This pretty much nails it. If everyone commits to using approximately the same definitions then (at the social scale) you get normative semantics as an uninten

This pretty much nails it. If everyone commits to using approximately the same definitions then (at the social scale) you get normative semantics as an unintentional by-product. Everybody in your tribe uses the same terminology/notation and means the same thing by "==". It's a desirable property because it minimises miscommunication and it enable effective asynchronous communication. Good luck trying to read a paper by somebody using different semantics. And then computer scientists come along and point out that all definitions (and by proxy - all Mathematics) are arbitrary. Because the chosen axioms are arbitrary.