Look again. We talked about defining things (in this case squares) and the combining them (in this case placing them besides each other) and then counting before and after combining them. Does it seem fairer now that I could interpret this as saying "2+2=5" in this system?

Many people when confronted with a situation like this will go back and modify their definitions so that normal arithmetic applies. This is why they can claim that normal arithmetic is universal and always applies. But there is another way of doing this.

You could modify your math so it describes the entities and your interaction with them as things really are! This might mean building the fuzziness and uncertainty directly into the mathematics!

It doesn't matter which way you do it. My hope is that you understand the flexible relationship between our mathematical systems, our perceptions of the world, and the symbolic manipulations we use to reason about reality. We are not passive observers.

Addendum: We statisticians, data scientists and other data analysts modify the math to fit reality in a hacky way. We attach reality to math with duct tape. The duct tape is called a mathematical model. We take advantage of standard math because it's a common language.

Our mathematical models are where all the fuzziness goes. Two data scientists can do the exact same analysis with the exact same general approach and get different numbers that more or less give essentially the same predictions! This is the reality of data analysis!