On Aug 28, 6:58 am, Brent Meeker <meeke...@dslextreme.com> wrote:

> So how are you going to get around Cox's 
> theorem?http://en.wikipedia.org/wiki/Cox%27s_theorem

Cox's theorem is referring to laws of probability for making
predictions.  I agree Bayesian inference is best for this.  But it
fails to capture the true basis for rationality, because true
explanation is more than just prediction.

See for example ‘Theory and Reality’  (Peter Godfrey Smith) and
debates in philosophy about prediction versus integration.  True
explanation is more than just prediction, and involves *integration*
of different models.  Bayes only deals with prediction.

> On the contrary, in Bohm's interpretation the particles are more like
> real classical objects that have definite positions and momenta.  What
> you describe as Bohmian is more like quantum field theory in which
> particles are just eigenstates of the momentum operator on the field.

In Bohm, reality is separated into two different levels of
organization, one for the particle level and one for the wave-level.
But the wave-level is regarded by Bohm is being deeper, the particles
are derivative.  See:


“In the enfolded [or implicate] order, space and time are no longer
the dominant factors determining the relationships of dependence or
independence of different elements. Rather, an entirely different sort
of basic connection of elements is possible, from which our ordinary
notions of space and time, along with those of separately existent
material particles, are abstracted as forms derived from the deeper
order. These ordinary notions in fact appear in what is called the
"explicate" or "unfolded" order, which is a special and distinguished
form contained within the general totality of all the implicate orders
(Bohm, 1980, p. xv).”

“In Bohm’s conception of order, then, primacy is given to the
undivided whole, and the implicate order inherent within the whole,
rather than to parts of the whole, such as particles, quantum states,
and continua.”

> I'd say analogies are fuzzy associations.  Bayesian inference applies
> equally to fuzzy associations as well as fuzzy causal relations - it's
> just math.  Causal relations are generally of more interest than other
> relations because they point to ways in which things can be changed.
> With apologies to Marx, "The object of inference is not to explain the
> world but to change it."

Associations are causal relations.  But  true explanation is more than
just causal relations, Bayes deals only with prediction of causal
relations..  A more important component of explanation is
categorization.  See:


"Categorization is the process in which ideas and objects are
recognized, differentiated and understood. Categorization implies that
objects are grouped into categories, usually for some specific

Analogies are concerned with Categorization, and thus go beyond mere
prediction. See ‘Analogies as Categorization’ (Atkins)

“I provide evidence that generated analogies are assertions of
categorization, and the
base of an analogy is the constructed prototype of an ad hoc category”

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