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.)