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Infinity, Causation, and Paradox (Hardcover)
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Infinity, Causation, and Paradox (Hardcover)
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Infinity is paradoxical in many ways. Some paradoxes involve
deterministic supertasks, such as Thomson's Lamp, where a switch is
toggled an infinite number of times over a finite period of time,
or the Grim Reaper, where it seems that infinitely many reapers can
produce a result without doing anything. Others involve infinite
lotteries. If you get two tickets from an infinite fair lottery
where tickets are numbered from 1, no matter what number you saw on
the first ticket, it is almost certain that the other ticket has a
bigger number on it. And others center on paradoxical results in
decision theory, such as the surprising observation that if you
perform a sequence of fair coin flips that goes infinitely far back
into the past but only finitely into the future, you can leverage
information about past coin flips to predict future ones with only
finitely many mistakes. Alexander R. Pruss examines this seemingly
large family of paradoxes in Infinity, Causation and Paradox. He
establishes that these paradoxes and numerous others all have a
common structure: their most natural embodiment involves an
infinite number of items causally impinging on a single output.
These paradoxes, he argues, can all be resolved by embracing
'causal finitism', the view that it is impossible for a single
output to have an infinite causal history. Throughout the book,
Pruss exposits such paradoxes, defends causal finitism at length,
and considers connections with the philosophy of physics (where
causal finitism favors but does not require discretist theories of
space and time) and the philosophy of religion (with a cosmological
argument for a first cause).
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