If somebody is a mereological nihilist they do not believe in ‘composite objects’ as things which really exist – they would say that the designations of ‘tables’ and ‘chairs’, ‘mountains’ and ‘bears’ are all simply conventional names for particular organizations of matter. This is called nominalism. However, presumably the nominalist believes, at least if she is anything like a materialist, that all objects to which we can ostensibly refer are composite objects. Composed of what? The corpuscularian doctrine of the early Empiricists answered by postulating a corpuscle, which was actually a physical atom. Here, it has to be understood that “physical-atom” is a philosophical term, and doesn’t refer to what physicists today call an ‘atom’. The word means indivisible, thus the concept is one of an indivisible smallest constituent particle of matter.
However, Leibniz famously offered a modal argument against the possibility of a physical atom, since any object extended in space must be in principle divisible (it must be logically possible, even if not physically possible, to divide such an object). Therefore (assuming we accept his argument), since there is no unit of matter smaller than which no unit of matter can be, how can there be any material composites? Any composite object must be ‘composed’, but composed of what? – If there are not true ‘atoms’, then there is simply an infinite regress of smaller composite parts. If, however, there must be some ‘basic units’, then it seems they cannot be physical – thus it seems the only logically possible option is that they be ‘substances’, or immaterial atoms.
In order to avoid calling composite objects subjects/substances (properly related to predicates), the nominalist must be a mereological nihilist, and they must hide behind a sort of physicalism or materialism which takes for granted that there are ‘atoms’. However, since physical atoms are not logically possible, something must be wrong with mereological nihilism. Nominalism, therefore, is metaphysically absurd precisely because it is stuck with an infinite regress of composite parts for any composite object. This is a good argument to think that something is wrong with nominalism in general. However, the Naturalist seems to have no option other than some kind of nominalism; therefore, naturalism is not true. A possible escape from this would be an idealist metaphysic, which I note many intelligent Naturalists already adopt. Therefore my argument probably only works to defeat materialism.
Notice that this charge I am throwing against Naturalism circumvents any discussion about bundle-theory; instead my concern is not with language and predication, but metaphysics.