Re: Lob + New Views On Mind-Body Connection

[Jacques Bailhache]

Hi Bruno, I'm back :-)
The axiom B(Bp->p)->Bp seems very strange to me.
Is it applicable only to machines or also to humans ?
Intuitively, let us consider for example p = "Santa Claus exists".
I don't believe that Santa Claus exists (~Bp).
If I consider the proposition "Bp->p" which means "If I believe that Santa 
Claus exists, then Santa Claus exists", this proposition seems true to me, 
because of le propositional logic rule "ex falso quodlibet sequitur" or 
false->p : the false proposition Bp implies any proposition, for example p.
So I can say thay I believe in the proposition Bp->p : B(Bp->p). According 
to the lobian formula B(Bp->p)->Bp, this implies Bp (I believe that Santa 
Claus exist) !

More formally :
The axiom ~Bp->B(~Bp) seems correct to me, isn't it ?
It seems also correct to me to say that the logical rules are valid inside 
believes, for example : (B(p->q) and B(q->r)) -> B(p->r), or B(F->p) where F 
is the false proposition.
Let us consider a p such that ~Bp, which is equivalent to (Bp)->F.
Then we have B(~Bp), which is equivalent to B(Bp->F).
From this and B(F->p) we can infer B(Bp->p).
Finally with the lobian formula B(Bp->p)->Bp we get Bp.
Is there an error anywhere ?
_
Trouvez l'âme soeur sur MSN Rencontres http://g.msn.fr/FR1000/9551

Re: Lob + New Views On Mind-Body Connection

[Bruno Marchal]

Hi Jacques,
Nice to see you back. Actually I just discovered your message
in the archive, I did not got them by the mail (?). Sorry for the delay.
I quote you from the archive:

>The axiom B(Bp->p)->Bp seems very strange to me.
I think it *is* strange. It is at the heart of "counter-intuition" in the sense
that you can derive from it (together with K = B(p->q)->(Bp->Bq) and the
two inference rule MP and NEC) all the consequences of incompleteness.
Do you see how to derive Godel second theorem of incompleteness theorem?
Boolos gives 5 reasons to find Lob's formula, that is B(Bp->p)->Bp,
"utterly astonishing", and he does not mention the placebo effect.
(have you read my last paper?
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.htm  )
>Is it applicable only to machines or also to humans ?
It is applicable to any consistent believer in
(classical) arithmetic, when belief are
checkable. If you prefer the B is for
provable, or Beweisbar (Godel).
For any machine-like entity (with or without
oracle) it gives even their complete
(propositional)
logic of provability and consistency.
It *is* the main axiom of G.
(Note that there is a corresponding
version for intuitionist arithmetic.)

>I don't believe that Santa Claus exists (~Bp).
>If I consider the proposition "Bp->p" which
>means "If I believe that Santa Claus exists,
>then Santa Claus exists", this proposition
>seems true to me, because of le
>propositional logic rule "ex falso quodlibet
>sequitur" or false->p : the false proposition
>Bp implies any proposition, for example p.
>So I can say thay I believe in the proposition
>Bp->p : B(Bp->p). According to the lobian
>formula B(Bp->p)->Bp, this implies Bp (I believe
>that Santa Claus exist) !
It is all correct  except that you cannot
prove (believe) your own consistency; so that
you cannot prove that you don't believe that Santa
Klaus does not exist. All formula beginning by ~B
are not believable (provable) by the consistent machine.

>More formally : The axiom ~Bp->B(~Bp)
>seems correct to me, isn't it ?   
It seems, but not for a notion of checkable or
verifiable belief. Any machine capable of proving
there is a proposition she cannot prove, would
be able to prove its consistency, and that's impossible
by Godel II.  (this follows from your "ex falso quodlibet":
a machine proving the f, will prove all propositions, so if
there is a proposition (like Santa Claus exists) that
you pretend you will never believe (prove) then you
are asserting that you prove (believe) you are consistent!.
All right? I use "believe" instead of "prove" because
we are following a little bit Smullyan's "Forever Undecided".
But this suits well with the "machine psychology".
Do you have that FU book?
Bruno
http://iridia.ulb.ac.be/~marchal/

Re: Lob + New Views On Mind-Body Connection

[Bruno Marchal]

Hi Jacques,
>What is the NEC rule ?
In modal logic it is the NECESSITATION RULE.
It means that if the machine proves p, then it will prove Bp.
Smullyan says such a machine is normal.
Put in another way, with Smullyan's self-referential
interpretation of the B logic: it means that Bp->BBp is true
for the machine. If furthemore the machine knows (correctly
believe) that she is normal, then we call it a type 4 reasoner
(again following Smullyan).
>>Do you see how to derive Godel second theorem
>>of incompleteness theorem?
>I think I see how to derive Gödel theorem :
>if we take p=F (false) we get B(BF->F)->BF
>or B(~BF)->BF. BF means that the machine
>is inconsistent, ~BF that it is consistent.
>If C means that the machine is consistent,
>then B(~BF)->BF becomes BC->~C,
>which means that if the consistency is
>provable, then the machine is not consistent.
Exact.
JB:
It is more clear to me if B means "provable" rather than "believe".
But I wonder if the notion of provability is equivalent to the notion of
belief. Intuitively I have the impression that if I don't believe that Santa
Claus exists, then I believe that I don't believe that Santa Claus exists.
One can believe sonething without having a proof of it. If it is a checkable
belief, why not say that the machine is sure that p, rather than believes p

BM:
B represents indeed "justifiable third person belief". But now, by GODEL II
this does not allow a "sure of" interpretation, and this justify somehow
the use of belief. This reminds us also that science (third person justifiable
propositions) is on the side of belief, and never on certainty. Now, as I told
you, I use the term "believe" because Smullyan uses it and it is quite
coherent with our psychological view of Godel's result.
The "proof" reading of B leads also to the belief that Bp->p, which is
actually true for Self-referentially correct machine, but unprovable
by those machine. Any choice of word has some defect. We are
in the counter-intuition country. "To be sure of p" will be defined by
   p & Bp
following Theaetetus (and Boolos, Goldblatt ...).
Bruno
PS Again, I did not get your post but find it in the archive.
Did you get mine? I wrote to Wei but did not get answers, perhaps
he is on Holiday.
http://iridia.ulb.ac.be/~marchal/

Re: Lob + New Views On Mind-Body Connection

[Jacques Bailhache]

Hi Bruno,
From: Bruno Marchal <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED]
Subject: Re: Lob + New Views On Mind-Body Connection
Date: Thu, 09 Sep 2004 15:46:10 +0200
Hi Jacques,
Nice to see you back. Actually I just discovered your message
in the archive, I did not got them by the mail (?). Sorry for the delay.
I quote you from the archive:

>The axiom B(Bp->p)->Bp seems very strange to me.
I think it *is* strange. It is at the heart of "counter-intuition" in the 
sense
that you can derive from it (together with K = B(p->q)->(Bp->Bq) and the
two inference rule MP and NEC) all the consequences of incompleteness.
What is the NEC rule ?
Do you see how to derive Godel second theorem of incompleteness theorem?
I think I see how to derive Gödel theorem : if we take p=F (false) we get 
B(BF->F)->BF or B(~BF)->BF. BF means that the machine is inconsistent, ~BF 
that it is consistent. If C means that the machine is consistent, then 
B(~BF)->BF becomes BC->~C, which means that if the consistency is provable, 
then the machine is not consistent.

Boolos gives 5 reasons to find Lob's formula, that is B(Bp->p)->Bp,
"utterly astonishing", and he does not mention the placebo effect.
(have you read my last paper?
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.htm  )
I had a look at it.

>Is it applicable only to machines or also to humans ?
It is applicable to any consistent believer in
(classical) arithmetic, when belief are
checkable. If you prefer the B is for
provable, or Beweisbar (Godel).
For any machine-like entity (with or without
oracle) it gives even their complete
(propositional)
logic of provability and consistency.
It *is* the main axiom of G.
(Note that there is a corresponding
version for intuitionist arithmetic.)
It is more clear to me if B means "provable" rather than "believe".
But I wonder if the notion of provability is equivalent to the notion of 
belief. Intuitively I have the impression that if I don't believe that Santa 
Claus exists, then I believe that I don't believe that Santa Claus exists. 
One can believe sonething without having a proof of it. If it is a checkable 
belief, why not say that the machine is sure that p, rather than believes p 
?



>I don't believe that Santa Claus exists (~Bp).
>If I consider the proposition "Bp->p" which
>means "If I believe that Santa Claus exists,
>then Santa Claus exists", this proposition
>seems true to me, because of le
>propositional logic rule "ex falso quodlibet
>sequitur" or false->p : the false proposition
>Bp implies any proposition, for example p.
>So I can say thay I believe in the proposition
>Bp->p : B(Bp->p). According to the lobian
>formula B(Bp->p)->Bp, this implies Bp (I believe
>that Santa Claus exist) !
It is all correct  except that you cannot
prove (believe) your own consistency; so that
you cannot prove that you don't believe that Santa
Klaus does not exist. All formula beginning by ~B
are not believable (provable) by the consistent machine.

>More formally : The axiom ~Bp->B(~Bp)
>seems correct to me, isn't it ?   
It seems, but not for a notion of checkable or
verifiable belief. Any machine capable of proving
there is a proposition she cannot prove, would
be able to prove its consistency, and that's impossible
by Godel II.  (this follows from your "ex falso quodlibet":
a machine proving the f, will prove all propositions, so if
there is a proposition (like Santa Claus exists) that
you pretend you will never believe (prove) then you
are asserting that you prove (believe) you are consistent!.
All right? I use "believe" instead of "prove" because
we are following a little bit Smullyan's "Forever Undecided".

But this suits well with the "machine psychology".
Do you have that FU book?
I don't have this book.
Bruno
http://iridia.ulb.ac.be/~marchal/
Jacques.
_
Bloquez les fenêtres pop-up, c'est gratuit ! http://toolbar.msn.fr

Re: Lob + New Views On Mind-Body Connection

[Bruno Marchal]

At 22:43 27/08/04 -0700, George Levy wrote:
Let's write Lob's formula as B2(B1p -> p) -> B1p
where B1, B2, and p are binary variables.
Note that B1 applies to p and B2 applies to the implication (B1p -> p). 
(Should I have done this differently?)
Why B1 and B2 ?   Lob's formula is really B(Bp->p)->Bp, meaning
(with our naive stance toward machine) that if the machine
ever believes that: [if I (the machine) ever believe p then p] then I will 
ever believe p).
We will come back to it. This is true, and actually believable by any
Self-Referentially Correct machine (and even by larger classes of machines,
but for the physics extraction I interview only the SRC machine).

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

RE: Lob + New Views On Mind-Body Connection

[Bruno Marchal]

At 21:02 28/08/04 +1000, Stathis Papaioannou wrote:
The paper cited below is consistent with the reductionist view that there 
must be a distinct brain state giving rise to each distinct mental state. 
"Whenever neurones A,B,C fire the subject experiences sensations X,Y,Z."

I agree (except that you assume some high level of description of the brain,
but what you say is compatible with comp, I don't need that assumption, I am
agnostic on the substitution level).


To include the phenomenon of first person experience one could add: 
"...and only the subject whose neurones are thus firing can know directly 
what it feels like to experience X,Y,Z." I believe this is as much as it 
is possible for an empirical science to say about the mind-body problem.

100% OK.   But then I illustrate (at least) that with some hypothesis you 
can extract
theories which explain much more (matter and mind in particular). But the 
experimental bets
you describe is always part of a "yes doctor" form of act of faith. Sure.

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

Re: Lob + New Views On Mind-Body Connection

[Bruno Marchal]

At 22:43 27/08/04 -0700, George Levy wrote:
Bruno
I am trying to visualize Lob formula as a block diagram to be implemented 
either in neural net, as computer program or as a digital cicuit. Digital 
circuits have the advantage of being very simple (binary) so let's try to 
express Lob's formula as a truth table that could be implemented with NAND 
gates.

Let's write Lob's formula as B2(B1p -> p) -> B1p
where B1, B2, and p are binary variables.
I am not sure I understand. It is better to see B as a (non truth 
functional) connector.


Note that B1 applies to p and B2 applies to the implication (B1p -> p). 
(Should I have done this differently?)
Let
~ = NOT
+ = OR
. = AND

We can convert the implication B1p -> p   to~(B1.p) + p
The Boolean equivalent to Lob is
 ~B2(~(B1p)+ p) + B1p
The truth table is
B2   B1   pB1p~B1p+p  ~B2(~(B1p)+ p))  ~B2(~(B1p)+ p) + B1p
0  0  0  01  1 
 1
0  0  1  01  1 
 1
0  1  0  01  1 
 1
0  1  1  11  1 
 1
1  0  0  01  0 
 0
1  0  1  01  0 
 0
1  1  0  01  0 
 0
1  1  1  11  0 
 1

I am now confused. The fifth column ~B1p+p surprisingly is all 1's. The 
last column ~B2(~(B1p)+ p) + B1p which is Lob's statement and which I 
expected to be all 1's is not. I have rechecked this table and I don't see 
anything wrong. Is there something wrong?

It may be that Boolean algebra is not adequate to express Lob. The 
question is how can Lob's formula be expressed simply by a digital circuit 
a block diagram or a neural net?

By making a system enough rich to represent B, like Godel did show
for provability in arithmetic. It is more comparable to a (lisp) interpretor
described in Lisp. In terme on electrical or neuronal nets it means it will
have feedback loops. Modal logic is not truth functional. You need delay and
close circuits (like flip-flop).
Boyer, if I remember well, as explicitly build Lobian theorem prover.
Smullyan presents toy systems in chapter 26 and 27 of FU. Of course
any reasonable formalisation of arithmetic is enough, so any universal
machine is Lobian extendible.
Bruno
http://iridia.ulb.ac.be/~marchal/

RE: Lob + New Views On Mind-Body Connection

[Stathis Papaioannou]

The paper cited below is consistent with the reductionist view that there 
must be a distinct brain state giving rise to each distinct mental state. 
"Whenever neurones A,B,C fire the subject experiences sensations X,Y,Z." To 
include the phenomenon of first person experience one could add: "...and 
only the subject whose neurones are thus firing can know directly what it 
feels like to experience X,Y,Z." I believe this is as much as it is possible 
for an empirical science to say about the mind-body problem.

--Stathis Papaioannou
From: Bruno Marchal <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED]
Subject: Lob + New Views On Mind-Body Connection
Date: Fri, 27 Aug 2004 13:19:42 +0200
A long time ago (1987), a french logician (a student at that time),
Philippe Balbiani, who did attend a talk I made
on the logic of self-reference (G) in Toulouse send me a letter
where he proposes informally to interpret the Lobian formula
(that is B(Bp->p)->Bp) as a form of closure for the french
self-persuading strategy known as "la méthode Coué" (la methode Coue)).
I must confess I was not really convinced. I thought this would be
somehow to beautiful to be true. My mind will slightly evolve on that
question when I will understand, in part through Smullyan's FU
(Forever Undecided) that the Lob formula does indeed capture,
at least formally, a form of self-fulfilling nature of machine's belief.
The Lob formula does indeed say that if a machine believes Bp->p for
some proposition p, then the machine will believe p.
This is very astonishing, and still quite mysterious to me. My thesis
has never been based directly on Lob formula, except that through
Solovay's theorem Lob formula formalize the entire discourse of
the self-referentially correct machine.
Then recently, when I was just explaining the Lob formula
in my Amsterdam paper, John Mikes send me the message below
which shows experimental evidence on the working of the placebo
effect (quite similar to the methode Coue). I have download many
papers on the placebo and eventually conclude that Lob formula
could indeed provide a formal explanation of the working of
that placebo phenomenon.
This makes reality still more "psychological" like if the universe(s)
was the product of a form of wishful thinking!  It also vindicates
in a deeper way the similarity between the Grand-Mother
psychology and the Lobian machine psychology. Thanks to John.
With the Knight Knaves Island Lob's theorem is not difficult
to explain and we can go back to that (but apparently some KK
posts are missing in the archive, and I don't know how to proceed,
and I will think the how and why for awhile).
A lot of physicians say the placebo effect is *subversive* with
respect to traditional science. What is clear is that it forces
even the therapist to address (at least) the mind body relation,
and this in some novel way (with respect to Aristotle).
Bruno
John Mikes wrote:
Bruno, your topic, maybe interesting novelty (I doubt). IMO the brain can 
encode data in el-chem perception, no indication so far how the qualia-gap 
is transcended into thought context. Not even in picture/music/taste 
apperceptions. The neuronal brain is a TOOL and the ongoing reductionist 
research stops at phenomenology of "the tool does it so the tool does it 
all". (Philosophy of "kill the messenger").
I hold the complexity to which "human" belongs unseparable in its 
functions unless one is a faithful dualist with a soul. Even then: does 
the 'soul' think?

John
- Original Message -
From: Robert Karl Stonjek
To: A Group MindBrain
Sent: Monday, August 02, 2004 5:50 PM
Subject: [Mind and Brain] Article: New Views On Mind-Body Connection

New Views On Mind-Body Connection


Studies into placebo effect and empathy suggest how the brain encodes 
subjective experience | By Eugene Russo


Courtesy of Fabrizio Benedetti
bkg_spacer.gif
access.jpgbkg_spacer.gif
captionarrow.gif UNPRECEDENTED ACCESS: During a deep brain stimulation 
clinical trial, researchers detected elements of the placebo effect. The 
pre-placebo neuron was recorded from the left subthalamic nucleus as a 
control. The post-placebo neuron was recorded from the right subthalamic 
nucleus. Other neurons demonstrated a similiar decrease in activity.
200px_dash.gif
bkg_spacer.gif

Revealing the complexities of the pain experience may offer a window into 
the mind-body interaction. Several recent studies into the placebo effect, 
human empathy, and their apparent interconnectedness are providing insight 
into the human subjective experience.

Such investigations, says Jon-Kar Zubieta, associate professor in 
psychiatry and radiology at the University of Michigan, help scientists 
understand the intersection of physical and emotional states. "The placebo 
effect gets at the core of how individuals react and modulate 
environmental events, whether positive or negative in nature," he says. If 
harnessed, 

Re: Lob + New Views On Mind-Body Connection

[George Levy]

Bruno

I am trying to visualize Lob formula as a block diagram to be
implemented either in neural net, as computer program or as a digital
cicuit. Digital circuits have the advantage of being very simple
(binary) so let's try to express Lob's formula as a truth table that
could be implemented with NAND gates.

Let's write Lob's formula as B2(B1p -> p) -> B1p
where B1, B2, and p are binary variables. 
Note that B1 applies to p and B2 applies to the implication (B1p ->
p). (Should I have done this differently?)
Let
~ = NOT
+ = OR
. = AND

We can convert the implication B1p -> p   to    ~(B1.p) + p

The Boolean equivalent to Lob is 

 ~B2(~(B1p)+ p) + B1p

The truth table is 

B2   B1   p    B1p    ~B1p+p  ~B2(~(B1p)+ p))  ~B2(~(B1p)+ p) +
B1p

0      0      0      0            1                  1                 
            1
0      0      1      0            1                  1                 
            1
0      1      0      0            1                  1                 
            1
0      1      1      1            1                  1                 
            1
1      0      0      0            1                  0                 
            0
1      0      1      0            1                  0                 
            0
1      1      0      0            1                  0                 
            0
1      1      1      1            1                  0                 
            1

I am now confused. The fifth column ~B1p+p surprisingly is all 1's. The
last column ~B2(~(B1p)+ p) + B1p which is Lob's statement and which I
expected to be all 1's is not. I have rechecked this table and I don't
see anything wrong. Is there something wrong?

It may be that Boolean algebra is not adequate to express Lob. The
question is how can Lob's formula be expressed simply by a digital
circuit a block diagram or a neural net?

George 

Bruno Marchal wrote:
A long time
ago (1987), a french logician (a student at that time),
Philippe Balbiani, who did attend a talk I made
on the logic of self-reference (G) in Toulouse send me a letter
where he proposes informally to interpret the Lobian formula
(that is B(Bp->p)->Bp) as a form of closure for the french 
self-persuading strategy known as "la méthode Coué" (la methode
Coue)).
I must confess I was not really convinced. I thought this would be
somehow to beautiful to be true. My mind will slightly evolve on
that
question when I will understand, in part through Smullyan's FU
(Forever Undecided) that the Lob formula does indeed capture,
at least formally, a form of self-fulfilling nature of machine's
belief.
The Lob formula does indeed say that if a machine believes Bp->p
for
some proposition p, then the machine will believe p.
This is very astonishing, and still quite mysterious to me. My
thesis
has never been based directly on Lob formula, except that through
Solovay's theorem Lob formula formalize the entire discourse of
the self-referentially correct machine.
Then recently, when I was just explaining the Lob formula
in my Amsterdam paper, John Mikes send me the message below
which shows experimental evidence on the working of the placebo
effect (quite similar to the methode Coue). I have download many
papers on the placebo and eventually conclude that Lob formula
could indeed provide a formal explanation of the working of
that placebo phenomenon. 
This makes reality still more "psychological" like if the
universe(s)
was the product of a form of wishful thinking!  It also
vindicates
in a deeper way the similarity between the Grand-Mother
psychology and the Lobian machine psychology. Thanks to John.
With the Knight Knaves Island Lob's theorem is not difficult
to explain and we can go back to that (but apparently some KK
posts are missing in the archive, and I don't know how to proceed,
and I will think the how and why for awhile). 
A lot of physicians say the placebo effect is *subversive* with
respect to traditional science. What is clear is that it forces
even the therapist to address (at least) the mind body relation,
and this in some novel way (with respect to Aristotle).
  
Bruno
  
John Mikes wrote:
  
  Bruno, your topic, maybe
interesting novelty (I doubt). IMO the brain can encode data in el-chem
perception, no indication so far how the qualia-gap is transcended into
thought context. Not even in picture/music/taste apperceptions. The
neuronal brain is a TOOL and the ongoing reductionist research stops at
phenomenology of "the tool does it so the tool does it all".
(Philosophy of "kill the messenger").
I hold the complexity to which "human" belongs unseparable in
its functions unless one is a faithful dualist with a soul. Even then:
does the 'soul' think? 
 
John
- Original Message - 
From: Robert Karl
Stonjek 
To: A Group
MindBrain 
Sent: Monday, August 02, 2004 5:50 PM
Subject: [Mind and Brain] Article: New Views On Mind-Body
Connection


New Views On Mind-Body
Connection