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Biology works on particular subjects. Because of its historicity, each biological entity is unique. Yet we need to bring them together to be able to talk about them in a general way. Our classifications are to communicate our concepts, and thus they reflect an intention. As we are in science, we prefer grouping (aka agglomerative) procedures to division procedures, which always end up isolating individuals. In systematics, the science of classifications, the geometry of our concepts is that of a hierarchy by nesting, from the most general to the most particular, rather than a stacking hierarchy (as in the case of scala naturae), because nesting is an inclusive practice while scaling is both inclusive and exclusive. Biological entities are crisscrossed by a host of different resemblances, and the overall resemblance, in trying to capture them all, does not capture any of them. It is indistinguishable from global difference. Yet we want to work on shared traits, not on differences, which wind up isolating entities. These shared traits are common attributes or shared properties. This is resemblance seen as a mosaic (which will lead to a phylogenetic mosaicism). Among the various types of resemblance, which is the one we choose? Topological resemblance, defined by the principle of connection, is the priority. Then come resemblance in forms and resemblance in developing processes (ontogeny). Functional resemblance is too misleading for consideration, with regards to our goals, since we classify in order to reflect common origins of entities. Modern classification of living things reflects their past genealogy, at least what we can reconstruct from it (phylogeny) based on our best inferences. For that purpose, topological resemblance is the most efficient.