Background Many areas of biology are open to mathematical and computational modelling. The application of discrete, logical formalisms defines the field of biomedical ontologies. Ontologies have been put to many uses in bioinformatics. The most widespread is for description of entities about which data have been collected, allowing integration and analysis across multiple resources. There are now over 60 ontologies in active use, increasingly developed as large, international collaborations. There are, however, many opinions on how ontologies should be authored; that is, what is appropriate for representation. Recently, a common opinion has been the “realist” approach that places restrictions upon the style of modelling considered to be appropriate. Methodology/Principal Findings Here, we use a number of case studies for describing the results of biological experiments. We investigate the ways in which these could be represented using both realist and non-realist approaches; we consider the limitations and advantages of each of these models. Conclusions/Significance From our analysis, we conclude that while realist principles may enable straight-forward modelling for some topics, there are crucial aspects of science and the phenomena it studies that do not fit into this approach; realism appears to be over-simplistic which, perversely, results in overly complex ontological models. We suggest that it is impossible to avoid compromise in modelling ontology; a clearer understanding of these compromises will better enable appropriate modelling, fulfilling the many needs for discrete mathematical models within computational biology.