Abstract
In this article, we present a new conception of internal relations between quantity
tropes falling under determinates and determinables. We begin by providing a novel
characterization of the necessary relations between these tropes as basic internal
relations. The core ideas here are that the existence of the relata is sufficient for their
being internally related, and that their being related does not require the existence of
any specific entities distinct from the relata. We argue that quantity tropes are, as
determinate particular natures, internally related by certain relations of proportion and
order. By being determined by the nature of tropes, the relations of proportion and
order remain invariant in conventional choice of unit for any quantity and give rise to
natural divisions among tropes. As a consequence, tropes fall under distinct
determinables and determinates. Our conception provides an accurate account of
quantitative distances between tropes but avoids commitment to determinable
universals. In this important respect, it compares favorably with the standard
conception taking exact similarity and quantitative distances as primitive internal
relations. Moreover, we argue for the superiority of our approach in comparison with
two additional recent accounts of the similarity of quantity tropes.