  A final division among conventionalist theories concerns whether the putative conventions inform pre-existing practice. Hume’s theory of property purports to unveil actual conventions at work in actual human societies. But some conventionalists instead urge that we must adopt a convention. Carnap’s conventionalist treatment of logic, mathematics, and ontology illustrates this approach. Carnap exhorts us to replace unformalized natural language with conventionally chosen formal languages. Carnap has no interest in describing pre-existing practice. Instead, he offers a “rational reconstruction” of that practice.