Metaphysical structure refers to the way entities, properties, and relations are organized in reality—what counts as fundamental versus derivative, how entities relate to their parts and properties, and what principles govern possible worlds. Formal metaphysics treats this structure as systematically analyzable, mapping the conceptual landscape that grounds all other facts.
In your prerequisite work on what metaphysics is and ontological categories, you learned that metaphysics asks foundational questions about what exists and how it is categorized. Metaphysical structure takes the next step: given that things exist and fall into categories, how are those categories and things *organized*? Reality isn't a flat list of equally basic items — there appears to be hierarchy, dependency, and architecture. Some things exist because of other things; some properties are built out of simpler properties; some facts obtain because of more fundamental facts. Mapping this architecture is what formal metaphysics does.
The key organizing concept is the distinction between fundamental and derivative entities. Something is fundamental if it doesn't exist in virtue of something else — it has no metaphysical explanation in terms of more basic things. Something is derivative if it does exist in virtue of something more basic. A shadow is derivative: it exists because of the light and the object blocking it. The particles making up that object might be fundamental, or they might themselves be derivative with respect to quantum fields. Metaphysical structure is the question: how deep does this hierarchy go, and what does it look like?
The formal relation that articulates this hierarchy is grounding: a relation of non-causal metaphysical determination. The fact that a ball is red and round *grounds* the fact that there is something colored. The physical facts about a brain *ground* the mental facts about its subject (if physicalism is true). Grounding is asymmetric, irreflexive, and transitive — it's a strict partial order on facts or entities. The structural question is whether grounding bottoms out in some set of fully ungrounded fundamentalia, or whether it could be infinitely descending.
This architectural picture has direct implications for ontological parsimony — the methodological preference for not multiplying entities beyond necessity. If mental facts are fully grounded in physical facts, we don't need an additional ontological category for minds: they're real but derivative. This is the strategy that physicalists use. Metaphysical structure lets you make these commitments precise: rather than asking "does X exist?" the more refined question is "at what level of the metaphysical hierarchy does X sit, and what grounds it?" Understanding this architecture is prerequisite to the more specific debates in grounding, fundamentality, and the theory of properties that this course builds toward.
Topics in reflective domains aren't scored by quiz answers. Read, reflect, and mark when you've thought it through.