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Random Emeralds
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Abstract
Suppose we observe many emeralds which are all green. This observation usually provides good evidence that all emeralds are green. However, the emeralds we have observed are also all grue, which means that they are either green and already observed or blue and not yet observed. We usually do not think that our observation provides good evidence that all emeralds are grue. Why? I argue that if we are in the best case for inductive reasoning, we have reason to assign low probability to the hypothesis that all emeralds are grue before seeing any evidence. My argument appeals to random sampling and the observation-independence of green, understood as probabilistic independence of whether emeralds are green and when they are observed.
Title: Random Emeralds
Description:
Abstract
Suppose we observe many emeralds which are all green.
This observation usually provides good evidence that all emeralds are green.
However, the emeralds we have observed are also all grue, which means that they are either green and already observed or blue and not yet observed.
We usually do not think that our observation provides good evidence that all emeralds are grue.
Why? I argue that if we are in the best case for inductive reasoning, we have reason to assign low probability to the hypothesis that all emeralds are grue before seeing any evidence.
My argument appeals to random sampling and the observation-independence of green, understood as probabilistic independence of whether emeralds are green and when they are observed.
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