As long as their beliefs aren’t totally independent of the facts, those beliefs will constitute evidence (one way or the other) of the facts. Thus learning their beliefs would be informative about pixies.
Learning people’s beliefs about Jesus is informative about Jesus, it’s just you already know that a lot of people believe in Jesus so there’s very little new information.
Do you dispute the truth of the sentence that precedes the one you quoted? Here it is again: “As long as their beliefs aren’t totally independent of the facts, those beliefs will constitute evidence (one way or the other) of the facts.”
Replacing “pixies” with “Jesus” should not change whether people’s beliefs are informative about Jesus. It may change the degree to which their beliefs are informative, for the reason /u/RowanE mentioned.
I am not suggesting that learning people’s beliefs about pixies would be incredibly informative. I am only suggesting that it would be more informative than not learning about such beliefs.
Here’s a thought experiment I often find helpful, tailored to the pixie-belief question:
Imagine Omega has come to you with a question: Are pixies real? She further tells you that a correct answer will result in an eternity of bliss for you and everyone you care about, and that an incorrect answer will result in unspeakable suffering for the same people. (The point is, a lot is at stake.) Then here is the key part of the scenario: Before you answer, she hands you an envelope marked “What People Believe About Pixies.” You can open it and get accurate information about people’s beliefs about pixies, or you can not open it. (Also, to make this work, we have to assume that you currently don’t know anything about people’s beliefs about pixies. Otherwise, the question becomes the value of info about pixie beliefs at the current margin, rather than simply the value of the info.) There’s no cost (or reward) from opening it, beyond the information you thereby obtain.
Would you open the envelope before answering?
If your answer is no, then we can conclude that you really do consider people’s pixie-beliefs to be completely devoid of information about the reality of pixies. But if you would open the envelope, can’t we conclude the opposite: that you consider their beliefs to be entangled with the truth, however tenuously?
(I like this thought experiment because in the past it has helped me see when I am believing in belief instead of, as I had supposed, just believing. I think I starting doing it after reading this 2011 Yvain post.)
As long as their beliefs aren’t totally independent of the facts, those beliefs will constitute evidence (one way or the other) of the facts. Thus learning their beliefs would be informative about pixies.
Learning their beliefs would be informative about something.
Do a mental experiment, replace pixies with Jesus.
Learning people’s beliefs about Jesus is informative about Jesus, it’s just you already know that a lot of people believe in Jesus so there’s very little new information.
Do you dispute the truth of the sentence that precedes the one you quoted? Here it is again: “As long as their beliefs aren’t totally independent of the facts, those beliefs will constitute evidence (one way or the other) of the facts.”
Replacing “pixies” with “Jesus” should not change whether people’s beliefs are informative about Jesus. It may change the degree to which their beliefs are informative, for the reason /u/RowanE mentioned.
I am not suggesting that learning people’s beliefs about pixies would be incredibly informative. I am only suggesting that it would be more informative than not learning about such beliefs.
Here’s a thought experiment I often find helpful, tailored to the pixie-belief question:
If your answer is no, then we can conclude that you really do consider people’s pixie-beliefs to be completely devoid of information about the reality of pixies. But if you would open the envelope, can’t we conclude the opposite: that you consider their beliefs to be entangled with the truth, however tenuously?
(I like this thought experiment because in the past it has helped me see when I am believing in belief instead of, as I had supposed, just believing. I think I starting doing it after reading this 2011 Yvain post.)