The subject of this thesis is the problem of the many - a problem which presents the challenge of there being many objects in situations in which we putatively take there to be one. The problem demands attention since it is paradoxical, ubiquitous in its extent, prompts a revision of the concepts it invokes (identity, distinctness, vagueness, and indeterminacy) , and promises a revelation of the relation between it and other philosophical problems. Chapters 2-3 establish what the problem of the many is and establishes its relationship to other problems and paradoxes. Chapters 3-9 consider the most standard responses to the problem and chapter 10 presents a new response called role theory. There are three main original contributions: 1. The introduction of a new delegic and aoristic modality which models theoretical commitment and indeterminacy (respect.). It is claimed that the modality is more appropriate to model indeterminacy than current methods of modeling indeterminacy which are based on alethic modality, such as those supplied by the supervaluationist and the ontic indeterminist. 2. The introduction of a new theory called role theory which is an axiomatic ontology that quantifies over roles and the objects that fill them. The theory is defended against presented responses to the problem of the many. 3. The demonstration of a significant difference between the sorites paradox and the problem of the many. This is achieved by contrasting the necessary conditions for the problems and by diagnosing the former as an instance of underdeterminacy and the latter as an instance of overdeterminacy. The difference gives us cause to revise the putative suitability of theories of vagueness as responses to the problem of the many especially due to a demonstrated inability of the theories to cope with situations in which there are instances of both problems.