natural vs formal language is a false dichotomy and accrues unwanted connotations

"Natural" here is meant to denote (at least according to Clark) "social" and "strategic" and "Schelling point built". "formal" is meant to denote "precise". Looks like a case of lifting a disambiguation into a type that accrues unwanted connotations: "natural" ought not be taken for "imprecise", nor ought "formal" to imply "apurposive" or "asocial".

Aside: is there a linguistics term for when a distinction is lifted into a definition?