Re: Bayes math hoax?

[Philip Thrift]

Suppose - vs. the edit and editors' disclaimer statement - *after the fact 
of publication *- that the article was just* removed* (erased!) from the 
journal!

What is not to say the removal of the article would be an example of CANCEL 
CULTURE?

Conservatives would go nuts.

Free speech (as advocated by the conservative community).

@philipthrift

On Monday, October 5, 2020 at 1:20:43 PM UTC-5 Brent wrote:

>
>
> On 10/5/2020 1:18 AM, Philip Thrift wrote:
>
> If this article were in an "Intelligent Design" blog or journal, then this 
> wouldn't be significant. 
>
> But this  is in a "secular scientific" journal. So I am curious about the 
> backlash.
>
> e.g.
>
> "Dembski, Axe, and Behe come up, and the paper includes essentially a 
> review of just about all ID arguments we’ve heard. This is a secular 
> journal, but does make me wonder about who the editor was and who reviewed 
> it. It is hard to imagine this paper surviving an unbiased review."
>
> Now there's this:
>
> *Editor’s Disclaimer* 
>
> *The Journal of Theoretical Biology and its co-Chief Editors do not 
> endorse in any way the ideology of nor reasoning behind the concept of 
> intelligent design. Since the publication of the paper it has now become 
> evident that the authors are connected to a creationist group (although 
> their addresses are given on the paper as departments in bona fide 
> universities). We were unaware of this fact while the paper was being 
> reviewed. Moreover, the keywords “intelligent design” were added by the 
> authors after the review process during the proofing stage and we were 
> unaware of this action by the authors. We have removed these from the 
> online version of this paper. We believe that intelligent design is not in 
> any way a suitable topic for the Journal of Theoretical Biology.*
>
>
> That sounds better, I guess.
>
>
> It sounds worse to me.  It sounds like "Let's keep the real message and 
> intent of the paper covered up."  I don't think the Editor's disclaimer 
> will show up when someone references the paper in the future.
>
> Brent
>

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Re: Bayes math hoax?

['Brent Meeker' via Everything List]

On 10/5/2020 1:18 AM, Philip Thrift wrote:
If this article were in an "Intelligent Design" blog or journal, then 
this wouldn't be significant.


But this  is in a "secular scientific" journal. So I am curious about 
the backlash.


e.g.

"Dembski, Axe, and Behe come up, and the paper includes essentially a 
review of just about all ID arguments we’ve heard. This is a secular 
journal, but does make me wonder about who the editor was and who 
reviewed it. It is hard to imagine this paper surviving an unbiased 
review."


Now there's this:

*Editor’s Disclaimer*

*The Journal of Theoretical Biology and its co-Chief Editors do not 
endorse in any way the ideology of nor reasoning behind the concept of 
intelligent design. Since the publication of the paper it has now 
become evident that the authors are connected to a creationist group 
(although their addresses are given on the paper as departments in 
bona fide universities). We were unaware of this fact while the paper 
was being reviewed. Moreover, the keywords “intelligent design” were 
added by the authors after the review process during the proofing 
stage and we were unaware of this action by the authors. We have 
removed these from the online version of this paper. We believe that 
intelligent design is not in any way a suitable topic for the Journal 
of Theoretical Biology.*



That sounds better, I guess.



It sounds worse to me.  It sounds like "Let's keep the real message and 
intent of the paper covered up."  I don't think the Editor's disclaimer 
will show up when someone references the paper in the future.


Brent

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Re: Bayes math hoax?

[John Clark]

On Mon, Oct 5, 2020 at 4:18 AM Philip Thrift  wrote:


> *> Editor’s Disclaimer**The Journal of Theoretical Biology and its
> co-Chief Editors do not endorse in any way the ideology of nor reasoning
> behind the concept of intelligent design. Since the publication of the
> paper it has now become evident that the authors are connected to a
> creationist group (although their addresses are given on the paper as
> departments in bona fide universities). We were unaware of this fact while
> the paper was being reviewed. Moreover, the keywords “intelligent design”
> were added by the authors after the review process during the proofing
> stage and we were unaware of this action by the authors. We have removed
> these from the online version of this paper. We believe that intelligent
> design is not in any way a suitable topic for the Journal of Theoretical
> Biology.*


*Good Darwin Almighty! Any publication that is so slipshod that it would
allow major changes to an article without the editors noticing could not be
called a reputable journal. Science and Nature have on rare occasions made
editing mistakes, but nothing as bad is that!  *


*John K Clark*

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Re: Bayes math hoax?

[Lawrence Crowell]

The problem with fine tuning is when it is used to argue for the existence 
of a fine tuner. Sure, if there is a fine tuner the world is then fine 
tuned. Where things go awry is when fine tuning is used to say there must 
be a fine tuner. The world on the level of quantum physics is Markovian, 
which means fluctuations at one time carry no information into a future 
time. There is an interface between that domain as mesoscopic physics where 
physics is subMarkovian or there is pink noise instead of white noise. In 
biology this is seen in a selection mechanism. This does not require a 
conscious entity.

With the universe at large it is possible there statistical set of 
cosmological states, say the vast landscape of string theory, or the more 
impoverished domain of swampland, there is a quantum cosmological 
interference process. This may act as a sort of selection process involving 
the extremization of complexity. Again there is no need, at least in 
principle, for there to be a conscious entity that is a fine tuner.

LC

On Monday, October 5, 2020 at 3:18:52 AM UTC-5 cloud...@gmail.com wrote:

> If this article were in an "Intelligent Design" blog or journal, then this 
> wouldn't be significant.
>
> But this  is in a "secular scientific" journal. So I am curious about the 
> backlash.
>
> e.g.
>
> "Dembski, Axe, and Behe come up, and the paper includes essentially a 
> review of just about all ID arguments we’ve heard. This is a secular 
> journal, but does make me wonder about who the editor was and who reviewed 
> it. It is hard to imagine this paper surviving an unbiased review."
>
> Now there's this:
>
> *Editor’s Disclaimer*
>
> *The Journal of Theoretical Biology and its co-Chief Editors do not 
> endorse in any way the ideology of nor reasoning behind the concept of 
> intelligent design. Since the publication of the paper it has now become 
> evident that the authors are connected to a creationist group (although 
> their addresses are given on the paper as departments in bona fide 
> universities). We were unaware of this fact while the paper was being 
> reviewed. Moreover, the keywords “intelligent design” were added by the 
> authors after the review process during the proofing stage and we were 
> unaware of this action by the authors. We have removed these from the 
> online version of this paper. We believe that intelligent design is not in 
> any way a suitable topic for the Journal of Theoretical Biology.*
>
>
> That sounds better, I guess.
>
>
> @philipthrift
>
>
> On Sunday, October 4, 2020 at 5:08:10 PM UTC-5 Brent wrote:
>
>> And we, and the biosphere, could exist without the universe being 
>> fine-tuned for us, IF there were a God who do miracles.  A miracle would be 
>> evidence for such a God.  So fine-tuning=no-miracle cannot be evidence for 
>> a God.  The same facts cannot be evidence both for and against a 
>> proposition.
>>
>> So for fine-tuning to count as evidence for some creator, it has to be a 
>> creator who is limited by natural laws, e.g. some super-alien engineers.  
>> Not  a god.
>>
>> Brent
>>
>>
>> On 10/4/2020 5:29 AM, John Clark wrote:
>>
>> On Sun, Oct 4, 2020 at 7:44 AM Philip Thrift  wrote:
>>
>> *Journal of Theoretical Biology*
>>> *Volume 501, 21 September 2020*
>>> *Using statistical methods to model the fine-tuning of molecular 
>>> machines and systems*
>>> https://www.sciencedirect.com/science/article/pii/S0022519320302071
>>>
>>
>>> * A science  journal publishes an article supporting Intelligent Design.*
>>
>>
>> I don't see how. If the universe really is fine-tuned (a very big if) 
>> then an explanation for that fine-tuning needs to be found, but the God 
>> Hypothesis is a very poor explanation for two reasons.
>>
>> 1) It does not say or even give a hint as to how God created the universe.
>> 2) It does not say or even give a hint as to how God came into existence 
>> other than to say He has always existed, but if you're  going to do that 
>> you might as well just say the universe always existed and save a step.
>>
>> It seems to me that when a mystery is found, and Science has plenty, a 
>> good honest "I don't know" would be a better response to it than offering a 
>> theory that is obviously silly. 
>>
>> John K Clark
>>
>> -- 
>> You received this message because you are subscribed to the Google Groups 
>> "Everything List" group.
>> To unsubscribe from this group and stop receiving emails from it, send an 
>> email to everything-li...@googlegroups.com.
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>>  
>> 
>> .
>>
>>
>>

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Re: Bayes math hoax?

[John Clark]

On Sun, Oct 4, 2020 at 12:09 PM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

 >>If the universe really is fine-tuned (a very big if) then an explanation
>> for that fine-tuning needs to be found, but the God Hypothesis is a very
>> poor explanation for two reasons.
>
> 1) It does not say or even give a hint as to how God created the universe.
>> 2) It does not say or even give a hint as to how God came into existence
>> other than to say He has always existed, but if you're  going to do that
>> you might as well just say the universe always existed and save a step.
>>
>
> > *The issue is whether fine tuning means a fine tuner. A fine tuner is a
> necessary condition, but probably not sufficient. *
>

I don't see why a fine tuner is necessary or sufficient.


> > *In the multiverse setting there may be a vast array of cosmologies*
>

Exactly. And it's no more surprising that we happen to be living in a
universe that is compatible with carbon based life then it's surprising
that even in this universe we live in a very atypical place. The average
place in this universe only contains about one atom per cubic meter, but
that's not where we live.


>  > It is also possible I think that many of these other cosmologies are
> off-shell conditions in a cosmological path integral. Cosmologies with
> larger vacuum energy densities may not be physically real, but quantum
> amplitudes off-shell from a physical cosmology. This may reduce the number
> of actual physical cosmologies, and that could mean just one.
>

As far as I know there is no evidence for that, but even if it turns out to
be true it wouldn't help because then God Himself would be asking pretty
much the same question that we do, "Why do I, God Almighty, exist in a
universe that allows me to always have existed?". So the God Hypothesis
brings us no closer to solving the mystery, it just kicks the question
upstairs and tells us not to ask any more questions about the enigma or
even to think about it again.

Another problem with the theory, in addition to the two that I already
mentioned, is it assumes a universe that has the physical constants ours
does is the only one that would allow large scale data processing. But we
don't know that, there could be universes that, despite having radically
different physical constance than ours, allow for structures of some sort
that can process data; structures that have nothing to do with what we
would call biology or electronics or even mechanics but can nevertheless
use their type of physics to process information and ask "Why are things
the way they are?", because I think it's just a brute fact that
consciousness is the way data feels when it is being processed.

 John K Clark

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Re: Bayes math hoax?

[Philip Thrift]

If this article were in an "Intelligent Design" blog or journal, then this 
wouldn't be significant.

But this  is in a "secular scientific" journal. So I am curious about the 
backlash.

e.g.

"Dembski, Axe, and Behe come up, and the paper includes essentially a 
review of just about all ID arguments we’ve heard. This is a secular 
journal, but does make me wonder about who the editor was and who reviewed 
it. It is hard to imagine this paper surviving an unbiased review."

Now there's this:

*Editor’s Disclaimer*

*The Journal of Theoretical Biology and its co-Chief Editors do not endorse 
in any way the ideology of nor reasoning behind the concept of intelligent 
design. Since the publication of the paper it has now become evident that 
the authors are connected to a creationist group (although their addresses 
are given on the paper as departments in bona fide universities). We were 
unaware of this fact while the paper was being reviewed. Moreover, the 
keywords “intelligent design” were added by the authors after the review 
process during the proofing stage and we were unaware of this action by the 
authors. We have removed these from the online version of this paper. We 
believe that intelligent design is not in any way a suitable topic for the 
Journal of Theoretical Biology.*


That sounds better, I guess.


@philipthrift


On Sunday, October 4, 2020 at 5:08:10 PM UTC-5 Brent wrote:

> And we, and the biosphere, could exist without the universe being 
> fine-tuned for us, IF there were a God who do miracles.  A miracle would be 
> evidence for such a God.  So fine-tuning=no-miracle cannot be evidence for 
> a God.  The same facts cannot be evidence both for and against a 
> proposition.
>
> So for fine-tuning to count as evidence for some creator, it has to be a 
> creator who is limited by natural laws, e.g. some super-alien engineers.  
> Not  a god.
>
> Brent
>
>
> On 10/4/2020 5:29 AM, John Clark wrote:
>
> On Sun, Oct 4, 2020 at 7:44 AM Philip Thrift  wrote:
>
> *Journal of Theoretical Biology*
>> *Volume 501, 21 September 2020*
>> *Using statistical methods to model the fine-tuning of molecular machines 
>> and systems*
>> https://www.sciencedirect.com/science/article/pii/S0022519320302071
>>
>
>> * A science  journal publishes an article supporting Intelligent Design.*
>
>
> I don't see how. If the universe really is fine-tuned (a very big if) then 
> an explanation for that fine-tuning needs to be found, but the God 
> Hypothesis is a very poor explanation for two reasons.
>
> 1) It does not say or even give a hint as to how God created the universe.
> 2) It does not say or even give a hint as to how God came into existence 
> other than to say He has always existed, but if you're  going to do that 
> you might as well just say the universe always existed and save a step.
>
> It seems to me that when a mystery is found, and Science has plenty, a 
> good honest "I don't know" would be a better response to it than offering a 
> theory that is obviously silly. 
>
> John K Clark
>
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-li...@googlegroups.com.
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>  
> 
> .
>
>
>

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Re: Bayes math hoax?

['Brent Meeker' via Everything List]

It doesn't really infer anything because it leaves "specificity" as a 
kind of I'll-know-it-when-I-see-it free parameter.


Brent

On 10/4/2020 12:16 PM, Philip Thrift wrote:


I think the key thing - from the fact this article was published (in a 
"reputable" science journal)  - is it provides an example (not a good 
example to follow, but others likely will) of how statistical (in 
particular, Bayesian) arguments can be used to deduce "design" (in 
effect, reject Darwinism),-  in the way this article formulates it in 
its probability model.


@philipthrift

On Sunday, October 4, 2020 at 11:09:26 AM UTC-5 Lawrence Crowell wrote:

On Sunday, October 4, 2020 at 7:30:15 AM UTC-5 johnk...@gmail.com
wrote:

On Sun, Oct 4, 2020 at 7:44 AM Philip Thrift
 wrote:

/Journal of Theoretical Biology/
/Volume 501, 21 September 2020/
*/Using statistical methods to model the fine-tuning of
molecular machines and systems/*
https://www.sciencedirect.com/science/article/pii/S0022519320302071


/ A science journal publishes an article supporting
Intelligent Design./


I don't see how. If the universe really is fine-tuned (a very
big if) then an explanation for that fine-tuning needs to be
found, but the God Hypothesis is a very poor explanation for
two reasons.

1) It does not say or even give a hint as to how God created
the universe.
2) It does not say or even give a hint as to how God came into
existence other than to say He has always existed, but if
you're  going to do that you might as well just say the
universe always existed and save a step.

It seems to me that when a mystery is found, and Science has
plenty, a good honest "I don't know" would be a better
response to it than offering a theory that is obviously silly.

John K Clark


The issue is whether fine tuning means a fine tuner. A fine tuner
is a necessary condition, but probably not sufficient. In the
multiverse setting there may be a vast array of cosmologies and
one could argue that just as Earth is one of many planets with the
right conditions for life, this cosmology is in a Goldilocks
situation. It is also possible I think that many of these other
cosmologies are off-shell conditions in a cosmological path
integral. Cosmologies with larger vacuum energy densities may not
be physically real, but quantum amplitudes off-shell from a
physical cosmology. This may reduce the number of actual physical
cosmologies, and that could mean just one. In this second
situation there is some condition in the structure of quantum
cosmology that selects exclusively for this cosmology.

LC

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Re: Bayes math hoax?

['Brent Meeker' via Everything List]

And we, and the biosphere, could exist without the universe being 
fine-tuned for us, IF there were a God who do miracles.  A miracle would 
be evidence for such a God.  So fine-tuning=no-miracle cannot be 
evidence for a God.  The same facts cannot be evidence both for and 
against a proposition.


So for fine-tuning to count as evidence for some creator, it has to be a 
creator who is limited by natural laws, e.g. some super-alien 
engineers.  Not  a god.


Brent

On 10/4/2020 5:29 AM, John Clark wrote:
On Sun, Oct 4, 2020 at 7:44 AM Philip Thrift > wrote:


/Journal of Theoretical Biology/
/Volume 501, 21 September 2020/
*/Using statistical methods to model the fine-tuning of molecular
machines and systems/*
https://www.sciencedirect.com/science/article/pii/S0022519320302071


/ A science  journal publishes an article supporting Intelligent
Design./


I don't see how. If the universe really is fine-tuned (a very big if) 
then an explanation for that fine-tuning needs to be found, but the 
God Hypothesis is a very poor explanation for two reasons.


1) It does not say or even give a hint as to how God created the universe.
2) It does not say or even give a hint as to how God came into 
existence other than to say He has always existed, but if you're 
 going to do that you might as well just say the universe always 
existed and save a step.


It seems to me that when a mystery is found, and Science has plenty, a 
good honest "I don't know" would be a better response to it than 
offering a theory that is obviously silly.


John K Clark
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Re: Bayes math hoax?

[Lawrence Crowell]

On Sunday, October 4, 2020 at 2:16:39 PM UTC-5 cloud...@gmail.com wrote:

>
> I think the key thing - from the fact this article was published (in a 
> "reputable" science journal)  - is it provides an example (not a good 
> example to follow, but others likely will) of how statistical (in 
> particular, Bayesian) arguments can be used to deduce "design" (in effect, 
> reject Darwinism),-  in the way this article formulates it in its 
> probability model. 
>
> @philipthrift
>

This may point to some extremal principle of complexity. For C complexity 
entropy is S ~ e^S, and the maximum entropy principle has a corollary with 
complexity. The evolution of systems may then be such that there is some 
extremal principle for the complexity of quantum states. 

I said above something wrong. I meant to say that fine tuning is a 
necessary condition for a fine tuner, which is sort of obvious, but that a 
fine tuner is not a sufficient condition.

LC
 

>
> On Sunday, October 4, 2020 at 11:09:26 AM UTC-5 Lawrence Crowell wrote:
>
>> On Sunday, October 4, 2020 at 7:30:15 AM UTC-5 johnk...@gmail.com wrote:
>>
>>> On Sun, Oct 4, 2020 at 7:44 AM Philip Thrift  wrote:
>>>
>>> *Journal of Theoretical Biology*
 *Volume 501, 21 September 2020*
 *Using statistical methods to model the fine-tuning of molecular 
 machines and systems*
 https://www.sciencedirect.com/science/article/pii/S0022519320302071

>>>
 * A science  journal publishes an article supporting Intelligent 
 Design.*
>>>
>>>
>>> I don't see how. If the universe really is fine-tuned (a very big if) 
>>> then an explanation for that fine-tuning needs to be found, but the God 
>>> Hypothesis is a very poor explanation for two reasons.
>>>
>>> 1) It does not say or even give a hint as to how God created the 
>>> universe.
>>> 2) It does not say or even give a hint as to how God came into 
>>> existence other than to say He has always existed, but if you're  going to 
>>> do that you might as well just say the universe always existed and save a 
>>> step.
>>>
>>> It seems to me that when a mystery is found, and Science has plenty, a 
>>> good honest "I don't know" would be a better response to it than offering a 
>>> theory that is obviously silly.
>>>
>>> John K Clark
>>>
>>
>> The issue is whether fine tuning means a fine tuner. A fine tuner is a 
>> necessary condition, but probably not sufficient. In the multiverse setting 
>> there may be a vast array of cosmologies and one could argue that just as 
>> Earth is one of many planets with the right conditions for life, this 
>> cosmology is in a Goldilocks situation. It is also possible I think that 
>> many of these other cosmologies are off-shell conditions in a cosmological 
>> path integral. Cosmologies with larger vacuum energy densities may not be 
>> physically real, but quantum amplitudes off-shell from a physical 
>> cosmology. This may reduce the number of actual physical cosmologies, and 
>> that could mean just one. In this second situation there is some condition 
>> in the structure of quantum cosmology that selects exclusively for this 
>> cosmology.
>>
>> LC
>>
>

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Re: Bayes math hoax?

[Philip Thrift]

I think the key thing - from the fact this article was published (in a 
"reputable" science journal)  - is it provides an example (not a good 
example to follow, but others likely will) of how statistical (in 
particular, Bayesian) arguments can be used to deduce "design" (in effect, 
reject Darwinism),-  in the way this article formulates it in its 
probability model. 

@philipthrift

On Sunday, October 4, 2020 at 11:09:26 AM UTC-5 Lawrence Crowell wrote:

> On Sunday, October 4, 2020 at 7:30:15 AM UTC-5 johnk...@gmail.com wrote:
>
>> On Sun, Oct 4, 2020 at 7:44 AM Philip Thrift  wrote:
>>
>> *Journal of Theoretical Biology*
>>> *Volume 501, 21 September 2020*
>>> *Using statistical methods to model the fine-tuning of molecular 
>>> machines and systems*
>>> https://www.sciencedirect.com/science/article/pii/S0022519320302071
>>>
>>
>>> * A science  journal publishes an article supporting Intelligent Design.*
>>
>>
>> I don't see how. If the universe really is fine-tuned (a very big if) 
>> then an explanation for that fine-tuning needs to be found, but the God 
>> Hypothesis is a very poor explanation for two reasons.
>>
>> 1) It does not say or even give a hint as to how God created the universe.
>> 2) It does not say or even give a hint as to how God came into existence 
>> other than to say He has always existed, but if you're  going to do that 
>> you might as well just say the universe always existed and save a step.
>>
>> It seems to me that when a mystery is found, and Science has plenty, a 
>> good honest "I don't know" would be a better response to it than offering a 
>> theory that is obviously silly.
>>
>> John K Clark
>>
>
> The issue is whether fine tuning means a fine tuner. A fine tuner is a 
> necessary condition, but probably not sufficient. In the multiverse setting 
> there may be a vast array of cosmologies and one could argue that just as 
> Earth is one of many planets with the right conditions for life, this 
> cosmology is in a Goldilocks situation. It is also possible I think that 
> many of these other cosmologies are off-shell conditions in a cosmological 
> path integral. Cosmologies with larger vacuum energy densities may not be 
> physically real, but quantum amplitudes off-shell from a physical 
> cosmology. This may reduce the number of actual physical cosmologies, and 
> that could mean just one. In this second situation there is some condition 
> in the structure of quantum cosmology that selects exclusively for this 
> cosmology.
>
> LC
>

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Re: Bayes math hoax?

[Lawrence Crowell]

On Sunday, October 4, 2020 at 7:30:15 AM UTC-5 johnk...@gmail.com wrote:

> On Sun, Oct 4, 2020 at 7:44 AM Philip Thrift  wrote:
>
> *Journal of Theoretical Biology*
>> *Volume 501, 21 September 2020*
>> *Using statistical methods to model the fine-tuning of molecular machines 
>> and systems*
>> https://www.sciencedirect.com/science/article/pii/S0022519320302071
>>
>
>> * A science  journal publishes an article supporting Intelligent Design.*
>
>
> I don't see how. If the universe really is fine-tuned (a very big if) then 
> an explanation for that fine-tuning needs to be found, but the God 
> Hypothesis is a very poor explanation for two reasons.
>
> 1) It does not say or even give a hint as to how God created the universe.
> 2) It does not say or even give a hint as to how God came into existence 
> other than to say He has always existed, but if you're  going to do that 
> you might as well just say the universe always existed and save a step.
>
> It seems to me that when a mystery is found, and Science has plenty, a 
> good honest "I don't know" would be a better response to it than offering a 
> theory that is obviously silly.
>
> John K Clark
>

The issue is whether fine tuning means a fine tuner. A fine tuner is a 
necessary condition, but probably not sufficient. In the multiverse setting 
there may be a vast array of cosmologies and one could argue that just as 
Earth is one of many planets with the right conditions for life, this 
cosmology is in a Goldilocks situation. It is also possible I think that 
many of these other cosmologies are off-shell conditions in a cosmological 
path integral. Cosmologies with larger vacuum energy densities may not be 
physically real, but quantum amplitudes off-shell from a physical 
cosmology. This may reduce the number of actual physical cosmologies, and 
that could mean just one. In this second situation there is some condition 
in the structure of quantum cosmology that selects exclusively for this 
cosmology.

LC

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Re: Bayes math hoax?

[John Clark]

On Sun, Oct 4, 2020 at 7:44 AM Philip Thrift  wrote:

*Journal of Theoretical Biology*
> *Volume 501, 21 September 2020*
> *Using statistical methods to model the fine-tuning of molecular machines
> and systems*
> https://www.sciencedirect.com/science/article/pii/S0022519320302071
>

> * A science  journal publishes an article supporting Intelligent Design.*


I don't see how. If the universe really is fine-tuned (a very big if) then
an explanation for that fine-tuning needs to be found, but the God
Hypothesis is a very poor explanation for two reasons.

1) It does not say or even give a hint as to how God created the universe.
2) It does not say or even give a hint as to how God came into existence
other than to say He has always existed, but if you're  going to do that
you might as well just say the universe always existed and save a step.

It seems to me that when a mystery is found, and Science has plenty, a good
honest "I don't know" would be a better response to it than offering a
theory that is obviously silly.

John K Clark

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Re: Bayes Destroyed?

[Dave]

I almost dread entering into this discussion, but I think it should be 
pointed out that this discussion occurs in various forms in both Leonard 
Jimmie Savage's Foundations of Statistics and E T Jaynes Probability 
Theory.  I would also point out that you are missing key elements of both 
the non-mathematical discussion of rationality (such as that from 
neuroscience) and the mathematical discussion of the properties of utility 
functions upon which a discussion of rationality must set.  There are 
probably a dozen good and separate formalizations of utility, the major 
ones are of course von Neumann's, Savages, Thaler's and Machina's.


Savage really formalized the discussion on personalistic statistics, but 
I really think you need to go back and look at both the axiomization he 
uses and the proofs.  Likewise, ET Jaynes really covers much of your 
discussion quite early on in his book.  Another person to consider is 
Moesteller, though I cannot remember where at the moment.  If it comes to 
me, I will post it.

Finally, there is an empiricism issue here.

I take some of the comments here as mistaking the model for the reality it 
models.  Models are valuable, by the definition of valuable, only to the 
extent they provide utility.  It follows from heterogeneous preferences 
that any discussion like this is foreclosed by the actors personal 
preferences.

Let us take some Bayesian mathematical construction as both all 
encompassing AND valid for the problem of reasoning.  This does not mean 
alternate constructions are invalid nor does it mean others cannot be all 
encompassing.  

It is dangerous to do mathematical reasoning by analogy, though it is 
valuable for the purpose of thrashing out the problem.

A second danger to your discussion is that it is confusing intuition with 
an action.

If intuition is seen as a set of perceptions following a stimulus given a 
state of the brain, then Bayesian reasoning must not only follow from it, 
but intuition creates a difference in the brain between the perceived 
likelihood function and the likelihood function actually happening in 
nature.

It does not seem rational to treat intuition as a rational process.  
Indeed, it is difficult to impossible to imagine intuition as rational.  
Rather it is a form of pattern association.  Bayesian reasoning must be 
framed in it, but it would be formulated either as a bias function in the 
registering of the likelihood or as part of the prior.  That is a very old 
discussion in psychology going back at least into the 1920's.  Brain scan 
studies on people whose brains prefer intuitive over concrete responses 
show that those that prefer concrete responses have high levels of activity 
in the limbic system with localized responses on the cortex while those who 
prefer intuitive response show very generalized response on the cortex.  
Put simply a person observing the details of the concrete response is not 
seeing the same perception as the person providing a more intuitive 
response.

It is important to note that perception must be irrational.  

I think this discussion partly exists because there are parts of the 
formalization that are taken as well behaved that when forgotten about 
raise questions.  I think you need to go back to the basics first and this 
discussion will solve itself.

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Re: Bayes Destroyed?

[Bruno Marchal]

On 31 Aug 2009, at 03:50, marc.geddes wrote:




 On Aug 31, 4:19 am, Bruno Marchal marc...@ulb.ac.be wrote:
 On 30 Aug 2009, at 10:12, marc.geddes wrote:




 But look at this. I decide to do the following experience. I prepare
 an electron so that it is in state up+down. I measure it in the base
 {up, down}, and I decide to take holiday in the North if I find it  
 up,
 and to the south, if I find it down.
 Not only that. I decide to go, after the holiday,  to the amnesia
 center where all my memories, from the state of the electron to
 everything which follows, except my feeling about how much I enjoy  
 the
 holliday. And I am asked to answer by yes or no to the question did
 you enjoy your holiday. Then, thanks to the amnesia my yes+no states
 will be used In this way.  I interfere with myself, and what will
 follow in the new branch where I have fuse with myself, my, and your,
 future is determined by my contentment qualia, in the two branches of
 the waves.

 This assumes that qualia are completely determined by the wave
 function, which (since Bohm is non-reductionist) I'm sure he'd
 dispute.  The wave function only predicts physical states, it does not
 neccesserily completely determine higher-level properties such qualia
 (although of course qualia depends on low-level physics).  If the wave
 function DID completely determine the qualia, your example would
 indeed contradict Bohm - but Bohm already admits he's non-
 reductionist.

Well, meaning that he is non computationalist. No problem, in free  
country.




 A weakness of MWI is that it does not describe the reality we actually
 see - additional steps are needed to convert wave function to human
 observables - Bohm makes this clear, MWI just disguises it.  Even in
 MWI, additional unexpected steps (Born probabilities derivation etc)
 are needed to convert wave function to what we actually observe.

I am not sure. Bohm has to use an unknwown and unspecified (but very  
vaguely) theory of mind.
The MWI has to use only comp (a modern version of a very old theory of  
mind).
(Then I point on the fact that if we take comp seriously the SWE has  
to be justified from numbers only, but that is nice because it points  
to a further simplification of the theory).

 But MWI has the same problem, it just states it in different terms, in
 MWI all worlds exist, but which one will we actually observe?  In
 Bohm, only one world is there, but which of the paths in the wave
 function is it?


Not at all. The question which world is reduced to the question why  
W or Why M in an WM self-duplication experiment, or to the child  
question why do I feel to be me and not my brother. Comp justifies  
why universal machine have to ask such question, and why they cannot  
answer them, and why they can explain that such question have no  
answer when assuming comp.
Bohm has to make special an observable (position), to threat away  
locality, to introduce hidden variables, and a supplementary equation,  
which describe necessarily hidden things.

Bruno


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




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Re: Bayes Destroyed?

[marc.geddes]

On Aug 31, 8:10 pm, Bruno Marchal marc...@ulb.ac.be wrote:
 On 31 Aug 2009, at 03:50, marc.geddes wrote:


  This assumes that qualia are completely determined by the wave
  function, which (since Bohm is non-reductionist) I'm sure he'd
  dispute.  The wave function only predicts physical states, it does not
  neccesserily completely determine higher-level properties such qualia
  (although of course qualia depends on low-level physics).  If the wave
  function DID completely determine the qualia, your example would
  indeed contradict Bohm - but Bohm already admits he's non-
  reductionist.

 Well, meaning that he is non computationalist. No problem, in free  
 country.

I don't know - does non-reductionist mean non-computationalist?  I
hope not.  Non-reductionist just means not all the high-level
properties of a system are determined by the lower-level properties.
I'm assuming its still all computational.





  A weakness of MWI is that it does not describe the reality we actually
  see - additional steps are needed to convert wave function to human
  observables - Bohm makes this clear, MWI just disguises it.  Even in
  MWI, additional unexpected steps (Born probabilities derivation etc)
  are needed to convert wave function to what we actually observe.

 I am not sure. Bohm has to use an unknwown and unspecified (but very  
 vaguely) theory of mind.
 The MWI has to use only comp (a modern version of a very old theory of  
 mind).
 (Then I point on the fact that if we take comp seriously the SWE has  
 to be justified from numbers only, but that is nice because it points  
 to a further simplification of the theory).

But the wave function does not describe the reality we actually
observe - that needs additional steps. Bohm just makes his explicit,
but MWI has them too (needs an additional step to convert wave
function to Born probabilities, MWI itself doesn't explain why for
instance we aren't aware of the other branches and don't see
superpositional states - needs additional theory of mind of some sort
too).





  But MWI has the same problem, it just states it in different terms, in
  MWI all worlds exist, but which one will we actually observe?  In
  Bohm, only one world is there, but which of the paths in the wave
  function is it?

 Not at all. The question which world is reduced to the question why  
 W or Why M in an WM self-duplication experiment, or to the child  
 question why do I feel to be me and not my brother. Comp justifies  
 why universal machine have to ask such question, and why they cannot  
 answer them, and why they can explain that such question have no  
 answer when assuming comp.
 Bohm has to make special an observable (position), to threat away  
 locality, to introduce hidden variables, and a supplementary equation,  
 which describe necessarily hidden things.

 Bruno


See above,  MWI needs supplementary theories too to convert wave
function into observables (things like procedure for deriving Born
probabilities etc), in practice position needs to be singled out to
make measurements.

Main problem with Bohm is the non-locality, but on the other hand its
picture of the world is much clearer and doesn't require huge
quantities of unobservables (alternative universes).  I'd rate the two
interpretations about equally good (50-50 toss up).  Will read your
links on locality and think over the example more.
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Re: Bayes Destroyed?

[Bruno Marchal]

On 31 Aug 2009, at 11:28, marc.geddes wrote:




 On Aug 31, 8:10 pm, Bruno Marchal marc...@ulb.ac.be wrote:
 On 31 Aug 2009, at 03:50, marc.geddes wrote:


 This assumes that qualia are completely determined by the wave
 function, which (since Bohm is non-reductionist) I'm sure he'd
 dispute.  The wave function only predicts physical states, it does  
 not
 neccesserily completely determine higher-level properties such  
 qualia
 (although of course qualia depends on low-level physics).  If the  
 wave
 function DID completely determine the qualia, your example would
 indeed contradict Bohm - but Bohm already admits he's non-
 reductionist.

 Well, meaning that he is non computationalist. No problem, in free
 country.

 I don't know - does non-reductionist mean non-computationalist?  I
 hope not.  Non-reductionist just means not all the high-level
 properties of a system are determined by the lower-level properties.
 I'm assuming its still all computational.


It has to be non-comp. If not he has to accept that my doppelganger  
has experience like you and me, guven that the branch implements the  
paralel computation. Bohm is non sensical with comp. Everett is really  
just QM + comp, and indeed, it is comp alone (assuming QM is correct).

Now, machanism, after Emil Post-Gödel  Co., can be explained to be  
the less reductionist theory possible, as I argue often with John.





 A weakness of MWI is that it does not describe the reality we  
 actually
 see - additional steps are needed to convert wave function to human
 observables - Bohm makes this clear, MWI just disguises it.  Even in
 MWI, additional unexpected steps (Born probabilities derivation etc)
 are needed to convert wave function to what we actually observe.

 I am not sure. Bohm has to use an unknwown and unspecified (but very
 vaguely) theory of mind.
 The MWI has to use only comp (a modern version of a very old theory  
 of
 mind).
 (Then I point on the fact that if we take comp seriously the SWE has
 to be justified from numbers only, but that is nice because it points
 to a further simplification of the theory).

 But the wave function does not describe the reality we actually
 observe -
 that needs additional steps. Bohm just makes his explicit,
 but MWI has them too (needs an additional step to convert wave
 function to Born probabilities, MWI itself doesn't explain why for
 instance we aren't aware of the other branches and don't see
 superpositional states - needs additional theory of mind of some sort
 too).


Everett insists and other have make this more precise that the  
probabilities emerge as first person constructs, and comp juutsifies  
those first person construct, without assuming QM.
Everett QM confirms comp, up to now.
Everett explains why we don't feel the split, why we cannot see or  
interact with the other branches, and provides the correct probability  
(quesi directly with Gleason theorem + frequentist proba).
And his the most parcimonious, à-la-Occam theory of nature.

Bohm needs non-comp, and an utterly weird theory of matter, with  
hidden particles having necessarily unknown initial condition. All  
that for transforming my quantum doppelganger into zombie.

Bohm-De Broglie is a sane reaction in front of Bohr-heisenberg fuzzy  
irrealism, or von Neumann-Wigner dualism, but has been made useless  
with Everett discovery that we really don't need a wave collapse. You  
can derive from the SWE only, why people appears and develop beliefs  
in classical reality.

The only (strong) critics you can do to Everett, is that he iis using  
comp, and UDA+MGA shows that if QM is empirically correct, then QM has  
to be derived purely arithmetically.

Comp makes elemntary Arithmetic the theory of Everything.








 But MWI has the same problem, it just states it in different  
 terms, in
 MWI all worlds exist, but which one will we actually observe?  In
 Bohm, only one world is there, but which of the paths in the wave
 function is it?

 Not at all. The question which world is reduced to the question  
 why
 W or Why M in an WM self-duplication experiment, or to the child
 question why do I feel to be me and not my brother. Comp justifies
 why universal machine have to ask such question, and why they cannot
 answer them, and why they can explain that such question have no
 answer when assuming comp.
 Bohm has to make special an observable (position), to threat away
 locality, to introduce hidden variables, and a supplementary  
 equation,
 which describe necessarily hidden things.

 Bruno


 See above,  MWI needs supplementary theories too to convert wave
 function into observables (things like procedure for deriving Born
 probabilities etc), in practice position needs to be singled out to
 make measurements.

Not at all. This is the point made clear by Zurek, and the decoherence  
theory. Everett theory does not need to sibgle out a base against the  
other. The position base singles out itself.




 Main problem with 

Re: Bayes Destroyed?

[marc.geddes]

On Aug 30, 7:23 pm, Bruno Marchal marc...@ulb.ac.be wrote:
 On 30 Aug 2009, at 07:06, marc.geddes wrote:


  It’s true that there is no wave function collapse in Bohm, so it uses
  the same math as Everett.  But Bohm does not interpret the wave
  function in ‘many world’ terms, in Bohm the wave function doesn’t
  represent concrete reality, its just an abstract field – the concrete
  reality is the particles, which are on a separate level of reality, so
  there are no ‘zombies’ in the wave function.

 In Bohm, the wave is not an abstract field, it plays a concrete role  
 in the determination of the position of the particles I can observed.  
 It is not a question of interpretation, it follows form the fact that  
 the wave guides the particles by simulating completely the parallel  
 branches. And in those branches the person acts exactly like believing  
 they are made of particles like us.
 How could we know that we belong to the branch with particles? We need  
 already to abandon CTM here.

Yes, in Bohm the wave is 'real' , but to interpret the wave as
actually referring to ordinary concrete things is already to
presuppose 'many worlds' ; reality has two levels, so really there's
two different definitions of 'real' in Bohm.  There are no 'people' in
the wave, its a more abstrast entity than ordinary concrete reality.


  Brent did make the point that it has trouble with field theory, but
  this problem is a feature of other interpretations also.  Brent also
  criticised the non-locality, but again, this problem is a feature of
  all other interpretations also.

 I disagree. Everett restores locality, as he explains himself. Deutsch  
 and Hayden wrote a paper explaining rather well how locality is  
 completely restored in the many-worlds view.
 And as I said, comp alone entails the many worlds (or many  
 dreams, ...). That part of the SWE confirms comp. If I remember well,  
 Bohm intuited this and made some case against the computationalist  
 hypothesis.

 Bruno

If MWI does eliminate non-locality, that would be a strong point in
its favor, but is there any conclusive paper demonstrating that its
done this?  I have not heard of one - I assume the Deutsch/Hayden
paper is just their attempt to restore locality which does not
succeed.

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Re: Bayes Destroyed?

[marc.geddes]

On Aug 30, 7:05 pm, Bruno Marchal marc...@ulb.ac.be wrote:

 This does not make sense.

You said;

The truth of Gödel sentences are formally trivial.
The process of finding out its own Gödel sentence is
mechanical.
The diagonilization is constructive. Gödel's
proof is constructive. That is what Penrose and Lucas are missing
(notably).

This contradicts Godel.  The truth of any particular Godel sentence
cannot be formally determined from within the given particular formal
system - surely that's what Godel says?

The points are addressed in ‘Shadows of The Mind’ (Section 2.6,
Q6).

The point of Penrose/Lucs is that you can only formally determine the
Godel sentence of a given system from *outside* that system.  We
cannot determine *our own* Godel sentences formally, and that's why we
have to rely on analogical reasoning  (which is the argument of
Hofstadler in  ‘I Am a Strange Loop’).


Analogies are then seen as a generalization of
morphism, which is the key notion of category theory.

Yes thats the sort of thing I'm suggesting, only I think its probably
the other way around, analogies are a particular type of morphism.
(morphism is more general)


You may develop. My feeling is that to compare category theory and
Bayesian inference, is like comparing astronomy and fishing. They
serve different purposes.

Well, Bayes is applied math, category theory is pure math.  But its
all math.  If category theory is the foundation of math, there must be
structures in there corresponding to Bayes.













  In ‘I Am a Strange Loop’, Hofstadter argues that the procedure for the
  determining the truth of Godel sentences  is actually a form of
  analogical reasoning.  (Chapters 10-12)

  (page 148)

  ‘by virtue of Godel’s subtle new code, which systematically mapped
  strings of symbols onto numbers and vice versa, many formulas could be
  read on a second level.  The first level of meaning obtained via the
  standard mapping, was always about numbers, just as Russell claimed,
  but the second level of meaning, using Godel’s newly revealed mapping…
  was about formulas’
  …
  (page 158)

  ‘all meaning is mapping mediated, which is to say, all meaning comes
  from analogies’

 This can make sense. Analogies are then seen as a generalization of  
 morphism, which is the key notion of category theory.







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

  Those are easily axiomatized.
  I see the relation analogy-category, but sets and functions are
  together, and not analogical imo.
  I don't see at all the link between Bayes and functions/relations.
  Actually, function/relations are the arrows in a category.

  See what I said in my first post this thread.  The Bayes theorem is
  the central formula for statistical inference.  Statistics in effect
  is about correlated variables.  Functions/Relations are just the
  abstract (ideal) version of this where the correlations are perfect
  instead of fuzzy (functions/relations map the elements of two sets).
  That’s why I say that Bayesian inference bears a strong ‘family
  resemblance’ to functions/relations.

  You agreed that analogies bear a strong ‘family resemblance’ to
  categories.

  Category theory *includes* the arrows. So if the arrows are the
  functions and relations (which I argued bears a strong family
  resemblance to Bayesian inference), and the categories (which you
  agreed bear a family resemblance to analogies) are primary, then this
  proves my point, Bayesian inferences are merely special cases of
  analogies, confirming that analogical reasoning is primary.

 You may develop. My feeling is that to compare category theory and  
 Bayesian inference, is like comparing astronomy and fishing. They  
 serve different purposes. Do you know Dempster Shafer theory of  
 evidence? This seems to me addressing aptly the weakness of Bayesian  
 inference.

 Bruno

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Re: Bayes Destroyed?

[Bruno Marchal]

On 30 Aug 2009, at 10:12, marc.geddes wrote:




 On Aug 30, 7:23 pm, Bruno Marchal marc...@ulb.ac.be wrote:
 On 30 Aug 2009, at 07:06, marc.geddes wrote:


 It’s true that there is no wave function collapse in Bohm, so it  
 uses
 the same math as Everett.  But Bohm does not interpret the wave
 function in ‘many world’ terms, in Bohm the wave function doesn’t
 represent concrete reality, its just an abstract field – the  
 concrete
 reality is the particles, which are on a separate level of  
 reality, so
 there are no ‘zombies’ in the wave function.

 In Bohm, the wave is not an abstract field, it plays a concrete role
 in the determination of the position of the particles I can observed.
 It is not a question of interpretation, it follows form the fact that
 the wave guides the particles by simulating completely the parallel
 branches. And in those branches the person acts exactly like  
 believing
 they are made of particles like us.
 How could we know that we belong to the branch with particles? We  
 need
 already to abandon CTM here.

 Yes, in Bohm the wave is 'real' , but to interpret the wave as
 actually referring to ordinary concrete things is already to
 presuppose 'many worlds' ;


Assuming the negation of computationalism in the cognitive science  
(like Bohm, I think). So why not.

But look at this. I decide to do the following experience. I prepare  
an electron so that it is in state up+down. I measure it in the base  
{up, down}, and I decide to take holiday in the North if I find it up,  
and to the south, if I find it down.
Not only that. I decide to go, after the holiday,  to the amnesia  
center where all my memories, from the state of the electron to  
everything which follows, except my feeling about how much I enjoy the  
holliday. And I am asked to answer by yes or no to the question did  
you enjoy your holiday. Then, thanks to the amnesia my yes+no states  
will be used In this way.  I interfere with myself, and what will  
follow in the new branch where I have fuse with myself, my, and your,  
future is determined by my contentment qualia, in the two branches of  
the waves.
In Everett universal wave (or Heisenberg universal matrix) and already  
in arithmetic, physicalness is an indexical, we don't need the  
notion of reality, just relative self-consistency.
We can cease to reify matter, and this is nice because I think that  
this is what stuck us on the mind-body problem so long.





 reality has two levels, so really there's
 two different definitions of 'real' in Bohm.


You say so.




 There are no 'people' in
 the wave, its a more abstrast entity than ordinary concrete reality.


Ordinary concrete reality is a projection of the ordinary universal  
machine from an infinity of them, to sum up roughly UDA conclusion.

A deep weakness of Bohm, is that we can do all the possible uses of QM  
from the SWE only, and then we have to solve a complex potential  
equation to just eliminate the possibility of life and consciousness  
in the parallel world?
And this by assuming weird things like non-locality (the root of Bohm  
non reductionism, I think), and non comp (or is this the root of non  
reductionism.

But then why not.

I find this not highly plausible, but if you make clear your theory  
and reason validly there is no problem, go for it.




 Brent did make the point that it has trouble with field theory, but
 this problem is a feature of other interpretations also.  Brent also
 criticised the non-locality, but again, this problem is a feature of
 all other interpretations also.

 I disagree. Everett restores locality, as he explains himself.  
 Deutsch
 and Hayden wrote a paper explaining rather well how locality is
 completely restored in the many-worlds view.
 And as I said, comp alone entails the many worlds (or many
 dreams, ...). That part of the SWE confirms comp. If I remember well,
 Bohm intuited this and made some case against the computationalist
 hypothesis.

 Bruno

 If MWI does eliminate non-locality, that would be a strong point in
 its favor,

Cool.



 but is there any conclusive paper demonstrating that its
 done this?  I have not heard of one - I assume the Deutsch/Hayden
 paper is just their attempt to restore locality which does not
 succeed.


The first time I understood this is in the reading of Everett long  
text. But it was still a bit unclear until I read the Everett FAQ  
(Michael Clive Price:  http://www.hedweb.com/manworld.htm), which  
convinces me that it should not been so much difficult to prove, from  
the SWE, that the worlds appears local for the normal observers. (no  
use of Bayes!)
A non rigorous yet convincing (!) proof of QM locality (in the normal  
branches) has been found by Tipler.
Deutsch and Hayden, makes this even more precise, using the Heisenberg  
picture. Somehow an experience (a preparation) is a partitioning of  
the local accessible part of the multiverse, and measurement are  
generalized self-localization in 

Re: Bayes Destroyed?

[Bruno Marchal]

On 30 Aug 2009, at 10:34, marc.geddes wrote:




 On Aug 30, 7:05 pm, Bruno Marchal marc...@ulb.ac.be wrote:

 This does not make sense.

 You said;

 The truth of Gödel sentences are formally trivial.
 The process of finding out its own Gödel sentence is
 mechanical.
 The diagonilization is constructive. Gödel's
 proof is constructive. That is what Penrose and Lucas are missing
 (notably).

 This contradicts Godel.  The truth of any particular Godel sentence
 cannot be formally determined from within the given particular formal
 system - surely that's what Godel says?

Not at all. Most theories can formally determined their Gödel  
sentences, and even bet on them.
They can use them to transform themselves into more powerful, with  
respect to probability, machines, inheriting new Gödel sentences, and  
they can iterate this in the constructive transfinite. A very nice  
book is the inexhaustibility by Torkel Franzen.

Machine can determined their Gödel sentences. They cannot prove them,  
but proving is not the only way to know the truth of a proposition.  
The fact that G* is decidable shows that a very big set of unprovable  
but true sentences can be find by the self-infering machine. The  
machine can prove that if those sentences are true, she cannot prove  
them, and she can know, every day, that they don't have a proof of  
them. They can instinctively believe in some of them, and they can be  
aware of some necessity of believing in some other lately.



 The points are addressed in ‘Shadows of The Mind’ (Section 2.6,
 Q6).

Hmm...



 The point of Penrose/Lucs is that you can only formally determine the
 Godel sentence of a given system from *outside* that system.

The cute thing is that you can find them by inside. You just can prove  
them, unless you take them as new axiom, but then you are another  
machine and get some new Godel sentences. Machines can infer that some  
arithmetical sentences are interesting question only. The machine  
can see the mystery, when she looks deep enough herself.

I would say it is very well known, by all logicians, that Penrose and  
Lucas reasoning are non valid. A good recent book is Torkel Franzen  
Use and abuse of Gödel's theorem.
Another classic is Judson Webb's book.
Ten years before Gödel (and thus 16 years before Church, Turing, ...)  
Emil Post has dicovered Church thesis, its consequences in term of  
absolutely insoluble problem and relatively undecidable sentences, and  
the Gödelian argument against mechanism, and the main error in those  
type of argument. Judson Webb has seen the double razor edge feature  
of such argument. If you make them rigorous, they flash back and you  
help the machines to make their points.


 We
 cannot determine *our own* Godel sentences formally,

We can, and this at each level of substitution we would choose. But  
higher third person level exists also (higher than the substitution  
level) and are close to philosophical paradoxes.

AUDA comes from the fact that ,not only machine can determined and  
study their Gödel sentences, but they can study how those sentences  
determined different geometries according to the points of view which  
is taken (cf the eight arithmetical hypostases in AUDA).

Bruno


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




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Re: Bayes Destroyed?

[Bruno Marchal]

On 30 Aug 2009, at 18:55, Bruno Marchal wrote:


 Not at all. Most theories can formally determined their Gödel
 sentences, and even bet on them.
 They can use them to transform themselves into more powerful, with
 respect to probability, machines, inheriting new Gödel sentences, and
 they can iterate this in the constructive transfinite. A very nice
 book is the inexhaustibility by Torkel Franzen.


I mean povability.   (the b is too much close to the v on my  
keyboard!)
Sorry.


 Machine can determined their Gödel sentences. They cannot prove them,
 but proving is not the only way to know the truth of a proposition.
 The fact that G* is decidable shows that a very big set of unprovable
 but true sentences can be find by the self-infering machine.

found. I guess.

I am so sorry for my english.


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




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Re: Bayes Destroyed?

[marc.geddes]

On Aug 31, 4:55 am, Bruno Marchal marc...@ulb.ac.be wrote:
 On 30 Aug 2009, at 10:34, marc.geddes wrote:







  On Aug 30, 7:05 pm, Bruno Marchal marc...@ulb.ac.be wrote:

  This does not make sense.

  You said;

  The truth of Gödel sentences are formally trivial.
  The process of finding out its own Gödel sentence is
  mechanical.
  The diagonilization is constructive. Gödel's
  proof is constructive. That is what Penrose and Lucas are missing
  (notably).

  This contradicts Godel.  The truth of any particular Godel sentence
  cannot be formally determined from within the given particular formal
  system - surely that's what Godel says?

 Not at all. Most theories can formally determined their Gödel  
 sentences, and even bet on them.
 They can use them to transform themselves into more powerful, with  
 respect to probability, machines, inheriting new Gödel sentences, and  
 they can iterate this in the constructive transfinite. A very nice  
 book is the inexhaustibility by Torkel Franzen.

Yes, ok, fair enough, they can formally FIND the Godel sentences, but
can't formally PROVE them, that's what I meant.

 Machine can determined their Gödel sentences. They cannot prove them,  
 but proving is not the only way to know the truth of a proposition.  
 The fact that G* is decidable shows that a very big set of unprovable  
 but true sentences can be find by the self-infering machine. The  
 machine can prove that if those sentences are true, she cannot prove  
 them, and she can know, every day, that they don't have a proof of  
 them. They can instinctively believe in some of them, and they can be  
 aware of some necessity of believing in some other lately.

Right, they can't formally prove them, and require an additional step
('instinctively believe')mathematical intuition (analogical reasoning)
to actualy believe in them.




  The points are addressed in ‘Shadows of The Mind’ (Section 2.6,
  Q6).

 Hmm...



  The point of Penrose/Lucs is that you can only formally determine the
  Godel sentence of a given system from *outside* that system.

 The cute thing is that you can find them by inside. You just can prove  
 them, unless you take them as new axiom, but then you are another  
 machine and get some new Godel sentences. Machines can infer that some  
 arithmetical sentences are interesting question only. The machine  
 can see the mystery, when she looks deep enough herself.

Sorry, see above, I meant to say,

 'the point of Penrose/Lucus is that you can only formally PROVE the
Godel senetence of a given systen from *outside* that system'

I accept that the 'machine can see the mystery', but not through any
ordinary reasoning methods. (you need analogical reasoning)


 I would say it is very well known, by all logicians, that Penrose and  
 Lucas reasoning are non valid. A good recent book is Torkel Franzen  
 Use and abuse of Gödel's theorem.
 Another classic is Judson Webb's book.
 Ten years before Gödel (and thus 16 years before Church, Turing, ...)  
 Emil Post has dicovered Church thesis, its consequences in term of  
 absolutely insoluble problem and relatively undecidable sentences, and  
 the Gödelian argument against mechanism, and the main error in those  
 type of argument. Judson Webb has seen the double razor edge feature  
 of such argument. If you make them rigorous, they flash back and you  
 help the machines to make their points.

  We
  cannot determine *our own* Godel sentences formally,

 We can, and this at each level of substitution we would choose. But  
 higher third person level exists also (higher than the substitution  
 level) and are close to philosophical paradoxes.

OK, sorry, I should have said 'we cannot PROVE *our own* Godel
sentences fomally - getting to the 'higher order' levels needs
acccepting Godel sentences as an axiom, and this needs 'mathematical
intuition' at each step (analogies)



 AUDA comes from the fact that ,not only machine can determined and  
 study their Gödel sentences, but they can study how those sentences  
 determined different geometries according to the points of view which  
 is taken (cf the eight arithmetical hypostases in AUDA).


OK.


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Re: Bayes Destroyed?

[marc.geddes]

On Aug 31, 4:19 am, Bruno Marchal marc...@ulb.ac.be wrote:
 On 30 Aug 2009, at 10:12, marc.geddes wrote:




 But look at this. I decide to do the following experience. I prepare  
 an electron so that it is in state up+down. I measure it in the base  
 {up, down}, and I decide to take holiday in the North if I find it up,  
 and to the south, if I find it down.
 Not only that. I decide to go, after the holiday,  to the amnesia  
 center where all my memories, from the state of the electron to  
 everything which follows, except my feeling about how much I enjoy the  
 holliday. And I am asked to answer by yes or no to the question did  
 you enjoy your holiday. Then, thanks to the amnesia my yes+no states  
 will be used In this way.  I interfere with myself, and what will  
 follow in the new branch where I have fuse with myself, my, and your,  
 future is determined by my contentment qualia, in the two branches of  
 the waves.

This assumes that qualia are completely determined by the wave
function, which (since Bohm is non-reductionist) I'm sure he'd
dispute.  The wave function only predicts physical states, it does not
neccesserily completely determine higher-level properties such qualia
(although of course qualia depends on low-level physics).  If the wave
function DID completely determine the qualia, your example would
indeed contradict Bohm - but Bohm already admits he's non-
reductionist.


 In Everett universal wave (or Heisenberg universal matrix) and already  
 in arithmetic, physicalness is an indexical, we don't need the  
 notion of reality, just relative self-consistency.
 We can cease to reify matter, and this is nice because I think that  
 this is what stuck us on the mind-body problem so long.

  reality has two levels, so really there's
  two different definitions of 'real' in Bohm.

 You say so.

  There are no 'people' in
  the wave, its a more abstrast entity than ordinary concrete reality.

 Ordinary concrete reality is a projection of the ordinary universal  
 machine from an infinity of them, to sum up roughly UDA conclusion.

 A deep weakness of Bohm, is that we can do all the possible uses of QM  
 from the SWE only, and then we have to solve a complex potential  
 equation to just eliminate the possibility of life and consciousness  
 in the parallel world?
 And this by assuming weird things like non-locality (the root of Bohm  
 non reductionism, I think), and non comp (or is this the root of non  
 reductionism.

A weakness of MWI is that it does not describe the reality we actually
see - additional steps are needed to convert wave function to human
observables - Bohm makes this clear, MWI just disguises it.  Even in
MWI, additional unexpected steps (Born probabilities derivation etc)
are needed to convert wave function to what we actually observe.


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Re: Bayes Destroyed?

[Brent Meeker]

marc.geddes wrote:

 On Aug 31, 4:19 am, Bruno Marchal marc...@ulb.ac.be wrote:
   
 On 30 Aug 2009, at 10:12, marc.geddes wrote:
 

   

   
 But look at this. I decide to do the following experience. I prepare  
 an electron so that it is in state up+down. I measure it in the base  
 {up, down}, and I decide to take holiday in the North if I find it up,  
 and to the south, if I find it down.
 Not only that. I decide to go, after the holiday,  to the amnesia  
 center where all my memories, from the state of the electron to  
 everything which follows, except my feeling about how much I enjoy the  
 holliday. And I am asked to answer by yes or no to the question did  
 you enjoy your holiday. Then, thanks to the amnesia my yes+no states  
 will be used In this way.  I interfere with myself, and what will  
 follow in the new branch where I have fuse with myself, my, and your,  
 future is determined by my contentment qualia, in the two branches of  
 the waves.
 

 This assumes that qualia are completely determined by the wave
 function, which (since Bohm is non-reductionist) I'm sure he'd
 dispute.  The wave function only predicts physical states, it does not
 neccesserily completely determine higher-level properties such qualia
 (although of course qualia depends on low-level physics).  If the wave
 function DID completely determine the qualia, your example would
 indeed contradict Bohm - but Bohm already admits he's non-
 reductionist.


   
 In Everett universal wave (or Heisenberg universal matrix) and already  
 in arithmetic, physicalness is an indexical, we don't need the  
 notion of reality, just relative self-consistency.
 We can cease to reify matter, and this is nice because I think that  
 this is what stuck us on the mind-body problem so long.

 
 reality has two levels, so really there's
 two different definitions of 'real' in Bohm.
   
 You say so.

 
 There are no 'people' in
 the wave, its a more abstrast entity than ordinary concrete reality.
   
 Ordinary concrete reality is a projection of the ordinary universal  
 machine from an infinity of them, to sum up roughly UDA conclusion.

 A deep weakness of Bohm, is that we can do all the possible uses of QM  
 from the SWE only, and then we have to solve a complex potential  
 equation to just eliminate the possibility of life and consciousness  
 in the parallel world?
 And this by assuming weird things like non-locality (the root of Bohm  
 non reductionism, I think), and non comp (or is this the root of non  
 reductionism.
 

 A weakness of MWI is that it does not describe the reality we actually
 see - additional steps are needed to convert wave function to human
 observables - Bohm makes this clear, MWI just disguises it.  Even in
 MWI, additional unexpected steps (Born probabilities derivation etc)
 are needed to convert wave function to what we actually observe.
But in Bohmian QM the guide-potential just determines where a particle 
goes.  So all but one of the possible paths are empty, which one is 
realized is just slipping the problem in the back door.

Brent

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Re: Bayes Destroyed?

[marc.geddes]

On Aug 31, 3:23 pm, Brent Meeker meeke...@dslextreme.com wrote:
 marc.geddes wrote:


  A weakness of MWI is that it does not describe the reality we actually
  see - additional steps are needed to convert wave function to human
  observables - Bohm makes this clear, MWI just disguises it.  Even in
  MWI, additional unexpected steps (Born probabilities derivation etc)
  are needed to convert wave function to what we actually observe.

 But in Bohmian QM the guide-potential just determines where a particle
 goes.  So all but one of the possible paths are empty, which one is
 realized is just slipping the problem in the back door.


But MWI has the same problem, it just states it in different terms, in
MWI all worlds exist, but which one will we actually observe?  In
Bohm, only one world is there, but which of the paths in the wave
function is it?


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Re: Bayes Destroyed?

[marc.geddes]

On Aug 29, 5:30 am, Brent Meeker meeke...@dslextreme.com 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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Re: Bayes Destroyed?

[Brent Meeker]

marc.geddes wrote:

 On Aug 29, 5:21 am, Brent Meeker meeke...@dslextreme.com 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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Re: Bayes Destroyed?

[Brent Meeker]

marc.geddes wrote:

 On Aug 29, 5:30 am, Brent Meeker meeke...@dslextreme.com 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 

Re: Bayes Destroyed?

[marc.geddes]

On Aug 29, 6:41 pm, Brent Meeker meeke...@dslextreme.com wrote:
 marc.geddes wrote:

  On Aug 29, 5:30 am, Brent Meeker meeke...@dslextreme.com 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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Re: Bayes Destroyed?

[marc.geddes]

On Aug 29, 6:16 pm, Brent Meeker meeke...@dslextreme.com 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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Re: Bayes Destroyed?

[marc.geddes]

On Aug 29, 6:50 pm, Brent Meeker meeke...@dslextreme.com 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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Re: Bayes Destroyed?

[Brent Meeker]

marc.geddes wrote:

 On Aug 29, 6:41 pm, Brent Meeker meeke...@dslextreme.com wrote:
   
 marc.geddes wrote:

 
 On Aug 29, 5:30 am, Brent Meeker meeke...@dslextreme.com 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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Re: Bayes Destroyed?

[Brent Meeker]

marc.geddes wrote:

 On Aug 29, 6:50 pm, Brent Meeker meeke...@dslextreme.com 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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Re: Bayes Destroyed?

[marc.geddes]

On Aug 29, 7:34 pm, Brent Meeker meeke...@dslextreme.com 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=186ID=4726

It remains to be seen how it gets developed.
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Re: Bayes Destroyed?

[Bruno Marchal]

On 29 Aug 2009, at 07:15, marc.geddes wrote:




 On Aug 29, 2:36 am, Bruno Marchal marc...@ulb.ac.be 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;

OK.
Computability is absolute,
Provability is relative.



 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?.

In principle. No ignorabimus as Hilbert said. Yet no machine or  
formal systems can prove propositions too much complex relatively to  
themselves, and there is a sense to say that some proposition are  
undecidable in some absolute way, relative to themselves.



 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.

Not really. The process of finding out its own Gödel sentence is  
mechanical. Machines can guess or infer their own consistency, for  
example. In AUDA intuition appears with the modality having  p in  
the definition (Bp  p, Bp  Dp  p).
Those can be related with Bergsonian time, intuitionistic logic,  
Plotinus universal soul, and sensible matter.




 So to find a math technique powerful enough to decide Godel
 sentences ,

This already exists. The diagonilization is constructive. Gödel's  
proof is constructive. That is what Penrose and Lucas are missing  
(notably).



 we look for a reasoning technique which is non-axiomatic,

This is the case for the  p modalities. They are provably  
necessarily non axiomatisable. They lead to the frst person, which,  
solipstically, does separate truth and provability.




 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


Those are easily axiomatized.
I see the relation analogy-category, but sets and functions are  
together, and not analogical imo.
I don't see at all the link between Bayes and functions/relations.  
Actually, function/relations are the arrows in a category.




 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

You may use some toposes (cartesian close category with a sub-object  
classifier). Those are mathematical mathematicians. But assuming  
comp, does not let you much choice on which topos you can choose. It  
has to be related to the S4Grz epistemic logic (in the ideal case).




 (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.


The truth of Gödel sentences are formally trivial. That is why  
consistency is a nice cousin of consciousness. It can be shown to be  
true easily by the system, and directly (in few steps), yet remains  
unprovable by the system, not unlike the fact that we can be quasi  
directly conscious, yet cannot prove it. Turing already exploited this  
in his system of logic based on ordinal (his thesis with Church).

Bruno

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




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Re: Bayes Destroyed?

[Bruno Marchal]

On 29 Aug 2009, at 08:09, marc.geddes wrote:

 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!


Bohm's QM is a variant of QM, which keeps the Everett many worlds, but  
use a very unclear theory of mind, and a very unclear notion of  
particle to make one hidden Everett branch of reality more real than  
the other, and this by reintroducing non-locality in the picture, and  
many zombies in the universal wave.

Bruno


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




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Re: Bayes Destroyed?

[Bruno Marchal]

On 29 Aug 2009, at 14:10, Bruno Marchal wrote:

 This is the case for the  p modalities. They are provably
 necessarily non axiomatisable. They lead to the frst person, which,
 solipstically, does separate truth and provability.



I mean does NOT separate truth and provability (like solipsist).

Sorry,

Bruno


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




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Re: Bayes Destroyed?

[marc.geddes]

On Aug 30, 12:10 am, Bruno Marchal marc...@ulb.ac.be wrote:


 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.

 Not really. The process of finding out its own Gödel sentence is  
 mechanical. Machines can guess or infer their own consistency, for  
 example. In AUDA intuition appears with the modality having  p in  
 the definition (Bp  p, Bp  Dp  p).
 Those can be related with Bergsonian time, intuitionistic logic,  
 Plotinus universal soul, and sensible matter.



  So to find a math technique powerful enough to decide Godel
  sentences ,

 This already exists. The diagonilization is constructive. Gödel's  
 proof is constructive. That is what Penrose and Lucas are missing  
 (notably).

 The truth of Gödel sentences are formally trivial. That is why
 consistency is a nice cousin of consciousness. It can be shown to be
 true easily by the system, and directly (in few steps), yet remains
 unprovable by the system, not unlike the fact that we can be quasi
 directly conscious, yet cannot prove it. Turing already exploited this
 in his system of logic based on ordinal (his thesis with Church).


Penrose deals with this point in ‘Shadows of The Mind’ (Section 2.6,
Q6);

‘although the procedure for obtaining (Godel sentences from a formal
system) can be put into the form of a computation, this computation is
not part of the procedures contained in (the formal system).  It
cannot be, because (the formal system) is not capable of ascertaining
the truth of (Godel sentences), whereas the new computation – together
with (the formal system) is asserted to be able to’


In ‘I Am a Strange Loop’, Hofstadter argues that the procedure for the
determining the truth of Godel sentences  is actually a form of
analogical reasoning.  (Chapters 10-12)

(page 148)

‘by virtue of Godel’s subtle new code, which systematically mapped
strings of symbols onto numbers and vice versa, many formulas could be
read on a second level.  The first level of meaning obtained via the
standard mapping, was always about numbers, just as Russell claimed,
but the second level of meaning, using Godel’s newly revealed mapping…
was about formulas’
…
(page 158)

‘all meaning is mapping mediated, which is to say, all meaning comes
from analogies’





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

 Those are easily axiomatized.
 I see the relation analogy-category, but sets and functions are  
 together, and not analogical imo.
 I don't see at all the link between Bayes and functions/relations.  
 Actually, function/relations are the arrows in a category.

See what I said in my first post this thread.  The Bayes theorem is
the central formula for statistical inference.  Statistics in effect
is about correlated variables.  Functions/Relations are just the
abstract (ideal) version of this where the correlations are perfect
instead of fuzzy (functions/relations map the elements of two sets).
That’s why I say that Bayesian inference bears a strong ‘family
resemblance’ to functions/relations.

You agreed that analogies bear a strong ‘family resemblance’ to
categories.

Category theory *includes* the arrows. So if the arrows are the
functions and relations (which I argued bears a strong family
resemblance to Bayesian inference), and the categories (which you
agreed bear a family resemblance to analogies) are primary, then this
proves my point, Bayesian inferences are merely special cases of
analogies, confirming that analogical reasoning is primary.


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Re: Bayes Destroyed?

[marc.geddes]

On Aug 30, 12:22 am, Bruno Marchal marc...@ulb.ac.be wrote:
 On 29 Aug 2009, at 08:09, marc.geddes wrote:

  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!

 Bohm's QM is a variant of QM, which keeps the Everett many worlds, but  
 use a very unclear theory of mind, and a very unclear notion of  
 particle to make one hidden Everett branch of reality more real than  
 the other, and this by reintroducing non-locality in the picture, and  
 many zombies in the universal wave.

 Bruno


It’s true that there is no wave function collapse in Bohm, so it uses
the same math as Everett.  But Bohm does not interpret the wave
function in ‘many world’ terms, in Bohm the wave function doesn’t
represent concrete reality, its just an abstract field – the concrete
reality is the particles, which are on a separate level of reality, so
there are no ‘zombies’ in the wave function.

The Bohm interpretation is actually the clearest of all
interpretations.  It does away with the enormous multiverse edifice of
unobservables, whilst at the same time maintaining a realist picture
of reality (agrees that wave function is real and doesn’t collapse,
whilst placing a single concrete reality on a different level).

You may like to look the volume (‘Quantum Implications’, B.J.Hiley,
F.David Peat) for examples of how the Bohm interpretation makes
problems which are unclear with other interpreations, very clear with
Bohm.  Since Bohm is non-reductionist and no conclusive rebuttals have
been found in over 50 years, it counts as evidence against the
reductionist world-view (and thus also evidence against Bayes).

Brent did make the point that it has trouble with field theory, but
this problem is a feature of other interpretations also.  Brent also
criticised the non-locality, but again, this problem is a feature of
all other interpretations also.

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Re: Bayes Destroyed?

[marc.geddes]

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
case;

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
inference (categories)

For each point, there's some evidence that analogical *can* handle the
problem:

(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
inference


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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Re: Bayes Destroyed?

[marc.geddes]

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:

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=186ID=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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Re: Bayes Destroyed?

[marc.geddes]

On Aug 27, 7:35 pm, Bruno Marchal marc...@ulb.ac.be 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/3012/01/statisti.pdf+%22bayesian+inference%22+%22problem+of+priors%22cd=9hl=enct=clnkgl=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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Re: Bayes Destroyed?

[Bruno Marchal]

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




 On Aug 27, 7:35 pm, Bruno Marchal marc...@ulb.ac.be 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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Re: Bayes Destroyed?

[Brent Meeker]

marc.geddes wrote:
 
 
 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.

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=186ID=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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Re: Bayes Destroyed?

[Brent Meeker]

marc.geddes wrote:
 
 
 On Aug 27, 7:35 pm, Bruno Marchal marc...@ulb.ac.be 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/3012/01/statisti.pdf+%22bayesian+inference%22+%22problem+of+priors%22cd=9hl=enct=clnkgl=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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Re: Bayes Destroyed?

[marc.geddes]

On Aug 29, 2:36 am, Bruno Marchal marc...@ulb.ac.be 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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Re: Bayes Destroyed?

[marc.geddes]

On Aug 29, 5:21 am, Brent Meeker meeke...@dslextreme.com 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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Re: Bayes Destroyed?

[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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Re: Bayes Destroyed?

[Brent Meeker]

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