marc.geddes wrote:
>
> On Aug 29, 5:30 am, Brent Meeker <meeke....domain.name.hidden> wrote:
>
>> marc.geddes wrote:
>>
>
>
>>> 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.
>>
>
> *Before* you can even begin to assign probabilities to anything, you
> first need to form symbolic representations of the things you are
> talking about; see Knowledge Representation:
>
> http://en.wikipedia.org/wiki/Knowledge_representation
>
> This is where categories come in – to represent knowledge you have to
> group raw sensory data into different categories, this is a
> prerequisite to any sort of ‘degrees of belief’, which shows that
> probabilities are not as important as knowledge representation. In
> fact knowledge representation is actually doing most of the work in
> science, and Bayesian ‘degrees of belief’ are secondary.
>
I have no problem with that. Certainly you form propositions
(representations of knowledge) before you can worry your degree of
belief in them. But you started with the assertion that you were going
to "destroy Bayesian reasoning" and since Bayes=reductionism this was
going to destroy reductionism. Now, you've settled down to saying that
forming categories is prior to Bayesian reasoning. People that post
emails with outlandish assertions simply to stir up responses are called
"Trolls".
>
>
>
>
>>> http://en.wikipedia.org/wiki/Implicate_and_Explicate_Order_according_...
>>>
>> 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
>>
>
> This is not a failing of the Bohemian interpretation, because *every*
> interpretation of quantum mechanics suffers from it ; no one has yet
> succeed in producing a consistent quantum field theory for the simple
> reason that general relatively contradicts quantum mechanics.
>
But Bohmian QM isn't even compatible with special relativity - which
quantum field theory is. QFT handles particle production just fine.
>
>
>>> 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.
>>
>
> But what justifies Cox's theorem?
Read it. It's an axiomatic deduction from some axioms about what
constitutes a rational adjust of belief based on data.
> Ultimately, to try to justify math
> you can’t use ‘degrees of belief’, but have to fall back on deep math
> like Set/Categoy theory (since Sets/Categories are the foundation of
> mathematics).
How do you justify set theory? By appeal to axioms that seem
intuitively true, with some adjustments to make the deductions
interesting. For example set theory says {{}}=/={} even though most
people find {{}}={} intuitive, but it would be hard to build things on
the empty set with the latter as an axiom.
> This shows that Bayes can’t be foundational
>
I never said it was. Although the fact that it has not been used in an
axiomatic foundation of math doesn't prove that it couldn't be.
>
>> 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-
>>
>
> Pure mathematics is a science which is not based on prediction,
> instead it is about finding structural relationships between different
> concepts (integrating different pieces of knowledge). Categories form
> the basis for knowledge representation and pure mathematics, which is
> prior to any sort of prediction. Category/Set Theory is utterly
> precise science, the opposite of mysticism.
>
But it's not based on analogical rules of inference either.
> Bohm's interpretation of QM is utterly precise and was published in a
> scientific journal (Phys. Rev, 1952). In the more than 50 years
> since, no technical rebuttal has yet been found, and it is fully
> consistent with all predictions of standard QM.
In fact it's mathematically equivalent to Schrodinger's equation with
just a different interpetation.
> In fact the Bohm
> interpretation is the only realist interpretation offering a clear
> picture of what’s going on – other interpretations such as Bohr deny
> that there’s an objective reality at all at the microscopic level,
> bring in vague ideas like the importance of ‘consciousness’ or
> ‘observers’ and postulate mysterious ‘wave functions collapses, or
> reference a fantastical ‘multiverse’ of unobservables, disconnected
> from actual concrete reality. Bohm is the *only* non-mystical
> interpretation!
>
It is mystical in that it assumes holism, so that the wave-function of
the universe is instantaneously changed by an interaction anywhere.
> In fact from;
> http://en.wikipedia.org/wiki/Implicate_and_Explicate_Order_according_to_David_Bohm
>
> "Bohm’s paradigm is inherently antithetical to reductionism, in most
> forms, and accordingly can be regarded as a form of ontological
> holism."
>
> Since Bohm's views are non-reductionist and still perfectly
> consistent, this casts serious doubt on the entire reductionist world-
> view on which Bayesian reasoning is based.
I don't know why the mere existence of some consistent holistic math
model - which cannot account for observed particle production - should
count as evidence against a reductionist world view.
Brent
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Received on Fri Aug 28 2009 - 23:41:09 PDT