marc.geddes wrote:
>
>
> On Aug 28, 6:58 am, Brent Meeker <meeke....domain.name.hidden> 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.
That depends on what interpretation you are assigning to the
probability measure. Often it is "degree of belief", not a
prediction. But prediction is the gold-standard for understanding.
>
>
>> 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:
>
> http://en.wikipedia.org/wiki/Implicate_and_Explicate_Order_according_to_David_Bohm
This is obviously written by an advocate of Bohm's philosophy - of
which his reformulation of Schrodinger's equation was on a small,
suggestive part. Note that Bohmian quantum mechanics implies that
everything is deterministic - only one sequence of events happens and
that sequence is strictly determined by the wave-function of the
universe and the initial conditions. Of course it doesn't account for
particle production and so is inconsistent with cosmogony and relativity.
Brent
>
> “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..
Bayes deals with whatever you put a probability measure on. Most
often it is cited as applying to degrees of belief, which is what
Cox's theorem is about.
>A more important component of explanation is
> categorization. See:
>
> http://en.wikipedia.org/wiki/Categorization
>
> "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
> purpose."
>
> Analogies are concerned with Categorization, and thus go beyond mere
> prediction. See ‘Analogies as Categorization’ (Atkins)
> :
> http://www.compadre.org/PER/document/ServeFile.cfm?DocID=186&ID=4726
>
> “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”
One may invent analogies and categories, but how do you know they are
not just arbitrary manipulation of symbols unless you can predict
something from them. This seems to me to be an appeal to mysticism
(of which Bohm would approve) in which "understanding" becomes a
mystical inner feeling unrelated to action and consequences.
Brent
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Received on Fri Aug 28 2009 - 10:30:09 PDT