What makes something an object rather than a property? Why can relations hold between things, but things cannot hold between relations? These questions seem almost too basic to ask—yet they reveal a remarkable fact about our conceptual framework.

Beneath every specific inquiry about what exists lies a deeper layer of structure. Whether we're cataloguing mental states, physical particles, or mathematical entities, we deploy the same fundamental categories: objects that bear properties, relations that connect things, wholes composed of parts. This structural scaffolding applies everywhere, regardless of domain.

Formal ontology investigates this universal framework. Unlike material ontology—which asks whether minds or numbers or quarks exist—formal ontology asks what it even means for something to be an object, a property, or a relation. It maps the architecture that any possible domain of being must exhibit. Understanding this architecture transforms how we approach every other metaphysical question.

Consider the difference between asking whether numbers exist and asking what kind of thing a number would be if it did exist. The first question belongs to material ontology—it concerns the inventory of a specific domain. The second belongs to formal ontology—it concerns categories applicable across all domains.

Material ontological categories carve up particular regions of being. Mental versus physical distinguishes domains of concrete existence. Abstract versus concrete separates mathematical and logical entities from spatiotemporal ones. These distinctions matter enormously, but they presuppose more fundamental categories.

Formal ontological categories apply universally. Object (or particular, or individual) designates whatever can bear properties and stand in relations. Property (or attribute, or quality) designates whatever characterizes objects. Relation designates whatever connects objects to one another. These categories make no reference to specific domains—mental objects bear properties just as physical ones do.

The formal/material distinction illuminates philosophical methodology. When philosophers debate whether properties are universals or tropes, they're doing formal ontology—asking about the nature of property-hood itself. When they debate whether mental properties reduce to physical ones, they're doing material ontology—asking about a specific domain. Both inquiries are legitimate, but confusing them generates pseudoproblems. Many disputes about abstract objects, for instance, conflate formal questions about what abstractness is with material questions about what abstract things exist.

Takeaway

Formal ontology provides the categories within which material ontological debates occur—you cannot argue about whether numbers exist until you understand what kind of existence is at stake.

Philosophers have proposed strikingly different categorical frameworks. Aristotle's Categories distinguished primary substances (individual things like Socrates) from secondary substances (kinds like human) and from nine accident categories including quantity, quality, and relation. His scheme privileged concrete individuals as the fundamental bearers of all other categories.

Roman Ingarden developed a more complex framework in the twentieth century. He distinguished modes of being (real, ideal, purely intentional, absolute) from existential moments (autonomy, dependence, originality, derivativeness). This allowed finer distinctions—fictional objects exist differently from mathematical objects, though both contrast with physical objects. Ingarden's scheme emphasizes that how something exists may vary even when categorial type remains constant.

Contemporary four-category ontologies, developed by philosophers like E.J. Lowe, propose a systematic grid. The scheme distinguishes substantial from non-substantial entities and particular from universal entities. This yields four fundamental categories: substantial particulars (individual objects), non-substantial particulars (property instances or tropes), substantial universals (kinds), and non-substantial universals (attributes). Each category has distinctive relations to the others—objects instantiate kinds, exemplify attributes, and are characterized by tropes.

These schemes are not merely competing lists. They embody different views about what formal relations are primitive and how categories depend upon one another. Aristotle makes substance fundamental; Ingarden emphasizes modes of existence; four-category ontologies balance particularity and universality. Evaluating these schemes requires asking which carves the space of possibilities at its joints—which reflects genuine metaphysical structure rather than mere conceptual convenience.

Takeaway

Different categorical schemes are not arbitrary classifications but competing hypotheses about the genuine joints in reality's structure—choosing between them requires asking which reflects deeper metaphysical necessity.

Formal ontology studies not only categories but the formal relations that structure them. These relations hold across all domains—wherever there are objects, properties, and relations, there are also parthood, exemplification, and dependence. Understanding their logic constrains what metaphysical theories are even coherent.

Parthood exhibits distinctive formal properties. It is reflexive (everything is part of itself), antisymmetric (if x is part of y and y is part of x, then x=y), and transitive (if x is part of y and y is part of z, then x is part of z). These aren't empirical discoveries but constraints any genuine parthood relation must satisfy. Mereology—the formal theory of parts and wholes—investigates what further principles hold. Does every collection of objects compose a further object? Classical mereology says yes; restricted composition says no. This question has no domain-specific answer—it concerns parthood as such.

Exemplification connects objects to properties. But its logic proves surprisingly complex. Does the exemplification relation itself require a further relation connecting it to what it relates? This generates Bradley's regress. Does exemplification admit of degrees, or is it all-or-nothing? The answer affects whether we can make sense of vague predication. These formal questions constrain theories of properties in any domain.

Ontological dependence comes in multiple varieties. Rigid dependence: x depends on y if x cannot exist without y existing. Generic dependence: x depends on Fs if x cannot exist without some F existing. Essential dependence: x depends on y if y figures in what x essentially is. Mapping these dependence structures reveals the grounding relations that make reality hierarchical rather than flat. Properties may depend on objects, or objects on properties, or both may depend on more fundamental facts. Formal ontology charts these possibilities without prejudging which obtains.

Takeaway

Formal relations like parthood, exemplification, and dependence have logical structures that constrain metaphysical theorizing—some theories fail not from empirical falsity but from violating these structural constraints.

Formal ontology occupies a peculiar position—more abstract than physics or psychology, yet more constrained than pure logic. It investigates categories and relations that any possible domain must exhibit, providing the framework within which specific ontological debates occur.

This framework shapes questions before we ask them. When we wonder whether minds are substances or bundles of properties, we presuppose the formal distinction between substance and property. When we debate whether wholes are more than their parts, we deploy formal mereological concepts. Making these presuppositions explicit is already philosophical progress.

The categories we uncover may reflect deep structural features of reality—or they may reflect our cognitive architecture projected outward. Formal ontology cannot settle this question alone. But it can clarify what we're asking, map the space of possibilities, and reveal which theoretical choices have which consequences.