A number of philosophers have argued that objects that have parts do not exist. The basis of their argument consists in claiming that our senses give us only foggy information about reality and thus they cannot be trusted; and for example, we fail to see the smallest building blocks that make up anything (and that's a pretty important aspect of reality to not have any perception of), and these smallest building blocks are individual and separate items that do not ever unify or come together into being non-individual. Thus they never compose anything. So, according to the concept of mereological nihilism, if the building blocks of reality never compose any whole items, then all of reality does not involve any whole items, even though we may think it does.
“Mereology (from the Greek μερος, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole. Its roots can be traced back to the early days of philosophy, beginning with the Presocratic atomists and continuing throughout the writings of Plato (especially the Parmenides and the Thaetetus), Aristotle (especially the Metaphysics, but also the Physics, the Topics, and De partibus animalium), and Boethius (especially In Ciceronis Topica).” (This citation is from the very beginning of his internet entry )
As can be seen from Varzi’s passage, classical mereology depends on the idea that there are metaphysical relations that connect part(s) to whole. Mereological nihilists maintain that such relations between part and whole do not exist, since wholes themselves do not exist.
Nihilists typically claim that our senses give us the (false) impression that there are composite material objects, and then attempt to explain why nonetheless our thought and talk about such objects is 'close enough' to the truth to be innocuous and reasonable in most conversational contexts.
Even though there are no tables or chairs, thinks van Inwagen, it is still permissible to assert sentences such as 'there are tables'. This is because such a sentence can be paraphrased as 'there are simples arranged tablewise'; it is appropriate to assert it when there are simples arranged a certain way. It is a common mistake to hold that van Inwagen's view is that tables are identical to atoms arranged tablewise. This is not his view: van Inwagen would reject the claim that tables are identical to atoms arranged tablewise because he rejects the claim that composition is identity, and because he does not admit the existence of atoms, which would have proper parts if they did exist--only living organisms and simples, such as electrons. Nonetheless, he maintains that an ordinary speaker who asserts, for instance, "There are four chairs in that room" will speak truly if there are, indeed, simples in the room arranged in the appropriate way (so as to make up, in the ordinary view, four chairs). He claims that the statement and its paraphrase "describe the same fact". (For details, see his book "Material Beings".)
One philosopher who has contended in favor of something close to pure mereological nihilism is Peter Unger, in his papers "There Are No Ordinary Things," and "I Do Not Exist."