We tell a story where an agent who chooses in such a way as to make the greatest possible profit on each of an infinite series of transactions ends up worse off than an agent who chooses in such a way as to make the least possible profit on each transaction. That is, contrary to what one might suppose, it is not necessarily rational always to choose the option that yields the greatest possible profit on each transaction.

In the paper below the authors describe three super-tasks. They show that although the abstract notion of a super-task may be, as Benacerraf suggested, a conceptual mismatch, the completion of the three super-tasks involved can be defined rather naturally, without leading to inconsistency, by means of a particular kinematical interpretation combined with a principle of continuity.

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_Paradoxes from A to Z, Third edition_ is the essential guide to paradoxes, and takes the reader on a lively tour of puzzles that have taxed thinkers from Zeno to Galileo, and Lewis Carroll to Bertrand Russell. Michael Clark uncovers an array of conundrums, such as Achilles and the Tortoise, Theseus’ Ship, and the Prisoner’s Dilemma, taking in subjects as diverse as knowledge, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at likely (...) solutions. This third edition is revised throughout, and adds nine new paradoxes that have important bearings in areas such as law, logic, ethics and probability. Paradoxes from A to Z, Third edition is an ideal starting point for those interested not just in philosophical puzzles and conundrums, but anyone seeking to hone their thinking skills. (shrink)