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Consequences of Collapse

Composition as identity is the strange and strangely compelling doctrine that the whole is in some sense identical to its parts. According to the most interesting and fun version, the one inspired1 by Donald Baxter, this is meant in the most straightforward way: a single whole is genuinely identical to its many parts taken together—identical in the very same sense of ‘identical’, familiar to philosophers, logicians, and mathematicians, in which I am identical to myself and 2+ 2 is identical to 4. Composition as identity implies the principle of Collapse: something is one of the X s iff it is part of the fusion of the X s. (Collapse is so-called because it in effect identi es mereologically equivalent pluralities.) In an earlier paper I pointed out that Collapse alters Boolos’s logic of plural quanti cation in various ways.2 Here I point out some further consequences of Collapse. For example, collapse implies that plural de nite descriptions do not function normally. (As we will see, this undermines Kris McDaniel’s (2008) recent argument against composition as identity.) Also it opens the door to drastic—though arguably unattractive—ideological simpli cations: parthood, identity, and the plural quanti ers may all be eliminated.