Categorical properties are intrinsic features an object possesses making no essential reference to what would happen in other situations (like being red); dispositional properties are characterized by what they would cause or manifest in appropriate circumstances (like fragility). Whether all properties are categorical, all dispositional, or mixed has profound implications for causation, modality, and laws of nature.
From your work on intrinsic and extrinsic properties, you know that some properties belong to a thing independently of its relations to other things, while others are relational. The categorical/dispositional distinction cuts across that one: it asks whether a property is defined by what a thing *is* right now, or by what it *would do* in some circumstances. Both categorical and dispositional properties can be intrinsic — but they differ in whether their complete specification requires reference to other possible situations.
A categorical property is one that is fully characterized by describing the current state of the object. The shape of a crystal, the charge distribution in a molecule, the mass of a particle — these seem describable without mentioning what would happen to the crystal under pressure, what the molecule would do in a reaction, or how the particle would respond to a force. You could in principle give a complete inventory of all the categorical properties of a thing by examining it here and now. The paradigm case is geometric shape: being spherical is just being spherical — there is no hidden "what it would do" built into the property.
A dispositional property is irreducibly defined by its potential manifestation in the right circumstances. Fragility is the canonical example: to say a glass is fragile is to say it *would* shatter if struck with sufficient force. The glass might never be struck; it might sit undisturbed forever. Yet it still has or lacks fragility right now. This is what makes dispositions philosophically puzzling: they seem to point toward possibilities, not just actualities. Other examples include solubility (would dissolve if submerged), flammability (would ignite if heated), toxicity (would poison if ingested). The dispositional property seems to "reach out" to counterfactual situations that haven't happened.
The debate about which properties are fundamental has deep consequences. Categoricalism holds that all fundamental properties are categorical, and dispositions are just regularities that happen to hold given those categorical grounds plus laws of nature. On this view, laws are external constraints imposed on a categorically described world. Dispositionalism (or the "powers" view) reverses this: the fundamental properties of nature are dispositions — mass is the disposition to attract, charge is the disposition to repel or attract — and laws of nature are not external constraints but expressions of what these powers necessarily do. This has major consequences for your understanding of causation: if properties are powers, causes necessitate their effects; if properties are categorical, causation requires contingent laws to bridge them.
The question connects to your study of causal relations because it determines what kind of work a property does in explaining why something happens. If fragility is a genuine dispositional property, then it helps explain why the glass broke — the breaking is the manifestation of a real power. If fragility is just a categorical description of microstructure plus a law, then the explanatory work is done by the underlying structure and the law, not the disposition per se. Deciding between these views requires going deep into debates about modality, laws of nature, and what kinds of features of the world are genuinely fundamental versus derived.
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