Phylogenetic methods unearth evolutionary history when supported by three starting points of reason: (1) the continuity axiom begs the existence of a “model” of evolutionary change, (2) the singularity axiom defines the historical ground plan (phylogeny) in which biological entities (taxa) evolve, and (3) the memory axiom demands identification of biological attributes (characters) with historical information. Axiom consequences are interlinked, making the retrodiction enterprise an endeavor of reciprocal fulfillment. In particular, establishing direction of evolutionary change (character polarization) roots phylogenies and enables testing the existence of historical memory (homology). Unfortunately, rooting phylogenies, especially the “tree of life,” generally follow narratives instead of integrating empirical and theoretical knowledge of retrodictive exploration. This stems mostly from a focus on molecular sequence analysis and uncertainties about rooting methods. Here, we review available rooting criteria, highlighting the need to minimize both ad hoc and auxiliary assumptions, especially argumentative ad hocness. We show that while the outgroup comparison method has been widely adopted, the generality criterion of nesting and additive phylogenetic change embodied in Weston rule offers the most powerful rooting approach. We also propose a change of focus, from phylogenies that describe the evolution of biological systems to those that describe the evolution of parts of those systems. This weakens violation of character independence, helps formalize the generality criterion of rooting, and provides new ways to study the problem of evolution.
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