When a conclusion feels wrong despite being derived logically, that usually means that the definitions are flawed. In math the defintions of structures don't ha

When a conclusion feels wrong despite being derived logically, that usually means that the definitions are flawed. In math the defintions of structures don't have to reflect anything real, it's all about starting with arbitrary rigorously stated definitions and exploring their implications. So when it feels like definitions are wrong in math, that's just a reflection of that "definitional gap". But the virtue of always siding with the logical-but-unintuitive isn't as valuable outside of mathematics, so it's maybe not the best point to bring up in an article that's about skills math teaches that are useful in "real life". In philosophy, definitions aren't arbitrary and rigorous, they're meant to be reflections of reality. So when a conclusion feels unintuitive, that's a decent argument against the definitions it was derived from. If mathematics teaches people to just pay attention to the definitional gap, that might be useful enough, but isn't that covered by "discussing definitions"?