Week 14: James Thomson, 'Tasks and Super-Tasks'

 

DQ1. Thomson's analysis of the Zeno paradox can be summarised as follows.

Thomson's analysis of the Zeno argument

  1. (Premise): If you complete any journey, then you must "complete an infinite number of journeys".
  2. (Premise): It is impossible to complete an infinite number of journeys.
  3. (Conclusion): Therefore, "you can't complete any journey".
  1. Do you agree with the first premise? With the second? Explain.
  2. Thomson writes: "the argument stated above is not valid. It commits the fallacy of equivocation. There is an element of truth in each of the premisses". What does he mean by this? What "element of truth" does he ascribes to each premise?

 

DQ2. Identify each of the supertasks that Thomson discusses in the text (there are several). Choose one of them: does it prove that supertasks are logically or physically impossible? Why or why not?

 

(Optional) DQ3. Recall the definition of Platonism and of Conventionalism from Lecture 13 on integers. Can a Platonist give an adequate account of what an infinite number is? Can a Conventionalist?