[Math] (Fictive) story of a time where people reasoned only up to isomorphism

Question

I seem to remember reading once a story that some mathematician had written to justify the use of categories, or isomorphisms or equivalences, or something like that. The story goes something like this:

Once upon a time, people did not know what equality was. Instead, they only thought about things up to isomorphism. For example, they did not say that two sets had the same number of elements, but that they were in bijection. Today with category theory go back to these roots.

Does anyone have an idea of who told this story and what the full story is?

Answer 1

This sounds an awful lot like TWF week 121:

To understand this, the following parable may be useful. Long ago, when shepherds wanted to see if two herds of sheep were isomorphic, they would look for an explicit isomorphism. In other words, they would line up both herds and try to match each sheep in one herd with a sheep in the other. But one day, along came a shepherd who invented decategorification. She realized one could take each herd and "count" it, setting up an isomorphism between it and some set of "numbers", which were nonsense words like "one, two, three,..." specially designed for this purpose. By comparing the resulting numbers, she could show that two herds were isomorphic without explicitly establishing an isomorphism! In short, by decategorifying the category of finite sets, the set of natural numbers was invented.