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Mereological nihilism (also called compositional nihilism, or rarely simply nihilism) is the mereological position that objects with proper parts do not exist. Only mereological simples, those basic building blocks without proper parts, exist. Or, more succinctly, "nothing is a proper part of anything." Mereological simples can be both spatial and temporal. Mereological nihilism also asserts that objects existing in time do not have any temporal parts.
The concepts of parts and wholes are used to describe common objects. For example, a ball is made up of two halves, so the ball is a whole that is made up of two parts. Every single object we experience in the world outside of us and around us is a whole that has parts, and we never experience an object that does not have parts. For example, a tail is a part of a lion, a cloud is a part of a greater weather system or, in visual terms, the sky, and a nucleobase is a part of a DNA strand. The only things we know of that do not have parts are the smallest items known to exist, such as leptons and quarks. These fundamental particles cannot be 'seen' and are not directly experienced. They may, however, be experienced indirectly through emergent properties. Thus all objects we directly experience have parts.
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. For example, we fail to see the smallest building blocks that make up anything. 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. According to the concept of mereological nihilism, if the building blocks of reality never compose any wholes, then no composite objects exist.
This seems to devolve into an error theory. If there are no composite objects, how can we make sense of our ordinary understanding of reality which accepts the existence of composite objects? Are we all deceived? Ted Sider (2013) has argued that we should think of composition as arrangement. According to Sider, when we say "there is a table", we mean there are mereological simples arranged table-wise.
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 Theaetetus), Aristotle (especially the Metaphysics, but also the Physics, the Topics, and De partibus animalium), and Boethius (especially In Ciceronis Topica).
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 only exist at the subatomic level.
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. Sider's linguistic revision that reformulates the existence of composite objects as merely the existence of arrangements of mereological simples is an example of this. Tallant (2013) has argued against this maneuver. Tallant has argued that mereological nihilism is committed to answering the following question: when is it that a group of mereological simples is arranged in a particular way? What relations must maintain among a group of mereological simples such that they are arranged table-wise? It seems the nihilist can determine when a group of objects compose another object: for them, never. But the nihilist, if he is committed to Sider's view, is committed to answering how mereological simples can be arranged in particular ways. No compelling answer has been provided in the literature. Mereological nihilism seems to pose the same amount of questions as it purports to answer. In fact, they are the very same questions re-formed in terms of arrangement.
The obvious objection that can be raised against nihilism is that it seems to posit far fewer objects than we typically think exist. The nihilist's ontology has been criticized for being too sparse as it only includes mereological simples and denies the existence of composite objects that we intuitively take to exist, like tables, planets, and animals. Another challenge that nihilists face arises when composition is examined in the context of contemporary physics. According to findings in quantum physics, there are multiple kinds of decomposition in different physical contexts. For example, there is no single decomposition of light; light can be said to be either composed of particles or waves depending on the context.  This empirical perspective poses a problem for nihilism because it does not look like material objects neatly decompose in the way nihilists imagine they do. In addition, some philosophers have speculated that there may not be a "bottom level" of reality. Atoms used to be understood as the most fundamental material objects, but were later discovered to be composed of subatomic particles and quarks. Perhaps what we take to be the most fundamental entities of current physics can actually be decomposed, and their parts can be further decomposed, on down the line. If matter is infinitely decomposable in this respect, then there are no mereological simples. This is a problem for nihilism because it then follows from their view that nothing exists, since they assert that only mereological simples exist. 
Partial vs. pure nihilism
Philosophers in favor of something close to pure mereological nihilism are Peter Unger, Cian Dorr, and Ross Cameron. There are a few philosophers who argue for what could be considered a partial nihilism, or what has been called quasi-nihilism, which is the position that only objects of a certain kind have parts. One such position is organicism: the view that living beings exist, but there are no other objects with parts, and all other objects that we believe to be composite—chairs, planets, etc.—therefore do not exist. Rather, other than living beings, which are composites (objects that have parts), there are only true atoms, or basic building blocks (which they call simples). The organicists include Trenton Merricks and Peter van Inwagen.
Van Inwagen's View
Peter Van Inwagen maintains that all material objects are mereological simples with the exception of biological life such that the only composite objects are living things. Van Inwagen’s view can be formulated like this: “Necessarily, for any non-overlapping xs, there is an object composed of the xs iff either (i) the activities of the xs contstitute a life or (ii) there is only one of the xs.” In other words, Van Inwagen contends that mereological atoms form a composite object when they engage in a sort special, complex activity which amounts to a life. 
One reason why Van Inwagen’s solution to the Special Composition Question is so attractive is that it allows us to account a conscious subject as a composite object. Nihilists have to maintain that the subject of a single consciousness is somehow the product of many discrete mereological atoms. Van Inwagen’s argument against nihilism can be characterized as such:
1. I exist
2. I am not a mereological simple
3. At least one object exists that is not a mereological simple
4. So, nihilism is false 
In addition to allowing for the existence of trees, cats, and human beings, Van Inwagen’s view is attractive because it inherits nihilism’s elegant solutions to traditional problems in mereology like the Ship of Theseus and the problem of the many.
One objection that can be offered against Van Inwagen’s view is the vagueness of the category of life and the ambiguity of when something gets “caught up” in a life. For example, if a cat takes a breath and inhales a carbon atom, it is unclear at what point that atom becomes officially incorporated into the cat’s body.
Even though there are no tables or chairs, van Inwagen thinks that 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 simples arranged tablewise. This is not his view: van Inwagen would reject the claim that tables are identical to simples arranged tablewise because he rejects the claim that composition is identity. 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". Van Inwagen suggests an analogy with the motion of the sun: an ordinary speaker who asserts that "the sun has moved behind the elms" will still speak truly, even though we accept the Copernican claim that this is not, strictly speaking, literally true. (For details, see his book "Material Beings".)
- Buddhist atomism
- Elementary particles
- Mereological essentialism
- Metaphysical nihilism
- Peter van Inwagen
- Trenton Merricks
- Sider, Theodore (2009), Nihilism and Ideology (PDF)
- Sider, Theodore (2013). Against Parthood. Oxford Studies in Metaphysics 8:237–293.
- Mereology, Stanford Encyclopedia of Philosophy
- Sider, Theodore (2013). Against Parthood. Oxford Studies in Metaphysics 8:237–293.
- Tallant, Jonathan (2013). Against mereological nihilism. Synthese 191 (7):1511-1527.
- Healy, Richard (2013). "Physical Composition". Studies in History and Philosophy of Modern Physics. 44: 48–62.
- Ney, Alyssa. Metaphysics: An Introduction. Routledge. pp. 111–112.
- Ned Markosian. Sider, Hawthorne, Zimmerman, ed. Contemporary Debates in Metaphysics. pp. 341–363.
- ney. Metaphysics: An Introduction. Routledge. ISBN 978-0415640756.
- Markosian. "Restricted Composition".