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.