The use of structured knowledge representations-ontologies and terminologies-has become standard in biomedicine. Definitions of ontologies vary widely, as do the values and philosophies that underlie them. In seeking to make these views explicit, we conducted and summarized interviews with a dozen leading ontologists. Their views clustered into three broad perspectives that we summarize as mathematics, computer code, and Esperanto. Ontology as mathematics puts the ultimate premium on rigor and logic, symmetry and consistency of representation across scientific subfields, and the inclusion of only established, non-contradictory knowledge. Ontology as computer code focuses on utility and cultivates diversity, fitting ontologies to their purpose. Like computer languages C++, Prolog, and HTML, the code perspective holds that diverse applications warrant custom designed ontologies. Ontology as Esperanto focuses on facilitating cross-disciplinary communication, knowledge cross-referencing, and computation across datasets from diverse communities. We show how these views align with classical divides in science and suggest how a synthesis of their concerns could strengthen the next generation of biomedical ontologies.