Bayes Destroyed?

[mjgeddes]

"That which can be destroyed by the truth should be."

-- P.C. Hodgell

Today, among logicians, Bayesian Inference seems to be the new dogma
for all encompassing theory of rationality.  But I have different
ideas, so I'm going to present an argument suggesting an alternative
form of reasoning.  In essence, I going to start to try to bring down
the curtain on the Bayesian dogma.  This is not the end, but it *is*
‘the beginning of the end’ (as Churchill once nicely put it).   I'm a
fan of David Bohm, the physicist who developed the 'Pilot Wave'
Interpretation of QM (which I like).  So I base my argument on his
ideas.

The genius of David Bohm was that he showed that there’s a perfectly
consistent interpretation of quantum mechanics which completely
reverses the normal way that physicists think about the relationship
between particles and background forces – physicists tend to think of
particles as real static objects moving around in a nebulous backdrop
of force fields.  Bohm turned this on its head and said why not regard
the *background forces* as primary and view particles as simply
temporary ‘pockets of stability’ in the background forces.  This idea
is implied by his interpretation of quantum mechanics,  where there’s
a ‘pilot wave’ (the quantum potential) which is primary and particles
are in effect ‘epiphenomen’ (mere aspects) of the deeper pilot wave.

Now my idea as regards rationality is exactly analogous to Bohm’s idea
as regards physics.  In the standard theory of rationality, causal
explanations (Bayesian reasoning) is primary and intuition (Analogies/
Narratives) is merely an imperfect human-invented ‘backdrop’ or
scaffolding.  My theory totally reverses the conevntional view.  I
say, why not take analogies/narratives as the primary ‘stuff’ of
thought, and causal explanations (Bayes) as merely
‘crystallized’ (unusually precise) analogies?

Bayesian reasoning is exactly analogous to algebra in pure math,
because with Bayes you are in effect trying to find correlations
between variables, where the correlations are imprecise or
fuzzy.  .Algebra is about *relations and functions* which in effect
maps two given sets of elements (correlate them).  So I suggest that
algebra is simply the ‘abstract ideal’ of Bayes, where the
correlations between variables are 100% precise (think of elements of
sets as the ‘variables’ of statistics).

Now…. Does algebra have any limitations?  Yes!  Algebra cannot fully
reason about algebra.  This is the real meaning of Godel’s theorem –
he showed that any formal system (which is in effect equivalent to an
algebraic system) complex enough to include both multiplication and
addition, has statements that cannot be proved within that system.
Since algebra is exactly analogous to Bayes, we can conclude that
Bayes cannot reason about Bayes, no system of statistical inference
can be used to fully reason about itself.

But is there a form of math more powerful than algebra?  Yes, Category/
Set Theory!  Unlike algebra, Category/Set theory really *can* fully
reason about itself, since Sets/categories can contain other Sets/
Categories.  Greg Cantor first explored these ideas in depth with his
transfinite arithmetic, and in fact it was later shown that the use of
transfinite induction can in theory bypass the Godel limitations. (See
Gerhard Gentzen)

By analogy, there’s another form of reasoning more powerful than
Bayes, the rationalist equivalent of Set/Category theory.  What could
it be?  Well, Sets/Category theory is very analogous to
categorization, a known form of inference involving grouping concepts
according to their degree of similarity – this is arguably the same
thing as…analogy formation!  Indeed, I’ve been using analogical
arguments throughout this post, showing that analogical inference is
perfectly capable of reasoning about itself.  My punch-line?  Bayesian
inference is merely a special case of analogy formation.

If all this seems hard to believe at first I suggest readers go back
and look at the analogy I gave with Bohm’s ideas about physics.
Remember Bohm’s ‘complete reversal’ of the normal way of thinking
about physics turned out to be fully consistent.  All I’ve done is
performed the same trick as Bohm in the field of cognitive science.
Just as ‘particles’ become mere epiphenomena of a ‘pilot wave’,
‘Bayes’ becomes a mere epiphenona of analogy formation.

Time for Bayesian logicians to fill their trousers? ;)

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[Bruno Marchal]

On 27 Aug 2009, at 08:19, marc.geddes wrote:

But is there a form of math more powerful than algebra?  Yes, Category/
Set Theory!  Unlike algebra, Category/Set theory really *can* fully
reason about itself, since Sets/categories can contain other Sets/
Categories.  Greg Cantor first explored these ideas in depth with his
transfinite arithmetic, and in fact it was later shown that the use of
transfinite induction can in theory bypass the Godel limitations. (See
Gerhard Gentzen)

Zermelo Fraenkel theory has full transfinite induction power, but is still limited by Gödel's incompleteness. What Gentzen showed is that you can prove the consistency of ARITHMETIC by a transfinite induction up to epsilon_0. This shows only that transfinite induction up to epsilon_0 cannot be done in arithmetic.

Algebra escapes Gödel's limitation by being to weak. Gödel's limitation applies to *any*effective and rich theory, like category theory or set theory.

I agree with your critics on Bayesianism, because it is a good tool but not a panacea, and it does not work for the sort of credibility measure we need in artificial intelligence.

Not sure about what you say about Bohm's formulation of QM. In my opinion he uses the many worlds, and selects one world by reintroducing particles or singularities in the field. This introduces zombie with no body, yet they talk and act like us.

(and it is Georg Cantor, not Greg).

Bruno

http://iridia.ulb.ac.be/~marchal/

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[Brent Meeker-2]

marc.geddes wrote:
> "That which can be destroyed by the truth should be."
>
> -- P.C. Hodgell
>
> Today, among logicians, Bayesian Inference seems to be the new dogma
> for all encompassing theory of rationality.  But I have different
> ideas, so I'm going to present an argument suggesting an alternative
> form of reasoning.  In essence, I going to start to try to bring down
> the curtain on the Bayesian dogma.  

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

>This is not the end, but it *is*
> ‘the beginning of the end’ (as Churchill once nicely put it).   I'm a
> fan of David Bohm, the physicist who developed the 'Pilot Wave'
> Interpretation of QM (which I like).  So I base my argument on his
> ideas.
>
> The genius of David Bohm was that he showed that there’s a perfectly
> consistent interpretation of quantum mechanics which completely
> reverses the normal way that physicists think about the relationship
> between particles and background forces – physicists tend to think of
> particles as real static objects moving around in a nebulous backdrop
> of force fields.  Bohm turned this on its head and said why not regard
> the *background forces* as primary and view particles as simply
> temporary ‘pockets of stability’ in the background forces.  This idea
> is implied by his interpretation of quantum mechanics,  where there’s
> a ‘pilot wave’ (the quantum potential) which is primary and particles
> are in effect ‘epiphenomen’ (mere aspects) of the deeper pilot wave.

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.

>
> Now my idea as regards rationality is exactly analogous to Bohm’s idea
> as regards physics.  In the standard theory of rationality, causal
> explanations (Bayesian reasoning) is primary and intuition (Analogies/
> Narratives) is merely an imperfect human-invented ‘backdrop’ or
> scaffolding.  

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."

>My theory totally reverses the conevntional view.  I
> say, why not take analogies/narratives as the primary ‘stuff’ of
> thought, and causal explanations (Bayes) as merely
> ‘crystallized’ (unusually precise) analogies?
>
> Bayesian reasoning is exactly analogous to algebra in pure math,
> because with Bayes you are in effect trying to find correlations
> between variables, where the correlations are imprecise or
> fuzzy.  .Algebra is about *relations and functions* which in effect
> maps two given sets of elements (correlate them).  So I suggest that
> algebra is simply the ‘abstract ideal’ of Bayes, where the
> correlations between variables are 100% precise (think of elements of
> sets as the ‘variables’ of statistics).
>
> Now…. Does algebra have any limitations?  Yes!  Algebra cannot fully
> reason about algebra.  This is the real meaning of Godel’s theorem –
> he showed that any formal system (which is in effect equivalent to an
> algebraic system) complex enough to include both multiplication and
> addition, has statements that cannot be proved within that system.
> Since algebra is exactly analogous to Bayes, we can conclude that
> Bayes cannot reason about Bayes, no system of statistical inference
> can be used to fully reason about itself.

You mean Bayesian inference is incomplete?  I think that would depend
on more than just the inference rule.  First order logic is complete,
so Bayesian inference without second order quantifiers would be complete.

>
> But is there a form of math more powerful than algebra?  Yes, Category/
> Set Theory!  Unlike algebra, Category/Set theory really *can* fully
> reason about itself, since Sets/categories can contain other Sets/
> Categories.  Greg Cantor first explored these ideas in depth with his
> transfinite arithmetic, and in fact it was later shown that the use of
> transfinite induction can in theory bypass the Godel limitations. (See
> Gerhard Gentzen)

On the contrary Gentzen showed that transfinite induction is an
example of the incompleteness that Godel proved.

>
> By analogy, there’s another form of reasoning more powerful than
> Bayes, the rationalist equivalent of Set/Category theory.  What could
> it be?  Well, Sets/Category theory is very analogous to
> categorization, a known form of inference involving grouping concepts
> according to their degree of similarity – this is arguably the same
> thing as…analogy formation!  Indeed, I’ve been using analogical
> arguments throughout this post, showing that analogical inference is
> perfectly capable of reasoning about itself.  My punch-line?  Bayesian
> inference is merely a special case of analogy formation.
>
> If all this seems hard to believe at first I suggest readers go back
> and look at the analogy I gave with Bohm’s ideas about physics.
> Remember Bohm’s ‘complete reversal’ of the normal way of thinking
> about physics turned out to be fully consistent.  All I’ve done is
> performed the same trick as Bohm in the field of cognitive science.
> Just as ‘particles’ become mere epiphenomena of a ‘pilot wave’,
> ‘Bayes’ becomes a mere epiphenona of analogy formation.

Note that Bohmian quantum mechanics is essentially barren.  It proved
to difficult, if not impossible, to create a relativistic version that
could account for particle production (a consequence of taking
particles as fundamental).

Brent

>
> Time for Bayesian logicians to fill their trousers? ;)
>
> >
>


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[mjgeddes]

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

http://en.wikipedia.org/wiki/Implicate_and_Explicate_Order_according_to_David_Bohm

“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:

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”

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[mjgeddes]

On Aug 27, 7:35 pm, Bruno Marchal <marc...@...> wrote:

>
> Zermelo Fraenkel theory has full transfinite induction power, but is  
> still limited by Gödel's incompleteness. What Gentzen showed is that  
> you can prove the consistency of ARITHMETIC by a transfinite induction  
> up to epsilon_0. This shows only that transfinite induction up to  
> epsilon_0 cannot be done in arithmetic.

Yes.  That's all I need for the purposes of my criticism of Bayes.
SInce ZF theory has full transfinite induction power, it is more
powerful than arithmetic.

The analogy I was suggesting was:

Arithmetic = Bayesian Inference
Set Theory =Analogical Reasoning

If the above match-up is valid, from the above (Set/Category more
powerful than Arithmetic), it follows that analogical reasoning is
more powerful than Bayesian Inference, and Bayes cannot be the
foundation of rationality as many logicians claim.

The above match-up is justified by (Brown, Porter), who shows that
there's a close match-up between analogical reasoning and Category
Theory.  See:

‘"Category Theory: an abstract setting for analogy and
comparison" (Brown, Porter)

http://www.maths.bangor.ac.uk/research/ftp/cathom/05_10.pdf

‘Comparison’ and ‘Analogy’ are fundamental aspects of knowledge
acquisition.
We argue that one of the reasons for the usefulness and importance
of Category Theory is that it gives an abstract mathematical setting
for analogy and comparison, allowing an analysis of the process of
abstracting
and relating new concepts.’

This shows that analogical reasoning is the deepest possible form of
reasoning, and goes beyond Bayes.


> I agree with your critics on Bayesianism, because it is a good tool
> but not a panacea, and it does not work for the sort of credibility
> measure we need in artificial intelligence.

The problem of priors in Bayesian inference is devastating.  Simple
priors only work for simple problems, and complexity priors are
uncomputable.  The deeper problem  of different models cannot be
solved by Bayesian inference at all:

See:
http://74.125.155.132/search?q=cache:_XQwv9eklmkJ:eprints.pascal-network.org/archive/00003012/01/statisti.pdf+%22bayesian+inference%22+%22problem+of+priors%22&cd=9&hl=en&ct=clnk&gl=nz


"One of the most criticized issues in the Bayesian approach is related
to
priors. Even if there is a consensus on the use of probability
calculus to
update beliefs, wildly different conclusions can be arrived at from
different
states of prior beliefs. While such differences tend to diminish with
increas-
ing amount of observed data, they are a problem in real situations
where
the amount of data is always finite. Further, it is only true that
posterior
beliefs eventually coincide if everyone uses the same set of models
and all
prior distributions are mutually continuous, i.e., assign non-zero
probabili-
ties to the same subsets of the parameter space (‘Cromwell’s rule’,
see [67];
these conditions are very similar to those guaranteeing consistency
[8]).
As an interesting sidenote, a Bayesian will always be sure that her
own
predictions are ‘well-calibrated’, i.e., that empirical frequencies
eventually
converge to predicted probabilities, no matter how poorly they may
have
performed so far [22].

It is actually somewhat misleading to speak of the aforementioned
crit-
icism as the ‘problem of priors’, as it were, since what is meant is
often at
least as much a ‘problem of models’: if a different set of models is
assumed,
differences in beliefs never vanish even with the amount of data going
to
infinity."


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[Bruno Marchal]

On 28 Aug 2009, at 10:47, marc.geddes wrote:

>
>
>
> On Aug 27, 7:35 pm, Bruno Marchal <marc...@...> wrote:
>
>>
>> Zermelo Fraenkel theory has full transfinite induction power, but is
>> still limited by Gödel's incompleteness. What Gentzen showed is that
>> you can prove the consistency of ARITHMETIC by a transfinite  
>> induction
>> up to epsilon_0. This shows only that transfinite induction up to
>> epsilon_0 cannot be done in arithmetic.
>
> Yes.  That's all I need for the purposes of my criticism of Bayes.
> SInce ZF theory has full transfinite induction power, it is more
> powerful than arithmetic.
>
> The analogy I was suggesting was:
>
> Arithmetic = Bayesian Inference
> Set Theory =Analogical Reasoning

This makes no sense for me.

Also, here arithmetic = Peano Arithmetic (the machine, or the formal  
system).

Obviously (?, by Gödel) Arithmetic (arithmetical truth) is infinitely  
larger that what you can prove in ZF theory.

Of course ZF proves much more arithmetical true statements than PA.
Interestingly enough, ZF and ZFC proves the same arithmetical truth.  
(ZFC = ZF + axiom of choice);
And of course ZFK (ZF + existence of inaccessible cardinals) proves  
much more arithmetical statements than ZF.
But all those theories proves only a tiny part of Arithmetical truth,  
which escapes all axiomatizable theories.

>
> If the above match-up is valid, from the above (Set/Category more
> powerful than Arithmetic), it follows that analogical reasoning is
> more powerful than Bayesian Inference, and Bayes cannot be the
> foundation of rationality as many logicians claim.
>
> The above match-up is justified by (Brown, Porter), who shows that
> there's a close match-up between analogical reasoning and Category
> Theory.  See:
>
> ‘"Category Theory: an abstract setting for analogy and
> comparison" (Brown, Porter)
>
> http://www.maths.bangor.ac.uk/research/ftp/cathom/05_10.pdf
>
> ‘Comparison’ and ‘Analogy’ are fundamental aspects of knowledge
> acquisition.
> We argue that one of the reasons for the usefulness and importance
> of Category Theory is that it gives an abstract mathematical setting
> for analogy and comparison, allowing an analysis of the process of
> abstracting
> and relating new concepts.’
>
> This shows that analogical reasoning is the deepest possible form of
> reasoning, and goes beyond Bayes.

I agree, but there are many things going beyond Bayes.

>
>
>> I agree with your critics on Bayesianism, because it is a good tool
>> but not a panacea, and it does not work for the sort of credibility
>> measure we need in artificial intelligence.
>
> The problem of priors in Bayesian inference is devastating.  Simple
> priors only work for simple problems, and complexity priors are
> uncomputable.  The deeper problem  of different models cannot be
> solved by Bayesian inference at all:

Like all theorems, Bayes theorems can be used with many benefits on  
some problems, and can generate total non sense when misapplied.

Bruno

http://iridia.ulb.ac.be/~marchal/




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[Brent Meeker-2]

marc.geddes wrote:

>
>
> On Aug 27, 7:35 pm, Bruno Marchal <marc...@...> wrote:
>
>> Zermelo Fraenkel theory has full transfinite induction power, but is  
>> still limited by Gödel's incompleteness. What Gentzen showed is that  
>> you can prove the consistency of ARITHMETIC by a transfinite induction  
>> up to epsilon_0. This shows only that transfinite induction up to  
>> epsilon_0 cannot be done in arithmetic.
>
> Yes.  That's all I need for the purposes of my criticism of Bayes.
> SInce ZF theory has full transfinite induction power, it is more
> powerful than arithmetic.
>
> The analogy I was suggesting was:
>
> Arithmetic = Bayesian Inference
> Set Theory =Analogical Reasoning
>
> If the above match-up is valid, from the above (Set/Category more
> powerful than Arithmetic), it follows that analogical reasoning is
> more powerful than Bayesian Inference,

 From analogies are only suggestive - not proofs.

>and Bayes cannot be the
> foundation of rationality as many logicians claim.
>
> The above match-up is justified by (Brown, Porter), who shows that
> there's a close match-up between analogical reasoning and Category
> Theory.

But did Brown and Porter justify Arithmetic=Bayesian inference?  ISTM
that Bayesian math is just rules of inference for reasoning with
probabilities replacing modal operators "necessary" and "possible".

> See:
>
> ‘"Category Theory: an abstract setting for analogy and
> comparison" (Brown, Porter)
>
> http://www.maths.bangor.ac.uk/research/ftp/cathom/05_10.pdf
>
> ‘Comparison’ and ‘Analogy’ are fundamental aspects of knowledge
> acquisition.
> We argue that one of the reasons for the usefulness and importance
> of Category Theory is that it gives an abstract mathematical setting
> for analogy and comparison, allowing an analysis of the process of
> abstracting
> and relating new concepts.’
>
> This shows that analogical reasoning is the deepest possible form of
> reasoning, and goes beyond Bayes.
>
>
>> I agree with your critics on Bayesianism, because it is a good tool
>> but not a panacea, and it does not work for the sort of credibility
>> measure we need in artificial intelligence.
>
> The problem of priors in Bayesian inference is devastating.  Simple
> priors only work for simple problems, and complexity priors are
> uncomputable.

Look at Winbugs or R.  They compute with some pretty complex priors -
that's what Markov chain Monte Carlo methods were invented for.
Complex =/= uncomputable.

> The deeper problem  of different models cannot be
> solved by Bayesian inference at all:

Actually Bayesian inference gives a precise and quatitative meaning to
  Occam's razor in selecting between models.

http://quasar.as.utexas.edu/papers/ockham.pdf

>
> See:
> http://74.125.155.132/search?q=cache:_XQwv9eklmkJ:eprints.pascal-network.org/archive/00003012/01/statisti.pdf+%22bayesian+inference%22+%22problem+of+priors%22&cd=9&hl=en&ct=clnk&gl=nz
>
>
> "One of the most criticized issues in the Bayesian approach is related
> to
> priors. Even if there is a consensus on the use of probability
> calculus to
> update beliefs, wildly different conclusions can be arrived at from
> different
> states of prior beliefs.

A feature, not a bug.


>While such differences tend to diminish with
> increas-
> ing amount of observed data, they are a problem in real situations
> where
> the amount of data is always finite.

And beliefs do not converge, even in probability - compare Islam and
Judaism.  Why would any correct theory of degrees of belief suppose
that finite data should remove all doubt?

>Further, it is only true that
> posterior
> beliefs eventually coincide if everyone uses the same set of models
> and all
> prior distributions are mutually continuous, i.e., assign non-zero
> probabili-
> ties to the same subsets of the parameter space (‘Cromwell’s rule’,
> see [67];
> these conditions are very similar to those guaranteeing consistency
> [8]).
> As an interesting sidenote, a Bayesian will always be sure that her
> own
> predictions are ‘well-calibrated’, i.e., that empirical frequencies
> eventually
> converge to predicted probabilities, no matter how poorly they may
> have
> performed so far [22].
>
> It is actually somewhat misleading to speak of the aforementioned
> crit-
> icism as the ‘problem of priors’, as it were, since what is meant is
> often at
> least as much a ‘problem of models’: if a different set of models is
> assumed,
> differences in beliefs never vanish even with the amount of data going
> to
> infinity."

But some models are more probable than others.

Brent

>
>
> >
>


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[Brent Meeker-2]

marc.geddes wrote:

>
>
> On Aug 28, 6:58 am, Brent Meeker <meeke...@...> 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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[mjgeddes]

On Aug 29, 2:36 am, Bruno Marchal <marc...@...> wrote:

>
> Obviously (?, by Gödel) Arithmetic (arithmetical truth) is infinitely  
> larger that what you can prove in ZF theory.

Godel’s theorem doesn’t mean that anything is *absolutely*
undecidable; it just means that not all truths can captured by
*axiomatic* methods; but we can always use mathematical intuition (non
axiomatic methods) to decide the truth of anything can't we?.

http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems

"The TRUE but unprovable statement referred to by the theorem is often
referred to as “the Gödel sentence” for the theory. "

The sentence is unprovable within the system but TRUE. How do we know
it is true?  Mathematical intuition.

So to find a math technique powerful enough to decide Godel
sentences , we look for a reasoning technique which is non-axiomatic,
by asking which math structures are related to which possible
reasoning techniques.  So we find;

Bayesian reasoning (related to) functions/relations
Analogical reasoning  (related to) categories/sets

Then we note that math structures can be arranged in a hierarchy, for
instance natural numbers are lower down the hierarchy than real
numbers, because real numbers are a higher-order infinity.  So we can
use this hierarchy to compare the relative power of epistemological
techniques.  Since:

Functions/relations <<<<  categories/sets

(Functions are not as general/abstract as sets/categories; they are
lower down in the math structure hierarchy)

Bayes <<<<<<  Analogical reasoning

So, analogical reasoning must be the stronger technique.  And indeed,
since analogical reasoning is related to sets/categories (the highest
order of math) it must the strongest technique.  So we can determine
the truth of Godel sentences by relying on mathematical intuition
(which from the above must be equivalent to analogical reasoning).
And nothing is really undecidable.

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[mjgeddes]

On Aug 29, 5:21 am, Brent Meeker <meeke...@...> wrote:

>
> Look at Winbugs or R.  They compute with some pretty complex priors -
> that's what Markov chain Monte Carlo methods were invented for.
> Complex =/= uncomputable.

 Techniques such the Monte Carlo method don’t scale well.
>

>
> Actually Bayesian inference gives a precise and quatitative meaning to
>   Occam's razor in selecting between models.
>
> http://quasar.as.utexas.edu/papers/ockham.pdf
>
>

The formal definitions of Occam’s razor are uncomputable. Remember,
the theory of Bayesian reasoning is *itself* a scientific model, so
differences of opinion about Bayesian models will result in mutually
incompatible science.  That’s why Bayes has serious problems. (see
below for more on this point)


>
> And beliefs do not converge, even in probability - compare Islam and
> Judaism.  Why would any correct theory of degrees of belief suppose
> that finite data should remove all doubt?


So how did people come to believe  things like Islam and Judaism in
the first place? (the beliefs PRIOR to collecting evidence)  Bayes
can’t tell you *what* to believe, it can only tell you how your
beliefs should *change* with new evidence.  The fact that you are free
to believe anything to start with shows that  Bayes has major
problems.

Stathis once pointed on this list that crazy people can actually still
perform axiomatic reasoning very well, and invent all sorts of
elaborate justifications, the problem is their priors, not their
reasoning; so if you try to use Bayes as the entire basis of your
logic, you’re crazy ;)



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[mjgeddes]

On Aug 29, 5:30 am, Brent Meeker <meeke...@...> 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.


>

>
> >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.


>
> > 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?  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).  This shows that Bayes can’t be foundational

>
> 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.

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 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!

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.


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[Brent Meeker-2]

marc.geddes wrote:

>
> On Aug 29, 5:21 am, Brent Meeker <meeke...@...> wrote:
>
>  
>> Look at Winbugs or R.  They compute with some pretty complex priors -
>> that's what Markov chain Monte Carlo methods were invented for.
>> Complex =/= uncomputable.
>>    
>
>  Techniques such the Monte Carlo method don’t scale well.
>  
>
>  

They do with Metropolis integration.

>> Actually Bayesian inference gives a precise and quatitative meaning to
>>   Occam's razor in selecting between models.
>>
>> http://quasar.as.utexas.edu/papers/ockham.pdf
>>
>>
>>    
>
> The formal definitions of Occam’s razor are uncomputable. Remember,
> the theory of Bayesian reasoning is *itself* a scientific model, so
> differences of opinion about Bayesian models will result in mutually
> incompatible science.  That’s why Bayes has serious problems. (see
> below for more on this point)
>  

And analogical reasoning is computable and doesn't produce any
differences of opinion??

>
>  
>> And beliefs do not converge, even in probability - compare Islam and
>> Judaism.  Why would any correct theory of degrees of belief suppose
>> that finite data should remove all doubt?
>>    
>
>
> So how did people come to believe  things like Islam and Judaism in
> the first place? (the beliefs PRIOR to collecting evidence)  Bayes
> can’t tell you *what* to believe, it can only tell you how your
> beliefs should *change* with new evidence.  The fact that you are free
> to believe anything to start with shows that  Bayes has major
> problems.
>  

The only reasons analogical reasoning seems better to you is that it's a
vague and ill defined method that encompasses anything you want it to.  
You are always free to believe anything.   Of course Bayesian inference
doesn't solve all problems - but at least it solves some of them.

> Stathis once pointed on this list that crazy people can actually still
> perform axiomatic reasoning very well, and invent all sorts of
> elaborate justifications, the problem is their priors, not their
> reasoning; so if you try to use Bayes as the entire basis of your
> logic, you’re crazy ;)
>  

Axiomatic reasoning =/= probabilistic reasoning.  Try basing all your
reasoning on analogies.

Brent

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[mjgeddes]

On Aug 29, 6:16 pm, Brent Meeker <meeke...@...> wrote:


>
> > Stathis once pointed on this list that crazy people can actually still
> > perform axiomatic reasoning very well, and invent all sorts of
> > elaborate justifications, the problem is their priors, not their
> > reasoning; so if you try to use Bayes as the entire basis of your
> > logic, you’re crazy ;)
>
> Axiomatic reasoning =/= probabilistic reasoning.  

Ok, probablistic/axiomatic, none of it works without the correct
priors, which Bayes can't produce.  Another exmaple would be dream
states, you could reason probalistically in your sleep, but without
the correct priors, your dreams will still be largely incoherent.

Don't get me wrong, I'm sure Bayes is very powerful- I just don't
think it's the be-all and end-all.

>Try basing all your
> reasoning on analogies.
>
> Brent

I do.  I think Bayes is just a special case of analogical reasoning ;)
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[Brent Meeker-2]

marc.geddes wrote:

>
> On Aug 29, 5:30 am, Brent Meeker <meeke...@...> 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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[Brent Meeker-2]

marc.geddes wrote:

>
> On Aug 29, 6:16 pm, Brent Meeker <meeke...@...> wrote:
>
>
>  
>>> Stathis once pointed on this list that crazy people can actually still
>>> perform axiomatic reasoning very well, and invent all sorts of
>>> elaborate justifications, the problem is their priors, not their
>>> reasoning; so if you try to use Bayes as the entire basis of your
>>> logic, you’re crazy ;)
>>>      
>> Axiomatic reasoning =/= probabilistic reasoning.  
>>    
>
> Ok, probablistic/axiomatic, none of it works without the correct
> priors, which Bayes can't produce.  

Bayes explicitly doesn't pretend to produce priors - although some have
invented ways of producing priors with minimum presumption (e.g. Jaynes
maximum entropy priors).  Analogical reasoning doesn't produce priors
either and it can produce false conclusions too.

> Another exmaple would be dream
> states, you could reason probalistically in your sleep, but without
> the correct priors, your dreams will still be largely incoherent.
>  
There's a huge difference between incoherent and incorrect.

> Don't get me wrong, I'm sure Bayes is very powerful- I just don't
> think it's the be-all and end-all.
>
>  
>> Try basing all your
>> reasoning on analogies.
>>
>> Brent
>>    
>
> I do.  I think Bayes is just a special case of analogical reasoning ;)

Then you can say analogical reasoning is just a special case of
reasoning.  Which then proves that reasoning is more fundamental than
analogical reasoning.  Then will you claim to have destroyed analogical
reasoning. ??

Brent

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[mjgeddes]

On Aug 29, 6:41 pm, Brent Meeker <meeke...@...> wrote:

> marc.geddes wrote:
>
> > On Aug 29, 5:30 am, Brent Meeker <meeke...@...> wrote:
>
> >> marc.geddes wrote:
>
>
> > *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".

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).  What I'm 'destroying'
is that claim.  And I've done that.  But of course Bayes is still very
useful and powerful.



>
> > 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.
>

Because if the reductionist world-view is the correct one, the non-
reductionist world view should have serious inconsistencies, the fact
that there's not yet a conclusive technical rebuttal of Bohm counts as
evidence against reductionism.
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[mjgeddes]

On Aug 29, 6:50 pm, Brent Meeker <meeke...@...> wrote:
> marc.geddes wrote:
>

>
> > Ok, probablistic/axiomatic, none of it works without the correct
> > priors, which Bayes can't produce.  
>
> Bayes explicitly doesn't pretend to produce priors - although some have
> invented ways of producing priors with minimum presumption (e.g. Jaynes
> maximum entropy priors).  Analogical reasoning doesn't produce priors
> either and it can produce false conclusions too.

Actually, I think that's exactly what analogical reasoning *does* do
(analogies can produce priors by biasing thoughts in the right
direction by viewing reality through the 'lens' of categories -see
above, analogy is categorization),


>
> > I do.  I think Bayes is just a special case of analogical reasoning ;)
>
> Then you can say analogical reasoning is just a special case of
> reasoning.  Which then proves that reasoning is more fundamental than
> analogical reasoning.  Then will you claim to have destroyed analogical
> reasoning. ??
>
> Brent-

No, I think the buck stops with analogical reasoning, since no form of
reasoning is more powerful. Analogical reasoning can produce priors
and handle knowledge representation (via categorization), Bayes can't.
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[Brent Meeker-2]

marc.geddes wrote:

>
> On Aug 29, 6:41 pm, Brent Meeker <meeke...@...> wrote:
>  
>> marc.geddes wrote:
>>
>>    
>>> On Aug 29, 5:30 am, Brent Meeker <meeke...@...> wrote:
>>>      
>>>> marc.geddes wrote:
>>>>        
>>    
>>> *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".
>>    
>
> 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?

> What I'm 'destroying'
> is that claim.  And I've done that.  But of course Bayes is still very
> useful and powerful.
>
>
>
>  
>>> 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.
>>
>>    
>
> Because if the reductionist world-view is the correct one, the non-
> reductionist world view should have serious inconsistencies, the fact
> that there's not yet a conclusive technical rebuttal of Bohm counts as
> evidence against reductionism.

What's a technical rebuttal if particle production isn't??   Failure to
predict what is observed is usually considered a severe defect in physics.

Also, note that there is no reason that there couldn't be both holistic
and reductionist accounts of the same thing.

Brent

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[Brent Meeker-2]

marc.geddes wrote:

>
> On Aug 29, 6:50 pm, Brent Meeker <meeke...@...> wrote:
>  
>> marc.geddes wrote:
>>
>>    
>
>  
>>> Ok, probablistic/axiomatic, none of it works without the correct
>>> priors, which Bayes can't produce.  
>>>      
>> Bayes explicitly doesn't pretend to produce priors - although some have
>> invented ways of producing priors with minimum presumption (e.g. Jaynes
>> maximum entropy priors).  Analogical reasoning doesn't produce priors
>> either and it can produce false conclusions too.
>>    
>
> Actually, I think that's exactly what analogical reasoning *does* do
> (analogies can produce priors by biasing thoughts in the right
> direction by viewing reality through the 'lens' of categories -see
> above, analogy is categorization),
>
>
>  
>>> I do.  I think Bayes is just a special case of analogical reasoning ;)
>>>      
>> Then you can say analogical reasoning is just a special case of
>> reasoning.  Which then proves that reasoning is more fundamental than
>> analogical reasoning.  Then will you claim to have destroyed analogical
>> reasoning. ??
>>
>> Brent-
>>    
>
> No, I think the buck stops with analogical reasoning, since no form of
> reasoning is more powerful. Analogical reasoning can produce priors
> and handle knowledge representation (via categorization),

Really?  How does analogy assign probabilities or degrees of belief?  
What degree of belief does it assign to "Global warming is caused by
burning fossil fuel" for example?

> Bayes can't.

But obviously reasoning, per se, is at least as powerful as analogical
reasoning, since it includes analogical as well as axiomatic,
probabilistic, metaphorical, intuitionist, etc.  My point is that you
have not given any definition of analogical reasoning.  By leaving it
vague and undefined you allow yourself to alternately identify every
kind of reasoning as analogical - or a special case of analogical.  
Which isn't wrong - but it doesn't have much content either.

Brent

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[mjgeddes]

On Aug 29, 7:34 pm, Brent Meeker <meeke...@...> wrote:
> marc.geddes wrote:
>
> > No, I think the buck stops with analogical reasoning, since no form of
> > reasoning is more powerful. Analogical reasoning can produce priors
> > and handle knowledge representation (via categorization),
>
> Really?  How does analogy assign probabilities or degrees of belief?  
> What degree of belief does it assign to "Global warming is caused by
> burning fossil fuel" for example?


Analogical reasoning is based on similarity measures (degrees of
similarities between two concepts), it remains to be seen how to
convert this to probabilities.



> But obviously reasoning, per se, is at least as powerful as analogical
> reasoning, since it includes analogical as well as axiomatic,
> probabilistic, metaphorical, intuitionist, etc.  My point is that you
> have not given any definition of analogical reasoning.  By leaving it
> vague and undefined you allow yourself to alternately identify every
> kind of reasoning as analogical - or a special case of analogical.  
> Which isn't wrong - but it doesn't have much content either.
>
> Brent

Sure, that's a good point, but that's because analogical reasoning has
not yet been well developed, since everyone has focused on Bayesian
reasoning... the point of this post was to show that there's a
neglected alternative.

There's are tentative definitions of analogical reasoning in the
literature, for instance ‘Analogies as Categorization’ (Atkins)
http://www.compadre.org/PER/document/ServeFile.cfm?DocID=186&ID=4726

It remains to be seen how it gets developed.
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