Logic

This chapter considers whether mereology should rightly be thought of as a first-order theory with parthood as a binary predicate. It considers extensions of classical mereology aimed at overcoming the expressive limits of standard first-order languages, focusing on second-order and plural formulations. Relatedly, Lewis’s megethology and applications to the philosophy of mathematics are discussed. Then, several ways of modifying the framework to make room for mereological considerations involving time and modality are presented, such as the possibility that an object may have different parts at different times, or that it could have had different parts from the ones it actually has. Finally, a number of theories are expounded that can be developed in order to deal with the phenomenon of mereological indeterminacy, i.e., the fact that in some cases the very question of whether something is part of something else does not appear to have a definite answer.