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The British Journal for the Philosophy of Science 1995 46(2):235-247; doi:10.1093/bjps/46.2.235
© 1995 by British Society for the Philosophy of Science
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DISCUSSION

On Some Paradoxes of the Infinite II

Victor Allis and Teun Koetsier

Department of Mathematics and Computer Science, Vrije Universiteit De Boelelaan 1081, 1081 Amsterdam, The Netherlands

In an earlier paper the authors discussed some super-tasks by means of a kinematical interpretation. In the present paper we show a semi-formal way that a more abstract treatment is possible. The core idea of our approach is simple: if a super-task can be considered as a union of (finite) tasks, it is natural to define the effect of the super-task as the union of the effects of the finite tasks it consists of. We show that this approach enables us to handle two of the three super-tasks that we discussed earlier. We also argue that recent objections against our original kinematical interpretation do not hold water. One of our arguments is based on the construction of an elegant correspondence between the first of those three super-tasks and Zeno's Achilles and the Tortois.


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