This is our monthly thread for collecting these little gems and pearls of wisdom, rationality-related quotes you've seen recently, or had stored in your quotesfile for ages, and which might be handy to link to in one of our discussions.
- Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
- Do not quote yourself.
- Do not quote comments/posts on LW/OB.
- No more than 5 quotes per person per monthly thread, please.
For any probablity p strictly between 0 and 1, and any distance r greater than 0, there exists a finite amount of evidence E that would convince a Bayesian that your point is within the distance r of the boundary with probablity greater than p.
Do you think that propositions about God are part of an uncountably large space? Is there a reasonable notion of "similar" such that you could be convinced with finite evidence that there is a true proposition arbitrarily "similar" to a proposition that a given God exists?
I think we need to taboo the word "finite". And stick to my example of the square for the time being.
If you had a uniform prior over the square, and then I inform you that my "random point" is on the edge, have I provided you with a 'finite' or an 'infinite' amount of evidence? A case could be made, I think, for either answer.
The same applies for the amount of evidence required to demonstrate something similar to the proposition that God exists, for many reasonable values of 'similar'.
Notice that "amount of evidence" is not just a property of the evidence. It also depends on what your prior was for receiving that evidence. It is a subjective number.