Portulacineae comprise a clade of eight ostensibly monophyletic families, four of which (Anacampserotaceae, Montiaceae, Portulacaceae s. str., and Talinaceae) and part of a fifth (Didiereaceae) had been classified traditionally in Portulacaceae s. lato. The clade also includes Basellaceae, Cactaceae, and Halophytaceae. While available evidence strongly supports recognition of major clades within Portulacineae, current analyses disagree with respect to relations among them, such that the Portulacineae “backbone” phylogeny remains “unresolved.” The disagreements might owe in part to incongruent data and/or poor analysis and/or known theoretical shortcomings of the analytical methods. But I argue here that it reflects mostly the failure to appreciate the fundamental property of living organisms, viz. their inherent determinism consequent to autopoiesis. This property renders the evolutionary process as idiosyncratic. This, in turn, renders phylogeny inherently unpredictable and, strictly speaking, unrecoverable. I also emphasize that the hierarchical organization of organisms predicts that phylogeny should not be strictly tree-like. Nonetheless, evolutionary history is materially tangible, hence is within the realm of scientific inquiry. I make two proposals here. One is that (often futile) efforts to resolve phylogeny as a tree reflect a constitutive cognitive proclivity to resolve trees even when phylogeny is not tree-like and/or otherwise “resolvable.” To mitigate this tendency, I propose that the objective of phylogenetic study should be reconciliation rather than resolution. In this way, the lack of tree-like phylogenetic resolution becomes useful knowledge. In this theoretical framework, I evaluate what can be considered tentatively known about the Portulacineae backbone phylogeny.