Decomposition

This chapter carefully attends to how decomposition principles are supposed to work, and how different variants and formulations affect the resulting theory in different ways. It begins with the philosophically familiar notion of Boolean complementation, and then gradually discusses ever weaker variants of this notion in the form of various supplementation principles. The chapter evaluates which of these principles are linked to extensionality and which (if any) are constitutive of the minimal concept of parthood. Other decomposition questions include: Can we continually decompose objects into smaller and smaller parts (gunk)? Must there be smallest parts (atoms)? Is there a mereological correlate to the empty set, namely the ‘null object’? Each of these questions is explored in full formal detail, including a characterization of the maximally consistent extensions of classical mereology.