[ExI] Bayesian epistemology

[Russell Wallace]

Lee Corbin wrote in another thread:
> Well, it's been a while since we've discussed Bayesianity.  My
> own views have shifted a bit.  Would you mind elaborating
> on your disagreement with Bayesianism, or providing some
> links?  (Preferably in a new thread.)

Sure. Like I said, I think Bayesianism is normative _where
applicable_, but that's not nearly as much of the time as one might
wish. The problematic ideas are:

1) All statements have a probability.

There are lots of statements for which the concept is extremely dubious, e.g.

The Tegmark multiverse exists. (I'm not even going to get into the
quagmire of probability assignment to "God exists".)
Theft is immoral.
Roses are pretty.
The Continuum Hypothesis is true.

2) All probabilities are in the range (0, 1) exclusive.

The probability that 2 + 2 = 4 (given the usual definitions of the
terms) is 1. The probability that Goldbach's conjecture is true is
either 0 or 1, though I don't know which. The probability that P = NP
is either 0 or 1; it's not proven yet, but I'm confident it's 0.

3) We should express uncertainty by making up numbers and calling them
probabilities.

There are situations where this is the right thing to do. What's the
probability that a fair coin will come up heads? 0.5. What's the
probability that I will die this year? I don't know, but life
insurance companies have tables that could be consulted for a number,
which could reasonably be interpreted as a probability _because it is
based on statistical data_.

But Bayesianism encourages us to make up numbers where there is no
such data. Not only do we not have any basis for calling these numbers
probabilities, but we have excellent reason to refrain from doing so.
One study showed that statements to which people attached "90%
confidence" were right about 30% of the time; nor is this at all
atypical.