Mathematics is largely already excepted from the above discussion—this post is talking about empirical clusters only (“When you draw a boundary around a group of extensional points empirically clustered in thingspace”), and mathematics largely operates in a priori truths derived from axioms. For example, no one needs to do a study of triangles to see whether their angle all do, indeed, add up to 180 degrees—when that’s not part of the definition of triangles, it follows from the other definitions and axioms.

Mathematics is largely already excepted from the above discussion—this post is talking about empirical clusters only (“When you draw a boundary around a group of extensional points empirically clustered in thingspace”), and mathematics largely operates in a priori truths derived from axioms. For example, no one needs to do a study of triangles to see whether their angle all do, indeed, add up to 180 degrees—when that’s not part of the definition of triangles, it follows from the other definitions and axioms.