Homogeneity and identity: A solution to the problem of minimal parts

Abstract

Plural and non-count nouns have been characterized as having homogeneous reference, the combination of the second-order properties of cumulative and divisive reference. Homogeneous reference is a useful property that captures similarities in the behavior of count plural and non-countable nouns. However, formal semantic definitions of divisive reference—the property that any part of what a noun refers to can also be referred to with that noun—run into the Problem of Minimal Parts. While both a portion of water and another portion of water that it is a part of can be referred to with the noun phrase water, both have parts such as hydrogen and oxygen atoms that are not water. This paper introduces a new formulation of homogeneous reference that avoids the Problem of Minimal Parts by making reference to the sum operation, rather than parthood relations.