Consequences of collapse

In Donald Baxter & Aaron Cotnoir (eds.), Composition as Identity. Oxford University Press (forthcoming)
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 inspired by Donald Baxter (1988a,b), this is meant in the most straightforward way: a single whole is genuinely identical to its many parts, in the very same sense of identity, 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 identifies mereologically equivalent pluralities.) In an earlier paper I pointed out that Collapse alters Boolos’s logic of plural quantification in various ways.1 Here I point out some further consequences of Collapse. For example, collapse implies that plural definite 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—albeit unattractive— ideological simplifications: parthood, identity, and the plural quantifiers may all be eliminated.
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