[ExI] Resend: Bayesian epistemology

[Jef Allbright]

On 8/6/07, Russell Wallace <russell.wallace at gmail.com> wrote:
>
> 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.

Bayesianism?  Apparently you're framing this in regard to the
religion, evidenced by your top-level emphasis on "normative, where
applicable".  It took me a moment to grasp your "...ianism" frame --
at first I kept thinking you meant "effective, where applicable", but
that would be nearly tautological.  It seemed you were somehow denying
the elegance, power,  and nearly universal applicability of the
principle known as Bayes' Rule.

However, your post seems to continually blur this distinction.



> The problematic ideas are:
>
> 1) All statements have a probability.

Presuming you mean by "statements", "all statements about future
observations of some state", then how could there not be a
probability?  Essentially, any such statement asserts the accuracy of
some aspects of an observer's model of reality, and any model is
necessarily ultimately incomplete.


> 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".)

These particular topics are difficult due to lack of relatively direct
evidence, but Bayes remains applicable since the aggregate of all your
evidence (and all evidence is indirect to some extent) contributes to
what approaches a necessarily single, unified model.


> Theft is immoral.

> Roses are pretty.

These assertions suffer not from lack of evidence, but from inadequate
specification.


> The Continuum Hypothesis is true.

This assertion too suffers from inadequate specification.  This may be
more difficult for some people to grasp, as here it is the
mathematical context that is inadequately specified.  As Gödel
famously showed, even mathematics can never be fully specified.

Heed ye, the Importance of Context!


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

Well yes, because every statement of probability refers to some aspect
of the difference between a model and putative reality.  Note that
while the model is highly dimensional, the difference (however
defined) can always be reduced to a scalar.


> 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.


These aren't statements of probability.  You're not turning Platonist
are you? ;-)


> 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_.


It appears you may be unclear about the distinction between
probability and likelihood.



> 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.

It appears we lack sufficient mutual background
here to  go much further.  It might be useful to point out though,
that even to frame a question necessarily entails some relevant prior
knowledge.

As for "Bayesianism", I'm not much of a joiner and tend to avoid
"isms" in general.

- Jef