The resolution of anaphora is dependent on a number of factors discussed in the literature: syntactic parallelism, topicality, etc. A system that attempts to resolve anaphora will have to represent many of these factors, and deal with their interaction. In addition, there must be a principle that simply says that the system needs to look for an antecedent. Without such a principle, if none of the factors recommend a clear winner, the system will be left without an antecedent. This principle should work in such a way that, if there is exactly one good candidate antecedent, the system will choose it; if there are more than one, the system will still attempt to identify one, or, at least, draw some inferences about the likely antecedent; and, in case there is no candidate, the system will produce an accommodated or deictic reading. Many systems embody some version of this principle procedurally, as part of the workings of their algorithm. However, because it is not explicitly formalized, it is hard to draw firm conclusions about what the system would do in any given case. In this paper I define a general principle of Equality by Default, formalize it in Default Logic, and demonstrate that it produces the desired behavior. Since all other factors can also be formalized in Default Logic, the principle does not need to be left implicit in the algorithm, and can be integrated seamlessly into the rest of the explicit rules affecting anaphora resolution.