Categorical properties are those with intrinsic natures that characterize how things are independent of what effects they produce. For example, mass might be categorical in determining an object's weight or acceleration. Some metaphysicians argue only categorical properties are truly fundamental.
You already understand the categorical/dispositional distinction: dispositional properties like *fragility* or *solubility* characterize what an object *would do* under certain circumstances, while categorical properties characterize what the object *is* independently of any conditional behavior. Categorical properties are the purely intrinsic, occurrent features of things — the way something actually is right now, not how it would behave if circumstances were different. The shape of a crystal, for instance, is often cited as a paradigm categorical property: it just *is* the geometric arrangement of atoms, regardless of what effects that arrangement produces.
The philosophical significance of this distinction lies in questions about grounding. If you hold that dispositions need to be grounded in something non-dispositional, then categorical properties play the role of the ultimate foundation. Consider: *solubility* is grounded in the molecular structure of a substance — its arrangement and bonding patterns. Those structural features are categorical. If you then ask what grounds the categorical structure, a committed categoricalist says "nothing further — it just is that way." The categorical properties are the bedrock. This picture is sometimes called Humean or categoricalist metaphysics: the world's fundamental layer consists entirely of categorical, non-dispositional qualities distributed across space-time, and all dispositions reduce to or are grounded in these categorical bases.
The sparse/abundant distinction you have encountered is relevant here. If we are asking what the *fundamental* categorical properties are, we want the sparse list — the genuine, natural joints in reality, not every gerrymandered predicate we can construct. Mass, charge, spin, and other fundamental physical quantities are strong candidates for fundamental categorical properties. These are not defined by what they would do; they are just *there*, intrinsic to their bearers. From these, all the dispositional features of objects — their fragility, conductivity, magnetic behavior — are supposed to follow as consequences.
Not everyone accepts this picture. Pure dispositionalists argue that categorical properties are themselves just unmanifested dispositions, or that the categorical/dispositional divide is not as sharp as it seems. Mass, they note, is precisely defined by its role in gravitational and inertial relations — it is characterized by how it *behaves*. If that's right, categoricalism may be an illusion. The debate ultimately connects to deep questions about whether properties have intrinsic natures independent of their causal roles, or whether being a property just *is* playing a certain causal role.
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