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.

"Using as"

I can use a fork as a backscratcher or my thumb and forefinger as the prongs of a slingshot.

I claim that when I do so, there isn't a backscratcher or a set of prongs that comes into existence when I do so.

For consider the three possibilities on which it is correct to say that prongs come into existence:

1. The thumb and forefinger cease to exist and prongs come into existence, made out of the former digits.
2. A set of prongs comes into existence in exactly the space occupied by the thumb and forefinger, and are made out of the same matter as the prongs.
3. The thumb and forefinger are both a thumb and forefinger and a pair of prongs after the transformation.

The first option is obviously false.  I didn't temporarily come to have only eight fingers when I did it for the purposes of the photo.

The second option doesn't match the how we talk.  I would say: "I used my fingers as the prongs of a slingshot."  But according to (2), I had the prongs of a slingshot right there in the very same region of space occupied by my fingers--why didn't I use them as the prongs of a slingshot, since they are surely at least as usable for that purpose.  Or did I use both my digits and the prongs as prongs?  But I need only two things for slingshot prongs, not four.

Moreover, as I am typing with both hands, surely the prongs no longer exist.  When did they cease to exist?  Right after the shot?  But when I took the picture, I didn't actually take a shot--I only used my fingers as prongs for show.  (I did take a shot on other occasions, shooting a little fuzzy ball from the kids' craft drawer.)  When I relaxed the fingers?  But why not, instead, think of the relaxed fingers as folded prongs?  A slingshot could, after all, fold.  It's not like I destroyed the prongs when I relaxed my fingers--they're ready for convenient use at any other time.  Yet if they do continue to exist, do I have forty-four other pairs of prongs on my hands (granted, 25 of the pairs--the ones with one finger from one hand and the other from the other--can only be used by having a friend pull back the pocket or by pulling the pocket back with the teeth) if I form the odd ambition to use a different pair every day for the next forty-four days?  And if the prongs ceased to exist, will the very same pair of prongs be resurrected the next time I use my thumb and forefinger as prongs?  These questions seem silly, and their silliness suggests that they are predicated on a mistake.

The third option fits better with our "use as" talk.  I used my fingers as prongs, and I used the prongs as prongs, but there aren't four things there, because the fingers were prongs.  But we get the wrong modal properties.  For suppose that I decided to reinforce the prongs by supergluing steel rods to them.  The steel rods would come to be a part of the prongs, but they wouldn't come to be a part of the fingers.  Hence the fingers are not identical with the prongs, by Leibniz's Law.  

All this fits with common sense.  I used fingers as slingshot prongs or a fork as a backscratcher, and there were no slingshot prongs or a backscratcher there.

But can this line be maintained?  Suppose I cease to use the fork as a fork, and start to use it exclusively as a backscratcher.  Suppose in our culture, everybody owns a backscratcher, as our greeting ritual is a light scratching of each other's backs.  And backscratchers look just like American forks.  Surely what I would have would be a backscratcher.  Yet, surely, whether a backscratcher comes into existence shouldn't depend on how permanently it is used as such.  Still, that seems to be how we talk.  If all we are doing is descriptive metaphysics, we may stop here.

But if we want to do more gutsy metaphysics, we might at this point question the initial intuition that I had a fork there.  Perhaps the fundamental concepts are not of backscratchers or slingshots (or prongs thereof) or even forks, but of using some thing or things (particles, say) as backscratcher, slingshot (or prongs thereof) or fork. To use as a backscratcher is like to dance a waltz--if we want to do serious metaphysics, we shouldn't ask where the token backscratcher is in the using or where the token waltz is in the dancing.

Rob Koons has defended the idea that artifacts are token social practices. What I am saying is quite similar, except that I do not want to identify the artifacts with social practices. But all the reality there is in artifacts is the reality of things used as, or meant to or designed to be used as something or other.

Privileging objects

Consider this criticism of traditional metaphysics: Traditional metaphysics privileges objects. A natural (though really not all that common) move for philosophers of a certain stripe is to move from a focus on objects to a focus on relationships between objects and to capture this by means of Category Theory. But Category Theory privileges relationships between pairs of objects, and that's at least as bad as privileging single objects.