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Kiekeben's Odd/Even Paradox
Suppose a point P is moving between points A and B (just like in the
original Racetrack). And suppose also that we stipulate that P is
in the state "even" for the first half of the journey, "odd"
for the next 1/4, "even" for the next 1/8, and so on. That
is, we simply decide to classify P based on where along the journey
it is, such that it alternates between what we call an "even"
and an "odd" state. We can in addition stipulate that once
it is in one state it remains in that state unless it gets switched
according to the above rule.
What state will P be in at B? Just as with Thomson's lamp, it cannot
be in either, yet it must be in one or the other. The only solution
to this paradox, it seems, is to claim that there is something wrong
with the way it is set up. The stipulated conditions simply cannot
form a consistent set. But why not?
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