A final division among conventionalist theories concerns whether theputative conventions inform pre-existing practice. Hume’s theoryof property purports to unveil actual conventions at work in actualhuman societies. But some conventionalists instead urge that we mustadopt a convention. Carnap’s conventionalist treatmentof logic, mathematics, and ontology illustrates this approach. Carnapexhorts us to replace unformalized natural language with conventionallychosen formal languages. Carnap has no interest in describingpre-existing practice. Instead, he offers a “rationalreconstruction” of that practice.


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