I put to William the following question:
Are you prepared to assert the following? It is never the case that whenever there are some things, there is a whole with those things as parts. Equivalently: For any xs, if the xs are two or more, there is no y such that the xs compose y.
To which he replied: "Agreed, if you are using xs as a plural quantifier, and by implication y as a singular quantifier."
I think William was too hasty in agreeing since his agreement makes him a mereological nihilist, or nihilist for short. Nihilism is the logical contrary, not contradictory, of mereological universalism, or universalism for short. Universalism is what is expressed by Unrestricted Composition:
UC. Whenever there are some things, then there exists a fusion [sum] of those things. (David Lewis, Parts of Classes, Basil Blackwell 1991, p. 74)
Given Extensionality -- no two wholes have the same parts -- (UC) says that whenever there are some individuals, no matter what their character or category, there is a unique individual that they compose. This is their mereological sum. Universalism is hard to swallow. I do not balk at the sum of the books in my house. But I balk at the sum of : the books in my house, William's last heartbeat, Peter's left foot, and the planet Mercury. But if, recoiling from Universalism, one embraces Nihilism, then one is committed to the proposition that there are no composite objects, there are only simples. And surely William does not want to be committed to that.