What if there is a box instead of a bag? |
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Suppose we have looked into many bags and found that they contain red marbles, and have achieved high confidence in our hypothesis, "bags contain red marbles". Now suppose we come to a box. Should we also assign it a high probability of containing red marbles? The question depends on whether or not we think the difference between "box" and "bag" is significant. If we see it as an insignificant difference, we will assign the box a high probability of containing red marbles. Again, it is not really about the hypothesis being "true", it is about it being a good approximation of reality, and up until now the rule has served us well. If we did see "box" as significantly different than "bag", then we would need to start over with a 50% chance of the box containing red marbles, for the same reason we gave the first bag a 50% probability after only one marble. Personally, if we had no other information, I think we would just think of the box and bag as "containers", and not see any significant difference, just like a young child will very often call every animal "dog" at first. How do we know if a difference is significant? Again, in practice, we'll need to use experience and induction. |