Bayes Destroyed?
marc.geddes
-- P.C. Hodgell
Today, among logicians, Bayesian Inference seems to be the new dogma
for all encompassing theory of rationality. But I have different
ideas, so I'm going to present an argument suggesting an alternative
form of reasoning. In essence, I going to start to try to bring down
the curtain on the Bayesian dogma. This is not the end, but it *is*
‘the beginning of the end’ (as Churchill once nicely put it). I'm a
fan of David Bohm, the physicist who developed the 'Pilot Wave'
Interpretation of QM (which I like). So I base my argument on his
ideas.
The genius of David Bohm was that he showed that there’s a perfectly
consistent interpretation of quantum mechanics which completely
reverses the normal way that physicists think about the relationship
between particles and background forces – physicists tend to think of
particles as real static objects moving around in a nebulous backdrop
of force fields. Bohm turned this on its head and said why not regard
the *background forces* as primary and view particles as simply
temporary ‘pockets of stability’ in the background forces. This idea
is implied by his interpretation of quantum mechanics, where there’s
a ‘pilot wave’ (the quantum potential) which is primary and particles
are in effect ‘epiphenomen’ (mere aspects) of the deeper pilot wave.
Now my idea as regards rationality is exactly analogous to Bohm’s idea
as regards physics. In the standard theory of rationality, causal
explanations (Bayesian reasoning) is primary and intuition (Analogies/
Narratives) is merely an imperfect human-invented ‘backdrop’ or
scaffolding. My theory totally reverses the conevntional view. I
say, why not take analogies/narratives as the primary ‘stuff’ of
thought, and causal explanations (Bayes) as merely
‘crystallized’ (unusually precise) analogies?
Bayesian reasoning is exactly analogous to algebra in pure math,
because with Bayes you are in effect trying to find correlations
between variables, where the correlations are imprecise or
fuzzy. .Algebra is about *relations and functions* which in effect
maps two given sets of elements (correlate them). So I suggest that
algebra is simply the ‘abstract ideal’ of Bayes, where the
correlations between variables are 100% precise (think of elements of
sets as the ‘variables’ of statistics).
Now…. Does algebra have any limitations? Yes! Algebra cannot fully
reason about algebra. This is the real meaning of Godel’s theorem –
he showed that any formal system (which is in effect equivalent to an
algebraic system) complex enough to include both multiplication and
addition, has statements that cannot be proved within that system.
Since algebra is exactly analogous to Bayes, we can conclude that
Bayes cannot reason about Bayes, no system of statistical inference
can be used to fully reason about itself.
But is there a form of math more powerful than algebra? Yes, Category/
Set Theory! Unlike algebra, Category/Set theory really *can* fully
reason about itself, since Sets/categories can contain other Sets/
Categories. Greg Cantor first explored these ideas in depth with his
transfinite arithmetic, and in fact it was later shown that the use of
transfinite induction can in theory bypass the Godel limitations. (See
Gerhard Gentzen)
By analogy, there’s another form of reasoning more powerful than
Bayes, the rationalist equivalent of Set/Category theory. What could
it be? Well, Sets/Category theory is very analogous to
categorization, a known form of inference involving grouping concepts
according to their degree of similarity – this is arguably the same
thing as…analogy formation! Indeed, I’ve been using analogical
arguments throughout this post, showing that analogical inference is
perfectly capable of reasoning about itself. My punch-line? Bayesian
inference is merely a special case of analogy formation.
If all this seems hard to believe at first I suggest readers go back
and look at the analogy I gave with Bohm’s ideas about physics.
Remember Bohm’s ‘complete reversal’ of the normal way of thinking
about physics turned out to be fully consistent. All I’ve done is
performed the same trick as Bohm in the field of cognitive science.
Just as ‘particles’ become mere epiphenomena of a ‘pilot wave’,
‘Bayes’ becomes a mere epiphenona of analogy formation.
Time for Bayesian logicians to fill their trousers? ;)
Bruno Marchal
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)
Brent Meeker
> "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.
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.
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.
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.
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)
example of the incompleteness that Godel proved.
>
> By analogy, there’s another form of reasoning more powerful than
> Bayes, the rationalist equivalent of Set/Category theory. What could
> it be? Well, Sets/Category theory is very analogous to
> categorization, a known form of inference involving grouping concepts
> according to their degree of similarity – this is arguably the same
> thing as…analogy formation! Indeed, I’ve been using analogical
> arguments throughout this post, showing that analogical inference is
> perfectly capable of reasoning about itself. My punch-line? Bayesian
> inference is merely a special case of analogy formation.
>
> If all this seems hard to believe at first I suggest readers go back
> and look at the analogy I gave with Bohm’s ideas about physics.
> Remember Bohm’s ‘complete reversal’ of the normal way of thinking
> about physics turned out to be fully consistent. All I’ve done is
> performed the same trick as Bohm in the field of cognitive science.
> Just as ‘particles’ become mere epiphenomena of a ‘pilot wave’,
> ‘Bayes’ becomes a mere epiphenona of analogy formation.
to difficult, if not impossible, to create a relativistic version that
could account for particle production (a consequence of taking
particles as fundamental).
Brent
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
>
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.
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."
just causal relations, Bayes deals only with prediction of causal
relations.. A more important component of explanation is
categorization. See:
http://en.wikipedia.org/wiki/Categorization
"Categorization is the process in which ideas and objects are
recognized, differentiated and understood. Categorization implies that
objects are grouped into categories, usually for some specific
purpose."
Analogies are concerned with Categorization, and thus go beyond mere
prediction. See ‘Analogies as Categorization’ (Atkins)
:
http://www.compadre.org/PER/document/ServeFile.cfm?DocID=186&ID=4726
“I provide evidence that generated analogies are assertions of
categorization, and the
base of an analogy is the constructed prototype of an ad hoc category”
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.
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.
priors only work for simple problems, and complexity priors are
uncomputable. The deeper problem of different models cannot be
solved by Bayesian inference at all:
See:
http://74.125.155.132/search?q=cache:_XQwv9eklmkJ:eprints.pascal-network.org/archive/00003012/01/statisti.pdf+%22bayesian+inference%22+%22problem+of+priors%22&cd=9&hl=en&ct=clnk&gl=nz
"One of the most criticized issues in the Bayesian approach is related
to
priors. Even if there is a consensus on the use of probability
calculus to
update beliefs, wildly different conclusions can be arrived at from
different
states of prior beliefs. While such differences tend to diminish with
increas-
ing amount of observed data, they are a problem in real situations
where
the amount of data is always finite. Further, it is only true that
posterior
beliefs eventually coincide if everyone uses the same set of models
and all
prior distributions are mutually continuous, i.e., assign non-zero
probabili-
ties to the same subsets of the parameter space (‘Cromwell’s rule’,
see [67];
these conditions are very similar to those guaranteeing consistency
[8]).
As an interesting sidenote, a Bayesian will always be sure that her
own
predictions are ‘well-calibrated’, i.e., that empirical frequencies
eventually
converge to predicted probabilities, no matter how poorly they may
have
performed so far [22].
It is actually somewhat misleading to speak of the aforementioned
crit-
icism as the ‘problem of priors’, as it were, since what is meant is
often at
least as much a ‘problem of models’: if a different set of models is
assumed,
differences in beliefs never vanish even with the amount of data going
to
infinity."
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
Brent Meeker
>
>
> 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.
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.
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:
Occam's razor in selecting between models.
http://quasar.as.utexas.edu/papers/ockham.pdf
>
> See:
> http://74.125.155.132/search?q=cache:_XQwv9eklmkJ:eprints.pascal-network.org/archive/00003012/01/statisti.pdf+%22bayesian+inference%22+%22problem+of+priors%22&cd=9&hl=en&ct=clnk&gl=nz
>
>
> "One of the most criticized issues in the Bayesian approach is related
> to
> priors. Even if there is a consensus on the use of probability
> calculus to
> update beliefs, wildly different conclusions can be arrived at from
> different
> states of prior beliefs.
>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.
Judaism. Why would any correct theory of degrees of belief suppose
that finite data should remove all doubt?
Brent
>
>
> >
>
Brent Meeker
>
>
> 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=186&ID=4726
>
> “I provide evidence that generated analogies are assertions of
> categorization, and the
> base of an analogy is the constructed prototype of an ad hoc category”
One may invent analogies and categories, but how do you know they are
not just arbitrary manipulation of symbols unless you can predict
something from them. This seems to me to be an appeal to mysticism
(of which Bohm would approve) in which "understanding" becomes a
mystical inner feeling unrelated to action and consequences.
Brent
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.
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.
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.
>
> 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 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?
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 ;)
marc.geddes
On Aug 29, 5:30 am, Brent Meeker <meeke...@dslextreme.com> 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.
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
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.
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.
>
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.
Brent Meeker
>
> 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 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
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.
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
Brent Meeker
>
> 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.
>
(representations of knowledge) before you can worry your degree of
belief in them. But you started with the assertion that you were going
to "destroy Bayesian reasoning" and since Bayes=reductionism this was
going to destroy reductionism. Now, you've settled down to saying that
forming categories is prior to Bayesian reasoning. People that post
emails with outlandish assertions simply to stir up responses are called
"Trolls".
>
>
>
>
>>> http://en.wikipedia.org/wiki/Implicate_and_Explicate_Order_according_...
>>>
>> This is obviously written by an advocate of Bohm's philosophy - of
>> which his reformulation of Schrodinger's equation was on a small,
>> suggestive part. Note that Bohmian quantum mechanics implies that
>> everything is deterministic - only one sequence of events happens and
>> that sequence is strictly determined by the wave-function of the
>> universe and the initial conditions. Of course it doesn't account for
>> particle production and so is inconsistent with cosmogony and relativity.
>>
>> Brent
>>
>
> This is not a failing of the Bohemian interpretation, because *every*
> interpretation of quantum mechanics suffers from it ; no one has yet
> succeed in producing a consistent quantum field theory for the simple
> reason that general relatively contradicts quantum mechanics.
>
But Bohmian QM isn't even compatible with special relativity - which
quantum field theory is. QFT handles particle production just fine.
>
>
>>> Associations are causal relations. But true explanation is more than
>>> just causal relations, Bayes deals only with prediction of causal
>>> relations..
>>>
>> Bayes deals with whatever you put a probability measure on. Most
>> often it is cited as applying to degrees of belief, which is what
>> Cox's theorem is about.
>>
>
> But what justifies Cox's theorem?
Read it. It's an axiomatic deduction from some axioms about what
constitutes a rational adjust of belief based on data.
> Ultimately, to try to justify math
> you can’t use ‘degrees of belief’, but have to fall back on deep math
> like Set/Categoy theory (since Sets/Categories are the foundation of
> mathematics).
How do you justify set theory? By appeal to axioms that seem
intuitively true, with some adjustments to make the deductions
interesting. For example set theory says {{}}=/={} even though most
people find {{}}={} intuitive, but it would be hard to build things on
the empty set with the latter as an axiom.
> This shows that Bayes can’t be foundational
>
I never said it was. Although the fact that it has not been used in an
axiomatic foundation of math doesn't prove that it couldn't be.
>
>> One may invent analogies and categories, but how do you know they are
>> not just arbitrary manipulation of symbols unless you can predict
>> something from them. This seems to me to be an appeal to mysticism
>> (of which Bohm would approve) in which "understanding" becomes a
>> mystical inner feeling unrelated to action and consequences.
>>
>> Brent-
>>
>
> Pure mathematics is a science which is not based on prediction,
> instead it is about finding structural relationships between different
> concepts (integrating different pieces of knowledge). Categories form
> the basis for knowledge representation and pure mathematics, which is
> prior to any sort of prediction. Category/Set Theory is utterly
> precise science, the opposite of mysticism.
>
But it's not based on analogical rules of inference either.
> Bohm's interpretation of QM is utterly precise and was published in a
> scientific journal (Phys. Rev, 1952). In the more than 50 years
> since, no technical rebuttal has yet been found, and it is fully
> consistent with all predictions of standard QM.
In fact it's mathematically equivalent to Schrodinger's equation with
just a different interpetation.
> In fact the Bohm
> interpretation is the only realist interpretation offering a clear
> picture of what’s going on – other interpretations such as Bohr deny
> that there’s an objective reality at all at the microscopic level,
> bring in vague ideas like the importance of ‘consciousness’ or
> ‘observers’ and postulate mysterious ‘wave functions collapses, or
> reference a fantastical ‘multiverse’ of unobservables, disconnected
> from actual concrete reality. Bohm is the *only* non-mystical
> interpretation!
>
It is mystical in that it assumes holism, so that the wave-function of
the universe is instantaneously changed by an interaction anywhere.
> In fact from;
> http://en.wikipedia.org/wiki/Implicate_and_Explicate_Order_according_to_David_Bohm
>
> "Bohm’s paradigm is inherently antithetical to reductionism, in most
> forms, and accordingly can be regarded as a form of ontological
> holism."
>
> Since Bohm's views are non-reductionist and still perfectly
> consistent, this casts serious doubt on the entire reductionist world-
> view on which Bayesian reasoning is based.
I don't know why the mere existence of some consistent holistic math
model - which cannot account for observed particle production - should
count as evidence against a reductionist world view.
Brent
Brent Meeker
>
> 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.
invented ways of producing priors with minimum presumption (e.g. Jaynes
maximum entropy priors). Analogical reasoning doesn't produce priors
either and it can produce false conclusions too.
> Another exmaple would be dream
> states, you could reason probalistically in your sleep, but without
> the correct priors, your dreams will still be largely incoherent.
>
There's a huge difference between incoherent and incorrect.
> Don't get me wrong, I'm sure Bayes is very powerful- I just don't
> think it's the be-all and end-all.
>
>
>> Try basing all your
>> reasoning on analogies.
>>
>> Brent
>>
>
> I do. I think Bayes is just a special case of analogical reasoning ;)
Then you can say analogical reasoning is just a special case of
reasoning. Which then proves that reasoning is more fundamental than
analogical reasoning. Then will you claim to have destroyed analogical
reasoning. ??
Brent
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".
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.
>
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.
marc.geddes
On Aug 29, 6:50 pm, Brent Meeker <meeke...@dslextreme.com> 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.
(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. ??
>
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.
Brent Meeker
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
Brent Meeker
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
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?
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
not yet been well developed, since everyone has focused on Bayesian
reasoning... the point of this post was to show that there's a
neglected alternative.
There's are tentative definitions of analogical reasoning in the
literature, for instance ‘Analogies as Categorization’ (Atkins)
http://www.compadre.org/PER/document/ServeFile.cfm?DocID=186&ID=4726
It remains to be seen how it gets developed.
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
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
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
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).
> 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).
>
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.
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.
marc.geddes
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.
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?
>
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! :)
Bruno Marchal
This does not make sense.
>
>
> 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
Bruno Marchal
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.
>
> The Bohm interpretation is actually the clearest of all
> interpretations.
It is not an interpretation. It is another theory. It is more sensical
than Copenhagen, but is a regression with respect to CTM, which
already explains why "observable reality" emerges from infinities of
computations.
> It does away with the enormous multiverse edifice of
> unobservables,
Nature has always contained many unobservable things, multiplied in
huge quantities, be it galaxies, before Hubble, or water molecules. It
is the basic motto of the "everything" idea that multiplying entities
can make our theories conceptually simpler.
> 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).
It is a form of cosmo-solipism. We always want to be unique, but that
is coquetry.
>
> 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.
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
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.
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
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.
marc.geddes
>The truth of Gödel sentences are formally trivial.
mechanical.
proof is constructive. That is what Penrose and Lucas are missing
(notably).
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.
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.
all math. If category theory is the foundation of math, there must be
structures in there corresponding to Bayes.
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
Bruno Marchal
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 usesthe same math as Everett. But Bohm does not interpret the wavefunction in ‘many world’ terms, in Bohm the wave function doesn’trepresent concrete reality, its just an abstract field – the concretereality is the particles, which are on a separate level of reality, sothere are no ‘zombies’ in the wave function.In Bohm, the wave is not an abstract field, it plays a concrete rolein the determination of the position of the particles I can observed.It is not a question of interpretation, it follows form the fact thatthe wave guides the particles by simulating completely the parallelbranches. And in those branches the person acts exactly like believingthey are made of particles "like us".How could we know that we belong to the branch with particles? We needalready 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, butthis problem is a feature of other interpretations also. Brent alsocriticised the non-locality, but again, this problem is a feature ofall other interpretations also.I disagree. Everett restores locality, as he explains himself. Deutschand Hayden wrote a paper explaining rather well how locality iscompletely restored in the many-worlds view.And as I said, comp alone entails the many "worlds" (or manydreams, ...). That part of the SWE confirms comp. If I remember well,Bohm intuited this and made some case against the computationalisthypothesis.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.
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
Bruno Marchal
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.
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.
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.
('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.
'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.
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).
>
marc.geddes
On Aug 31, 4:19 am, Bruno Marchal <marc...@ulb.ac.be> 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.
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".
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.
Brent Meeker
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
marc.geddes
> > 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.
>
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?
Bruno Marchal
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 preparean 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 amnesiacenter where all my memories, from the state of the electron toeverything which follows, except my feeling about how much I enjoy theholliday. And I am asked to answer by yes or no to the question "didyou enjoy your holiday. Then, thanks to the amnesia my yes+no stateswill be used In this way. I interfere with myself, and what willfollow in the new branch where I have fuse with myself, my, and your,future is determined by my contentment qualia, in the two branches ofthe 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.
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 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?
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.
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).
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
>
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.
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 Bohm is the non-locality,
and non computationalism. And this makes its theory more reductionist
than computationalism.
> but on the other hand its
> picture of the world is much clearer
I have work on comp to understand what is matter, because the naïve
conception leads to many difficulties, both with QM, but also with
comp, and even by itself (try to define matter without matter, for
example).
The reappartion of particles would be a problem for comp, and a
problem for those who does not believe in particles.
> and doesn't require huge
> quantities of unobservables (alternative universes).
This is a quality of the theory. Not only because it confrims the comp
many dreams, but because a unique physical universe would have been
arguably an ontological aberration.
In any case, Everett is a step by physicist toward comp, and in comp,
at the ontic level, we need the least ontology possible: numbers (with
+ and *). All the rest can be explained, and *is* explained by the
discurses of self-observing universal machine.
> 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.
Don't hesitate to dig on those issues. No doubt that Bohm provides an
interesting and indeed coherent non local and non computaionalist
theory.
But it looks for me as a sophisticate attempt to dodge the mind-body
problem, and to make very complex, with his non covariant potential,
what is really much more simple (the SWE).
Bruno