify precision as though it speaks to something that exists physically.

The higher the abstraction the less this must be true.

Math is a lens that is chosen, one that comes with definite epistemic costs. It is a way of communicating, not a way of describing.

A description is perceived by the reader as an account of how things actually happen.

Being extremely precise about things that are abstract does not elucidate, it actively interferes with deeper understanding by pretending to be rigorous.

To speak exactly about things that are not exact is to obscure.

Like all choices, math comes with a cost. Let’s not pretend otherwise.