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This paper draws on the Supertask literature in order to better understand the conceptual and physical possibility of an infinite decision puzzle presented by Barrett and Arntzenius (1999, 2002). The first section presents the puzzle and two possible objections documented in the literature. The next section argues that cardinality and tracking considerations play a key role in understanding the puzzle. The paper concludes with a discussion about some implications for the decision theory.Barrett and Arntzenius (1999, 2002) proposed a puzzle where one-step rationality contradicts the global rationality. Cardinality and tractability considerations give a proper account of the puzzle.
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