Fundamental and Derivative Properties: Sparse and Abundant Ontologies

Core Idea

Abundant theories count as properties any condition expressible by a predicate (redness, being-a-table, being-north-of-Boston); sparse theories restrict properties to fundamental, causally-efficacious ones required to explain all other facts. The choice shapes understanding of causation, laws of nature, and scientific ontology.

Explainer

From your study of intrinsic and extrinsic properties you know that some features of an object belong to it independently of its environment (its mass, its charge) while others depend on relationships (being north of Boston, being the most famous). And from your study of grounding and fundamentality you know that some facts hold in virtue of other facts — derivative truths are grounded in more basic ones. The sparse/abundant debate asks: which of all the things we can truly predicate of an object correspond to genuine, metaphysically substantive properties, and which are merely useful classifications we project onto a world that doesn't carve quite that way?

The abundant theory of properties is maximally permissive: for every predicate that can be truly applied to some object, there is a corresponding property. Being-a-prime-number, being-located-within-ten-miles-of-Paris, being-such-that-snow-is-white — all of these correspond to real properties if the predicate is coherent and applicable. The advantage of abundance is logical tractability: properties proliferate as freely as predicates, and no selection problem arises. The disadvantage is that abundant properties cannot do explanatory work. If everything has a property corresponding to every true predicate, you can't use property-sharing to explain causal similarity, natural law, or projectibility. Two things both have the property being-such-that-Plato-existed — that doesn't make them causally alike in any interesting way.

The sparse theory holds that only some predicates track genuine, natural properties — the ones that "carve nature at its joints," to use Plato's phrase. David Lewis, the sparse theory's most influential defender, argued that sparse properties are those picked out by physics: mass, charge, spin, and a few others. These are the perfectly natural properties that ground resemblance, causal power, and nomological necessity. Everything else is derivative. The predicate "is jade" picks out what turns out to be two natural kinds (jadeite and nephrite) loosely grouped by appearance — it doesn't correspond to a single sparse property. The predicate "is an electron" plausibly does correspond to a sparse property.

The practical stakes are high for philosophy of science. Laws of nature are typically understood as regularities among natural properties, not among arbitrary abundant ones. "All electrons repel each other" is a candidate law because "electron" tracks a sparse property; "all things within ten miles of the Eiffel Tower expand when heated" is not, even if accidentally true, because the property is not natural. Similarly, causation: only sparse properties can genuinely be causes, on many theories. If the "property" of being red causes nothing (redness just is a certain complex of physical surface reflectance properties that do the causal work), then color language is causally otiose — a useful shorthand, not a report of causal structure. The choice between sparse and abundant theories thus determines whether the predicates of ordinary language and the special sciences carve reality or merely slice a convenient path through it.