 A different philosophical use of a formal ontology is one that aims to be descriptive. A descriptive formal ontology aims to correctly describe a certain domain of entities, say sets, or numbers, as opposed to all things there are. Take common conceptions of set theory as one example. Many people take set theory to aim at correctly describing a domain of entities, the pure sets. This is, of course, a controversial claim in the philosophy of set theory, but if it is correct then set theory could be seen as a descriptive formal ontology of pure sets. It would imply that among incompatible formal theories of sets only one could be correct. If set theory were merely representational then both of the incompatible theories could be equally useful as representational tools, though probably for different representational tasks.