With and without end

Philosophical Investigations 30 (2):105–126 (2007)
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Ways and words about infinity have frequently hidden a continuing paradox inspired by Zeno. The basic puzzle is the tortoise's – Mr T's – Extension Challenge, the challenge being how any extension, be it in time or space or both, moving or still, can yet be of an endless number of extensions. We identify a similarity with Mr T's Deduction Challenge, reported by Lewis Carroll, to the claim that a conclusion can be validly reached in finite steps. Rejecting common solutions to both challenges, we use a Wittgensteinian approach for dissolution, noting also that other paradoxes, such as the Surprise Examination and Yablo's, trap us inconsistently into similar endlessnesses. In so doing, we encounter a hopping flea, generate a proportionality paradox and consider the knight's move in chess.



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Peter Cave
Cambridge University

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The Complete Works: The Rev. Oxford Translation.Jonathan Barnes (ed.) - 1984 - Princeton, N.J.: Princeton University Press.
Philosophical grammar.Ludwig Wittgenstein - 1974 - Oxford [Eng.]: Blackwell. Edited by Rush Rhees.
Philosophical remarks.Ludwig Wittgenstein - 1975 - Chicago: University of Chicago Press. Edited by Rush Rhees.

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