THE PERIODIC TABLE OF THE VIRTUES: A Coordinate Classification of Moral Forms, Their Occupations, and Their Compounds

Abstract

Abstract A periodic table is not a list with headings. It is a coordinate system in which position carries predictive content, vacancies are falsifiable predictions, and the classification is closed under the operations of the underlying theory. This paper constructs such a system for the virtues on the basis of the Ontological Virtue Formula (V = F ⊕ D), the Inversion Theorem, and the Dynamic Freedom Theorem (S = F·A/R), and applies it to the 101-virtue catalogue of the Filosofia das Virtudes together with its ten cross-traditionally attested extensions. Four results are structural rather than taxonomic. First, virtues and vices are not distinct populations: a vice is the same form under a different master, so a catalogue of 101 virtues and 101 inversions describes 101 entities, not 202. Compounds receive formulas and metastable states receive names; neither enlarges the table. Second, no order-1 virtue modulates all three terms of the Dynamic Freedom Theorem. The all-terms signature belongs to unrendered Freedom alone. This is derived as the Restriction Principle from a stated axiom, the Occasion Premise, with the Defiance Exclusion as a corollary; a damage assessment states in advance what survives if the axiom fails. Third, the channel by which a form inverts is determined not by its position alone but by two dispositional properties of its domain — whether its output is appropriable by an occupying power, and whether its performance carries display value. This capture mechanism screens off the weak regime–channel association it replaces, explaining both why that association exists and why it is weak. Fourth, the rendering block predicts not how a form is captured but where a catalogue has failed to look: three-quarters of the truth-rendered and form-rendered cells stood empty against under a fifth of the act-rendered ones. The system is validated against evidence it was not built from: seven of ten independently identified cross-traditional candidates fall into cells the coordinates had marked vacant, and the remaining three fall into occupied cells that the source catalogue had independently judged only partially distinct. The census closes 32 of 36 vacancies with 27 predicted elements carrying pre-registered inversion channels, tiered by confidence, with the weakest marked against the elements they are most likely to collapse into. Sixteen compounds are registered and none admitted. Criteria are given at three levels: adequacy conditions on the classification, admission conditions for elements, and admission conditions for compounds and mixed states. Applied to a body of proposed extensions, they reject most “virtue ⊗ vice hybrids” as counterfeits of exactly the kind the occupation thesis describes: a configuration whose value is claimed to depend on retaining an occupying power is an occupation with a rationale attached. All coding is single-coder. No human virtue has been measured. The verification protocol, decision rules, and falsifiers are stated in §11 and the limits of every claim in §12. Keywords: virtue theory · classification · Inversion Theorem · measurement regimes · Dynamic Freedom Theorem · moral ontology · institutional capture