Substance and Bundle Theories

Strip the postbox of its properties one at a time. Take away the red, and you have a grey or black one. Take away the cylindrical shape, the cast iron, the weight, the slot for letters, the place on the pavement. At some point the list of properties runs out. Is anything left?

The previous article asked what it is for the postbox and the tomato to share a colour, and assumed throughout that there is a postbox which has the colour. That assumption was deliberately left unexamined. It is the subject of this article: whether an ordinary particular is something over and above the properties it has, or is nothing more than those properties gathered together.

What a substance is for

The idea has accumulated several jobs, and it helps to separate them, because different theories drop different ones.

The first job is to be the bearer. Properties are ways of being, and a way of being seems to need something that is that way. Redness on its own is not a thing that can sit on a pavement and collect letters. There must be something that is red, and the sentence "the postbox is red" seems to say so.

The second job is to unify. The postbox is red, cylindrical, heavy and made of iron, and these do not float together by accident. A natural thought is that they belong together because they are all properties of one thing, which holds them.

The third job is to survive change. The postbox is repainted from green to red and is still the same postbox. If it were merely its colour, together with its shape and weight, repainting would produce a different thing. Something must stay constant while the properties alter, and the substance is the obvious candidate.

These jobs are logically separate. A theory could supply a bearer without supplying anything that survives change, or the reverse. What the two positions in this article disagree about is whether a single entity needs to do them, and whether that entity has to be distinct from the properties it carries.

Substrata and bare particulars

Locke's Essay (1689) gave the idea its most famous and least flattering statement. Asked what supports the qualities of a thing, we are driven to say a substance, which Locke described as something, "I know not what". He treated it as a placeholder we cannot do without and cannot say anything about.

The modern version sharpens the placeholder.

Gustav Bergmann developed the view in the 1960s, and Edwin Allaire's "Bare Particulars" (1963) defended it under the name it has kept. On the bare particular view, a thing is a particular plus the universals or tropes it exemplifies, and the particular is the bearer and the unifier. It is the same bare particular whatever properties it has, so it also survives change.

The argument for it is an inference to the best account of the three jobs.

The argument pushes on the second premise, and the bundle theorist will deny it. For now notice what the conclusion requires. The substratum must be distinct from every property it bears, or it would be one of the things being united and not the thing doing the uniting. So it can have none of the postbox's properties as part of what it is. That is the bareness.

Bundle theory

Hume's treatment of the mind in the Treatise (1739) is the classic source. Looking inward he finds no self apart from a "bundle or collection" of perceptions, and the same attitude applied to the postbox yields a thing that is only its qualities. Bertrand Russell developed the view for physical objects, most clearly in An Inquiry into Meaning and Truth (1940), taking a particular to be a collection of qualities that are compresent: there together, in the same place at the same time.

The motive is economy. A substratum is an entity no one has observed or could observe, introduced only to be a bearer, and the bundle theorist denies that any bearer is needed. A red cylindrical heavy thing is a case of redness, cylindricality and heaviness occurring together. The unity that the substratum was supposed to provide is supplied by compresence, which holds among the properties directly and requires no further subject.

The view comes in two versions, and they are the ones the previous article prepared. A bundle of universals is a collection of the shared properties redness, cylindricality and so on, so that the postbox is a certain collection of repeatable items. A bundle of tropes is a collection of particular qualities, this redness and this shape, so that the postbox is made of items that are each particular already. Keith Campbell defended the second in Abstract Particulars (1990). The choice matters for the problems that follow, since a good many of them bear on one version and not on the other.

Problems for bundles

The pressure on bundle theory comes from three directions.

The first is the question of what compresence is. If it is a relation among properties, then it is another item in the ontology, and the question of what unites the properties has moved to the question of what unites the compresence relation to its relata. If it is a mere fact that the properties occur together, then the bundle theorist has accepted the unity as brute, which is where the substratum theorist stood. The bundle theorist's best reply is that this is the same dilemma the substratum theorist faces about instantiation, so that on this score the two are no worse than each other.

The second concerns change and the persistence of the thing. If the postbox is the bundle of its properties, then a repainted postbox is a different bundle, since one member has been replaced. On a strict reading the postbox did not survive repainting. Bundle theorists have to say that a persisting object is a series of bundles linked by continuity or resemblance, which is a perfectly good position but one the theory gets by adding to it, and which meets the difficulties the ship of Theseus brought out.

The third concerns modality, and it is the sharpest.

The argument is a use of the distinction between essential and accidental properties that the beginner tier drew. A bundle seems to have its members essentially: change a member and the bundle is a different one. An ordinary thing has most of its properties accidentally. The bundle theorist can answer by treating the postbox's modal profile through counterparts, so that "could have been blue" is a claim about a similar bundle, or by weakening the identity to a relation of constitution. Each answer concedes something. The substratum theorist, by contrast, locates the thing's modal flexibility in the particular, which can lose or gain properties without ceasing to be itself.

The identity of indiscernibles

The principle should be kept apart from Leibniz's law, with which it is easily confused. Leibniz's law says that identical things share all properties. The identity of indiscernibles says the converse: things that share all properties are identical. The first is nearly trivial. The second is a substantive claim about what the world can contain, and it has been denied far more often.

It matters here because it is the point at which bundle theory is exposed. If an object just is a bundle of universals, then two objects with exactly the same universals are the same bundle, and so one object. The bundle theory of universals therefore entails the identity of indiscernibles, and anything that counts against the principle counts against it.

Max Black's counterexample, in "The Identity of Indiscernibles" (1952), is the standard test. Imagine a universe containing nothing but two iron spheres, alike in size, temperature, colour and chemical make-up, and some distance apart. They have the same intrinsic properties, and each stands in the same relations to a sphere of just that kind, so they share their relational properties too. If this universe is possible, the principle is false: there are two things and no property that distinguishes them.

Defenders of the principle have resisted each premise. Robert Adams, in "Primitive Thisness and Primitive Identity" (1979), considered the reply that the spheres differ after all: the first has the property of being distinct from the second, which the second lacks, since it is not distinct from itself. Adams argued that such properties are no help to a purely qualitative form of the principle, because they presuppose the numerical difference they were meant to explain, and so are not purely qualitative. Ian Hacking argued in 1975 that the description of Black's world underdetermines the facts: the same appearances fit a world containing a single sphere in a space that closes back on itself, so the case does not clearly secure two things. And some philosophers accept the case as possible and reject the principle, which leaves the bundle theory of universals in trouble.

Where the two views meet

The bundle theory of tropes escapes Black's case without further argument. Each sphere is a bundle of its own tropes: this sphere's grey, that sphere's grey, this sphere's roundness, that sphere's roundness. The tropes exactly resemble one another across the two bundles, but they are two sets of tropes, so there are two bundles. Numerical difference is carried by the particularity of the tropes and does not need a qualitative difference. That is a real advantage, and it is a reason bundle theorists with a taste for economy are often trope theorists.

It also reveals what the substratum was doing. A bare particular is a way of securing numerical difference without qualitative difference: two bare particulars, one in each sphere, and nothing else needed. Tropes secure the same difference by making the qualities themselves particular. The two views offer different sources of particularity, one in a bare bearer and the other in the properties, and neither needs numerical difference to come from qualitative difference.

A third position sits between. Armstrong's thick particular, and the Aristotelian substance it descends from, has its properties as constituents and is not a bare core with properties attached. On this view the postbox is a particular-with-its-properties from the start, and neither part can exist apart from the other. It escapes the unknowable core, since there is no core to be unknown, and it keeps the bearer, since the particular remains a constituent. Its cost is that it takes the unity of the thing as primitive, which the bundle theorist and the substratum theorist each attempted to explain.

What the dispute turns on, then, is where one is prepared to stop explaining. The substratum theorist stops at the instantiation tie, the bundle theorist at compresence, and the thick particular theorist at the thing itself. Each also takes a stand on whether numerical difference can outrun qualitative difference, which is the question Black's spheres put. The next article asks what else the world contains besides things and their properties: facts, events and states of affairs.