Science aims to develop an accurate understanding of reality through a variety of rigorously empirical and formal methods. Ontologies are used to formalize the meaning of terms within a domain of discourse. The Basic Formal Ontology (BFO) is an ontology of particular importance in the biomedical domains, where it provides the top-level for numerous ontologies, including those admitted as part of the OBO Foundry collection. The BFO requires that all classes in an ontology are actually instantiated in reality. Despite the fact that it is hard to show whether entities of some kind exist or do not exist in reality (especially for unobservable entities like elementary particles), this criterion fails to satisfy the need of scientists to communicate their findings and theories unambiguously. We discuss the problems that arise due to the BFO's realism criterion and suggest viable alternatives.