Here I explore the biological relevance, origin and meaning of the concept of cladogram (rooted, directed branching diagrams representing the hypothesized phylogenetic relationships among the terminal taxa under study) and argue that cladograms do not necessarily entail synapomorphies, but synapomorphies are required to test and ultimately falsify cladograms. Both cladograms and synapomorphies are required to achieve phylogenetic explanation. I conclude that within a phylogenetic, scientific context, testability refers to the logical relationship among cladograms (hypotheses), synapomorphies (evidence), and background knowledge (descent with modification). It is the relationship between evidence and hypothesis that underlies a logically consistent relationship between synapomorphies and cladograms. The capacity of a given cladogram, as a hypothesis, to explain synapomorphies complements this relationship and conforms phylogenetic explanation.