Methodology

A direct account of how this ontology was constructed, what it does and does not preserve, and the specific limits of the source-text mapping. Read this before citing or critiquing the artifact.

How this ontology was constructed

This artifact is distinctive among the BFO-aligned philosophical ontologies hosted under this domain. The companion Spinoza and Leibniz ontologies were extracted by BFO-Agent's dialogue pipeline, with each class produced by an LLM proposer, validated by the HermiT reasoner, and reviewed by a human before commit. Their source-text provenance is preserved at the moment of extraction.

The Geometry of the Good ontology was built differently. The ontology was constructed by the author during the writing of the book and refined separately from the prose. It was then imported into BFO-Agent as a finalized OWL artifact, with consistency confirmed by HermiT but without the per-passage extraction trail that the dialogue pipeline produces. The construction is closer to traditional ontology engineering — Protégé-style work informed directly by the author's developing philosophical view — than to the LLM-driven extraction used for the historical philosophers.

The source-text mapping shown on this site was therefore reconstructed after the ontology was finalized. The reconstruction was produced semi-automatically by matching each OWL class to the chapter sections in the published PDF whose textual content best aligns with the class name. Where matches were strong (multi-word class names whose constituent terms appeared densely in a given section) the class was assigned to that section. Where matches were ambiguous or weak, the class was left unmapped.

BFO mapping decisions worth flagging

The book deploys a relational metaphysics that does not always map cleanly to BFO categories. Several mapping decisions are worth surfacing for scholarly review.

Obligation as relational structure

The book's central claim is that obligation is ontologically real — it is the structural fact of one being's directedness toward another. In BFO, obligation is rendered predominantly as a specifically dependent continuant: a relational structure that inheres in the relation between obligor and obligee, neither reducible to a quality of the obligor alone nor to a contractual artifact between them. Many subtypes (InheritedObligation, ObligationGeneratingCondition, FutureDirectedObligation, ObligationSedimentation) develop this base mapping in ways the book's later chapters require.

Directedness as quality and as structure

Directedness — the proto-ethical orientation of one being toward another that the book treats as foundational — appears in the ontology in two roles. As a quality (BFO_0000019), it inheres in a directed being. As a structural feature (RelationalDirectedness, NetworkOfDirectedness, ObligationDirectedness), it characterizes the relational field within which obligation arises. The book moves between these two uses depending on context; the ontology preserves both.

Recognition as ontological disposition

Recognition is typed as a disposition (BFO_0000016) of recognizing beings, realized in actual acts of recognition (which are processes). The framework distinguishes ontological recognition (necessary in being-with) from institutionalized recognition (the form recognition takes in law and political life). The latter is treated as a generically dependent continuant that the institution bears.

Rupture as ontological event

Rupture — the failure of directedness, the breach of the relational field — is rendered as a process (BFO_0000015). The book's central argument is that rupture is not just a moral wrong but an ontological event that disrupts the structure of being-with. The ontology preserves this by typing all eight rupture subclasses (MoralRupture, OntologicalRupture, RelationalRupture, MoralFieldRupture, etc.) under BFO process, with participants drawn from the bearers of the violated relation.

Fidelity as the form of the good

Chapter 6 argues that fidelity, not flourishing or duty or maximization, is the form of the good. The ontology represents fidelity as a complex of disposition (capacity for fidelity), process (fidelity as enacted), and quality (the relational quality of being faithful). Several subclasses (RelationalFidelity, StructuralFidelity, OntologicalFidelity, FidelityToRelation) make explicit the different senses in which fidelity is the good.

The contradiction of denial

Chapter 13's central argument — that denying one's relational situation is materially contradictory, not merely false — is represented primarily through named individuals (axioms) rather than classes. Individuals such as DirectednessImpliesObligation, UncertaintyDoesNotAbsolveObligation, and PossibilityGroundedObligation function as ontological commitments rather than mere typing assertions. They state the structural facts the book argues are non-negotiable.

The limits of the source-text mapping

The mapping shown in the source-text view of this site is post-hoc and semi-automated. Some specific limits readers should keep in mind:

Density-weighted matching favors longer passages. The preface is the longest single passage in the book and absorbs nearly a third of the OWL's classes by the matching algorithm. This is not entirely wrong — the preface really does introduce most of the framework's vocabulary — but it does mean that more granular passages within chapters get less attribution than the actual textual development warrants.

Single-best-match assumption. Each class is assigned to one canonical passage, even when the class is developed across multiple chapter sections. The book's actual argumentation often returns to the same concept across chapters with different emphases; the mapping does not preserve those returns.

Approximate name-to-text alignment. The matching uses the CamelCase-split words of each class name and locates sections where those words appear in the prose. This catches well-named classes (Directedness, Fidelity, Recognition) and the canonical sections that introduce them. It does worse with structural classes whose names are technical compositions (OntologicalGroundingOfObligationByDirectednessAsymmetry) that may not appear verbatim in the prose.

Unmapped classes remain in the OWL. About 1% of the ontology's classes did not match any section with high enough confidence. They appear in the BFO tree and search without source-text linkage. The methodology page documents this honestly rather than hiding the unmapped tail.

A planned improvement

A more precise mapping is planned. The most reliable approach would be a hand-mapping by the author, identifying for each class the passage(s) where it is most centrally developed. This would take serious sustained work but would produce the best-quality artifact. In the interim, the semi-automated mapping is the right tradeoff between fidelity and time-to-publication.

Limitations

Single rendering. The ontology represents one structural reading of the book — the author's own. Different readers would produce different ontologies. Treat this as a starting point.

Reasoner caveats. HermiT validates consistency under standard OWL 2 DL semantics. The book's claims about modal necessity (some obligations are necessary in the strong sense), about phenomenological priority (relational structure is prior to cognition), and about normative weight (some obligations matter more than others) are not expressible directly in OWL 2 DL and are rendered only approximately.

Self-representation. Unlike Spinoza and Leibniz, this is the author rendering his own framework. Readers should approach with appropriate caution: the structural commitments shown here are the author's account of his own commitments, not an independent reading.

References

Arp, R., Smith, B., and Spear, A. D. (2015). Building Ontologies with Basic Formal Ontology. MIT Press.

Glimm, B., Horrocks, I., Motik, B., Stoilos, G., and Wang, Z. (2014). HermiT: An OWL 2 reasoner. Journal of Automated Reasoning 53(3), 245–269.

Koepsell, D. R. (2025). The Geometry of the Good: The Architecture of Social Being, Book 1.

Smith, B. and Ceusters, W. (2010). Ontological realism: A methodology for coordinated evolution of scientific ontologies. Applied Ontology 5(3-4), 139–188.