I’d say that a P this high for each statement, given this example, is well nigh impossible.
I can state with P=.94 (much higher) that you know how to read English. Is that an impossible level of certainty?
The real question isn’t probability assigned, but prior probability distribution, and evidence. You’re on Less Wrong—I’ve yet to meet somebody on Less Wrong, out of hundreds of conversations, who can’t speak English, so I have a prior much higher than .94 starting off. (I don’t care to calculate it, since I don’t even know the exact sample size, but somewhere in the vicinity of .99) I have evidence that you read and write English, pushing the prior slightly higher.
Somebody could throw this statement into a list of several others about any given Less Wrongian without influencing the overall probabilities.
It’s the relationship of the statements to their prior probabilities that matters.
I can state with P=.94 (much higher) that you know how to read English. Is that an impossible level of certainty?
The real question isn’t probability assigned, but prior probability distribution, and evidence. You’re on Less Wrong—I’ve yet to meet somebody on Less Wrong, out of hundreds of conversations, who can’t speak English, so I have a prior much higher than .94 starting off. (I don’t care to calculate it, since I don’t even know the exact sample size, but somewhere in the vicinity of .99) I have evidence that you read and write English, pushing the prior slightly higher.
Somebody could throw this statement into a list of several others about any given Less Wrongian without influencing the overall probabilities.
It’s the relationship of the statements to their prior probabilities that matters.