Mereology and constituent ontology

I’ve just realized that one can motivate belief in bare particulars as follows:

1. Constituent ontology of attribution: A thing has a quality if and only if that quality is a part of it.

2. Universalism: Every plurality has a fusion.

3. Weak supplementation: If x is a proper part of y, then y has a part that does not overlap x.

4. Anti-bundleism: A substance (or at least a non-divine substance) is not the fusion of its qualities.

For, let S be a substance. If S has no qualities, it’s a bare particular, and the argument is done.

So, suppose S has qualities. By universalism, let Q be the fusion of the qualities that are parts of S. This is a part of S by uncontroversial mereology. By anti-bundleism, Q is a proper part of S. By weak supplementation, S has a part P that does not overlap Q. That part has no qualities as a part of it, since if it had any quality as a part of it, it would overlap Q. Hence, P is a bare particular. (And if we want a beefier bare particular, just form the fusion of all such Ps.)

It follows that every substance has a bare particular as a part.

[Bibliographic notes: Sider thinks that something like this argument means that the debate between constituent metaphysicians overlap bare particulars is merely verbal. Not all bare particularists find themselves motivated in this way (e.g., Smith denies 1).]

To me, universalism is the most clearly false claim. And someone who accepts constituent ontology of attribution can’t accept universalism: by universalism, there is fusion of Mt. Everest and my wedding ring, and given constituent ontology, the montaineity that is a part of Everest and the goldenness of my ring will both be qualities of EverestRing, so that EverestRing will be a golden mountain, which is absurd.

But universalism is not, I think, crucial to the argument. We use universalism only once in the argument, to generate the fusion of the qualities of S. But it seems plausible that even if universalism in general is false, there can be a substance S such that there is a fusion Q of its qualities. For instance, imagine a substance that has only one quality, or a substance that has a quality Q₁ such that all its other qualities are parts of Q₁. Applying the rest of the argument to that substance shows that it has a bare particular as a part of it. And if some substances have bare particular parts, plausibly so do all substances (or at least all non-divine substances, say).

If this is right, then we have an argument that:

5. You shouldn’t accept all of: constituent ontology, weak supplementation, anti-bundleism and anti-bare-particularism.

I am an anti-bundleist and an anti-bare-particularist, but constituent ontology seems to have some plausibility to me. So I want to deny weak supplementation. And indeed I think it is plausible to say that the case of a substance that has only one quality is a pretty good counterexample to weak supplementation: that one quality lacks even a weak supplement.