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We define two ‘problems of altruism’. The first is the classic problem of altruism, defined as the issue of how a behavior which decreases an individual’s lifetime reproductive success, while helping another individual (or individuals) increase their lifetime reproductive success, can evolve. We also define a ‘second-order problem of altruism’, where different authors have different conceptions of what does, and does not, constitute ‘altruism’, including approaches based on kin selection, multi-level selection theory, short-term altruism and psychological altruism.