Logical Impossibility: Infinity Machines & Super-Tasks1.On this reading, Zeno’s argument attempts to show that it is logically impossiblefor Rto reach G. That is, Zeno’s puzzle is not that the runner has to run too far, or that the runner has to run for too long a time, but that the claim that the runner has completed all the Z-runs leads to a contradiction.2.Following James Thomson [“Tasks and Super-Tasks,” on reserve], let us define a super-taskas an infinite sequence of tasks. Can one perform a super-task? Bertrand Russell thought that one could, as Thomson explains [“Tasks and Super-Tasks,” p. 93]: “Russell suggested that a man’s skill in performing operations of some kind might increase so fast that he was able to perform each of an infinite sequence of operations after the first in half the time he had required for its predecessor. Then the time required for all of the infinite sequence of tasks would be only twice that required for the first. On the strength of this Russell said that the
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Philosophy of mathematics, Bertrand Russell, lamp, James Thomson, infinite sequence