On Aug 29, 7:12 pm, Brent Meeker <meeke...@dslextreme.com> wrote:
> marc.geddes wrote:
> > There are many logicians who think that Bayesian inference can serve
> > as the entire foundation of rationality and is the most powerful form
> > of reasoning possible (the rationalist ideal).
> Cox showed it is a rational ideal for updating one's beliefs based on
> new evidence. Has anyone shown that analogical reasoning is optimum in
> any sense?
At this point I'm going to give a 'prosecution summing up' of my
arguments that Bayes is not foundational, and that analogical
reasoning might be more powerful than Bayes, with Bayes just a special
Here were my main points:
(1) Bayes can’t handle mathematical reasoning, and especially, it
can’t deal with Godel undecidables
(2) Bayes has a problem of different priors and models
(3) Formalizations of Occam’s razor are uncomputable and
approximations don’t scale.
(4) Most of the work of science is knowledge representation, not
prediction, and knowledge representation is primary to prediction
(5) The type of pure math that Bayesian inference resembles (functions/
relations) is lower down the math hierarchy than that of analogical
For each point, there's some evidence that analogical *can* handle the
(1) Analogical reasoning can engage in mathematical reasoning and
bypass Godel (see Hoftstadler, Godelian reasoning is analogical)
(2) Analogical reasoning can produce priors, by biasing the mind in
the right direction by generating categories which simplify (see
Analogy as categorization)
(3) Analogical reasoning does not depend on huge amounts of data thus
it does not suffer from uncompatibility.
(4) Analogical reasoning naturally deals with knowledge representation
(analogies are categories)
(5) The fact that analogical reasoning closely resembles category
theory, the deepest form of math, suggests it’s the deepest form of
Finally, since Bayes is tied to the reductionist world-view, I had to
present an alternative non-reductionist physics model; I pointed out
that the Bohm interpretation (which is non-reductionist) is precise
and clear, was published in a scientific journal and has not been
conclusively rebutted in over 50 years (although Brent did point out a
copuple of valid criticisms).
You could say, to sum up, that Bayes has been 'Bohm'ed! :)
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