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In recent years, a scholarly community has coalesced around questions of fairness, accountability, and transparency (FAT) in algorithmic systems. This community originates in computer science and statistics, but has been enrolling participants from other disciplines including law, policy, philosophy, and the social sciences. While ostensibly united by a shared set of concerns, the key terms of FAT have been difficult to grapple with, particularly in the absence of an agreed upon scope for the community's work. This paper argues that central to this missing basis for agreement is a rift that has developed between those who seek technological repairs to the problem of 'unfair algorithms' and those who understand these problems to be rooted in the technosocial nature of algorithmic systems themselves. This has led to the development of multiple, separate assumptions about FAT, which may undermine the viability of any unified community dedicated to such concerns. This paper surveys the discursive space of FAT by mapping out the ways in which fairness, accountability, and transparency are understood and elaborated by various groups within the community, as well as what the status of "the algorithm" is across these various understandings. The paper discusses how differently-positioned actors understand the goals and scope of the FAT project, what pragmatic, and political, and institutional challenges may limit the interventions that are possible for this project to make, and how the project can be understood in the context of developing understandings of fairness, accountability, and transparency in society.