Bundle Theory versus Substratum

Take a tomato and enumerate its properties: red, round, ripe, of such-and-such mass, at such-and-such place. Have you enumerated the tomato, or have you enumerated the properties of something that is not itself among them?

Bundle theory says the first: the object is the properties, held together by a relation of compresence, and there is nothing else there. Substratum theory says the second: besides the properties there is a bearer that has them and is not constituted by them.

The dispute is the sharpest form of the question the substance page raised, and each side's objection to the other is strong enough that the debate has produced more compromises than victories.

Bundle theory

The object is a bundle: a complex whose constituents are properties and whose unifying relation is compresence — the relation properties bear to one another when they are properties of the same thing. Russell held a version; so does any trope theorist who wants a one-category ontology.

Its appeal is economy and empiricism. Nothing is posited beyond what can be encountered; there is no unknowable je ne sais quoi of the kind Locke was reduced to.

The fatal objection, if properties are universals. Suppose the constituents are universals. Then two objects with all the same properties are two bundles with all the same constituents — and a bundle is individuated by its constituents, so they are one bundle. Bundle theory with universals therefore entails the identity of indiscernibles necessarily: it is not merely true but impossible that two things share all their properties.

That is a very strong claim, and Black's two-spheres case is designed to refute it (see individuation). If it is even possible that a symmetric universe contain two exactly similar spheres, bundle-with-universals is false.

The trope repair. Substitute tropes for universals and the objection dissolves. Two exactly similar spheres are two bundles of numerically distinct though exactly resembling tropes; there is no shared constituent to collapse them. This is why most contemporary bundle theorists are trope theorists — the position is far more defensible in that form, and the cost is inherited from trope theory rather than added.

The change objection. A bundle is individuated by its members, so a bundle that loses a member is a different bundle. But the tomato survives ripening from green to red. The bundle theorist must therefore either individuate objects by a privileged subset of properties — the nuclear bundle theory, on which a core of essential properties constitutes the thing and the rest are attached to it — or adopt temporal parts, so that the green bundle and the red bundle are successive stages of a perduring whole. Both are substantial further commitments.

The compresence problem. Compresence must bind the properties into one object. Is it itself a constituent of the bundle? If so, what binds it to the rest, and Bradley's regress begins. If not, the bundle has a unifying element that is not one of its members — which sounds very much like the substratum the theory was avoiding, differing only in being a relation rather than a thing.

Substratum theory

The alternative posits a bare particular or substratum: an entity that bears properties without being constituted by them, and which accounts for both the object's unity and its numerical distinctness from qualitatively identical objects.

It handles everything the bundle theory struggles with. Two exactly similar spheres are two because their substrata are two. The tomato survives ripening because the substratum persists while properties come and go. The unity of the object is the unity of a single bearer.

The objections are correspondingly about the bearer's intelligibility:

• It is unintelligible. A thing with no properties of its own is not a thing at all; to conceive it we must conceive it as something, which is to attribute a property.
• It is unknowable. Locke's complaint: we encounter qualities, never the bearer. Any epistemology on which we know objects by their features leaves the substratum permanently out of reach.
• It is self-contradictory. A bare particular has the property of being bare, hence is not bare.

The standard defence is that these misread the position. The bare particular is not an entity without properties; it is an entity that is not constituted by its properties. "Bare" describes how it is considered, not how it is. The substratum has all the properties of the object — it is what has them — and is called bare only when abstracted from them for the purpose of analysis. On this reading the third objection is a pun and the first is a confusion between having no properties and not being a collection of properties.

Armstrong's thin particular is exactly this: the particular considered in abstraction from its properties, which is not a further entity alongside the thick particular but the same thing under a different consideration.

The middle positions

Because both extremes are costly, most actual views are hybrids:

• Trope bundle theory — the majority position. Bundles, but of particulars, so the PII objection lapses.
• Nuclear bundle theory (Simons) — a core bundle of essential tropes forms the individual; accidental tropes attach to the core. Handles change without temporal parts.
• Substance–attribute with tropes (Lowe) — objects are basic and irreducible; tropes are the modes they bear. Gives up one-category economy for a scheme in which each category does one job.
• States of affairs (Armstrong) — the fundamental unit is neither bundle nor bearer but the fact of a particular's having a universal, with both constituents abstractions from it.

The last is worth attention because it changes the question. The bundle/substratum dispute assumes the object is built from something, and asks what the parts are. Armstrong's answer is that the built thing is not the object but the state of affairs, and that the object and its properties are both got by abstraction from something more basic — which dissolves the dispute rather than settling it.

Where this sits

This is the category question applied to the internal structure of a particular, and its outcome constrains everything downstream. Whether qualitatively identical objects are possible, whether objects can survive change, and what individuates them are all decided, or at least sharply constrained, by the answer.

The next page takes the question that the bundle theory's difficulties make urgent: what makes two things two, if not a difference in their properties? That is the problem of individuation.