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dspeyer comments on Your existence is informative - Less Wrong
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Isn't "I observe X" equivalent to "someone chosen for reasons unrelated to this observation observed X"? That solves the "at some point somebody will make most mistaken measurements" problem because the likelihood of randomly choosing the scientist making that mistake is small.
You can't use this logic for observations of the form "I'm alive" because if you weren't alive you wouldn't be observing. What you can use that as evidence of is a hard problem. But it isn't a general problem.
Perhaps, but then there is the question of how you should pretend they were chosen. This is controversial.
If you weren't alive you wouldn't be observing "I'm alive". If X wasn't true you wouldn't be observing X. Could you be more clear on how you think the logic differs?
Slight double-meaning in the word observing:
When I said "if you weren't alive you wouldn't be observing" I meant you wouldn't be seeing whether you were alive or not.
When you said "If X wasn't true you wouldn't be observing X" you meant you wouldn't be seeing that X is true.
I'm finding my second paragraph surprisingly hard to reword.
If your existence depends on X, there are two possibilities: you observe X, you observe nothing
If your existence doesn't depend on X but you have some other way of observing whether X is true, the possibilities are: you observe X, you observe not X.
Do you think that observing X provides different information about something else in these two cases?