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Vaniver comments on Absence of Evidence Is Evidence of Absence - Less Wrong
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This is all fine and good, but it does not address what "evidence" is. I cannot gather evidence of extra solar planets (either evidence for or against existence) with my naked eyes. So in this experiment, even though I see no "evidence" of extra solar planets by looking up into the sky, I still do not have evidence of absense, because in fact I have no evidence at all.
Evidence, from the aspect of probability theory, is only meaningful when the experiment is able to differential between existence and absence.
Then the real question becomes: do we have evidence that our experiment is able to yield evidence? And the only way to prove this to the affirmative, is to find something. You cannot *know* you experiment is designed correctly.
Really, the issue here is whether evidence has to increase probability (of existence or nonexistence) by a positive amount or a non-negative amount. The difference between those two sets is the very important "zero."
You are interested in the question: "Are there extra-solar planets?", with possibilities "Yes" and "No". You wonder how to answer the question, and decide to try the experiment "look with my naked eyes." You sensibly decide that if you can see any extra-solar planets, then it's not less likely that there are extra-solar planets, and if you can't see extra-solar planets, then it's not more likely that there are extra-solar planets. The strength of those effects is determined by the quality of the experiment; in this case, that strength is 0.
The specific fallacy in question is saying that all outcomes of an experiment make a claim more likely- that is inconsistent with how probability works. Similarly, one can argue that you should have a good estimate of the quality of an experiment before you get the results. That estimate doesn't have to be perfect- you can look at the results and say "I'm going to doublecheck to make sure I didn't screw up the experiment"- but changing your bet after you lose should not be allowed.