Mereological nihilism denies that any composite objects exist. There are only fundamental simples; everything we ordinarily call a 'composite object' is really just a scattered collection of atoms with no genuine unity. This radical view challenges our ordinary understanding of objects like tables and people.
From your study of mereology, you know that mereological composition is the process by which parts combine to form a whole. Different theories give different answers to the Special Composition Question: under what conditions do some objects compose something? Unrestricted mereology says composition always occurs — any collection of objects, however scattered or unrelated, composes a whole. Restricted mereology tries to identify principled conditions. Mereological nihilism takes the most radical restricted position: composition *never* occurs. There are no composite objects at all — only simples, the fundamental particles that have no parts.
On the nihilist view, when you look at what you ordinarily call a table, there is no table there. There are atoms (or quarks, or whatever the fundamental physical simples are) arranged in a table-like configuration — what philosophers call being arranged tablewise — but no further object that is *the table* over and above those particles. The table-talk is a useful fiction or a convenient shorthand, but the ontological inventory of the universe contains only simples. Similarly, when you seem to see yourself in the mirror, there is no "you" as a composite object — there are particles arranged human-wise, but no further entity that is you.
This might seem like an obviously absurd view, but it has genuine philosophical motivations. One is ontological parsimony: if you admit that tables exist in addition to the atoms, you face a combinatorial explosion of objects — every arbitrary collection of simples composes something, generating an enormous number of entities most of which have no naturalness or causal relevance. Nihilism avoids this by simply denying all composite objects. A second motivation comes from puzzles about material constitution. The Ship of Theseus problem — is the ship rebuilt plank-by-plank the same ship? — arises only if we assume there is a ship-object in addition to the planks. If there is no ship, only planks-arranged-shipwise, the puzzle loses its grip. Similar dissolving moves work on puzzles about fission, statue-and-lump coincidence, and sortal-relative identity.
The deepest challenge for mereological nihilism is explaining ordinary discourse. We all talk about tables, persons, and planets as if they were real. The nihilist owes an account of how this is possible if those things don't exist. The standard response is paraphrase: every apparent reference to a composite object can be paraphrased into quantification over simples arranged appropriately. "The table is brown" becomes "There are simples arranged tablewise, and they are brown" (or collectively appear brown under observation). Whether all ordinary object-talk can be successfully paraphrased this way without loss of meaning is a sustained research program, and many philosophers think the paraphrase strategy fails for persons — it is especially counterintuitive to deny that you exist as a composite object, since your mental states seem to be properties of a unified subject, not of scattered particles.
The view most famously associated with Peter van Inwagen comes close to nihilism but makes an exception: van Inwagen's position is that composite objects exist *only* when their parts are caught up in the right kind of life (biological organisms). This saves persons from dissolution but gives up strict nihilism for a hybrid view. Pure mereological nihilism avoids this uneasy compromise by being consistent — nothing composes anything — but pays the price of committing to the non-existence of literally everything you are looking at right now.
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