Abstract: Beginning from the assumption that quantities are (rich) relational structures, I ask, what kind of ontology arises from attributing this sort of structure to physical attributes. There are three natural questions to ask about relational structures: What are the relations, what are the relata, and what is the relationship between relata and relations? I argue that for quantities, the choicepoints available in response to these questions are:
1) intrinsicalism vs. structuralism
2) substantivialism vs. anti-substantivalism
3) absolutism vs. comparativism
In the remainder of the talk I sketch, which of these choices make for coherent candidate ontologies for quantities.