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Bundled Vortices: Relation over Constituents

Is the idea that particulars are bundles of properties defensible?

The defensibility of bundle theory depends on the definition. I shall flesh out a minimal definition and consider three objections, two of which can be handled expeditiously. The third I shall argue is equally a problem for substratum theory, after which I shall attempt a solution based on my own interpretive definition.

Bundle theory is described as concrete particulars – ordinary objects – being constituted of properties. However, this is a broad outline and details vary between presenters. As such ‘bundle theory’ is more an umbrella term of loosely associated theories than a single well-defined theory. It is tempting, therefore, to assert that its defensibility is solely dependent upon – to borrow a phrase from Van Cleve – which ‘unpacking of the ‘bundle’ metaphor’ we are partial to (p. 28). While containing a grain of truth, such a blunt dismissal would nevertheless be premature. However, it is worthy of note since the dance between the theory’s detractors and proponents follows a general pattern.

Ideally detractors should wish to show that certain objections can be raised against any version of bundle theory. Since most are proponents of substratum theory, this usually pans out in attempts at required inclusions of bare substrata. These attempts consist of finding some feature of concrete particulars which cannot be accounted for by mere reduction to properties. The counter step is then taken up by the proponent of bundle theory; usually in an attempt to show that ‘Aha! You failed to consider this particular redefinition, which deftly avoids your objections like so-and-so.’

This makes the dance intricately interesting but unfortunately also renders a definitive analysis nearly impossible.

James Van CleveSophisticated defenders of the bundle theory do not say that a thing is nothing but a bundle of properties; they say that it is a bundle whose elements all stand to one another in a certain very important relation. Let us call the relation co-instantiation (Van Cleve, p. 29).

The nature of this relation therefore takes centre stage in our considerations. The issue of defining bundle theory (and by extension its defensibility) is compounded by a further schism between realism and nominalism, which effects the applicability of certain objections. Loux, for instance, holds that the ‘Identity of Indiscernibles’ objection applies only to realist versions of bundle theory (p. 97). However, I am more interested in where the objections lead than in our starting point.

So returning to our important relation, it requires elaboration.

Michael J. Loux[…] however it is labelled, the relation is treated in the same way. It is taken to be an unanalyzable or ontologically primitive relation, but it is explained informally as the relation of occurring together, of being present together, or being located together; and it is always construed as a relation that attributes enter into only contingently (Loux, p. 91).

To make a recap of bundle theory then, it is the proposition that a concrete thing is wholly reducible to attributes and the contingent relation they share by mutual occurrence. In contrast substratum theorists agree with bundle theorists that a concrete particular is reducible to attributes and their mutual relation; they disagree about the ‘wholly’ part. Instead substratum theorists argue for the inclusion of a bare substratum, ‘that functions as the literal bearer or possessor of the attributes (Loux, p. 87).’ Allaire uses the example ‘this is red,’ which the substratum theorist would take as a subject-predicate proposition where ‘red’ refers to a universal property and ‘this’ is the literal exemplifier of that property (pp. 1-2).

This might seem a bit puzzling and an uncharitable reaction is to dismiss it as an example of what Whitehead called ‘the fallacy of misplaced concreteness (Irvine; Loux mentions ‘it is raining’ as an example of a doerless doing, p. 93, though without referring to Whitehead explicitly).’ However, we would then fail to take into account what I consider the true motives behind each opposing stance. The motives of substratum and bundle theorists alike seem to arise from a disconcert with the opposed position rather than merely the merits of their own. A short passage by Russell draws upon the worries of both parties.

Bertrand RussellThe continuity of a human body is a matter of appearance and behaviour, not of substance. The same thing applies to the mind. We think and feel and act, but there is not, in addition to thoughts and feelings and actions, a bare entity, the mind or the soul, which does or suffers these occurrences. The mental continuity of a person is a continuity of habit and memory; there was yesterday one person whose feelings I can remember, and that person I regard as myself of yesterday; but in fact, myself of yesterday was only certain mental occurrences which are now remembered, and are regarded as part of the person who now recollects them. All that constitutes a person is a series of experiences connected by memory and by certain similarities of the sort we call habit (pp. 42-43).

The crux of the matter is our intuitive conception of identity – in this case the temporal persistence of personal identity – which riles us ever more once we realise that some madman might include us among the concrete particulars to be dissected! And although the existence of bare particulars does not necessarily entail the existence of souls, it would be quite benighted to gloss over the similarities; one being that empiricists ought to find both equally problematic. On the other hand, whereas an ineffable anchor to some inaccessible reality is brutish, it is not desirable that the ship of Theseus dissolves into the ocean entirely – even if today it has a different mast than yesterday.

What we have just outlined is the temporal persistence objection to bundle theory, which features among five other objections in Van Cleve’s paper. However, Van Cleve readily abandons the first three at the advent of ‘co-instantiation (p. 29).’ The three objections left are: the temporal persistence, the essentiality, and the identity of indiscernibles objections.

I shall not devote much effort to temporal persistence. Firstly, as Loux points out, the objection does not arise for bundle theory alone, but is an instance of a more general principle (p. 93). Secondly, Casullo has, to my satisfaction, shown that by construing enduring things as a contingently related series of momentary things – a move available to both bundles and substrata – the objection is only a problem if bundle theory cannot account for momentary things (pp. 127-128).

The essentiality objection – if a thing were a complex of properties, those properties would be essential to it since it could not have different properties and retain its identity – is not dealt with by Casullo as much as accepted as not really a problem. Casullo maintains that the essentiality of properties is only true of momentary things and not enduring things, since the latter are a series of the former (p. 129).

One might wonder if this is not merely a one-step regression. I.e. if an enduring thing were a series of momentary things, would it not be the case that those momentary things were essential to the series? Casullo wants to deny this but it is unclear to me how he can, given the fact that he accepted the argument one step down, avoiding it only by moving up. I see only one way out of an infinite regress; instead of identifying the series primarily with its members and secondarily with the relation we must do the opposite. What gives Series A its individuated identity is not its constituent momentary members but its relational structure of an unbroken causal chain.

The upshot is that if we want to avoid a commitment to temporal instances – as a series of momentary things would demand – we could simply move back down and solve temporal persistence in the same way; albeit at the cost of having to reconsider most of our nouns as verbs. We could always rename it bundling theory if it is too far from its parent.

Last we come to the identity of indiscernibles objection, generally considered the strongest. The Stanford Encyclopedia’s definition is:

Peter ForrestThe Identity of Indiscernibles (hereafter called the Principle) is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

F(FxFy) → x=y.


The objection goes that bundle theory demands the necessary truth of the Principle (PII) since two concrete particulars cannot possibly share all their properties without thereby being the same particular. However, PII is not a necessary truth because we can conceive of two numerically distinct particulars who do share all their properties.

There are many ways in which a bundle theorist might want to respond – some bad (as held by ‘A’ in Zimmerman’s imagined dialogue), some better (as held by Casullo). However, for the sake of brevity I shall not dwell on them. Rather I shall argue that the identity of indescernibles is equally a problem for the substratum theorist.

If we compare PII as expressed by Forrest in the Stanford to its Loux counterpart, it becomes immediately clear that something is amiss. Loux states the Principle as follows:

Necessarily, for any concrete objects, a and b, if for any attribute, Ø, Ø is an attribute of a if and only if Ø is an attribute of b, than a is numerically identical with b (p. 97).

Why have Forrest’s objects x and y been narrowed down from any objects to only concrete objects? Luckily Loux presents us with a retraceable line of argument.

(i)                  Necessarily, for any concrete entity, a, if for any entity, b, b is a constituent of a, then b is an attribute.

(ii)                Necessarily, for any complex objects, a and b, if for any entity, c, c is a constituent of a if and only if c is a constituent of b, then a is numerically identical with b (p. 98).

For convenience I have altered Loux’ (BT) for ‘bundle theory’ and (PCI) for ‘Principle of Constituent Identity’ to (i) and (ii) respectively. Now, (i) seems fine although Casullo suggests changing the necessity to a contingency (p. 131), which would render appeals to conceivable possibilities moot. Yet if we grant (i) and (ii), we should also grant Loux’ version of PII. However, my issue is with (ii). The specification of ‘complex objects’ effectively shields bare substrata from the onslaught of PCI but this begs the question against the bundle theorist. Bare substrata have neither attributes nor constituents so what accounts for their individuated identity? Both the original PII and (ii) – barring arbitrary exclusions – can be applied to bare substrata.

For any bare substrata, a and b, if for any entity, c, c is a constituent/attribute of a if and only if c is a constituent/attribute of b, then a is identical with b.

This holds true since for any given constituent or attribute any substratum will, in and of itself, only possess it if and only if all other substrata also possess it – i.e. no substrata will possess any whatsoever. This means there can be only one substratum. If all substrata are identical, in and of themselves, then Loux’ version of the PII applies equally to concrete objects of substratum theory.

My suggested solution is the same as the one I gave to the temporal persistence and essentiality objections:

A thing is a causal relation of a complex of properties.

I can imagine this would seem completely counter-intuitive to some. However, we are already familiar with at least some things, which we would describe like this. For instance vortices are not constituted by any specific constituents. Nevertheless we should not hesitate to speak of that particular vortex every time we saw it; even if it were to contain none of the same water molecules as last.

VortexThe way in which this solves the PII objection is that if we have a specific complex of constituents, there is no contradiction in imagining those constituents performing the qualitatively the same relational event today as yesterday. Neither is it contradictory to suppose that a specific complex of constituents could perform the same relational event twice simultaneously, though it does tax us with a higher level of abstraction. However, it should be noted that the phrase ‘the same relational event’ is misleading in the context of simultaneity, since unless there is a continuous causal connection between instantiations, they give rise to individuated concrete particulars – i.e. twin synchronised vortices.

If doing away with momentary particulars is cause for worry, they can always be reintroduced by a one-step regression as considered in the essentiality objection. I readily grant that a substratum theorist could easily adopt my solution. However, I see no reason to disturb parsimony by an unnecessary multiplicity of entities.

I have argued that the defensibility of bundle theory depends upon the definition and considered three objections; temporal persistence, essentiality, and identity of indiscernibles. The first two were answered by a definition stressing the relation over the complex. I argued the third is equally a problem for substratum, suggesting the previous definition as solution usable by both theories, ultimately favouring bundle as more parsimonious.





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One Response to “Bundled Vortices: Relation over Constituents”

  1. What a data of un-ambiguity and preserveness of precious knowledge
    about unpredicted feelings.

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