Parts and plurals
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This dissertation consists of four independent papers on the foundations of mereology and the logic of plural expressions. The first chapter shows that the standard formal definition of atomicity–the thesis that everything is ultimately composed of atoms–fails to exclude nonatomistic models and is therefore inadequate. It then formulates a new definition of atomicity in a plural logic framework. The second chapter argues that the bundle theory of objects is consistent with the principle of the identity of indiscernibles when the relation between properties and objects is interpreted as parthood. The third chapter develops a semantics and axiom system for a logic of compound terms. This logic extends the expressive and inferential power of standard first-order logics that leave compound terms unanalyzed or, worse, misrepresent their logical properties entirely. The final chapter argues against the ontological innocence of plural reference. It appeals to formal, epistemological, and metaphysical principles endorsed by a variety of philosophers to show that ‘some things exist’ does not entail ‘something exists.’ If this is correct, then plural quantification works very differently than most philosophers think.