Science progresses through the development of integrative theories that unify more and more subsidiary theories. Progress in phylogenetic theory comes from mutual reconciliation with the theoretical structure of other branches of evolutionary biology, such as developmental biology, population biology, and population genetics. The notions of species, individuality, and scalar hierarchy are keys to this reconciliation. Conflation of the results and simplifying assumptions of particular discovery operations with the nature of the entities that we search for is a continuing problem in inferential biology. Other problems extend from the fact that scientific discovery operations address sets of entities and sets of interactions, even when the definitions employed by the operations are not rigorous set-definers, but rather generalized descriptive approximations which summarize similarities among the parts of hierarchically more general entities. As an example, in the discovery methods of phylogenetic systematics, organisms (parts of species) are treated as if they are extensions of a set (the lineage considered as a set), rather than as indefinable parts of a particular (the lineage as a system). This simplifying assumption constitutes treating scalar hierarchies as if they are specification hierarchies and, although this may be necessary for scientific progress, it can lead to over-reductionism if applied uncritically. We expect all analytical techniques to fail at some frequency in part because the limits and reality of the entities that scientists attempt to discover do not extend from definitions used in discovery operations, For this reason, all operational definitions in systematics must be patched by theoretical (= process) claims to one degree or another to give us a more complete representation of evolutionary history. In our view, ontology is the result of reconciliation of theoretical expectations and lines of operational evidence (both of “direct” observation and logical techniques). This “consilience of inductions” provides a general picture of the world and illuminates the limitations of particular discovery operations. As our understanding of the lawful nature of the universe improves, we are able to refine the definitions used by our discovery operations. Against the backdrop of the payoffs to evolutionary biology, the various definitions of species are most starkly compared. In cases where tokogeny is not inherently hierarchical, the level of organization chosen as the basic unit that maximizes the explanatory power of phylogenetic hypotheses is the level of Evolutionary Species, which is that of largest integrating lineages, rather than the level of individual organisms. Nevertheless, we recognize that our discovery operations rest on observations of organismal characteristics. The Phylogenetic Species Concept is, at best, the operational equivalent of Evolutionary Species, but may identify parts of Evolutionary Species that are only temporarily isolated. The cost of this kind of error is judged to be small compared with the alternative of recognizing paraphyletic “species” on the basis of potential to recombine. Metaphyly, concerns about exclusiveness of lineages as something more than an analytical issue, and “an escape from species” through operationalism are judged to stem from errors of overreduction.