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Benardete's Paradox of the
Gods
Another modern version of the Racetrack that brings out the conceptual
difficulties inherent in infinite tasks is the paradox of the gods.
Suppose Achilles wants to run the length of a racetrack but there
are an infinite number of gods who have the following intentions:
the first god intends to paralyze Achilles if he reaches the halfway
mark; the second intends to paralyze Achilles if he reaches the quarter
mark; the third, if he reaches the one-eighth mark; and so on. As
in the Reverse Dichotomy, Achilles cannot even start running: to do
so would violate the intentions of an infinite number of gods. However,
it is not clear why he cannot start running, for until he does, no
god has actually paralyzed him.
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