Yet another bundle theory of objects

I will offer a bundle theory with one primitive symmetric relationship. Moreover, the primitive relationship is essential to pairs. I don’t like bundle theories, but this one seems to offer a nice and elegant solution to the bundling problem.

Here goes. The fundamental entities are tropes. The primitive symmetric relationship is partnership. As stated above, this is essential to pairs: if x and y are partners in one world, they are partners in all worlds in which both exist. If x and y are tropes that exist and are partners, then we say they are coinstantiated.

Say that two possible tropes, existing in worlds w₁ and w₂ respectively, are immediate partners provided that there is a possible world where they both exist and are partners. Then derivative partnerhood is defined to be the transitive closure of immediate partnerhood.

The bundles in any fixed world are in one-to-one correspondence with the maximal non-empty pluralities of pairwise-partnered tropes, and each bundle is said to have each of the tropes that makes up the corresponding plurality. We have an account of transworld identity: a bundle in w₁ is transworld identical with a bundle in w₂ just in case some trope in the first bundle is a derivative partner of some trope in the second bundle. (This is a four-dimensionalist version. If we want a three dimensionalist one, then replace worlds throughout with world-time pairs instead.) So we have predication (or as good as a trope theorist is going to have) and identity. That seems enough for a reductive story about objects.

We can even have ersatz objects if we have the ability to form large transworld sets of possible tropes: just let an ersatz object be a maximal set of pairwise derivately partnered tropes. An ersatz object then is said to ersatz-exist at a world w iff some trope that is a member of the ersatz object exists at w. We can then count objects by counting the ersatz objects.

This story is compatible with all our standard modal intuitions without any counterpart theoretic cheats.

Of course, the partnership relationship is mysterious. But it is essential to pairs, so at least it doesn’t introduce any contingent brute facts. And every story in the neighborhood has something mysterious about it.

There are two very serious problems, however:

1. On this story we don’t really exist. All that really exist are the tropes.

2. This story is incompatible with transsubstantiation—as we would expect of a story on which there is no substance.

So what’s the point of this post? Well, I think it is nice to develop a really good version of an opposing theory, so as to be able to focus one’s critique on what really matters.

From bundles to bare particulars and back again

Here's a compelling narrative. Start with the bundle theory of substance: substances are nothing but bundles of properties. Then observe that this suffers from serious problems. If a substance is nothing but a bundle of properties, it is unclear how a substance could have had other properties than it does. Further, intuitively it should be possible to have two indiscernible substances--ones with all the same properties. This motivates a move to bare particular theory. According to bundle theory, substances were constituted by one kind of thing: properties. Bare particular theory makes substances be constituted by both properties and a special entity, the bare particular. Introducing the bare particular solves the modal problem, since we can say that the identity of substances is grounded in the identity of the bare particulars, so you can have a substance in one world with different properties than the very same substance in another world, as long as the same bare particular is found in both. Further, there is no difficulty with indiscernibles, as long as you have two bare particulars.

Note that this narrative isn't quite the standard narrative about bare particulars. The standard narrative introduces bare particulars to solve the problem of predication, by making the bare particular be the subject of predication. That standard narrative, however, falls prey to a problem that Andrew Bailey points out: we don't want to say that the bare particular has the ordinary properties of the host substance (for then we get reduplication), but if it does not, then it's not the subject of predication.

So let's stick to my from-bundles-to-bare-particulars narrative. But at this point there is a really interesting move possible, one that was pointed out in my undergraduate metaphysics class by a brilliant freshman, Rose Brugger. According to bare particular theory, substances are constituted by two kinds of things: properties and a bare particular. But Brugger suggested that we take the bare particular to just be an individuating property. Namely, a haecceity.

The result is a really interesting theory. It is a kind of bundle theory. However, first, the motivations for bare particular theory continue to be satisfied: we can ground identity between substances in identity of the haecceity. Second, we solve the puzzle of the mysterious "bareness" of the bare particular: the haecceity isn't some weird propertyless individual, but just a property, albeit a special one. Third, the resulting theory is more parsimonious, because it posits one fewer fundamental category: all it needs are substances and their constituent properties, without a separate category of bare particulars.

The resulting theory is superior to both standard bundle theory and standard bare particular theory, being only slightly more complex than standard bundle theory but solving a number of problems.

Coinstantiation

One of the fundamental concepts of bundle theory is a coinstantiation relation between properties. Interestingly, it may be possible to reduce coinstantiation to instantiation and entailment. Specifically, a bundle theorist may say that the Ps (some plurality of properties) are coinstantiated if and only if there is a property Q such that (a) Q entails each of the Ps and (b) Q is instantiated.

Pluralist theories of predication

According to anti-pluralist theories of predication, there is only a small handful of fundamental predicates and they are all of a highly general and abstract nature.  Sometimes there is only one.  For instance, strong Platonism has as fundamental only the multigrade predicate Instantiates.  All other predications should be analyzed in terms of it.  Resemblance nominalism has the fundamental predicate ResemblesInRespect and then needs some story about respects (which story may involve one or two more fundamental predicate).  Bundle theory will have the fundamental predicate CobundledWith, plus perhaps the predicates of set theory (∈ and IsASet) or of some other highly general theory for constructing objects out of bundles.

According to pluralist theories of predication, there are many fundamental predicates and many of them are of a very concrete nature.  For instance, the pluralist is likely to have predicates like Horse, Daphnia and NegativelyCharged.  She may also have highly abstract predicates like ∈ as well.

Ostrich nominalists are pluralists.  But one can also be a weak Platonist and a pluralist.  I am inclined to think that the solution to the problem of the unity of form and matter given in Metaphysics H.6 commits Aristotle to pluralism.

The big insight of the pluralist is that the puzzle of predication is no less of a puzzle when that puzzle concerns a small handful of fundamental predicates.  There may be theoretical simplicity grounds to prefer particular anti-pluralist theories of predication over particular pluralist theories, but I suspect these will result in a stalemate.  And then the pluralist will win, as her fundamental predicates fit better with our intuitions, I think.

A regress for bundle theory

According to bundle theory, each individual is a bundle of properties. But what is an individual? Presumably, individuals are existing entities that we can individuate, quantify over and predicate things of. Take that as a sufficient condition for being an individual. But then a property is also an individual. (If one balks at this, I expect that it is simply because one has stipulated this fact away, say by defining individuals as existing entities that we can individuate, quantify over and predicate things of which are not properties. If so, then the class of "individuals" is gerrymandered. But we needn't worry about words. Call something that we can individuate, quantify over and predicate things of an "individual*", and construe what I say below as about individuals*.)

But now the regress is obvious. Socrates, let us say, is a bundle of humanity, maleness, snubnosedness, smartness, hellenicity, etc. Fine. But humanity is also an individual. So, humanity is itself a bundle of properties. What properties? I don't know. Maybe properties like propertyhood, unchangingness, animal-kind-hood, rational-being-kind-hood, etc. Already it gets weird—we have no idea what to say. And then the problem returns for the properties that humanity is a bundle of. What, say, is propertyhood a bundle of? What is animal-kind-hood a bundle of? Obviously, a regress ensues. Is it vicious? I suspect so. We have bundles of bundles of bundles of .... If the bundling is done set-wise, then the sets will violate regularity.

And in any case if the individuation of bundles is by their members, that never bottoms out. On an abundant theory of properties, our non-property individuals all look like {{{...},{...},{...},...},{...},{...}},{...},...}, with exactly the same structure of braces. (That's for the set-theoretic construction. Otherwise, replace the braces by whatever bundling method we have.) On a sparse theory of properties, if it turns out that non-property individuals have finitely many properties, and that properties all have finitely many properties, maybe then we can differentiate these things by the structure of the rooted property-tree (individual x has 7 properties at the first level, the first of which branches has 19 properties, etc.) But that's as crazy as Pythagoreanism.

So maybe the bundle theorist will limit her theory of predication to individuals that are not themselves properties. But if she does that, she still needs a story about how we manage to predicate things of properties. For we do. Humanity is a universal. It is unchanging. It is non-spatio-temporal. It is different from hellenicity. And so on. And whatever non-bundle theory of predication that we give for the properties of properties, the opponent of bundle theory will say: Why not just simplify and give that for the individuals that are not properties?

Or one might take first-order properties to be bundles of individuals. But that's terrible. First, they'd have to be bundles of possible individuals. Second, we now have circularity in place of regress, which is worse.

This arguments seems to force the bundle theorist to say that eventually we get to properties that have no properties (what about their abstractness? their propertyhood? maybe we say that these are not genuine properties--maybe abstractness is just the denial of concreteness). Todd Buras then points out to me that these properties with no properties are just like the bare particulars avoiding which was one of the main motives for bundle theory!

Note: The argument works equally well if we have bundles of tropes instead of bundles of universals.

I know that these issues have been worked over, and regress-finding is a fun game for the philosophical family, so this regress is quite likely known. (If you have a reference, please let me know.)