Samadi and Barberousse attempt to provide a precise, formal definition of the species category that is faithful to the internodal species concept (Samadi S, Barberousse A. 2006. The tree, the network, and the species. Biological Journal of the Linnean Society89: 509–521). Here, it is argued that their study is technically flawed. Most of the necessary corrections to their definitions are provided in order to accurately portray the internodal concept. It is then argued that the internodal concept is fundamentally flawed; it does not solve the ‘classical problems’ that Samadi and Barberousse claim it does. In particular, it does not allow for the possibility of interspecies hybridization. In addition, the proposal is unworkable in practice, and also theoretically problematic because it entails that, in many lineages, speciation events are taking place every few generations.