Re: Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Hi John,


Le 11-nov.-07, à 23:33, John Mikes a écrit :

> Bruno, I hope it will be accessible to me, too, by simple computerese 
> software.


Normally there should be no difficulties. My goal is not to explain all 
the technics, but the minimal things which I estimate to be necessary 
for having a basic general idea of what is going on.

My first goal, perhaps my main goal, is to explain Church Thesis CT.  
To explain why CT is a very strong hypothesis, with a uniform deep 
impact on everything, and mainly on "theories of everything".

I want also to explain more clearly the difference between Tegmark, 
Schmidhuber, and "comp", etc.

But this needs a minimal amount of "modern math", so as to make clear 
Cantor's role, and then Church, Kleene.

Not really the time today, but hopefully (normally) I will have more 
time tomorrow,

Thanks for letting me know your interest, and your patience,

Best,

Bruno








>
> On Nov 8, 2007 11:31 AM, David Nyman <[EMAIL PROTECTED] > wrote:
>>
>> On Nov 6, 2:37 pm, Bruno Marchal < [EMAIL PROTECTED]> wrote:
>>
>> > I have almost finished the posts on the lobian machine I have 
>> promised.
>> > I have to make minor changes and to look a bit the spelling. I 
>> cannot
>> > do that this week, so I will send it next week. Thanks for your
>> > patience.
>>
>> Thanks - I'll keep an eye out.
>>
>> David
>>
>> > Hi David,
>> >
>> > I have almost finished the posts on the lobian machine I have 
>> promised.
>> > I have to make minor changes and to look a bit the spelling. I 
>> cannot
>> > do that this week, so I will send it next week. Thanks for your
>> > patience. I give you the plan, though, which I will actually also
>> > follow for the beginning (and the end) of the ULB-saturday course 
>> this
>> > year:
>> >
>> > 1) Cantor's diagonal
>> > 2) Does the universal digital machine exist?
>> > 3) Lobian machines,  who and what are they?
>> > 4) The 1-person and the 3- machine.
>> > 5) Lobian machines' theology
>> > 6) Lobian machines' physics
>> > 7) Lobian machines' ethics
>> >
>> > BTW, if some people are near Belgium, I have been invited for doing 
>> a
>> > talk on the UDA at a colloquium on "Logic and Reality" at 
>> Namur/Louvain
>> > in BELGIUM. The other talks seems quite interesting (too, if I may 
>> say
>> > :). Most will be done in english. Program and informations can be 
>> found
>> > here:
>> >
>> > http://www.logic-center.be/acts/logrea.html
>> >
>> > Best regards to David, and all of you
>> >
>> > Bruno
>> >
>> > http://iridia.ulb.ac.be/~marchal/
>>
>>  >>
>>
http://iridia.ulb.ac.be/~marchal/

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Re: Rép : Observer Moment = Sigma1-Sentences

[John Mikes]

Bruno, I hope it will be accessible to me, too, by simple computerese
software.
John

On Nov 8, 2007 11:31 AM, David Nyman <[EMAIL PROTECTED] > wrote:

>
> On Nov 6, 2:37 pm, Bruno Marchal < [EMAIL PROTECTED]> wrote:
>
> > I have almost finished the posts on the lobian machine I have promised.
> > I have to make minor changes and to look a bit the spelling. I cannot
> > do that this week, so I will send it next week. Thanks for your
> > patience.
>
> Thanks - I'll keep an eye out.
>
> David
>
> > Hi David,
> >
> > I have almost finished the posts on the lobian machine I have promised.
> > I have to make minor changes and to look a bit the spelling. I cannot
> > do that this week, so I will send it next week. Thanks for your
> > patience. I give you the plan, though, which I will actually also
> > follow for the beginning (and the end) of the ULB-saturday course this
> > year:
> >
> > 1) Cantor's diagonal
> > 2) Does the universal digital machine exist?
> > 3) Lobian machines,  who and what are they?
> > 4) The 1-person and the 3- machine.
> > 5) Lobian machines' theology
> > 6) Lobian machines' physics
> > 7) Lobian machines' ethics
> >
> > BTW, if some people are near Belgium, I have been invited for doing a
> > talk on the UDA at a colloquium on "Logic and Reality" at Namur/Louvain
> > in BELGIUM. The other talks seems quite interesting (too, if I may say
> > :). Most will be done in english. Program and informations can be found
> > here:
> >
> > http://www.logic-center.be/acts/logrea.html
> >
> > Best regards to David, and all of you
> >
> > Bruno
> >
> > http://iridia.ulb.ac.be/~marchal/ 
>
>
> >
>

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Re: Rép : Observer Moment = Sigma1-Sentences

[David Nyman]

On Nov 6, 2:37 pm, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> I have almost finished the posts on the lobian machine I have promised.
> I have to make minor changes and to look a bit the spelling. I cannot
> do that this week, so I will send it next week. Thanks for your
> patience.

Thanks - I'll keep an eye out.

David

> Hi David,
>
> I have almost finished the posts on the lobian machine I have promised.
> I have to make minor changes and to look a bit the spelling. I cannot
> do that this week, so I will send it next week. Thanks for your
> patience. I give you the plan, though, which I will actually also
> follow for the beginning (and the end) of the ULB-saturday course this
> year:
>
> 1) Cantor's diagonal
> 2) Does the universal digital machine exist?
> 3) Lobian machines,  who and what are they?
> 4) The 1-person and the 3- machine.
> 5) Lobian machines' theology
> 6) Lobian machines' physics
> 7) Lobian machines' ethics
>
> BTW, if some people are near Belgium, I have been invited for doing a
> talk on the UDA at a colloquium on "Logic and Reality" at Namur/Louvain
> in BELGIUM. The other talks seems quite interesting (too, if I may say
> :). Most will be done in english. Program and informations can be found
> here:
>
> http://www.logic-center.be/acts/logrea.html
>
> Best regards to David, and all of you
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/


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Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Hi David,

I have almost finished the posts on the lobian machine I have promised. 
I have to make minor changes and to look a bit the spelling. I cannot 
do that this week, so I will send it next week. Thanks for your 
patience. I give you the plan, though, which I will actually also 
follow for the beginning (and the end) of the ULB-saturday course this 
year:


1) Cantor's diagonal
2) Does the universal digital machine exist?
3) Lobian machines,  who and what are they?
4) The 1-person and the 3- machine.
5) Lobian machines' theology
6) Lobian machines' physics
7) Lobian machines' ethics



BTW, if some people are near Belgium, I have been invited for doing a 
talk on the UDA at a colloquium on "Logic and Reality" at Namur/Louvain 
in BELGIUM. The other talks seems quite interesting (too, if I may say 
:). Most will be done in english. Program and informations can be found 
here:

http://www.logic-center.be/acts/logrea.html

Best regards to David, and all of you

Bruno


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

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Re: Rép : Observer Moment = Sigma1-Sentences

[Günther Greindl]

Dear Bruno,

> No. But making it precise and searching consequences helps to avoid 
> misunderstanding. The comp hyp is really a religious belief: it *is* a 
> belief in the fact that you can be reincarnated through a digital 
> reconstitution of yourself relatively to some hopefully stable set of 
> computational histories (on which you can only bet). So the question is 
> not "is comp true"? The question is really: "do you accept your 
> daughter marries a computationalist".

Ok, I'm with you :-)

> And my point is only that IF comp is true then the mind body problem is 
> reduced into a derivation of physics (the eventually stable physical 
> beliefs) from ... addition and multiplication (and there is a gift: it 

Why would this only be true in comp?
What I find strange is the following: why do people find "mind" 
something strange - why not accept it as something fundamental like 
electromagnetism or gravity? (Of course, it is not a force (or is it?))

Many people say a materialist/physicalist attitude fails to explain the 
mind. I agree if one remains in a dualist view of the world, but not if 
"mind" is accepted as something natural - something which occurs 
automatically if certain organizational criteria are met.

> Yes indeed! But then how is it possible to convince someone who does 
> not reason correctly, of the advantage of reasoning correctly?
> Answer: by letting him learn the consequences of reasoning incorrectly, 
> if he can still learn after!
> Problem: about fundamental questions, this can take millennia, and more 

Agreed.


Best,
Günther

-- 
Günther Greindl
Department of Philosophy of Science
University of Vienna
[EMAIL PROTECTED]
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org

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Re: Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 14-sept.-07, à 00:17, John Mikes a écrit :

> Bruno, that was quite a response. Let me just include those part to 
> which I have something to say - in most cases your 'half-agreement' 
> cuts my guts.
> ==
> "...I like very much David Deutsch's
> idea that if we are scientist we are in principle willing to know that
> our theory is wrong, but to discover this we have to take them
> seriously enough."
>
> I never said I am a scientist, I just speculate (and allow to change 
> my mind).


That's what I call, with Popper, a scientist, more or less... Perhaps 
the scientist just try to be as clear as possible, and submit papers 
from time to time.





> What I brought together is in my distsinction a 'narrative', not a 
> theory, not even a hypothesis.


I think this corresponds to the points of view (both in the UDA and 
after in the arithmetical UDA). I think I agree with you, but I know we 
disagree on this!
It just happen that I am enough open minded toward machine that I am 
listening to their many points of view.




>
> "(JM)> And i still did not get an acceptable explanation why 'numbers' 
> are
> > the basics of everything (and WHAT they may be).
> (BM) Nobody can KNOW that. The fact is that ONCE you take the comp hyp
> seriously enough into consideration, then you can, by work, be
> eventually convince that our own immateriality (which follows easily by
> comp) has to be "contagious" on our possible neighborhoods."<
>
> (JM):
> Why don't I take the 'comp hyp (whatever it is) seriously BEFORE I 
> know about numbers?
> I see it circular: unless 'comp' has nothing to do with numbers. I 
> cannot take seriously a 'thing' to get to that 'thing'. As you wrote:


Sure! You have perhaps a good intuition about numbers, we cannot define 
them without using them. That is why there are a good starting point. 
Now comp and numbers are related because comp concerns notably 
transformation of finite things into finite things, like when you are 
using your computer, and numbers give the most easy and known way to 
represented finite things. But you should not fix yourself too much on 
numbers; if you insist I will come back to the combinators! (One reason 
to use numbers, beside that with + and * and logic, is that  they are 
enough for the ontic view, another is that we learn numbers in primary 
school; combinators belongs to mathematical logics, and are less 
known).
Anyway, once you have the combinators and their relations you got the 
numbers, and vice verça.






>
> (BM):
> "...we are not talking about those numbers humans
> (re)invented, but on those which have to exist independently of us once
> we accept some minimal amount of computer science, without which we
>  could infer nothing fron comp (our, well mine, working 
> hypothesis)"
>
> (JM):  -RE-invented? if we agreed (D. Bohm) that the numbers we use as 
> numbers
> are human inventions, how did they exist independentloy of us?


As I discussed a lot with Peter D. Jones, I just mean that the 
propositions about numbers, and about  relation between numbers, are 
true or false independent of me. Do you sincerely believe that the fact 
that you cannot build a rectangle at least two row large with the 
following items I depends of you? (yes, there are 17 
strokes, well normally).




> Is even the 'littlest' computer science feasible without numbers?


According to Hartree Field, the whole science can be done without 
numbers, but his prospects fails for number theory (!) and computer 
science indeed. So we agree.



> And I would not accept something to exist before it came into 
> existence just to make
> a 'hyp' workable - which I don't see feasible without such circularity.


I don't think there is any circularity: I make clear the distinction 
between the hypothesis and the consequences.



>
> BM:  (Bohm) denies comp -
> (JM): I do not. I don't know what it is.


Comp is :
- Church thesis (a scientific (= refutable) hypothesis in the 
foundation of math and computer science)
- The assumption of the existence of a level of description of myself 
such that I can say "yes" to a doctor who proposes me an artificial 
body made at that level, without which I would die in the ordinary 
sense. Ex: 1) Ray Kurzweil is a comp practionners (hopers, ...).  2) 
All scientist except Penrose (but even Searle and Rosen although this 
is not obvious and I guess debatable). Comp is a very weak hypothesis, 
but with "devastatting consequences" once we take it seriously enough, 
due to CT, mainly.



>  I hope it is not that embryonic digitality-churner we have on our 
> desk (don't even mention 'binary'), but if it is named ptoperly 
> (comp?) it has 'something' to do with computationality (involving 
> numbers to handle). Now this may be your mystical unknowable 'number' 
> what I was willing to call (not condoning) the Almighty Creator, or 
> anything else - of course not emulable by an (embryonic level) Turing 
> machine.

Yes;

Re: Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Dear Günther,


Le 13-sept.-07, à 21:37, Günther Greindl a écrit :

>
>>> The problem is: in math what follows from the axioms is true per
>>> definition (that is what following from the axioms mean).
>>
>> Not at all. If you were true, no inconsistent theory in math would
>> appear.
>
> You are right, my above sentence was too simple.
>
> New try:
>
> All sentences that follow from axioms which do not lead to a
> contradiction - and therefore an inconsistency - we call true in this
> system. Better "valid" than "true", so new refinement:
>
> All sentences that follow from axioms which do not lead to a
> contradiction - and therefore an inconsistency - we call valid in this
> system.



I am more or less ok. Strictly speaking "validity" is for a deduction, 
and you can deduce, in a valid way, a contradiction (for example from 
some other contradiction), like when Bertrand Russel derives in some 
valid way, the identity of himself with the pope from 0 = 1.






>
> We have now freed the word true for a different use (see below).
>
>> "Axioms" are just provisory statements on which we agree. For
>> simple filed like number theory, it happens that nobody doubts them,
>> and in that case I am willing to say I do believe them true, but I am 
>> a
>> few bit less sure for ZF set theory, and quite skeptical for a theory
>> like NF (Quine's new foundation).
>
> Axioms and inferential rules can be formed arbitrarily. If they are
> consistent, they may be interesting.


As they may be uninteresting ! Like PA + (PA is inconsistent). That is 
a consistent theories which is not very interesting. Of course the 
existence of such unreasonable but consistent arithmetical theories 
*is* interesting!




>
> If the axioms and the inferential rules are chosen in a way that an
> isomorphic mapping with the physical world is possible, we call them
> true.


(I could call them illusory and I think they are asking for deeper 
explanations; as a platonist (say) the observable world is just the 
border of what we cannot observe, but we can learn to infer it from the 
observations, or still better, learn to deduce it from a deeper theory, 
or by lobian machine's introspection (à-la UDA, or its purely 
arithmetical version, I refer you to my url for more)).






> (I am somewhat unhappy with the word true here - I am trying to
> adopt your choice of words here; I would never use "true" in describing
> mappings of formal systems into reality: I would only call the mappings
> consistent/usefull with preservation of inferential validity.


That's an excellent move. (Actually that move is the main one well 
captured by the category theory approach of logic).



>
> True should IMHO be reserved to propositions made about reality
> (propositions which relate formal systems to reality, for instance, but
> distinct from the formal system).


Yes, but eventually "true about any reality concerning me" is not even 
definable by a lobian machine, and that is why, again with Plato, the 
notion of truth, once encompassing enough to concern *you*, becomes 
something unameable by *you*. It is the God of Plato: Truth. But lobian 
machine can still deduce the complete theology of simpler lobian 
machine (and understand she has to lift those theology only by *hope* 
in self "soundness). Many "quotes" to insist that a lobian 
machine cannot define its own soundness (its own relation with truth or 
its "intended model").




>
>
>> Well, you can doubt the axioms indeed, but this could lead
>> to long and useless debate. It is better, imo, to try to make the
>> postulate (axioms) sufficiently precise so that we can infer some
>> absurdity (internal or empirical).
>
> I agree. I also think it is interesting to develop this idea precisely.
> But do you think that discussing the assumptions is really useless?


No. But making it precise and searching consequences helps to avoid 
misunderstanding. The comp hyp is really a religious belief: it *is* a 
belief in the fact that you can be reincarnated through a digital 
reconstitution of yourself relatively to some hopefully stable set of 
computational histories (on which you can only bet). So the question is 
not "is comp true"? The question is really: "do you accept your 
daughter marries a computationalist".
And my point is only that IF comp is true then the mind body problem is 
reduced into a derivation of physics (the eventually stable physical 
beliefs) from ... addition and multiplication (and there is a gift: it 
gives the quanta and the qualia, thanks to the G/G* separation 
discovered by Godel, Lob, Solovay: see my url for more on this, Russell 
says some words on it in his book)


>
>> I don't think so. Teaching in science, for adult,  is (I mean  ideal
>> teaching *should* be) an invitation to deduction in hypothetical
>> context, inductive inference and then the art of observation and
>> verification.
>
> Ok, that is of course correct - but you have to at least convince the
> people

Re: Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 13-sept.-07, à 19:52, Brent Meeker a écrit :

> A theory also can be contradicted by a fact.  The theory need not be
> contradictory, i.e. capable of proving false, in order to be 
> contradicted.


Yes sure! Actually the second incompleteness theorem (GODEL II) makes 
this remark genuine even just for a simple theory like Peano Arithmetic 
(the escherichia coli of the Lobian Machines).

For example, anyone who knows a bit PA is confident that PA's theorems 
fit the facts (here: the true arithmetical statements). In particular 
everyone believes that PA is consistent. So the proposition "PA is 
consistent" fits the facts (once tranlated into an arithmetical 
proposition like Godel did).. So the proposition "PA is not consistent" 
does not fit the arithmetical facts. But by GODEL II, PA + (as new 
axiom) "PA is not consistent" is consistent (if not PA would be able to 
prove its consistency). It is just that, like in the situation you 
describe, PA cannot prove false the proposition PA is inconsistent, 
which is indeed false.

But then that is why I prefer to say that a machine is sound when it is 
correct relatively to its intended (standard) model, and to keep the 
notion of consistency (and inconsistency, contradiction) in a pure 
syntactical sense: a machine is inconsistent if proves a contradiction. 
Of course Godel "completeness" relates the two notions for the first 
order theories (such a theory has a model (logician's sense, see below) 
iff it is consistent).

For the non-mathematically minded, perhaps this could help: imagine a 
museum in which there is the VENUS DE MILO sculpture, and machine 
describing, "by heart" but accurately,  the VENUS DE MILO sculpture. 
Now, unless you believe there is something contradictory in the reality 
itself of the VENUS DE MILO sculpture, you can understand that the 
machine is consistent and sound (correct). Now take that machine and 
put in front of some other sculpture in the museum. There is no reason 
the machine becomes inconsistent by that move, but the machine become 
unsound, it loses correctness ... relatively to its intended model.

(Note that in the average, when a physician talks on "model", he means 
what a logician calls a "theory". Logicians use the word "model" for 
mathematical structures "satisfying" (= "making true" in some precise 
mathematical sense) formula belonging to a theory (=, in my context, 
provable by a lobian machine). This significant departure in vocabulary 
does not help the dialogs between logicians and physicians 'course.

Those mathematical structures plays the role of (and actually *are*, 
for platonists) the realities *realities*. For example, the natural 
number structure (N, +, x) plays the role of the intended reality for 
the PA theory (mechanical or syntactical generator of theorems).

Bruno

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


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Re: Rép : Observer Moment = Sigma1-Sentences

[John Mikes]

Bruno, that was quite a response. Let me just include those part to which I
have something to say - in most cases your 'half-agreement' cuts my guts.
==
"...I like very much David Deutsch's
idea that if we are scientist we are in principle willing to know that
our theory is wrong, but to discover this we have to take them
seriously enough."

I never said I am a scientist, I just speculate (and allow to change my
mind). What I brought together is in my distsinction a 'narrative', not a
theory, not even a hypothesis.

"(JM)> And i still did not get an acceptable explanation why 'numbers' are
> the basics of everything (and WHAT they may be).
(BM) Nobody can KNOW that. The fact is that ONCE you take the comp hyp
seriously enough into consideration, then you can, by work, be
eventually convince that our own immateriality (which follows easily by
comp) has to be "contagious" on our possible neighborhoods."<

(JM):
Why don't I take the 'comp hyp (whatever it is) seriously BEFORE I know
about numbers?
I see it circular: unless 'comp' has nothing to do with numbers. I cannot
take seriously a 'thing' to get to that 'thing'. As you wrote:

(BM):
"...we are not talking about those numbers humans
(re)invented, but on those which have to exist independently of us once
we accept some minimal amount of computer science, without which we
could infer nothing fron comp (our, well mine, working hypothesis)"

(JM):  -RE-invented? if we agreed (D. Bohm) that the numbers we use as
numbers
are human inventions, how did they exist independentloy of us?
Is even the 'littlest' computer science feasible without numbers?
And I would not accept something to exist before it came into existence just
to make
a 'hyp' workable - which I don't see feasible without such circularity.

BM:  (Bohm) denies comp -
(JM): I do not. I don't know what it is. I hope it is not that embryonic
digitality-churner we have on our desk (don't even mention 'binary'), but if
it is named ptoperly (comp?) it has 'something' to do with computationality
(involving numbers to handle). Now this may be your mystical unknowable
'number' what I was willing to call (not condoning) the Almighty Creator, or
anything else - of course not emulable by an (embryonic level) Turing
machine.
 I just wonder WHY NUMBER? because Plato talked numbers? That was 2500 years
ago at the epistemic cognitive level of that time!  OK, our mind is still
not capable of thinking beyond the level it can think, but to substitute the
ORIGIN by something invented in the course much much later on, because we
have some idea about THAT, does not seem to me 'scientific' enough.
Unless you give me a better explanation - if you care.

(BM):
All proof in math are particular case of thought experiments. In
philosophy-of-mind, theology, theoretical physics and math, the only
tools available are the thought experiments.

(JM):
(I wrote: > I also keep away from ANY thought experiences, they are products
of
> OUR state of the mind at the time they are 'invented'<
in which "experience" is a typo, it should read "experiment". Sorry about
it)

I was referring to those 'thought experiments' (EPR, teleportation etc.)
which imagined physical tests on imaginary (unreal?) circumstances to prove
a position. To "test" ideas
in mental domains is a mental  effort, not what I would call a 'thought
experiment'.

(JM):
> I am in subconscious trouble with the machine, which is differently
> identified by Robert Rosen and I find a lot acceptable in his ideas.
(BM):
Imo, Rosen is wrong on Church thesis. But this could wait when I
succeed to explain more about CT later ..
(JM):
I was referring to his nomenclature of the 'formal' (reductionist,
conventional) terms vs his tems in the impredicative view of the total
interconnective 'cpmplexity'. "His" machine is computer-emulable while his
'natural systems' always have noncomputable elements.
I consider the latter as part of the world, while the restricted view -
mostly topically selected within boundaries we set for our presently
accessible observations - is what I call  "model", encompass the
conventional sciences. He worked in math and theor. biology as well.
(I am looking forward to reading your explanatory piece about the CT. )
Interesting match in your par:
"Just keep track of the definitions. By angels and gods (note the
plural) I mean things which are not turing-emulable, or if you prefer,
any entities which are provably not machines."
(JM):
"provably" is ambiguous. i would accept "per definitionem".

(BM): What is conventional sciences.
(JM): basically: what you and Nietzsche described. I consider it the
historical figment of the ever changing (advancing?) observational skills
and explanational levels, built upon the previous flight of knowledge-base
in the human (scientific) establishment. It applies math to calfculate the
quantities deduced from the developing observations on the 'model-view' (see
above). Such incomplete information may lead to parado

Re: Rép : Observer Moment = Sigma1-Sentences

[Günther Greindl]

Dear Bruno,

>> The problem is: in math what follows from the axioms is true per
>> definition (that is what following from the axioms mean).
> 
> Not at all. If you were true, no inconsistent theory in math would 
> appear.

You are right, my above sentence was too simple.

New try:

All sentences that follow from axioms which do not lead to a 
contradiction - and therefore an inconsistency - we call true in this 
system. Better "valid" than "true", so new refinement:

All sentences that follow from axioms which do not lead to a 
contradiction - and therefore an inconsistency - we call valid in this 
system.

We have now freed the word true for a different use (see below).

> "Axioms" are just provisory statements on which we agree. For 
> simple filed like number theory, it happens that nobody doubts them, 
> and in that case I am willing to say I do believe them true, but I am a 
> few bit less sure for ZF set theory, and quite skeptical for a theory 
> like NF (Quine's new foundation).

Axioms and inferential rules can be formed arbitrarily. If they are 
consistent, they may be interesting.

If the axioms and the inferential rules are chosen in a way that an 
isomorphic mapping with the physical world is possible, we call them 
true. (I am somewhat unhappy with the word true here - I am trying to 
adopt your choice of words here; I would never use "true" in describing 
mappings of formal systems into reality: I would only call the mappings 
consistent/usefull with preservation of inferential validity.

True should IMHO be reserved to propositions made about reality 
(propositions which relate formal systems to reality, for instance, but 
distinct from the formal system).


> Well, you can doubt the axioms indeed, but this could lead 
> to long and useless debate. It is better, imo, to try to make the 
> postulate (axioms) sufficiently precise so that we can infer some 
> absurdity (internal or empirical). 

I agree. I also think it is interesting to develop this idea precisely.
But do you think that discussing the assumptions is really useless?

> I don't think so. Teaching in science, for adult,  is (I mean  ideal 
> teaching *should* be) an invitation to deduction in hypothetical 
> context, inductive inference and then the art of observation and 
> verification.

Ok, that is of course correct - but you have to at least convince the 
people that it is worthwile to _reason_ correctly :-)
(not all people seem to share this opinion, even at university!)

Best Regards,
Günther

-- 
Günther Greindl
Department of Philosophy of Science
University of Vienna
[EMAIL PROTECTED]
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org

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Re: Rép : Observer Moment = Sigma1-Sentences

[Brent Meeker]

Bruno Marchal wrote:
> ...
>
> I agree with this. You can rule out a theory when it leads to a 
> contradiction, but only *once* you get that contradiction. (A theory 
> can be contradictory without you ever knowing that fact).
>   

A theory also can be contradicted by a fact.  The theory need not be 
contradictory, i.e. capable of proving false, in order to be contradicted.

Brent Meeker


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Re: Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Dear Günther,


Le 12-sept.-07, à 16:49, Günther Greindl a écrit :

> The problem is: in math what follows from the axioms is true per
> definition (that is what following from the axioms mean).


Not at all. If you were true, no inconsistent theory in math would 
appear. "Axioms" are just provisory statements on which we agree. For 
simple filed like number theory, it happens that nobody doubts them, 
and in that case I am willing to say I do believe them true, but I am a 
few bit less sure for ZF set theory, and quite skeptical for a theory 
like NF (Quine's new foundation).
All the first theories extending the lambda calculus or the combinators 
were inconsistent.




>
> How would you be able to "refute" comp? There is no way to do that, one
> can only call the axioms into question (and that is what John is 
> doing).


Not at all. Well, you can doubt the axioms indeed, but this could lead 
to long and useless debate. It is better, imo, to try to make the 
postulate (axioms) sufficiently precise so that we can infer some 
absurdity (internal or empirical). Many years ago I thought comp was 
easy to refute because it makes the indirect evidence of "many world" 
necessary, but then QM did confirm this.
You can read the UD Argument; it shows comp is refutable because it put 
very strong constraints on the possible physics. Comp and its 
consequences would have been discovered at Newton time, it would have 
been considered as refuted by many philosophers. Probably not by Newton 
himself, because Newton has seen quickly that "classical mechanics" 
could not really been the end of the history in physics.





>
>>> because the Flat Earth did not prove true later, either.
>> We have no proof that the earth is round, only solid evidence that the
>> roundity of earth is a solid *local* truth.
>
> In which models would the Earth not be round? (I am speaking here of
> models which have the property "roundness" in them and which other
> objects similar to Earth are also round - I guess that is as close to
> what we can call as something being true.) In this sense I would call
> the Earth as being round true.


In the model were I wake up and realize that the earth is flat, in all 
serious appearances. My point was trivial here: I'm not arguing against 
the round aspect of earth, I am just arguing that we cannot pretend to 
have a proof. There are just no proof about reality. It is a simple 
triviality I am recalling. Proofs occur only through theories, and 
theories or just "world views" are only inferred.




>
>> No serious scientist will ever try to convince others (except for the
>> mundane purpose of getting some funds). As I said a scientist, not 
>> only
>> does not want to convince others, he want others to show him wrong
>> instead. You confuse scientists, and mediatico-pseudo-scientists, 
>> which
>> can exist still today due to 1500 years of abandon of the fundamental
>> question to political pseudo-religious authorities. Of course they 
>> have
>> had no choice, because it is best to do pseudo-science than to burn
>> alive ... (I don't judge them here).
>
> I agree strongly with you Bruno that science is about doubt and 
> modesty.
> But I do not think that a scientist has to be so agnostic as to never
> want to convince anybody else of some positions (which is what teaching
> essentially is);


I don't think so. Teaching in science, for adult,  is (I mean  ideal 
teaching *should* be) an invitation to deduction in hypothetical 
context, inductive inference and then the art of observation and 
verification.




>
> I am adopting a critical rationalist position here: a scientist can 
> look
> at the models and assign different plausibilities to them; he can say
> that the evidence speaks more for A than for B. But he sometimes can
> also say that C is strictly ruled out


I agree with this. You can rule out a theory when it leads to a 
contradiction, but only *once* you get that contradiction. (A theory 
can be contradictory without you ever knowing that fact).



> (of course, this is often said too
> soon in practice, but if one is careful one can nevertheless say this,
> of inconsistent theories for instance).


... of some of them. You can have an inconsistent theory in which the 
shorter proof of the falsity is *very* long.


Best,

Bruno



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


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Re: Rép : Observer Moment = Sigma1-Sentences

[Günther Greindl]

Dear Bruno, Dear List,

> You could be right. The point we are addressing is the question of 
> making our hypotheses clear enough so that we can refute them or make 
> sense of how we could have them refuted at least in principle.
> 

>> I also keep away from ANY thought experiences, they are products of 
>> OUR state of the mind at the time they are 'invented'. 
> 
> All proof in math are particular case of thought experiments. In 
> philosophy-of-mind, theology, theoretical physics and math, the only 
> tools available are the thought experiments.

The problem is: in math what follows from the axioms is true per 
definition (that is what following from the axioms mean).

How would you be able to "refute" comp? There is no way to do that, one 
can only call the axioms into question (and that is what John is doing).

>> because the Flat Earth did not prove true later, either.
> We have no proof that the earth is round, only solid evidence that the 
> roundity of earth is a solid *local* truth.

In which models would the Earth not be round? (I am speaking here of 
models which have the property "roundness" in them and which other 
objects similar to Earth are also round - I guess that is as close to 
what we can call as something being true.) In this sense I would call 
the Earth as being round true.

> No serious scientist will ever try to convince others (except for the 
> mundane purpose of getting some funds). As I said a scientist, not only 
> does not want to convince others, he want others to show him wrong 
> instead. You confuse scientists, and mediatico-pseudo-scientists, which 
> can exist still today due to 1500 years of abandon of the fundamental 
> question to political pseudo-religious authorities. Of course they have 
> had no choice, because it is best to do pseudo-science than to burn 
> alive ... (I don't judge them here).

I agree strongly with you Bruno that science is about doubt and modesty. 
But I do not think that a scientist has to be so agnostic as to never 
want to convince anybody else of some positions (which is what teaching 
essentially is);

I am adopting a critical rationalist position here: a scientist can look 
at the models and assign different plausibilities to them; he can say 
that the evidence speaks more for A than for B. But he sometimes can 
also say that C is strictly ruled out (of course, this is often said too 
soon in practice, but if one is careful one can nevertheless say this, 
of inconsistent theories for instance).

Cheers,
Günther


-- 
Günther Greindl
Department of Philosophy of Science
University of Vienna
[EMAIL PROTECTED]
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org

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Re: Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 12-sept.-07, à 00:41, John Mikes a écrit :

> Bruno, you ARE a teacher (a good and passionate one) but your 
> imagination is insufficient. You cannot imagine how much I don't 
> know.  pick up 'words' and 'phrases' and apply common sense to them 
> with a certain authoritative flair, so  those who understand the topic 
> can think that I am talking sense. As I already confessed: I never 
> studied logics and cannot 'read' the signs (nor can I 'decipher' those 
> equational formats) you all apply in otherwise human sentences. They 
> look like math to me.



They are math! It is the game I play. I like very much David Deutsch's 
idea that if we are scientist we are in principle willing to know that 
our theory is wrong, but to discover this we have to take them 
seriously enough.





> And i still did not get an acceptable explanation why 'numbers' are 
> the basics of everything (and WHAT they may be). 


Nobody can KNOW that. The fact is that ONCE you take the comp hyp 
seriously enough into consideration, then you can, by work, be 
eventually convince that our own immateriality (which follows easily by 
comp) has to be "contagious" on our possible neighborhoods.





>  Those numbers applied in mathematical formal language are definitely 
> products of the human mind,


yes sure. But we are not talking about those numbers humans 
(re)invented, but on those which have to exist independently of us once 
we accept some minimal amount of computer science, without which we 
could infer nothing fron comp (our, well mine, working hypothesis).




> as David Bohm so clearly stated.


No problem, Bohm is a serious guy, he makes clear he does not accept 
the comp hyp at the start. Bohm is serious, and as far as I can jujudge 
by my reding, he is 100% correct. But he denies comp.



> I know: you represent the opposite way: not numbers from thinking, but 
> existence, ith all pertinent to it FROM numbers, which I reject just 
> as the 'personalized creator'  in an any other form.


You could be right. The point we are addressing is the question of 
making our hypotheses clear enough so that we can refute them or make 
sense of how we could have them refuted at least in principle.




> I also keep away from ANY thought experiences, they are products of 
> OUR state of the mind at the time they are 'invented'. 


All proof in math are particular case of thought experiments. In 
philosophy-of-mind, theology, theoretical physics and math, the only 
tools available are the thought experiments.




>  In deducing some explanations from 'phenomena' we think we 
> experienced (depends upon the actual level of our observational and 
> explanatory cpacity)  I always put an uncertainty in it,


I totally agree with you here!



> because the Flat Earth did not prove true later, either.


We have no proof that the earth is round, only solid evidence that the 
roundity of earth is a solid *local* truth.



> (Now geocentrism is true again, after Einstein, because it is quite 
> arbitrary that we can decide as a (relative) center for all others, no 
> matter how complicated the math would be...).
> I am in subconscious trouble with the machine, which is differently 
> identified by Robert Rosen and I find a lot acceptable in his ideas.


Imo, Rosen is wrong on Church thesis. But this could wait when I 
succeed to explain more about CT later ...


>  God and the angels are also hard: I do not go for assumption-based 
> consequences (not true: everything is such), in fairytales of 
> non-logical hearsay.


Just keep track of the definitions. By angels and gods (note the 
plural) I mean things which are not turing-emulable, or if you prefer, 
any entities which are provably not machines.




> I go with Colin's "mini solipsism" as I call it, the world is what we 
> make of it for ourselves.


I am a realist. I guess there is something more than me. The rest, the, 
can be justified as first person points of view.



>  I use my own logic, it served me well for many decades, and my 
> 'narrative' about the world and its installation is such (and only 
> such) as it entertains me and my logic. Not the conventional sciences.


What is conventional sciences. If by this you mean that sometimes the 
academy gives grades and honours wrongly, then you are right but this 
is really "human too much human" as Nietzche said once. We have no 
choice to learn with this facts. I prefer to talk about science, and 
describe some science has being wrong from time to time (like when Bohr 
dismissed Everett, just because what Everett said contradicted his 
(Bohr) wishfull thinking. Science = doubt and modesty. When scientist 
pretend to know the truth, they are mad, that's all.



> After 5 decades of successful polymer chemistry (38 patents, 3 
> continent consulting) I do not accept the existence of atoms and 
> molecules,


Nor do I believe in the primary nature of those notion. Plotinus (+300) 
did already understand that such notions were 

Re: Rép : Observer Moment = Sigma1-Sentences

[John Mikes]

Bruno, you ARE a teacher (a good and passionate one) but your imagination is
insufficient. You cannot imagine how much I don't know.  pick up 'words' and
'phrases' and apply common sense to them with a certain authoritative flair,
so  those who understand the topic can think that I am talking sense. As I
already confessed: I never studied logics and cannot 'read' the signs (nor
can I 'decipher' those equational formats) you all apply in otherwise human
sentences. They look like math to me.
And i still did not get an acceptable explanation why 'numbers' are the
basics of everything (and WHAT they may be).  Those numbers applied in
mathematical formal language are definitely products of the human mind, as
David Bohm so clearly stated. I know: you represent the opposite way: not
numbers from thinking, but existence, ith all pertinent to it FROM numbers,
which I reject just as the 'personalized creator'  in an any other form.
I also keep away from ANY thought experiences, they are products of OUR
state of the mind at the time they are 'invented'.  In deducing some
explanations from 'phenomena' we think we experienced (depends upon the
actual level of our observational and explanatory cpacity)  I always put an
uncertainty in it, because the Flat Earth did not prove true later, either.
(Now geocentrism is true again, after Einstein, because it is quite
arbitrary that we can decide as a (relative) center for all others, no
matter how complicated the math would be...).
I am in subconscious trouble with the machine, which is differently
identified by Robert Rosen and I find a lot acceptable in his ideas.
 God and the angels are also hard: I do not go for assumption-based
consequences (not true: everything is such), in fairytales of non-logical
hearsay.
I go with Colin's "mini solipsism" as I call it, the world is what we make
of it for ourselves. I use my own logic, it served me well for many decades,
and my 'narrative' about the world and its installation is such (and only
such) as it entertains me and my logic. Not the conventional sciences.
After 5 decades of successful polymer chemistry (38 patents, 3 continent
consulting) I do not accept the existence of atoms and molecules, they are
'math' based explanatory sweat-products of the past 2-300 years for
observations mostly misunderstood. Natural law is a statistical mistake by
counting matching observations(?) within a selected 'model' (cut-off domain)
of vision. Use a wider 'model' and different 'laws' will appear.
If you have some empty Google time, I wrote a 'worldview'-like (now
obsolete) piece on the KARL JASPERS FORUM (TA-62MIK) on networks of networks
in 2003.
And one thing: I am an anti-teacher, I don't want to persuade anybody to
accept MY views. I offer them for consideration - period.
Sorry for the longwinded chit-chat.

John

On 9/11/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>
>
> Le 10-sept.-07, à 21:03, John Mikes a écrit :
>
> > Dear Bruno, i failed to acknowledge your kind reply - and others
> > joining in - for the past month, not because I have been tied up with
> > 'other' WEB lists, but because I realized that i have nothing to say
> > "in kind" of the language you use.
>
>
> No problem. But note that you can ask about language question in case
> of trouble.
>
>
>
>
> > Not only are the terms unfamiliar (I have to think hard to put them
> > into 'meaning' (proper or not), but the underlying and firmly supposed
> > to 'known' math-phys theories are vague at best (some, others
> > unknown). So are the words used lately.
>
>
> Don't hesitate, in case you have the time to tell us which one. You
> could be surprise how simple things are, and why sometimes things seems
> complex but are not (alas, sometimes the contrary is true too; they are
>   manay things which seems obvious, but are not, like Church's thesis to
> name just one important example).
>
>
>
> > So I did not want to bore you with my uneducated remarks.
>
>
> The "average lobian machine" is even less educate than you. And the
> understanding of what I'm trying to do is 50% based on the fact that
> lobian machine can already understand it, even discover it.
>
>
>
> > This discussion penetrated the technical (?) level of the few adepts
> > and alas I am not part of it.
>
> You are, imo (judging from you posts). But it asks for work, and I can
> understand it is hard to find the time and sometimes even just the
> necessary serene atmosphere for thinking ...
>
>
>
> > In the meantime Marc G published his tabels restricting all that can
> > be known (his ontology?) into the domains he presently knows. That
> > also threw me out from a desire to participate:
> >  I start from our ignorance and consider whatever we think we know as
> > our increasing epistemy.
>
>
> A good path. Note that eventually we have to come back to ignorance.
> Bohr said something similar to "the more you dig on the quantum the
> less you understand".  With comp, this is also correct, but in this
> case you can a

Re: Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 10-sept.-07, à 21:03, John Mikes a écrit :

> Dear Bruno, i failed to acknowledge your kind reply - and others 
> joining in - for the past month, not because I have been tied up with 
> 'other' WEB lists, but because I realized that i have nothing to say 
> "in kind" of the language you use.


No problem. But note that you can ask about language question in case 
of trouble.




> Not only are the terms unfamiliar (I have to think hard to put them 
> into 'meaning' (proper or not), but the underlying and firmly supposed 
> to 'known' math-phys theories are vague at best (some, others 
> unknown). So are the words used lately.


Don't hesitate, in case you have the time to tell us which one. You 
could be surprise how simple things are, and why sometimes things seems 
complex but are not (alas, sometimes the contrary is true too; they are 
  manay things which seems obvious, but are not, like Church's thesis to 
name just one important example).



> So I did not want to bore you with my uneducated remarks.


The "average lobian machine" is even less educate than you. And the 
understanding of what I'm trying to do is 50% based on the fact that 
lobian machine can already understand it, even discover it.



> This discussion penetrated the technical (?) level of the few adepts 
> and alas I am not part of it.

You are, imo (judging from you posts). But it asks for work, and I can 
understand it is hard to find the time and sometimes even just the 
necessary serene atmosphere for thinking ...



> In the meantime Marc G published his tabels restricting all that can 
> be known (his ontology?) into the domains he presently knows. That 
> also threw me out from a desire to participate:
>  I start from our ignorance and consider whatever we think we know as 
> our increasing epistemy.


A good path. Note that eventually we have to come back to ignorance. 
Bohr said something similar to "the more you dig on the quantum the 
less you understand".  With comp, this is also correct, but in this 
case you can at least understand why it is necessarily so. The more you 
dig on comp, the less you understand, but at least you can understand 
why. Eventually lobian ignorance appears as something powerful and 
creative. Also, that digging is a major step to "more freedom", but 
also, I think, to more humanity (because of its "less certainty" 
consequences; many inhuman aspects of humanity come from people having 
certainties about humans.




> I keep lurking and when my mouse starts squeaking in common sense, I 
> will put in a post.
> With appreciation for your (plural) advanced knowledge


Thanks. Take it easy. What I propose to explain to David is the minimal 
background in 19th century mathematics which has led to Church's 
thesis, which is really somehow the "Schroedinger equation" of comp. 
Church thesis makes the universal machine really "universal", and it 
makes the universal dovetailer really universally dovetailing.

If you stick literally to the idea of complaining each time you miss a 
technical world, then you will eventually understand what I am trying 
to prove. There is not so much difficulties (beside newness or 
novelty). I propose a thought experiment (UDA) which shows why IF we 
are (digital) machine then the laws of physics have to be justified 
from the many possible relations existing between numbers/machines, and 
then I show how to put this into practice by interviewing some 
Universal Machine (the one I call lobian, which are just a slight 
extension of what a universal machine is).

The real bomb is just the discovery/apparition of those universal 
machines last century. They are the "heroes" of our time, not because 
they are powerful, but because they indicate a path which can help a 
lot to realize our own abyssal ignorance. And adding knowledge about 
those beasts can only makes our (creative) ignorance even bigger.

John, you don't have to justify your silence, but if that silence is 
based on vocabulary questions, please just dare to ask. As a teacher I 
have eventually understood that everybody can understand math, but not 
everybody can be motivated. Motivations are personal. Now, sometimes 
people are motivated, but they can be discouraged for bad reasons, like 
the feeling something is not for them, when they have actually just 
miss a definition. In *that* case I can help (and I am interested 
personally to help). The questions addressed in this list *are* 
complex; the math is needed to simplify things, not making them more 
complex ...

Best,

Bruno

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


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Re: Rép : Observer Moment = Sigma1-Sentences

[John Mikes]

Dear Bruno, i failed to acknowledge your kind reply - and others joining in
- for the past month, not because I have been tied up with 'other' WEB
lists, but because I realized that i have nothing to say "in kind" of the
language you use. Not only are the terms unfamiliar (I have to think hard to
put them into 'meaning' (proper or not), but the underlying and firmly
supposed to 'known' math-phys theories are vague at best (some, others
unknown). So are the words used lately.
So I did not want to bore you with my uneducated remarks. This discussion
penetrated the technical (?) level of the few adepts and alas I am not part
of it.
In the meantime Marc G published his tabels restricting all that can be
known (his ontology?) into the domains he presently knows. That also threw
me out from a desire to participate: I start from our ignorance and consider
whatever we think we know as our increasing epistemy.
I keep lurking and when my mouse starts squeaking in common sense, I will
put in a post.
With appreciation for your (plural) advanced knowledge

John Mikes


On 8/13/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
> Dear John,
>
>
> Le 12-août-07, à 18:00, John Mikes a écrit :
>
> > Dear Bruno,
> > did your scientific emotion just trapped you into showing that your
> > theoretical setup makes no sense?
> > Angels have NO rational meaning, they are phantsms of a (fairy?)tale
> > and if your math-formulation can be applied to a (really) meaningless
> > phantasy-object, the credibility of it suffers.
> > How can your formalism be applied to something nonexistent? What does
> > it say about the 'real' value of it?
>
>
> I think you have missed the posts where I defined Angels, Gods,
> Supergods, etc.  By definition they refer to lobian entities which are
> NOT emulable by Turing Machines. They exists mathematically. They are
> the main object study of a branch of mathematical logic known as
> recursion theory or computability theory (which could be called
> uncomputability theory aswell).
> A detailed example of a very powerful, yet lobian, "angel" is given in
> Boolos 93, and called "Analysis + Omega-rule", and I have often refer
> to it by calling it Anomega.
>
> Perhaps later I will explain that the full (first order modal logical
> system) which I use to interpret Plotinus "divine intellect" is really
> an angel too, actually more powerful than the unnameable "god" (the
> plotinus' ONE) of the machine.
>
>
>
> >
> > I read Kim's question as a joke, you took it seriously with some
> > (imagined) meaning you had in mind. Faith?
>
>
> I remind you that we have already talk a lot about the necessity of
> some "faith" from the part of lobian entities (machine or not). The
> machine cannot prove its own consistency, but can bet on it, and use
> that bet in many different ways.
>
>
>
> > Please, do not tell me that your theories are as well applicable to
> > faith-items! Next time sopmebody will calculate the enthalpy of the
> > resurrection.
>
> Don't worry. each term I am using have been well defined. By "Angel" I
> just mean those lobian entities which are not machines. I did already,
> in 2000, in this list called G* the "guardian angel" of the machine,
> because it knows a lot about the machine that the machine cannot know
> or prove about itself. Now, with the arithmetical interpretation of
> Plotinus, I have to use those terms in a bit more systematic ways. The
> G/G* type of theology works for (ideally correct) machine, but also on
> many self-referentially correct entities which are NOT machine. OK?
>
> Best,
>
>
> Bruno
>
>
>
> >
> > John
> >
> > On 8/9/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> >>
> >> Le 09-août-07, à 11:22, Kim Jones a écrit :
> >>
> >> >
> >> > What is "lobian" apart from la machine, Bruno? Are you referring to
> >> > "angels" here?
> >> >
> >> > Aren't angels machines too?
> >>
> >>
> >> Angels are not machine. Unless you extend the meaning of machine
> >> 'course, but Angels' provability extend the provability of any
> >> turing-emulable machine. Sometimes people use the term "supermachine"
> >> for what I call angel, but mathematically, in principle,  angels have
> >> nothing to do with machine. Angels can prove any sentence having the
> >> shape AxP(x) with P(x) decidable. (AxP(x) = For all x P(x)). Universal
> >>  machine are Sigma_1 complete. Angels are PI_1 complete. A sigma_1
> >> sentence asserts something like "It exists a number having such or
> >> such
> >> verifiable (decidable) property". PI_1 sentences asserts something
> >> like
> >> "all numbers have such or such verifiable (decidable) property".
> >> The most famous PI_1 sentences is the *machine* consistency statement:
> >> it is indeed equivalent with: all number have the (verifiable)
> >> property
> >> of not being the Godel number (or any arithmetical encoding) of a
> >> proof
> >> of f.
> >> (f = any arithmetical contradiction, like (1+1=2 & ~(1+1=2)).
> >> Angels can be shown to be lobian. They obey G and G*,

Re: SV: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Hi David,


Le 02-sept.-07, à 17:00, David Nyman a écrit :

>
> On 02/09/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> You could have chosen a better moment because next week I have exams
>> and will not be in my office, but the week after I will try to explain
>> this. It is necessary to get the UDA, and even more for the AUDA (the
>> lobian interview).
>
> Hi Bruno
>
> Given your current commitments, I'll continue my reading, and also
> thinking about the various issues recently posted.  Let's continue the
> dialogue the week after the exams.


No problem. I hope you don't mind if I give little exercises from time 
to time. My goal is not to teach logic on the list but only to explain 
the minimal amount so that I can explain better some result, so that 
people are not mislead by the vocabulary. It is just OK to ask me for 
answesr if only for the benefits of the others. It is obvious that comp 
makes sense only through some COMPuter science ...





>
> BTW, I've also been intermittently reading Schopenhauer (and Bryan
> Magee's book on him) and ISTM that maybe comp is a way to approach the
> Kant-Schopenhauer noumenon, at least in the sense that what is below
> our substitution level is indiscernible, and hence in that way
> inescapably 'noumenal', for us (i.e. it's constitutive of us, but
> never an object of our knowledge).


It is bit more complex, in the sense that it is not just because those 
sublevel substitution are indiscernible, but also because we have to 
bet on a substitution level at the start: so, eventually, the 
theological part is more related to the G/G* distinction than to the 
unknowability of what happens below the subtitution level, but again we 
are anticipating ... Of course those points are related.




> Is this in any way similar to what
> you mean by machine 'theology', in the sense that its theology (or
> noumenon) is equivalent to a machine's beliefs about its ontology
> (i.e. its constitutive or 'substitution' level), but that these
> beliefs can never be formulated as proofs about its epistemic (or
> 'phenomenal') world?

It is related. Actually I am not yet sure about the best way to define 
this 'machine theology'. But the simplest way is to define the theology 
of machine M by the difference between TRUTH ABOUT the machine M, and 
what the machine M can prove about herself, once she bets on some 
substitution level (and once she bets on comp, also).
This is a non normative definition of theology. Nobody pretends to know 
truth about us. But it is a fact that rich lobian machine can *prove* 
everything about simpler machine theology (at the propositional level).


> If so, the content of such a belief would then
> be what Wittgenstein, taking his lead from Schopenhauer, claimed
> (though he stressed its primacy) that we couldn't make intelligible
> statements about (i.e. the mystery *that* the world is); but the
> notion of substitution level in comp would in fact give us a way of
> speaking about it in a relative way.


Yes, again this is related. In "CONSCIENCE ET MECANISME" I make that 
relation explicit. I take as axiom what I did call the WITTGENSTEIN 
principle: such content is an x such that, well not only we cannot 
prove x, but the truth of x entails the non-provability of x. That is, 
we have both:

~Bx, and
x -> ~Bx

with "B" meaning "provable by M", in the language of the (ideally 
correct) machine M. Note that any falsity, like "0 = 1" satisfies the 
first formula trivially: ~B'0=1' is true for an ideally correct 
machine. But that very fact is a truth which, by the second 
incompleteness result, cannot be given by the machine. So x = 
consistency (x = ~B'0=1') statisfies the second formula: ~B"0=1' -> 
~B(~B'0=1'), or ~Bf -> ~B(~Bf). OK?

To sum up: theology of machine M = truth about M minus provability by M 
about M. (Tell me if this makes some sense for you, or nothing, but 
again we are anticipating).

best,

Bruno


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


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Re: SV: Observer Moment = Sigma1-Sentences

[David Nyman]

On 02/09/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> You could have chosen a better moment because next week I have exams
> and will not be in my office, but the week after I will try to explain
> this. It is necessary to get the UDA, and even more for the AUDA (the
> lobian interview).

Hi Bruno

Given your current commitments, I'll continue my reading, and also
thinking about the various issues recently posted.  Let's continue the
dialogue the week after the exams.

BTW, I've also been intermittently reading Schopenhauer (and Bryan
Magee's book on him) and ISTM that maybe comp is a way to approach the
Kant-Schopenhauer noumenon, at least in the sense that what is below
our substitution level is indiscernible, and hence in that way
inescapably 'noumenal', for us (i.e. it's constitutive of us, but
never an object of our knowledge).  Is this in any way similar to what
you mean by machine 'theology', in the sense that its theology (or
noumenon) is equivalent to a machine's beliefs about its ontology
(i.e. its constitutive or 'substitution' level), but that these
beliefs can never be formulated as proofs about its epistemic (or
'phenomenal') world?  If so, the content of such a belief would then
be what Wittgenstein, taking his lead from Schopenhauer, claimed
(though he stressed its primacy) that we couldn't make intelligible
statements about (i.e. the mystery *that* the world is); but the
notion of substitution level in comp would in fact give us a way of
speaking about it in a relative way.

David
>
>
> Le 31-août-07, à 16:54, Lennart Nilsson a écrit :
>
>
> >
> > Bruno says:
> >
> > "...the notion of computability is absolute."
> >
> > David Deutsch says: 
>
>
>
> OK, but on this point David, as he says himself, disagrees with 100% of
> the mathematicians.
> OK, this *is* not an argument 
>
>
>
>
>
>
> >
> > "We see around us a computable universe;
>
>
> I am already not sure we can *see* a universe. But I am definitely sure
> we don't see a computable universe. This is only something which has to
> be inferred. Also, would Copenhagen QM be correct, we could as well say
> we see around us a non computable universe. You have to infer the MW
> for keeping Church thesis intact (this is not obvious to show).
> Also, I recall you that platonists insists that seeing gives only
> appearances, and then comp implies (by UDA) that such appearances have
> to have non computationnal components.
>
>
>
>
> > that is to say, of all
> > possible mathematical objects and relationships, only an infinitesimal
> > proportion
> > are ever instantiated in the relationships of physical objects and
> > physical
> > processes. (These are essentially the computable functions.)
>
>
> David postulates here both comp and physical realism. This is simply
> not working by the UDA (and weak Occam).
> Recall that: IF I am a Machine, then, whatever the "appearance of
> universe" can be it cannot be computable.
>
>
> > Now it might
> > seem that one approach to explaining that amazing fact, is to say "the
> > reason
> > why physical processes conform to this very small part of mathematics,
> > 'computable mathematics,' is that physical processes really are
> > computations
> > running on a computer external to what we think of as physical
> > reality."
>
>
> Note that here comp really entails that physical processes cannot be
> computable. If I am a digitalizable machine then the universe cannot be
> a digitilizable machine. Don't confuse constructive physics or
> computational physics with computationnalist physics: which is the
> physics you have to derive from numbers once you take seriously enough
> the comp hyp. I know that all this is a bit counter-intuitive, that is
> why I like to ask people where in the UDA they stop to be convinced.
>
>
>
> >  But
> > that relies
>
> relies wrongly
>
>
> > on the assumption that the set of computable functions -- the
> > Turing computable functions, or the set of quantum computable
> > operations
> > -- is somehow inherently privileged within mathematics.
>
>
> This is Church thesis, and David agrees (and I think is even the first
> to show) that Quantum Computer does not violate Church thesis. The set
> of functions computable from N to N with a quantum computer is the same
> as the set of functions from N to N computable with Babbage machine or
> the one that can be described in  Python, Lisp, Fortran, Game-of-life, etc.>.
>
>
>
> > So that even a
> > computer
> > implemented in unknown physics (the supposed computer that we're
> > all simulations on) would be expected to conform to those same notions
> > of
> > computability, to use those same functions that mathematics designates
> > as
> > computable.
>
> Yes.
>
>
> > But in fact, the only thing that privileges the set of all
> > computational
> > operations that we see in nature, is that they are instantiated by
> > the laws of physics.
>
> I don't believe in this at all (and again, here I'm on the side of all
> mathematicians b

Re: SV: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 31-août-07, à 16:54, Lennart Nilsson a écrit :


>
> Bruno says:
>
> "...the notion of computability is absolute."
>
> David Deutsch says: 



OK, but on this point David, as he says himself, disagrees with 100% of 
the mathematicians.
OK, this *is* not an argument 






>
> "We see around us a computable universe;


I am already not sure we can *see* a universe. But I am definitely sure 
we don't see a computable universe. This is only something which has to 
be inferred. Also, would Copenhagen QM be correct, we could as well say 
we see around us a non computable universe. You have to infer the MW 
for keeping Church thesis intact (this is not obvious to show).
Also, I recall you that platonists insists that seeing gives only 
appearances, and then comp implies (by UDA) that such appearances have 
to have non computationnal components.




> that is to say, of all
> possible mathematical objects and relationships, only an infinitesimal
> proportion
> are ever instantiated in the relationships of physical objects and 
> physical
> processes. (These are essentially the computable functions.)


David postulates here both comp and physical realism. This is simply 
not working by the UDA (and weak Occam).
Recall that: IF I am a Machine, then, whatever the "appearance of 
universe" can be it cannot be computable.


> Now it might
> seem that one approach to explaining that amazing fact, is to say "the
> reason
> why physical processes conform to this very small part of mathematics,
> 'computable mathematics,' is that physical processes really are 
> computations
> running on a computer external to what we think of as physical 
> reality."


Note that here comp really entails that physical processes cannot be 
computable. If I am a digitalizable machine then the universe cannot be 
a digitilizable machine. Don't confuse constructive physics or 
computational physics with computationnalist physics: which is the 
physics you have to derive from numbers once you take seriously enough 
the comp hyp. I know that all this is a bit counter-intuitive, that is 
why I like to ask people where in the UDA they stop to be convinced.



>  But
> that relies

relies wrongly


> on the assumption that the set of computable functions -- the
> Turing computable functions, or the set of quantum computable 
> operations
> -- is somehow inherently privileged within mathematics. 


This is Church thesis, and David agrees (and I think is even the first 
to show) that Quantum Computer does not violate Church thesis. The set 
of functions computable from N to N with a quantum computer is the same 
as the set of functions from N to N computable with Babbage machine or 
the one that can be described in .



> So that even a
> computer
> implemented in unknown physics (the supposed computer that we're
> all simulations on) would be expected to conform to those same notions 
> of
> computability, to use those same functions that mathematics designates 
> as
> computable.

Yes.


> But in fact, the only thing that privileges the set of all
> computational
> operations that we see in nature, is that they are instantiated by
> the laws of physics.

I don't believe in this at all (and again, here I'm on the side of all 
mathematicians but OK don't take this as an argument).



>  It is only through our knowledge of the physical world
> that we know of the difference between computable and not computable.


Not at all, except in the weak sense that you have to live to begin 
with for  being interested in question like that.. Wait until I explain 
Church Thesis, there are deep purely arithmetical reasons to believe in 
the necessity of the computable and the many uncomputables.




> So
> it's only through our laws of physics that the nature of computation 
> can be
> understood. It can never be vice versa."


I don't believe in this. It has not been proved, and actually this 
cannot be maintained if comp is true.



>
> http://www.qubit.org/people/david/Articles/PPQT.pdf
>
>
> If it is only through our knowledge of the physical world
> that we know of the difference between computable and not computable, 
> and I
> don´t see any flaw in David´s argument that leads up to that 
> statement, then
> the notion of computability definitely is not absolute.


Well, thank you for providing me still more motivations to explain why 
the concept of computability is the most absolute epistemological 
notion ever discovered by the mathematician, and why Church thesis, 
although a very strong statement (philosophically) is very well 
grounded both with the facts and conceptually.

You could have chosen a better moment because next week I have exams 
and will not be in my office, but the week after I will try to explain 
this. It is necessary to get the UDA, and even more for the AUDA (the 
lobian interview).

Bruno

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


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Re: SV: Observer Moment = Sigma1-Sentences

[Brent Meeker]

Lennart Nilsson wrote:
> Bruno says:
> 
> "...the notion of computability is absolute." 
> 
> David Deutsch says:
> 
> "We see around us a computable universe; that is to say, of all
> possible mathematical objects and relationships, only an infinitesimal
> proportion
> are ever instantiated in the relationships of physical objects and physical
> processes. (These are essentially the computable functions.) 

But if there is inherent randomness in QM that is not computable.  So Deutsch 
and others insist on the MWI so that everything happens computably and then 
they turn around and conclude that the universe is computable.  A clearly 
circular argument.

Brent Meeker

>Now it might
> seem that one approach to explaining that amazing fact, is to say "the
> reason
> why physical processes conform to this very small part of mathematics,
> 'computable mathematics,' is that physical processes really are computations
> running on a computer external to what we think of as physical reality." But
> that relies on the assumption that the set of computable functions -- the
> Turing computable functions, or the set of quantum computable operations
> -- is somehow inherently privileged within mathematics. So that even a
> computer
> implemented in unknown physics (the supposed computer that we're
> all simulations on) would be expected to conform to those same notions of
> computability, to use those same functions that mathematics designates as
> computable. But in fact, the only thing that privileges the set of all
> computational
> operations that we see in nature, is that they are instantiated by
> the laws of physics. It is only through our knowledge of the physical world
> that we know of the difference between computable and not computable. So
> it's only through our laws of physics that the nature of computation can be
> understood. It can never be vice versa."
> 
> http://www.qubit.org/people/david/Articles/PPQT.pdf
> 
> 
> If it is only through our knowledge of the physical world
> that we know of the difference between computable and not computable, and I
> don´t see any flaw in David´s argument that leads up to that statement, then
> the notion of computability definitely is not absolute.
> 
> LN
> 
> 
> 
> > 
> 
> 


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SV: Observer Moment = Sigma1-Sentences

[Lennart Nilsson]

Bruno says:

"...the notion of computability is absolute." 

David Deutsch says:

"We see around us a computable universe; that is to say, of all
possible mathematical objects and relationships, only an infinitesimal
proportion
are ever instantiated in the relationships of physical objects and physical
processes. (These are essentially the computable functions.) Now it might
seem that one approach to explaining that amazing fact, is to say "the
reason
why physical processes conform to this very small part of mathematics,
'computable mathematics,' is that physical processes really are computations
running on a computer external to what we think of as physical reality." But
that relies on the assumption that the set of computable functions -- the
Turing computable functions, or the set of quantum computable operations
-- is somehow inherently privileged within mathematics. So that even a
computer
implemented in unknown physics (the supposed computer that we're
all simulations on) would be expected to conform to those same notions of
computability, to use those same functions that mathematics designates as
computable. But in fact, the only thing that privileges the set of all
computational
operations that we see in nature, is that they are instantiated by
the laws of physics. It is only through our knowledge of the physical world
that we know of the difference between computable and not computable. So
it's only through our laws of physics that the nature of computation can be
understood. It can never be vice versa."

http://www.qubit.org/people/david/Articles/PPQT.pdf


If it is only through our knowledge of the physical world
that we know of the difference between computable and not computable, and I
don´t see any flaw in David´s argument that leads up to that statement, then
the notion of computability definitely is not absolute.

LN



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Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Hi David,


Le 29-août-07, à 16:57, I (Bruno Marchal)  wrote :

>
> I must go. Tomorrow I begin to explain the idea of a computable
> function. To let you think in advance I give you a problem: have you an
> idea why NON computable functions have to exist?


I feel a bit guilty because, 'course, that is a *very* tricky question, 
and I have made quite a jump here!

Let me continue in that vein!

Could we even hope that a the notion of computability can be defined 
mathematically? Is not "computable" an epistemic notion?
How could we think that a function computable by the french is 
necessarily computable by the belgians, and vice versa?

Should not John Mikes interrupt me, and tell me: "Bruno, whatever 
definition of computability you will give to us, it will only define, 
at the best, a notion of *human* computability, certainly not an 
absolute notion!

Where does my confidence that John would be wrong here comes from?

Well, most of you know the answer, my confidence comes from  what 
is known as "Church's Thesis"  CT (sometimes by Post Law, or 
Church-Turing thesis, or Post-Markov-Kleene thesis, ...).


David, here is a little roadmap:

GOAL: to get a thorough understanding that the notion of computability 
is absolute. This is needed, not only for grasping that the universal 
dovetailer is really universal (and thus for the grasping of the 
informal UDA), but is also needed to get a thorough understanding that 
the notion of provability is not absolute, and cannot been made 
universal. John would be right to criticize  any notion of absolute 
provability; but for the notion of computability, well, a miracle will 
occur (Godel's eventual wording on CT).

MEANS: I think, if you are patient enough, that I will go back were the 
story starts, and I think it starts with GALILEO. Galileo is indeed the 
first, as far as I know, to realize that there is a bijection between N 
and 2N (by which I mean the set of even numbers). Galileo was disturbed 
by the fact a set (N) could be put in one-one correspondence with a 
proper subset of itself (2N). I will come back on this, but for now I 
am thinking on the following roadmap:

Bijection
Enumeration (bijection with N)
Non enumerable set

And only when this will be clear, can we introduce the subtler and most 
important concept of mechanical or effective or recursive enumeration 
and introduce Church thesis and computability. And then we will proceed 
toward the notion of provability, and only then can we address the 
notion of "machine theology"  OK? We have to address that Church 
Miracle.

So:

Do you see that there is a bijection between N = {0, 1, 2, 3, 4 ...} 
and 2N = {0, 2, 4, 6, 8, ...}. Which one?
Do you see that there is a bijection between N and NXN (= the set of 
couple (x, y) with x and y belonging to N)?

Bruno




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


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Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 28-août-07, à 18:26, David Nyman a écrit :

>
> On 28/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
 If you drop a pen, to
 compute EXACTLY what will happen in principle, you have to consider
 all
 comp histories in UD* (the complete development of the UD) going
 through your actual state (the higher level description of it, which
 exists by comp, but which is actually not knowable by you. Of course
 this cannot be used in practice, but has to be used to derive the 
 more
 usable laws of physics.
>>>
>>> I hope this will become clearer as we proceed.
>>
>>
>> I hope too. Perhaps it would help us if you could tell me which step 
>> of
>> the UDA you find unclear.
>
> I'm sorry, I should have been clearer myself.  It isn't the UDA per se
> that I don't find clear, but some of your specific statements and
> language above.  For example, what specifically enables us to 'derive
> the usable laws of physics'?


I'm afraid "usable" is a fatal typo mistake. I dont see what I was 
trying to say! My fault. Do you understand that to predict the exact 
behavior of the pen, you have to take into account all computations 
going through your state? (your state = your third person comp state 
when you are looking at the pen before you drop it, which exists by 
comp.
Of course nobody are interested in something as exact as that in any 
application, for the same reason nobody will use Schroedinger equation 
to study the trajectory of a satellite, nor will anybody use string 
theory for doing a pizza. Even if we succeed in deriving physics from 
the comp hyp, it could be that such a physics would be always too much 
exact for any practical use. Still, it could give general idea, like 
the existence of interfering many worlds, the refutation of 
in-exploitability of sub-level comp computation (the comp-"quantum" 
computing ability, etc.





> But perhaps I'm anticipating.  I'm also
> not sure exactly what you mean by 'comp histories going through your
> actual state'.

I mean the set of computations which are going through your third 
person state (in the UD*), but as seen from your first person pov.



> I think you mean that an 'actual state' (i.e. first
> person OM) that I'm experiencing can be attributed to any of these
> histories - yes?

OK. A bit more exact would be  can be attributed to some 3-state 
occurring in those histories/computations. Let us be more specific 
later, when we will have a bit more vocabulary to put the right 
nuances.


>
>> Remember that we *assume* the comp hyp. Sometimes some people does not
>> understand because they (more or less unconsciously believe that I am
>> arguing for comp, but that is something I am never doing since a very
>> long time: I really take it as a working hypothesis with no 
>> (conscious)
>> prejudice about where this can lead us.
>
> Yes, I accepted this a while back.


OK. (I knew, but sometimes I add little things for the benefice of some 
others so that they doesn't miss the train, just in case ...).



>
>> By linearity the cat
>> will be in the superposition state. What prevent us of seeing the cat
>> in that superposition state is not that the cat is macroscopic but
>> comes from the fact that we cannot isolate the cat sufficiently well
>> from us, so that, very quickly we will find ourselves in a
>> superposition seeing the cat in such state + seeing the cat in the
>> orthe state. The "quickly" here is not due to some magical quick wave
>> collapse, but is due to the rapidity of the decoherence process, which
>> mainly describes the (linear) way superposition are contagiopus to
>> their neighborhood.
>
> OK, so 'the cat' quickly becomes us + the cat in two orthogonal
> states?  BTW, I've never seen the cat referred to as a 'contagio-puss'
> before, but it might catch on!

OK.


>
>> Now with comp, it is the same. You cannot known, by the first person
>> indeterminacy, which computations support your conscious state among
>> all computations that you cannot discerned. To make this clearer, I
>> will wait you telling me where exactly you have some trouble in the
>> UDA. OK?
>
> I think this is what I intended above - i.e. the UD* entails
> computations that support both versions of 'me' + the cat; which one
> "I" experience in a given OM is indeterminate.


OK (I think).


>
>> A state by itself cannot change the probabilities. It is the relative
>> number of possible continuations of a state, relative to the "number"
>> of comp histories going through that state which counts, up to some
>> (extraordinarily complex) equivalence relation.
>
> Are you still talking about the equivalence relation between the mind
> and the brain?  I'm sorry to be so picky, but I'm really trying to be
> sure I understand each sentence.


I'm not sure I have ever talk about an equivalence relation between the 
mind and the brain, unless you mean the relation between one mind (one 
person) and the infinity of computation going through in

Re: Observer Moment = Sigma1-Sentences

[David Nyman]

On 28/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> >> If you drop a pen, to
> >> compute EXACTLY what will happen in principle, you have to consider
> >> all
> >> comp histories in UD* (the complete development of the UD) going
> >> through your actual state (the higher level description of it, which
> >> exists by comp, but which is actually not knowable by you. Of course
> >> this cannot be used in practice, but has to be used to derive the more
> >> usable laws of physics.
> >
> > I hope this will become clearer as we proceed.
>
>
> I hope too. Perhaps it would help us if you could tell me which step of
> the UDA you find unclear.

I'm sorry, I should have been clearer myself.  It isn't the UDA per se
that I don't find clear, but some of your specific statements and
language above.  For example, what specifically enables us to 'derive
the usable laws of physics'?  But perhaps I'm anticipating.  I'm also
not sure exactly what you mean by 'comp histories going through your
actual state'.  I think you mean that an 'actual state' (i.e. first
person OM) that I'm experiencing can be attributed to any of these
histories - yes?

> Remember that we *assume* the comp hyp. Sometimes some people does not
> understand because they (more or less unconsciously believe that I am
> arguing for comp, but that is something I am never doing since a very
> long time: I really take it as a working hypothesis with no (conscious)
> prejudice about where this can lead us.

Yes, I accepted this a while back.

> By linearity the cat
> will be in the superposition state. What prevent us of seeing the cat
> in that superposition state is not that the cat is macroscopic but
> comes from the fact that we cannot isolate the cat sufficiently well
> from us, so that, very quickly we will find ourselves in a
> superposition seeing the cat in such state + seeing the cat in the
> orthe state. The "quickly" here is not due to some magical quick wave
> collapse, but is due to the rapidity of the decoherence process, which
> mainly describes the (linear) way superposition are contagiopus to
> their neighborhood.

OK, so 'the cat' quickly becomes us + the cat in two orthogonal
states?  BTW, I've never seen the cat referred to as a 'contagio-puss'
before, but it might catch on!

> Now with comp, it is the same. You cannot known, by the first person
> indeterminacy, which computations support your conscious state among
> all computations that you cannot discerned. To make this clearer, I
> will wait you telling me where exactly you have some trouble in the
> UDA. OK?

I think this is what I intended above - i.e. the UD* entails
computations that support both versions of 'me' + the cat; which one
"I" experience in a given OM is indeterminate.

> A state by itself cannot change the probabilities. It is the relative
> number of possible continuations of a state, relative to the "number"
> of comp histories going through that state which counts, up to some
> (extraordinarily complex) equivalence relation.

Are you still talking about the equivalence relation between the mind
and the brain?  I'm sorry to be so picky, but I'm really trying to be
sure I understand each sentence.

> Can you compute how many functions from A to B there are, in case A has
> n elements and B has m elements? Answer: m^n. Can you see that?

Yes, I can see it now I understand the notation better.

> By "proof" here, I mean an argument which convinces you,
> or better, an argument which you have the feeling that it can be used
> to convince your "little sister" (which I suppose not to be a
> mathematician).

In fact I have two little sisters (and one little brother), and none
are mathematicians.

David

>
>
> Le 27-août-07, à 13:27, David Nyman a écrit :
>
> >
> > On 16/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> >
> >> If you drop a pen, to
> >> compute EXACTLY what will happen in principle, you have to consider
> >> all
> >> comp histories in UD* (the complete development of the UD) going
> >> through your actual state (the higher level description of it, which
> >> exists by comp, but which is actually not knowable by you. Of course
> >> this cannot be used in practice, but has to be used to derive the more
> >> usable laws of physics.
> >
> > I hope this will become clearer as we proceed.
>
>
> I hope too. Perhaps it would help us if you could tell me which step of
> the UDA you find unclear.
> cf the paper:
> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.htm
>
> and the single summary slide PDF:
> http://iridia.ulb.ac.be/~marchal/publications/SANE2004Slide.pdf
>
> Normally the first seven steps should not be too much difficult.
> Remember that we *assume* the comp hyp. Sometimes some people does not
> understand because they (more or less unconsciously believe that I am
> arguing for comp, but that is something I am never doing since a very
> long time: I really take it as a working hypothesis with no (conscious)
> prejudice about where this c

Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 27-août-07, à 13:27, David Nyman a écrit :

>
> On 16/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> If you drop a pen, to
>> compute EXACTLY what will happen in principle, you have to consider 
>> all
>> comp histories in UD* (the complete development of the UD) going
>> through your actual state (the higher level description of it, which
>> exists by comp, but which is actually not knowable by you. Of course
>> this cannot be used in practice, but has to be used to derive the more
>> usable laws of physics.
>
> I hope this will become clearer as we proceed.


I hope too. Perhaps it would help us if you could tell me which step of 
the UDA you find unclear.
cf the paper:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.htm

and the single summary slide PDF:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004Slide.pdf

Normally the first seven steps should not be too much difficult. 
Remember that we *assume* the comp hyp. Sometimes some people does not 
understand because they (more or less unconsciously believe that I am 
arguing for comp, but that is something I am never doing since a very 
long time: I really take it as a working hypothesis with no (conscious) 
prejudice about where this can lead us.



>
>> Empirically we can expect that the 'substitution level" is more 
>> related
>> to a notion of "isolation" than of scaling. Nevertheless, we cannot
>> really use this here, given that we have to extract quantum physics
>> from the existence of that "level".
>
> I don't understand this yet.


I guess you have some understanding of the first sentence, given that 
this is something happening in any version of QM without collapse. 
Sometime ago, some people argued that QM is confined to the 
microscopic, and they believed that that was the reason why a 
macroscopic quantum superposition (like Schroedinger's Cat) could not 
exist. Today we have plenty of evidences that this is not correct, and 
that it is even quite easy to generate a cat in a superposition eating 
+ drinking (say). Indeed it is enough to *isolate* sufficiently well 
the cat, and then to force him/her/it to choose between drinking and 
eating according to the result of a measurement of a quantum 
superposition state state of some local photon. By linearity the cat 
will be in the superposition state. What prevent us of seeing the cat 
in that superposition state is not that the cat is macroscopic but 
comes from the fact that we cannot isolate the cat sufficiently well 
from us, so that, very quickly we will find ourselves in a 
superposition seeing the cat in such state + seeing the cat in the 
orthe state. The "quickly" here is not due to some magical quick wave 
collapse, but is due to the rapidity of the decoherence process, which 
mainly describes the (linear) way superposition are contagiopus to 
their neighborhood.
Now with comp, it is the same. You cannot known, by the first person 
indeterminacy, which computations support your conscious state among 
all computations that you cannot discerned. To make this clearer, I 
will wait you telling me where exactly you have some trouble in the 
UDA. OK?



>
>> The
>> 3-brain is just not a physical device for producing consciousness, it
>> is a local and relative "description" of a state making greater the
>> probability that you will be able to manifest your first person
>> experience relatively to some "dream", itself being an infinite set of
>> histories.
>
> Do you mean here that: there exists a 'state that [increases] the
> probability that you will be able to manifestetc.' and that the
> 3-brain 'is a local and relative "description"' of such a state?


A state by itself cannot change the probabilities. It is the relative 
number of possible continuations of a state, relative to the "number" 
of comp histories going through that state which counts, up to some 
(extraordinarily complex) equivalence relation.



>
>> Can you explain why the set of all binary sequences *is* closed
>> for diagonalization
>
> Because any additional members generated by diagonalisation must also
> be binary sequences?

OK.


>
>> and why any *enumerable* set of binary sequences
>> is *not* close for diagonalization?
>
> Because new members can always be generated by diagonalisation that go
> outside the original enumerable set (as distinct from the larger set
> of *all* sequences)?

OK.


>
>> A bit more difficult: can you show that for any set A, the set of
>> functions from A to {0,1} is bigger than A?
>
> Could you please elucidate "functions from A to {0,1}" ?


I recall that *a* function (without "s") from a set A to a set B, is 
just any association to each member of A of a member of B, in such a 
way that no element of A is associate to more than one element of B.
It is usual to describe a function by either a table of associations, 
or by a graph, etc. I will represent them by the set of associations. 
For example, the function FACTORIAL from N to N is represented b

Re: Observer Moment = Sigma1-Sentences

[David Nyman]

On 16/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> If you drop a pen, to
> compute EXACTLY what will happen in principle, you have to consider all
> comp histories in UD* (the complete development of the UD) going
> through your actual state (the higher level description of it, which
> exists by comp, but which is actually not knowable by you. Of course
> this cannot be used in practice, but has to be used to derive the more
> usable laws of physics.

I hope this will become clearer as we proceed.

> Empirically we can expect that the 'substitution level" is more related
> to a notion of "isolation" than of scaling. Nevertheless, we cannot
> really use this here, given that we have to extract quantum physics
> from the existence of that "level".

I don't understand this yet.

> The
> 3-brain is just not a physical device for producing consciousness, it
> is a local and relative "description" of a state making greater the
> probability that you will be able to manifest your first person
> experience relatively to some "dream", itself being an infinite set of
> histories.

Do you mean here that: there exists a 'state that [increases] the
probability that you will be able to manifestetc.' and that the
3-brain 'is a local and relative "description"' of such a state?

> Can you explain why the set of all binary sequences *is* closed
> for diagonalization

Because any additional members generated by diagonalisation must also
be binary sequences?

> and why any *enumerable* set of binary sequences
> is *not* close for diagonalization?

Because new members can always be generated by diagonalisation that go
outside the original enumerable set (as distinct from the larger set
of *all* sequences)?

> A bit more difficult: can you show that for any set A, the set of
> functions from A to {0,1} is bigger than A?

Could you please elucidate "functions from A to {0,1}" ?

David

>
>
> Le 15-août-07, à 17:00, David Nyman a écrit :
>
>
> >
> >> What comp (by UDA+FILMED-GRAPH) shows, is that, once the digitalness
> >> of
> >> your local relative description is taken seriously, you can no more
> >> distinguish the comp stories existing below your comp substitution
> >> level.
> >
> > So, 'materiality' - for you - can consist in effect only of what is at
> > or above this level?
>
>
> Yes. The visible will appear as a sum of the invisible.
>
>
>
> >
> >> Eventually the laws of physics will be the law of what remains
> >> or emerges as observable in all computations.
> >
> > Again - for all observers - what emerges at or above their
> > substitution level?
>
>
> This is exactly what we will have to compute.
>
>
>
> >
> >> From inside this has to
> >> interfere statistically (by UDA).
> >
> > That is, from inside comp reality, not inside 'matter'?  Then, given
> > this, statistical interference leads to first person indeterminacy.
>
>
> I would say the contrary. The first person indeterminacy comes from the
> fact that (relative) computational histories can diverge, and does
> diverge in case of self-differentiation or bifurcation like in the WM
> duplication experiment. Then the statistical interference emerges from
> the first (plural, hopefully) indeterminacy. If you drop a pen, to
> compute EXACTLY what will happen in principle, you have to consider all
> comp histories in UD* (the complete development of the UD) going
> through your actual state (the higher level description of it, which
> exists by comp, but which is actually not knowable by you. Of course
> this cannot be used in practice, but has to be used to derive the more
> usable laws of physics.
>
>
>
> >
> >> How? I would say by self-measurement relatively to their most probable
> >> (or credible ...) comp histories. There is always an infinity of them.
> >
> > How does 'self-measurement' lead to the observables of physics?  By
> > 'most probable' I assume you mean the convergence of first person
> > experience on such histories.  Is this what you mean by
> > 'self-measurement' (i.e. the convergence by self-sampling on a
> > first-personal 'measure')?
>
>
> Yes. And after the 8th step of the UDA, you should understand that the
> "physical implementation of the UD" is not relevant, because a UM
> cannot distinguish "reality" ("real" or virtual) from purely
> arithmetical reality,
>
>
> >
> >> You can see my thesis either as a the showing that comp necessitates
> >> to
> >> generalize Everett embedding of the subject into the physical world.
> >> (Cf also Rossler endophysiocs). Indeed comp forces us to embed the
> >> arithmetician (or any memory machine) in numberland (something for
> >> which we will never have a complete unification).
> >
> > Is comp therefore in effect a 'many minds' view?  In this case, do the
> > 'many worlds' emerge as the observables contingent on the povs of the
> > many minds (from the background of numberland)?
>
>
> I would say yes. I have often used the expression "many dreams" where a
> dream is an infinite set of (non inter

Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 17-août-07, à 18:12, David Nyman a écrit :



>
> On 16/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> OK. I will come back on this too.
>
> I'm away until next Thursday, so I'll continue to think about - and
> reserve my response to  - your last post until I return.  I've
> received Albert, Cutland, and Franzen, so I've got plenty of bed-time
> reading :-)





You are more lucky than me. I have ordered "Logical number theory" by 
Smorynski since years, and Amazon keeps up asking me if I really want 
it, and I have to confirm each time! Then, recently they abandon the 
search  Could books disappear?

Take your time, and enjoy the reading. At the same time, I would say 
you can also just consult them, ... (don't expect to get that stuff in 
some quick linear way ...).

I propose to focus on Cantor theorem. It is a good first step, even for 
just the less technical Universal Dovetailer Argument (UDA), or even 
just Church's Thesis.

See you (electronically) next week,

Good week-end for all of you,

Bruno


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


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Re: Observer Moment = Sigma1-Sentences

[David Nyman]

On 16/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> OK. I will come back on this too.

I'm away until next Thursday, so I'll continue to think about - and
reserve my response to  - your last post until I return.  I've
received Albert, Cutland, and Franzen, so I've got plenty of bed-time
reading :-)

David


>
>
> Le 15-août-07, à 17:00, David Nyman a écrit :
>
>
> >
> >> What comp (by UDA+FILMED-GRAPH) shows, is that, once the digitalness
> >> of
> >> your local relative description is taken seriously, you can no more
> >> distinguish the comp stories existing below your comp substitution
> >> level.
> >
> > So, 'materiality' - for you - can consist in effect only of what is at
> > or above this level?
>
>
> Yes. The visible will appear as a sum of the invisible.
>
>
>
> >
> >> Eventually the laws of physics will be the law of what remains
> >> or emerges as observable in all computations.
> >
> > Again - for all observers - what emerges at or above their
> > substitution level?
>
>
> This is exactly what we will have to compute.
>
>
>
> >
> >> From inside this has to
> >> interfere statistically (by UDA).
> >
> > That is, from inside comp reality, not inside 'matter'?  Then, given
> > this, statistical interference leads to first person indeterminacy.
>
>
> I would say the contrary. The first person indeterminacy comes from the
> fact that (relative) computational histories can diverge, and does
> diverge in case of self-differentiation or bifurcation like in the WM
> duplication experiment. Then the statistical interference emerges from
> the first (plural, hopefully) indeterminacy. If you drop a pen, to
> compute EXACTLY what will happen in principle, you have to consider all
> comp histories in UD* (the complete development of the UD) going
> through your actual state (the higher level description of it, which
> exists by comp, but which is actually not knowable by you. Of course
> this cannot be used in practice, but has to be used to derive the more
> usable laws of physics.
>
>
>
> >
> >> How? I would say by self-measurement relatively to their most probable
> >> (or credible ...) comp histories. There is always an infinity of them.
> >
> > How does 'self-measurement' lead to the observables of physics?  By
> > 'most probable' I assume you mean the convergence of first person
> > experience on such histories.  Is this what you mean by
> > 'self-measurement' (i.e. the convergence by self-sampling on a
> > first-personal 'measure')?
>
>
> Yes. And after the 8th step of the UDA, you should understand that the
> "physical implementation of the UD" is not relevant, because a UM
> cannot distinguish "reality" ("real" or virtual) from purely
> arithmetical reality,
>
>
> >
> >> You can see my thesis either as a the showing that comp necessitates
> >> to
> >> generalize Everett embedding of the subject into the physical world.
> >> (Cf also Rossler endophysiocs). Indeed comp forces us to embed the
> >> arithmetician (or any memory machine) in numberland (something for
> >> which we will never have a complete unification).
> >
> > Is comp therefore in effect a 'many minds' view?  In this case, do the
> > 'many worlds' emerge as the observables contingent on the povs of the
> > many minds (from the background of numberland)?
>
>
> I would say yes. I have often used the expression "many dreams" where a
> dream is an infinite set of (non interacting or independent) infinite
> computations. Logicians, like modal logicians are using the term
> "world" as something primitive and indefinite: a world is just an
> element of a set. They uses it intechangeably with "states", "points",
> "elements" etc. Does the many dreams generates anything like a singular
> physical world: well probably not. Does the many dreams generate a
> quantum multiverse? Well, if comp (and my reasoning) is correct then it
> has to do that. Does it, up to now yes (Again I anticipate).
>
>
> >
> >> I said in Siena, and already in this list, that for Plato, what *you*
> >> see (observe, measure) is the border of what *you* don't see. In the
> >> universal machine context this can lead to a recursive but solvable
> >> equation where physical reality is a sort of border of the comp-
> >> indeterminacy or the comp intrinsical ignorance.
> >
> > When you refer to the observables as the border of what you don't see,
> > or the border of the comp indeterminacy, are you again referring to
> > the indistinguishability of what lies below one's substitution level?
>
>
> Absolutely.
>
>
>
> > If so, would this not imply the potential existence of an infinity of
> > levels of observables, or physics(s), depending on the substitution
> > levels of classes of observers?
>
> All right, but note that we have no choice concerning our level of
> substitution. And the physics (observables) will be a "sum" on all
> possible fine grained histories consistent with your actual state. If
> comp is really at the origin of the quantum empirical interference, the
> 

Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 15-août-07, à 17:00, David Nyman a écrit :


>
>> What comp (by UDA+FILMED-GRAPH) shows, is that, once the digitalness 
>> of
>> your local relative description is taken seriously, you can no more
>> distinguish the comp stories existing below your comp substitution
>> level.
>
> So, 'materiality' - for you - can consist in effect only of what is at
> or above this level?


Yes. The visible will appear as a sum of the invisible.



>
>> Eventually the laws of physics will be the law of what remains
>> or emerges as observable in all computations.
>
> Again - for all observers - what emerges at or above their 
> substitution level?


This is exactly what we will have to compute.



>
>> From inside this has to
>> interfere statistically (by UDA).
>
> That is, from inside comp reality, not inside 'matter'?  Then, given
> this, statistical interference leads to first person indeterminacy.


I would say the contrary. The first person indeterminacy comes from the 
fact that (relative) computational histories can diverge, and does 
diverge in case of self-differentiation or bifurcation like in the WM 
duplication experiment. Then the statistical interference emerges from 
the first (plural, hopefully) indeterminacy. If you drop a pen, to 
compute EXACTLY what will happen in principle, you have to consider all 
comp histories in UD* (the complete development of the UD) going 
through your actual state (the higher level description of it, which 
exists by comp, but which is actually not knowable by you. Of course 
this cannot be used in practice, but has to be used to derive the more 
usable laws of physics.



>
>> How? I would say by self-measurement relatively to their most probable
>> (or credible ...) comp histories. There is always an infinity of them.
>
> How does 'self-measurement' lead to the observables of physics?  By
> 'most probable' I assume you mean the convergence of first person
> experience on such histories.  Is this what you mean by
> 'self-measurement' (i.e. the convergence by self-sampling on a
> first-personal 'measure')?


Yes. And after the 8th step of the UDA, you should understand that the 
"physical implementation of the UD" is not relevant, because a UM 
cannot distinguish "reality" ("real" or virtual) from purely 
arithmetical reality,


>
>> You can see my thesis either as a the showing that comp necessitates 
>> to
>> generalize Everett embedding of the subject into the physical world.
>> (Cf also Rossler endophysiocs). Indeed comp forces us to embed the
>> arithmetician (or any memory machine) in numberland (something for
>> which we will never have a complete unification).
>
> Is comp therefore in effect a 'many minds' view?  In this case, do the
> 'many worlds' emerge as the observables contingent on the povs of the
> many minds (from the background of numberland)?


I would say yes. I have often used the expression "many dreams" where a 
dream is an infinite set of (non interacting or independent) infinite 
computations. Logicians, like modal logicians are using the term 
"world" as something primitive and indefinite: a world is just an 
element of a set. They uses it intechangeably with "states", "points", 
"elements" etc. Does the many dreams generates anything like a singular 
physical world: well probably not. Does the many dreams generate a 
quantum multiverse? Well, if comp (and my reasoning) is correct then it 
has to do that. Does it, up to now yes (Again I anticipate).


>
>> I said in Siena, and already in this list, that for Plato, what *you*
>> see (observe, measure) is the border of what *you* don't see. In the
>> universal machine context this can lead to a recursive but solvable
>> equation where physical reality is a sort of border of the comp-
>> indeterminacy or the comp intrinsical ignorance.
>
> When you refer to the observables as the border of what you don't see,
> or the border of the comp indeterminacy, are you again referring to
> the indistinguishability of what lies below one's substitution level?


Absolutely.



> If so, would this not imply the potential existence of an infinity of
> levels of observables, or physics(s), depending on the substitution
> levels of classes of observers?

All right, but note that we have no choice concerning our level of 
substitution. And the physics (observables) will be a "sum" on all 
possible fine grained histories consistent with your actual state. If 
comp is really at the origin of the quantum empirical interference, the 
"reason" why "an electron" can go through two holes simultaneously, is 
that the electron "choice" has no impact at all, even in principle, 
with your actual and successor  comp histories.
Empirically we can expect that the 'substitution level" is more related 
to a notion of "isolation" than of scaling. Nevertheless, we cannot 
really use this here, given that we have to extract quantum physics 
from the existence of that "level".


>
>> In a nutshell, you cannot use Godel incompleteness 

Re: Observer Moment = Sigma1-Sentences

[David Nyman]

On 15/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> David, please recall that one half of the propositions I assert are
> false.

Yes, but which half?

> Also, my "s" spelling seems to be uncomputable.

In that case it must lie outside comp reality! :-)

David


>
> Hi David, and all,
>
>
>
> Le 15-août-07, à 13:36, Bruno Marchal a écrit :
>
> > Where a layman says: the temperature in Toulouse is 34.5,  the logician
> > says:   temperature(Toulouse) = 17.
>
>
>
> read instead:
>
>
> > Where a layman says: the temperature in Toulouse is 34.5,  the logician
> > says:   temperature(Toulouse) = 34.5.
>
>
> Logicians are not that special!
>
> David, please recall that one half of the propositions I assert are
> false.
>
> Also, my "s" spelling seems to be uncomputable.
>
> Apology,
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
> >
>

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Re: Observer Moment = Sigma1-Sentences

[David Nyman]

On 15/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> Like Stathis argued a lot, if you identify yourself with your
> history/personality there is a sense to be 50 years old, but if you
> identify yourself with your matter, you disappear a bit by eating and
> shitting (is this correct? polite?)

It's correct - and fine with me - but not perhaps quite polite.

> What comp (by UDA+FILMED-GRAPH) shows, is that, once the digitalness of
> your local relative description is taken seriously, you can no more
> distinguish the comp stories existing below your comp substitution
> level.

So, 'materiality' - for you - can consist in effect only of what is at
or above this level?

> Eventually the laws of physics will be the law of what remains
> or emerges as observable in all computations.

Again - for all observers - what emerges at or above their substitution level?

> From inside this has to
> interfere statistically (by UDA).

That is, from inside comp reality, not inside 'matter'?  Then, given
this, statistical interference leads to first person indeterminacy.

> How? I would say by self-measurement relatively to their most probable
> (or credible ...) comp histories. There is always an infinity of them.

How does 'self-measurement' lead to the observables of physics?  By
'most probable' I assume you mean the convergence of first person
experience on such histories.  Is this what you mean by
'self-measurement' (i.e. the convergence by self-sampling on a
first-personal 'measure')?

> You can see my thesis either as a the showing that comp necessitates to
> generalize Everett embedding of the subject into the physical world.
> (Cf also Rossler endophysiocs). Indeed comp forces us to embed the
> arithmetician (or any memory machine) in numberland (something for
> which we will never have a complete unification).

Is comp therefore in effect a 'many minds' view?  In this case, do the
'many worlds' emerge as the observables contingent on the povs of the
many minds (from the background of numberland)?

> I said in Siena, and already in this list, that for Plato, what *you*
> see (observe, measure) is the border of what *you* don't see. In the
> universal machine context this can lead to a recursive but solvable
> equation where physical reality is a sort of border of the comp-
> indeterminacy or the comp intrinsical ignorance.

When you refer to the observables as the border of what you don't see,
or the border of the comp indeterminacy, are you again referring to
the indistinguishability of what lies below one's substitution level?
If so, would this not imply the potential existence of an infinity of
levels of observables, or physics(s), depending on the substitution
levels of classes of observers?

> In a nutshell, you cannot use Godel incompleteness to show that we are
> not machine (or that we are not lobian), but you can use Godel
> incompleteness to argue that IF we are sound lobian machine then we
> cannot know which machine we are, still less which computations support
> us. It gives the arithmetical origin of the first person comp
> indetermincacy, which you are supposed to have already intuitively
> swallow from the UDA, OK?

OK.  However, I still have in reserve my question about how we are
supposed to think about the relation between, say, our minds and some
observable version of our brains.  For example, how are we supposed to
account for how changes to some version of our brains seem to
correlate with changes of mind, or how the physical evolution of
brains relates to that of minds?

> Where a layman says: the temperature in Toulouse is 34.5,  the logician
> says:   temperature(Toulouse) = 17.

Is it colder for logicians?

> So an arbitrary function from n-tuple to number will
> be denote by f(x_1, x_2, ..., x_n). Exactly like in the definition of
> an arbitrary derivative in calculus: the limit, if it exists, for h
> going near zero of the quotient f(x + h) - f(x) with h. OK?

OK, thanks.

> I propose to go, from the Cantor non-enumerability of the reals (or
> things equivalent) to Kleene non recursive enumerability of the
> recursive reals, by Church thesis. Comp, both in the UDA, and in the
> arithmetical UDA, is mainly Church thesis. I want to show you how
> strong and deep that thesis is. OK?

OK

> Now diagonalization will appear to be a sort of "transcendental
> operation". Its main use is for going outside some set, and I would
> like to convey why the fact that the set  "programmable functions" is
> closed for diagonalization is truly a miracle! (to borrow Godel's
> expression). It is really that miracle which makes the set of
> programmable or computable function fitting so well the search for
> universal everything theory.

I think I see what you mean - i.e. that extensions to the set by
diagonalisation are also programmable functions, which makes the set
in effect a closed but infinite universe.

> Well, ok, sorry. Instead of "the non enumerability of the subset of N",
> read "the non en

Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Hi David, and all,



Le 15-août-07, à 13:36, Bruno Marchal a écrit :

> Where a layman says: the temperature in Toulouse is 34.5,  the logician
> says:   temperature(Toulouse) = 17.



read instead:


> Where a layman says: the temperature in Toulouse is 34.5,  the logician
> says:   temperature(Toulouse) = 34.5.


Logicians are not that special!

David, please recall that one half of the propositions I assert are 
false.

Also, my "s" spelling seems to be uncomputable.

Apology,

Bruno



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


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Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 13-août-07, à 17:37, David Nyman a écrit :

> On 11/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> That the 'comp reality' is founded on the number realm, is almost
>> trivial. What is not trivial at all, and this is what the UDA shows, 
>> is
>> that, once you say "yes" to the digital doctor, for some level of
>> substitution, then your immateriality (somehow like the quantum
>> superpositions) is contagious on your most probable neighborhoods. So
>> that physics has to be shown to emerge statistically from the 
>> "measure"
>> on the UD accessible relative states.
>
> This perhaps needs to be explained more slowly.  What - exactly - do
> you mean by "immateriality", and "contagious on your most probable
> neighbourhoods"?


Nothing magical. For example the game of bridge is immaterial, despite 
you need some local matter to implement some particular bridge game. 
All abstract concepts are immaterial. You don't have the need to 
explain what bosons and fermions are to explain what is a number.
Like Stathis argued a lot, if you identify yourself with your 
history/personality there is a sense to be 50 years old, but if you 
identify yourself with your matter, you disappear a bit by eating and 
shitting (is this correct? polite?) and respiring, etc. and never 
really exist for more than seven years, etc... In the first case you 
admit somehow your immateriality despite contingent and local 
appearance of being composed in some substancial way.
What comp (by UDA+FILMED-GRAPH) shows, is that, once the digitalness of 
your local relative description is taken seriously, you can no more 
distinguish the comp stories existing below your comp substitution 
level. Eventually the laws of physics will be the law of what remains 
or emerges as observable in all computations. From inside this has to 
interfere statistically (by UDA).






> Also, precisely what do you intend to be included in
> - or excluded from - the notion of 'physics' in this context?  Is it
> to be equated with what is observable, and if so, how and by whom?


By lobian machine. By lobian machine, as they are emulated by a weaker 
machine (the universal dovetailer, alias the arithmetical Sigma1 
sentences).
How? I would say by self-measurement relatively to their most probable 
(or credible ...) comp histories. There is always an infinity of them.

I said in Siena, and already in this list, that for Plato, what *you* 
see (observe, measure) is the border of what *you* don't see. In the 
universal machine context this can lead to a recursive but solvable 
equation where physical reality is a sort of border of the comp- 
indeterminacy or the comp intrinsical ignorance.



>
>> To be sure, it is needed,
>> however, for the understanding that with comp, we *have to* derive the
>> physics from "intensional numbers prevailing discourses". With comp,
>> postulating a physical world cannot be used as an explanation relating
>> mind and appearance of matter (memory-stable observations).
>> It is not that (aristotelian primary )substance does not exist, but
>> that such primary substance is provably (with the comp hyp) void of
>> explanation power.
>
> It strikes me, reading the above, that it might be a good idea to find
> a way to limit ourselves -


Yes. (but hard!)



> at this deliberately elementary stage - to
> an agreed set of terms with which to designate each of your key ideas,
> for example with respect to physics deriving from "intensional number
> prevailing discourses".  Perhaps what we need is not so much
> grandmother-version, but a kindergarten-level introduction to the key
> terms and concepts, which we can then use slowly and clearly to build
> up the argument.



I have to explain enough notions so as to be able to explain Solovay 
theorem, which links precisely the modal logic G and G* with the 
discourse of the ideally correct lobian machines. "Machine theology" is 
really captured by the study of G*, G* \ G, and their intensional 
(modal) variants (but this is again an anticipation).

Most key terms and concepts are from mathematical logic and computer 
science key terms and concepts, at least for the arithmetical part.


You can see my thesis either as a the showing that comp necessitates to 
generalize Everett embedding of the subject into the physical world. 
(Cf also Rossler endophysiocs). Indeed comp forces us to embed the 
arithmetician (or any memory machine) in numberland (something for 
which we will never have a complete unification).

But you can also see the technical part of the thesis as a 
reconstruction of Lucas-Penrose godelian argument. This reconstruction 
has a long history which, paradoxically enough precedes both Lucas 
(1960) or Penrose (Much latter). The line is: Post, Benecerraf, Wang, 
Reinhardt, (myself), Webb, etc.

In a nutshell, you cannot use Godel incompleteness to show that we are 
not machine (or that we are not lobian), but you can use Godel 
incompleteness to argue that IF we are sound l

Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Hi Mirek,

Welcome to the list,

Le 13-août-07, à 16:54, Mirek Dobsicek a écrit :

> Hello Bruno !
>
> I am a freshman to this list and it seems to me that some kind of a
> 'course' is going to happen.


Let us say that I try to give some information linking my (already old) 
work and the main discussion on this list.

In the case you know french the most extensive description of what I 
have done is in "Conscience et Mécanisme", or in some preceding papers.
In English my last papers could perhaps help, you can find them here:

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



> I checked a couple of last messages and it
> looks interesting. Please, would you mind to repeat what is
> approximately the starting point of your explanations and where do you
> aim? Hopefully, I'll be able to follow.


The starting point of this list is the idea that "everything exist" 
could be an easier explanation than any assumption of the kind 
"something exists".
My own starting point is what I called the "indexical digital mechanist 
thesis", which is called also "computationalism", and which is a 
digital version of Milinda-Descartes mechanism thesis. When Milinda 
asked Nagarjuna, what is the nature of a person, Nagarjuna answered by 
an informal exposition of the mechanist thesis.
What I show (or try to show) is that once we take the idea that "I am a 
machine" seriously enough, then this entails a reversal between physics 
and "intensional number theory", or "mathematical computer science" or 
(as I can justify) "machine theology", and this in a sufficiently 
precise way so that the physics extracted from the computationalist 
"machine theology" can be compared with the empirical facts.





Lennart Nilsson wrote:

> Bruno wrote:
>> I don't think Church thesis can be grasped
>> conceptually without the understanding that the class of programmable
>> functions is closed for the diagonalization procedure.
>
> This is something I never grasped but would love to understand.


Thanks for saying; it is indeed a key point, which, I realize now,  is 
rarely understood, although in my opinion Emil Post has seen this point 
in the 1920, and Judson Webb has written a genuine book in the 1980 
(ref in my thesis).

But at the computability meeting in Siena 2007, I have heard that some 
people still believe that Church thesis could be viewed as a definition 
(of computable function), which, as I hope being able to explain, is 
complete  nonsense.  Actually, when Church did propose what he did 
consider as a definition, Stephen Kleene makes clear it has to be a 
thesis (i.e. an hypothesis). I will come back on this.

I will have to come back on Cantor. Meanwhile people can consult my old 
post on diagonalization.
Actually you can search for diagonalisation (with a s) for my older and 
more basic posts, and then search for diagonalization (with a z) for 
some more recent one.

Well, the list archive are no so easy to search in: here is my older 
"diagonalisation" post, send to George Levy on the list, the 21 
augustus 2001, shortly after the sudden death of James Higgo.

 copy of my first diagonalzation 
post
 in memory of James,


Hi George, Hi People,

I guess most of you know the famous proof by diagonalisation
  of the uncountability or non enumerability of the reals.

To my knowledge diagonalisation appears in the work of
  Dubois-Reymond, but it is Cantor who first used it for proving
  that the set of reals is bigger, in some sense, than the set of
  natural numbers N, or the set of integers Z or the set of
  rational numbers Q.

Here I want recall Cantor proof, and then I want to show you
  a weird, similar but false diagonalisation reasoning.

The  correction of that reasoning will give a shortcut to Godel's
  incompleteness result, which is itself a step toward G and G*.

In this post I prove Cantor theorem, and then I give you the
  similar but wrong proof. I will let you search the error.

I hope you see that Q is countable. There are simple
  drawing proof of that. But without drawing, it is enough
  to realise that a rational numbers like -344/671 is described
  by a finite string in the alphabet {O, 1, 2, 3, ... 9, -, /}.
  And finite strings can be ordered by length, and those
  with the same length which remains can be ordered by some
  chosen alphabetical order. I call this order (on string) the
  *lexicographic* order.

Actually we will be interested by the functions of N to N.
  N is the set of natural numbers (positive integers).



So here is a variant of Cantor theorem:

1. Theorem: The set of functions from N to N is NOT countable.

(Note: if you know Cantor proof, just skip it and go to 2. below).

Proof: (by absurdum and diagonalisation)

 I recall that a function from N to N is just an assignment for each
   natural number (called the argument or input) of a natural numbers,
   called the output or va

Re: Observer Moment = Sigma1-Sentences

[Russell Standish]

On Wed, Aug 01, 2007 at 11:31:51AM +0200, Bruno Marchal wrote:
> >
> > No, I mean all information known by the observer (including, but not
> > exclusively information know by the observer about erself).
> 
> 
> OK, but then adding "about the universe" is confusing at this stage. 
> You interpret the quantum state as describing knowledge. (And then I am 
> not sure I follow what you mean by quantum state: you are supposing the 
> quantum hyp. here, aren't you (or perhaps your linearity hyp. only? 
> Again where would that linearity come from?).
> 

Sorry, I realised I hadn't responded to this before. Things have got
away from me, including recovering from a harddisk crash.

I am using universe somewhat colloquially here, to help intuition. But
sometime it doesn't help.

What we have are observer moments, which somehow contain all
knowledge, or are circumscribed by all knowledge that an observer has
at an instant of time.

The use of the word "universe" was meant to make some connection back
to discussions of "many universes", or "many worlds", but to be
precise we are just talking about observer moments which are in a
sense primitive.

> 
> >
> >>
> >>
> >>> this led me to identify the observer moment
> >>> and the quantum state vector.
> >>
> >>
> >> ... and the partial relative quantum state vector corresponding to the
> >> observer. OK, but at this stage this would be cheating. We can not yet
> >> explain why the quantum histories wins over the comp/number relations.
> >>
> >
> > Well I have my own reasons, considering knowledge acquisition as an
> > evolutionary process. But I disagree about it being cheating, because
> > I don't a priori assume quantum states are elements of a Hilbert
> > space. That is a derived property.
> 
> 
> So, how do you define quantum state?
> 

I don't define quantum state. I use the word state as a synonym of
observer moment, again as a means of contact with quantum
terminology. I make the statement "identify observer moment with
quantum state" as a shorthand for the following argument.

Assume that the state (or observer moment) undergoes evolution (I'm
refraining from qualifiying this with Darwinian) in that:

1) subsequent OMs (obviously a successor relationship is a
   prerequisite here - something I call the TIME postulate) are
   related closely to the previous OM, ie they inherit.

2) There is variation between successor OMs - ie the "many worlds"
   idea.

3) That a particular successor OM x_i of OM y is what is observed
   ("anthropically selected"), with a probability P(x_i|y). The
   probability function P(x|y) satisfies the Kolmogorov probability
   axioms. This also implies that OMs must satisy set axioms. I also
   call this third assumption the "PROJECTION postulate".

There is a final assumption. The initial OMs are drawn from the set of
all OMs according to some sort of measure, which happens to be complex. Since
measures can be more general than complex measures, I'm not entirely
sure why the measure should be restricted to being complex.

And that is it. From this idea (that OMs evolve), the following three
postulates of QM follow by a mechanistic proof

1. States are elements of a Hilbert space over a complex field
2. States evolve unitarily (ie according to a Schroedinger equation)
 i\hbar d\psi/dt = H\psi
   between measurements
3. The probability function P(x_i|y) satisfies the Born rule 
 P(x_i|y) = ||^2 / 

Now some people have complained about how one can derive quantum
probabilities from the Kolmogorov axioms. It seems
counterintuitive. But this part is the most rigorous. The argument has
been put for the last seven years, and a number of very smart people
have looked at it without finding a flaw. Of course that doesn't mean
there isn't a flaw, but it would have to be quite subtle.

> 
> >
> >>
> >>
> >>> This is not incompatible with with your
> >>> notion of the OM being a Sigma1 sentence, but it places severe
> >>> restrictions on the form of the quantum state vector.
> >>
> >>
> >> The OM are the Sigma1 sentences, when they are considered as third
> >> person constructs.
> >
> > Third person is that which is accessible to all observers.
> 
> 
> ? (This correspond more to the first person plural notion as I have 
> defined it in most of my papers: observers appeared in the fourth and 
> fifth hypostases, and perhaps already a part of it appears in the third 
> one; but there are no observer in the second or first hypostases).
> 
> cf:
> 1  p  (truth, 0-person)
> 2 Bp (provable, 3-person)
> 3 Bp & p  (knowable, 1-person)
> 4 Bp & Dp (observable, measurable; 1-plural-person)
> 5 Bp & Dp & p (sensationalisable, feelable, personally 
> observable/measurable, 1 person again)
> 

Thinking about it, I'm not sure our x-person terminology is completely
compatible. And it comes down to the problems I've had even in
understanding (or grokking, more to the point) the Theatetus
definition of knowledge. I can understand it from a purely
intellectual

Re: Rép : Observer Moment = Sigma1-Sentences

[Mirek Dobsicek]

Bruno Marchal wrote:
> 
> Question to David, and others who could be interested:  is the notion 
> of enumerable and non enumerable set clear? Can you explain why the set 
> of functions from N to N is not enumerable?
> 
> 

> Let us go slow and deep so that everybody can understand, once and for 
> all.  OK?

Hello Bruno !

I am a freshman to this list and it seems to me that some kind of a
'course' is going to happen. I checked a couple of last messages and it
looks interesting. Please, would you mind to repeat what is
approximately the starting point of your explanations and where do you
aim? Hopefully, I'll be able to follow.

Best regards,
 Mirek

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Re: Observer Moment = Sigma1-Sentences

[David Nyman]

On 11/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> That the 'comp reality' is founded on the number realm, is almost
> trivial. What is not trivial at all, and this is what the UDA shows, is
> that, once you say "yes" to the digital doctor, for some level of
> substitution, then your immateriality (somehow like the quantum
> superpositions) is contagious on your most probable neighborhoods. So
> that physics has to be shown to emerge statistically from the "measure"
> on the UD accessible relative states.

This perhaps needs to be explained more slowly.  What - exactly - do
you mean by "immateriality", and "contagious on your most probable
neighbourhoods"?  Also, precisely what do you intend to be included in
- or excluded from - the notion of 'physics' in this context?  Is it
to be equated with what is observable, and if so, how and by whom?

> To be sure, it is needed,
> however, for the understanding that with comp, we *have to* derive the
> physics from "intensional numbers prevailing discourses". With comp,
> postulating a physical world cannot be used as an explanation relating
> mind and appearance of matter (memory-stable observations).
> It is not that (aristotelian primary )substance does not exist, but
> that such primary substance is provably (with the comp hyp) void of
> explanation power.

It strikes me, reading the above, that it might be a good idea to find
a way to limit ourselves - at this deliberately elementary stage - to
an agreed set of terms with which to designate each of your key ideas,
for example with respect to physics deriving from "intensional number
prevailing discourses".  Perhaps what we need is not so much
grandmother-version, but a kindergarten-level introduction to the key
terms and concepts, which we can then use slowly and clearly to build
up the argument.  At each stage, perhaps you could refer to the
appropriate points in the UDA, or other key papers, that could then be
consulted for comparison and further elucidation.  Would this work?

> The best book is without
> doubt the one by Cutland:
>
> CUTLAND N. J., 1980, Computability An introduction to recursive
> function theory,
> Cambridge University Press.

Thanks

> OK. I will begin by saying two words on the language we will use when
> discussing with the machine. I can already explain the difference
> between the layman (or grandmother) and the logician. This is not just
> for you (I guess you know what I will say) but for those who just
> abandon logic for reason of notation.
>
> The main difference is that where a layman says "Alfred is serious",
> the logician says serious(Alfred).
>
> Where the layman will say there is a ferocious dog, a logician will say
> that it exists something such that that something is a dog and is
> ferocious. Because of laziness he will write Ex(dog(x) & ferocious(x)).
> For saying that all dogs are ferocious, he will say that for all dogs
> (i.e. choose any thing that is a dog) that things will be ferocious:
> and he will write Ax (dog(x) -> ferocious(x)).
>
> Of course, there is perhaps no effective test to see if a dog is
> ferocious or not, perhaps the notion is not well defined, but we have
> to live with things like that: even in the pure realm of numbers we
> will encounter some unexpected (I guess) complexity.

Thanks, this is useful.

> By the way, David, do you know what is called "classical propositional
> calculus", the truth table method? Do you need some refreshing?
> Some refreshing is in Smullyan's FU, but I can do it, or focus on some
> difficulty (classical propositional calculus is not so simple indeed,
> even if simpler than most other logics).

I can always use wikipedia - which I've looked at - or other sources
online, but anything you would also be prepared to do here would be
most helpful.

David
>
> Le 10-août-07, à 22:32, David Nyman a écrit :
>
> >
> > On 10/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> >
> >> OK. Have you seen that this is going to made physics a branch of
> >> "intensional number theory", by which I mean number theory from the
> >> points of view of number ... ?
> >
> > Insofar as we accept that the foundation of 'comp reality' is the
> > number realm, comp physics must indeed be a branch of this (e.g. as
> > per my previous example of 'digital digestion').
>
>
> That the 'comp reality' is founded on the number realm, is almost
> trivial. What is not trivial at all, and this is what the UDA shows, is
> that, once you say "yes" to the digital doctor, for some level of
> substitution, then your immateriality (somehow like the quantum
> superpositions) is contagious on your most probable neighborhoods. So
> that physics has to be shown to emerge statistically from the "measure"
> on the UD accessible relative states. Withouth this, the arithmetical
> interview would not lead to making comp testable.
> This reasoning shows really the incompleteness of Everett's work: once
> you accept the observer can be locally described by its digi

Re: Rép : Observer Moment = Sigma1-Sentences

[David Nyman]

On 13/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> Question to David, and others who could be interested:  is the notion
> of enumerable and non enumerable set clear? Can you explain why the set
> of functions from N to N is not enumerable?

Do please remind us.  "Off the top of my head", do you mean, by
non-enumerable, arbitrary extensibility by the generation of new
members via diagonalisation?

> Do you people know the difference between ordinal and cardinal (I know
> some knows 'course).

Yes

> I don't think Church thesis can be grasped
> conceptually without the understanding that the class of programmable
> functions is closed for the diagonalization procedure.

Please explain 'programmable functions' and 'closed for the
diagonalisation procedure'.

> Do everyone
> (interested) know how to prove the non enumerability of the subset of N
> by diagonalization?

Which subset do you mean?  I've encountered the
diagonalisation/enumerability argument, assuming it's the one I
referred to above.

> Let us go slow and deep so that everybody can understand, once and for
> all.  OK?

Definitely OK.

David

>
>
> Le 13-août-07, à 13:29, Kim Jones a écrit :
>
> > where he appears to serve the option of being machine or some other
> > order of being. I must confess that I still don't understand the
> > ontology of angels as opposed to machines but I'm sure his reply
> > contains the reason
>
>
> Don't worry, I will try to explain.
>
>
> Question to David, and others who could be interested:  is the notion
> of enumerable and non enumerable set clear? Can you explain why the set
> of functions from N to N is not enumerable?
>
> Just say no, and I go back to Cantor, the one who discussed with the
> pope about the question of naming infinities (!), and indeed the one
> who will discover (or invent) the varieties of infinities.
>
> Do you people know the difference between ordinal and cardinal (I know
> some knows 'course). I don't think Church thesis can be grasped
> conceptually without the understanding that the class of programmable
> functions is closed for the diagonalization procedure. Do everyone
> (interested) know how to prove the non enumerability of the subset of N
> by diagonalization?
>
> Let us go slow and deep so that everybody can understand, once and for
> all.  OK?
>
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
> >
>

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SV: Rép : Observer Moment = Sigma1-Sentences

[Lennart Nilsson]

-Ursprungligt meddelande-
Från: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] För Bruno Marchal
Skickat: den 13 augusti 2007 16:36
Till: [EMAIL PROTECTED]
Ämne: Re: Rép : Observer Moment = Sigma1-Sentences


>I don't think Church thesis can be grasped 
>conceptually without the understanding that the class of programmable 
>functions is closed for the diagonalization procedure. 

This is something I never grasped but would love to understand.

LN



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Re: Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 13-août-07, à 13:29, Kim Jones a écrit :

> where he appears to serve the option of being machine or some other 
> order of being. I must confess that I still don't understand the 
> ontology of angels as opposed to machines but I'm sure his reply 
> contains the reason


Don't worry, I will try to explain.


Question to David, and others who could be interested:  is the notion 
of enumerable and non enumerable set clear? Can you explain why the set 
of functions from N to N is not enumerable?

Just say no, and I go back to Cantor, the one who discussed with the 
pope about the question of naming infinities (!), and indeed the one 
who will discover (or invent) the varieties of infinities.

Do you people know the difference between ordinal and cardinal (I know 
some knows 'course). I don't think Church thesis can be grasped 
conceptually without the understanding that the class of programmable 
functions is closed for the diagonalization procedure. Do everyone 
(interested) know how to prove the non enumerability of the subset of N 
by diagonalization?

Let us go slow and deep so that everybody can understand, once and for 
all.  OK?


Bruno


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


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Re: Rép : Observer Moment = Sigma1-Sentences

[Kim Jones]

Just to clarify - my question to Bruno was serious. He has mentioned  
angels before. I thank him for his considered response which I am  
still studying.

The part of his post which prompted my question was:


Also, if we are machine (or just lobian), we can indeed contemplate the
consistency of *little part* of math, but certainly not the consistency
of the whole of math, still less the consistency of the whole of
creation.

where he appears to serve the option of being machine or some other  
order of being. I must confess that I still don't understand the  
ontology of angels as opposed to machines but I'm sure his reply  
contains the reason

regards,

Kim


On 13/08/2007, at 2:00 AM, John Mikes wrote:

> Dear Bruno,
> did your scientific emotion just trapped you into showing that your  
> theoretical setup makes no sense?
> Angels have NO rational meaning, they are phantsms of a (fairy?) 
> tale and if your math-formulation can be applied to a (really)  
> meaningless phantasy-object, the credibility of it suffers.
> How can your formalism be applied to something nonexistent? What  
> does it say about the 'real' value of it?
>
> I read Kim's question as a joke, you took it seriously with some  
> (imagined) meaning you had in mind. Faith?
> Please, do not tell me that your theories are as well applicable to  
> faith-items! Next time sopmebody will calculate the enthalpy of the  
> resurrection.
>
> John
>
> On 8/9/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>
> Le 09-août-07, à 11:22, Kim Jones a écrit :
>
> >
> > What is "lobian" apart from la machine, Bruno? Are you referring to
> > "angels" here?
> >
> > Aren't angels machines too?
>
>
> Angels are not machine. Unless you extend the meaning of machine
> 'course, but Angels' provability extend the provability of any
> turing-emulable machine. Sometimes people use the term "supermachine"
> for what I call angel, but mathematically, in principle,  angels have
> nothing to do with machine. Angels can prove any sentence having the
> shape AxP(x) with P(x) decidable. (AxP(x) = For all x P(x)). Universal
> machine are Sigma_1 complete. Angels are PI_1 complete. A sigma_1
> sentence asserts something like "It exists a number having such or  
> such
> verifiable (decidable) property". PI_1 sentences asserts something  
> like
> "all numbers have such or such verifiable (decidable) property".
> The most famous PI_1 sentences is the *machine* consistency statement:
> it is indeed equivalent with: all number have the (verifiable)  
> property
> of not being the Godel number (or any arithmetical encoding) of a  
> proof
> of f.
> (f = any arithmetical contradiction, like (1+1=2 & ~(1+1=2)).
> Angels can be shown to be lobian. They obey G and G*, and G and G*
> describe completely their propositional provability logic.
> (btw, I call "god" any non turing emulable entity obeying G and G*,  
> but
> for which G and G* are not complete (you need more axioms to
> characterize their provability power; and I call supergods, entities
> extending vastly the gods.
> All that is really the subject matter of recursion theory, alias
> computability theory (which should have been called, like someone said
> in Siena, the theory of un-computability). recursion theory is really
> the science of Angels and Gods, well before being the science of
> Machines. But (and this is a consequence of incompleteness), you  
> cannot
> seriously study machines without studying angels too  For example
> the quantifies version of G* (the first order modal logic of
> provability, the one I note qG*) can be shown to be a superangel:  
> it is
> P1-complete *in* Arithmetical Truth (making bigger than the  
> "unnameable
> God of the machine). This means that the divine intellect, or the
> Plato's "NOUS"  is bigger, in some sense than "God" (Plotinus' ONE).
> Plato would have appreciate, and perhaps Plotinus too because he wants
> the ONE to be simple , but yes the divine intellect is much more
> powerful than the "God" (accepting the arithmetical interpretation of
> the hypostases: see my Plotinus papert).
>
> I will certainly come back on all definitions. But roughly speaking, a
> machine is (Turing)-universal (Sigma_1 complete) if it proves all true
> Sigma_1 sentences. A machine is lobian if not only the machine proves
> all true Sigma_1 sentences, but actually proves, for each Sigma_1
> sentence, that if that sentence is true then she can prove it. Put in
> another way, a machine is universal if, for any Sigma_1 sentence S, it
> is true that S->BS (B = beweisbar, provable). A machine is lobian if
> she proves, for any Sigma_1 sentence S, S->BS. For a universal machine
> (talking a bit of classical logic) S->BS is true about the machine.  
> For
> a lobian machine S->BS is not only true, but provable (again with S
> representing Sigma_1 sentence).
>
> But all this is a theorem. My "abstract" definition of lobianity is:
> any entity proving B(Bp->p)->Bp where B is her provabi

SV: Rép : Observer Moment = Sigma1-Sentences

[Lennart Nilsson]

Le 12-août-07, à 18:00, John Mikes a écrit :
>Please, do not tell me that your theories are as well applicable to
faith-items! Next time sopmebody will calculate the enthalpy of the
resurrection.

Frank Tipler calculated the probability of the resurrection in his last book
"The Physics of Christianity" as follows: 
 
"This probability is 10 raised to the power of -100. We must then raise this
enormously small number to a power equal to the number of atoms in a human
body, something like 10 raised to the power of 29".

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Re: Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Dear John,


Le 12-août-07, à 18:00, John Mikes a écrit :

> Dear Bruno,
> did your scientific emotion just trapped you into showing that your 
> theoretical setup makes no sense?
> Angels have NO rational meaning, they are phantsms of a (fairy?)tale 
> and if your math-formulation can be applied to a (really) meaningless 
> phantasy-object, the credibility of it suffers.
> How can your formalism be applied to something nonexistent? What does 
> it say about the 'real' value of it?


I think you have missed the posts where I defined Angels, Gods, 
Supergods, etc.  By definition they refer to lobian entities which are 
NOT emulable by Turing Machines. They exists mathematically. They are 
the main object study of a branch of mathematical logic known as 
recursion theory or computability theory (which could be called 
uncomputability theory aswell).
A detailed example of a very powerful, yet lobian, "angel" is given in 
Boolos 93, and called "Analysis + Omega-rule", and I have often refer 
to it by calling it Anomega.

Perhaps later I will explain that the full (first order modal logical 
system) which I use to interpret Plotinus "divine intellect" is really 
an angel too, actually more powerful than the unnameable "god" (the 
plotinus' ONE) of the machine.



>
> I read Kim's question as a joke, you took it seriously with some 
> (imagined) meaning you had in mind. Faith?


I remind you that we have already talk a lot about the necessity of 
some "faith" from the part of lobian entities (machine or not). The 
machine cannot prove its own consistency, but can bet on it, and use 
that bet in many different ways.



> Please, do not tell me that your theories are as well applicable to 
> faith-items! Next time sopmebody will calculate the enthalpy of the 
> resurrection.

Don't worry. each term I am using have been well defined. By "Angel" I 
just mean those lobian entities which are not machines. I did already, 
in 2000, in this list called G* the "guardian angel" of the machine, 
because it knows a lot about the machine that the machine cannot know 
or prove about itself. Now, with the arithmetical interpretation of 
Plotinus, I have to use those terms in a bit more systematic ways. The 
G/G* type of theology works for (ideally correct) machine, but also on 
many self-referentially correct entities which are NOT machine. OK?

Best,


Bruno



>
> John
>
> On 8/9/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>>
>> Le 09-août-07, à 11:22, Kim Jones a écrit :
>>
>> >
>> > What is "lobian" apart from la machine, Bruno? Are you referring to
>> > "angels" here?
>> >
>> > Aren't angels machines too?
>>
>>
>> Angels are not machine. Unless you extend the meaning of machine
>> 'course, but Angels' provability extend the provability of any
>> turing-emulable machine. Sometimes people use the term "supermachine"
>> for what I call angel, but mathematically, in principle,  angels have
>> nothing to do with machine. Angels can prove any sentence having the
>> shape AxP(x) with P(x) decidable. (AxP(x) = For all x P(x)). Universal
>>  machine are Sigma_1 complete. Angels are PI_1 complete. A sigma_1
>> sentence asserts something like "It exists a number having such or 
>> such
>> verifiable (decidable) property". PI_1 sentences asserts something 
>> like
>> "all numbers have such or such verifiable (decidable) property".
>> The most famous PI_1 sentences is the *machine* consistency statement:
>> it is indeed equivalent with: all number have the (verifiable) 
>> property
>> of not being the Godel number (or any arithmetical encoding) of a 
>> proof
>> of f.
>> (f = any arithmetical contradiction, like (1+1=2 & ~(1+1=2)).
>> Angels can be shown to be lobian. They obey G and G*, and G and G*
>> describe completely their propositional provability logic.
>> (btw, I call "god" any non turing emulable entity obeying G and G*, 
>> but
>> for which G and G* are not complete (you need more axioms to
>> characterize their provability power; and I call supergods, entities
>> extending vastly the gods.
>> All that is really the subject matter of recursion theory, alias
>> computability theory (which should have been called, like someone said
>> in Siena, the theory of un-computability). recursion theory is really
>> the science of Angels and Gods, well before being the science of
>> Machines. But (and this is a consequence of incompleteness), you 
>> cannot
>> seriously study machines without studying angels too  For example
>> the quantifies version of G* (the first order modal logic of
>> provability, the one I note qG*) can be shown to be a superangel: it 
>> is
>> P1-complete *in* Arithmetical Truth (making bigger than the 
>> "unnameable
>> God of the machine). This means that the divine intellect, or the
>> Plato's "NOUS"  is bigger, in some sense than "God" (Plotinus' ONE).
>> Plato would have appreciate, and perhaps Plotinus too because he wants
>> the ONE to be simple , but yes the divine intellect is much more
>> 

Re: Rép : Observer Moment = Sigma1-Sentences

[John Mikes]

Dear Bruno,
did your scientific emotion just trapped you into showing that your
theoretical setup makes no sense?
Angels have NO rational meaning, they are phantsms of a (fairy?)tale and if
your math-formulation can be applied to a (really) meaningless
phantasy-object, the credibility of it suffers.
How can your formalism be applied to something nonexistent? What does it say
about the 'real' value of it?

I read Kim's question as a joke, you took it seriously with some (imagined)
meaning you had in mind. Faith?
Please, do not tell me that your theories are as well applicable to
faith-items! Next time sopmebody will calculate the enthalpy of the
resurrection.

John

On 8/9/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>
>
> Le 09-août-07, à 11:22, Kim Jones a écrit :
>
> >
> > What is "lobian" apart from la machine, Bruno? Are you referring to
> > "angels" here?
> >
> > Aren't angels machines too?
>
>
> Angels are not machine. Unless you extend the meaning of machine
> 'course, but Angels' provability extend the provability of any
> turing-emulable machine. Sometimes people use the term "supermachine"
> for what I call angel, but mathematically, in principle,  angels have
> nothing to do with machine. Angels can prove any sentence having the
> shape AxP(x) with P(x) decidable. (AxP(x) = For all x P(x)). Universal
> machine are Sigma_1 complete. Angels are PI_1 complete. A sigma_1
> sentence asserts something like "It exists a number having such or such
> verifiable (decidable) property". PI_1 sentences asserts something like
> "all numbers have such or such verifiable (decidable) property".
> The most famous PI_1 sentences is the *machine* consistency statement:
> it is indeed equivalent with: all number have the (verifiable) property
> of not being the Godel number (or any arithmetical encoding) of a proof
> of f.
> (f = any arithmetical contradiction, like (1+1=2 & ~(1+1=2)).
> Angels can be shown to be lobian. They obey G and G*, and G and G*
> describe completely their propositional provability logic.
> (btw, I call "god" any non turing emulable entity obeying G and G*, but
> for which G and G* are not complete (you need more axioms to
> characterize their provability power; and I call supergods, entities
> extending vastly the gods.
> All that is really the subject matter of recursion theory, alias
> computability theory (which should have been called, like someone said
> in Siena, the theory of un-computability). recursion theory is really
> the science of Angels and Gods, well before being the science of
> Machines. But (and this is a consequence of incompleteness), you cannot
> seriously study machines without studying angels too  For example
> the quantifies version of G* (the first order modal logic of
> provability, the one I note qG*) can be shown to be a superangel: it is
> P1-complete *in* Arithmetical Truth (making bigger than the "unnameable
> God of the machine). This means that the divine intellect, or the
> Plato's "NOUS"  is bigger, in some sense than "God" (Plotinus' ONE).
> Plato would have appreciate, and perhaps Plotinus too because he wants
> the ONE to be simple , but yes the divine intellect is much more
> powerful than the "God" (accepting the arithmetical interpretation of
> the hypostases: see my Plotinus papert).
>
> I will certainly come back on all definitions. But roughly speaking, a
> machine is (Turing)-universal (Sigma_1 complete) if it proves all true
> Sigma_1 sentences. A machine is lobian if not only the machine proves
> all true Sigma_1 sentences, but actually proves, for each Sigma_1
> sentence, that if that sentence is true then she can prove it. Put in
> another way, a machine is universal if, for any Sigma_1 sentence S, it
> is true that S->BS (B = beweisbar, provable). A machine is lobian if
> she proves, for any Sigma_1 sentence S, S->BS. For a universal machine
> (talking a bit of classical logic) S->BS is true about the machine. For
> a lobian machine S->BS is not only true, but provable (again with S
> representing Sigma_1 sentence).
>
> But all this is a theorem. My "abstract" definition of lobianity is:
> any entity proving B(Bp->p)->Bp where B is her provability predicate.
> A machine is weakly lobian if B(Bp->p)->Bp is true about the machine
> (not necessarily provable). A typical weakly lobian system which is not
> lobian is the modal logic K, I have talk about sometimes ago.
> B(Bp->p)->Bp is the Lob formula (Loeb, or better Löb; better if well
> printed!).
>
> Don't panic with all that vocabulary and formula, I will try, perhaps
> with the help of people in the list, like David (if everything goes
> well), to be more systematic. Please, indulge the fact that I could
> change a definition in the course of the explanation, for a matter of
> making things easier.
>
> But of course, ask any question, even if I decide to postpone the
> comment, it can help me to figure out where are the difficulties.
>
>
> Bruno
>
>
> http://iridia.ulb.ac.be/

Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 10-août-07, à 22:32, David Nyman a écrit :

>
> On 10/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> OK. Have you seen that this is going to made physics a branch of
>> "intensional number theory", by which I mean number theory from the
>> points of view of number ... ?
>
> Insofar as we accept that the foundation of 'comp reality' is the
> number realm, comp physics must indeed be a branch of this (e.g. as
> per my previous example of 'digital digestion').


That the 'comp reality' is founded on the number realm, is almost 
trivial. What is not trivial at all, and this is what the UDA shows, is 
that, once you say "yes" to the digital doctor, for some level of 
substitution, then your immateriality (somehow like the quantum 
superpositions) is contagious on your most probable neighborhoods. So 
that physics has to be shown to emerge statistically from the "measure" 
on the UD accessible relative states. Withouth this, the arithmetical 
interview would not lead to making comp testable.
This reasoning shows really the incompleteness of Everett's work: once 
you accept the observer can be locally described by its digital memory 
states, the laws of physics have to emerge from all comp histories.
We can discuss that too, although it is not entirely needed for 
grasping how to derive physics from comp. To be sure, it is needed, 
however, for the understanding that with comp, we *have to* derive the 
physics from "intensional numbers prevailing discourses". With comp, 
postulating a physical world cannot be used as an explanation relating 
mind and appearance of matter (memory-stable observations).
It is not that (aristotelian primary )substance does not exist, but 
that such primary substance is provably (with the comp hyp) void of 
explanation power.


>
>> OK. Don't buy it if you decide to buy only one book on Godel, and let
>> me think which is the best one. But if you are willing to buy/read two
>> books, then get it asap.
>
> 'In for a penny, in for a pound' (old English saying) - I've ordered a
> cheap(ish) copy of Franzen on Godel.  But let me know which you think
> is the best one.


Well, I should perhaps take the opportunity of your book open mindness 
to suggest some books I have already advertized on the list.
Comp is related to computations, computing, and computability. 
Fortunately we will need mainly the computability theory, which in some 
sense is more easy than computing theory. The best book is without 
doubt the one by Cutland:

CUTLAND N. J., 1980, Computability An introduction to recursive 
function theory,
Cambridge University Press.


Then, you have a "recreative" introduction to the modal logic of 
self-reference, the system known as G (but also GL, Prl, K4W, etc.). 
Unfortuantely the most important chapter "the heart of the matter" need 
a good understanding of Cutland (say) to make the link.

SMULLYAN R., 1987, Forever Undecided, Alfred A. Knopf, New York.

Then, the best textbook on mathematical self-reference is the book by 
Boolos 1993. But this one is probably a bit heavy to begin with. So 
wait to see if your curiosity will be enough high. It does contain a 
full chapter on the "third hypostase"; alias the first person, alias 
the knower, alias the modal logic S4Grz, or its purely arithmetical 
interpretation.

BOOLOS, G. 1993, The Logic of Provability. Cambridge University Press, 
Cambridge.

Or perhaps better (lighter) is its predecessor book on the subject, in 
the lucky case you find it (in a library?). I would be Dover Edition, I 
would print a paperback of that book;


BOOLOS, G. 1979,  The unprovability of consistency. Cambridge 
University Press, London.


Actually, if you have good eyes, the textbook by Smorynski is also 
quite valuable (and complementary to Boolos on many aspects):

SMORYNSKI, C., 1985,  Smoryński, P. (1985). Self-Reference and Modal 
Logic. Springer Verlag, New York.



>>> I think we may have to come back later to this question of subjective
>>> time.  But for now I rely on you to set the agenda of our more
>>> structured modus operandi.
>>
>>
>> Ok thanks.
>
> Then for the rest, I'll wait for your next post.




OK. I will begin by saying two words on the language we will use when 
discussing with the machine. I can already explain the difference 
between the layman (or grandmother) and the logician. This is not just 
for you (I guess you know what I will say) but for those who just 
abandon logic for reason of notation.

The main difference is that where a layman says "Alfred is serious", 
the logician says serious(Alfred).

Where the layman will say there is a ferocious dog, a logician will say 
that it exists something such that that something is a dog and is 
ferocious. Because of laziness he will write Ex(dog(x) & ferocious(x)). 
For saying that all dogs are ferocious, he will say that for all dogs 
(i.e. choose any thing that is a dog) that things will be ferocious: 
and he will write Ax (dog(x) -> ferocious(x)).

Of course, there i

Re: Observer Moment = Sigma1-Sentences

[David Nyman]

On 10/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> OK. Have you seen that this is going to made physics a branch of
> "intensional number theory", by which I mean number theory from the
> points of view of number ... ?

Insofar as we accept that the foundation of 'comp reality' is the
number realm, comp physics must indeed be a branch of this (e.g. as
per my previous example of 'digital digestion').

> OK. Don't buy it if you decide to buy only one book on Godel, and let
> me think which is the best one. But if you are willing to buy/read two
> books, then get it asap.

'In for a penny, in for a pound' (old English saying) - I've ordered a
cheap(ish) copy of Franzen on Godel.  But let me know which you think
is the best one.

> > I think we may have to come back later to this question of subjective
> > time.  But for now I rely on you to set the agenda of our more
> > structured modus operandi.
>
>
> Ok thanks.

Then for the rest, I'll wait for your next post.

David

>
>
> Le 10-août-07, à 14:26, David Nyman a écrit :
>
> >
> > On 09/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> >
> >> I hope you will not mind if I ask you "stupid" question, like "Do you
> >> know what mathematicians mean by "function?".
> >> Sometimes I realize that some people does not grasp what I say because
> >> they just miss some elementary vocabulary, or they have a problem with
> >> the notation.
> >> Of course anyone can ask any questions. Math is something easy (the
> >> easiest of all sciences) but if you miss a definition then it *looks*
> >> difficult.
> >
> > Thank you for asking, it's very important to ensure full understanding
> > at all points.  My maths are indeed a bit rusty, but fortunately
> > resources are easily available as needed to refresh the memory.  Would
> > you be happy with the wikipedia treatment of 'function'?
> >
> > http://en.wikipedia.org/wiki/Mathematical_function
>
>
> It is ok. I will say more in a post on the difference between the
> layman and the logician.
>
>
> >
> >> OK. But for this I need to be sure you grasp well the UD argument, at
> >> least the seven first step. The steps will always refer to the 8-steps
> >> presentation of the summary PDF Slides available here:
> >> http://iridia.ulb.ac.be/~marchal/publications/
> >> SANE2004MARCHALAbstract.html
> >
> > How can I best demonstrate this to your satisfaction?  I accept the
> > validity of the demonstration in the UDA (which I believe that I'd
> > already intuited as a consequence of the 'solipsism of the One') that
> > the first person or reflexive OM must be indeterminate with respect to
> > its third person manifestations.
>
>
> OK. Have you seen that this is going to made physics a branch of
> "intensional number theory", by which I mean number theory from the
> points of view of number ... ?
>
>
> >  However, I also wanted to ask
> > whether it was important in this context to define in detail the
> > content and informational limits of a given OM (e.g. its temporal
> > scope or 'duration')?
>
>
> ? The third person OM are outside time and space. time and space will
> emerge from the way OMs combine each other. They do combine through
> their intrinsic relative content eventually. But here we are
> anticipating.
>
>
>
>
> >
> >> Well, the UDA can already be seen as a 'grandmother' way of making
> >> this
> >> intuitive. What you have to understand is the turing-universality of
> >> addition and multiplication, in the first order logic framework. I
> >> will
> >> explain this in all detail, but I have to begin with Church thesis. I
> >> propose we try to organize ourself through a well defined sequence of
> >> posts, which we can from time to time transform into a pdf, so that we
> >> can refer to the pages of that pdf, instead of post messages with
> >> fragile addresses. OK?
> >
> > OK indeed.
> >
> >> Peter was putting too much philosophical weight to the notion of
> >> existence. Recall that the "ontic base of reality" will just be te
> >> numbers, and that when I say a number exist, I mean it in the usual
> >> sense of elementary high school arithmetic. The key point is that a
> >> machine which can prove all the true sigma1-sentence is turing
> >> universal. this is already well explained in Torkel Franzen's book (in
> >> his first appendix).  Again, don't worry I will explain.
> >
> > Do I need Franzen's book too?
>
>
> Hmmm The problem with the logicians is that they have a tendency to
> write beautiful books (and often quite expensive).
> So yes, buy or find an exemplar of Franzen's book, but honestly I could
> mention some other good book. But in our context Franzen's book could
> be a good if not the best beginning. His other book on inexhaustibility
> is quite interesting too, even as an introduction to PA (the
> Escherichia Coli of the "lobian machine").
> OK. Don't buy it if you decide to buy only one book on Godel, and let
> me think which is the best one. But if you are willing to buy/read two
> books, th

Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 10-août-07, à 14:26, David Nyman a écrit :

>
> On 09/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> I hope you will not mind if I ask you "stupid" question, like "Do you
>> know what mathematicians mean by "function?".
>> Sometimes I realize that some people does not grasp what I say because
>> they just miss some elementary vocabulary, or they have a problem with
>> the notation.
>> Of course anyone can ask any questions. Math is something easy (the
>> easiest of all sciences) but if you miss a definition then it *looks*
>> difficult.
>
> Thank you for asking, it's very important to ensure full understanding
> at all points.  My maths are indeed a bit rusty, but fortunately
> resources are easily available as needed to refresh the memory.  Would
> you be happy with the wikipedia treatment of 'function'?
>
> http://en.wikipedia.org/wiki/Mathematical_function


It is ok. I will say more in a post on the difference between the 
layman and the logician.


>
>> OK. But for this I need to be sure you grasp well the UD argument, at
>> least the seven first step. The steps will always refer to the 8-steps
>> presentation of the summary PDF Slides available here:
>> http://iridia.ulb.ac.be/~marchal/publications/
>> SANE2004MARCHALAbstract.html
>
> How can I best demonstrate this to your satisfaction?  I accept the
> validity of the demonstration in the UDA (which I believe that I'd
> already intuited as a consequence of the 'solipsism of the One') that
> the first person or reflexive OM must be indeterminate with respect to
> its third person manifestations.


OK. Have you seen that this is going to made physics a branch of 
"intensional number theory", by which I mean number theory from the 
points of view of number ... ?


>  However, I also wanted to ask
> whether it was important in this context to define in detail the
> content and informational limits of a given OM (e.g. its temporal
> scope or 'duration')?


? The third person OM are outside time and space. time and space will 
emerge from the way OMs combine each other. They do combine through 
their intrinsic relative content eventually. But here we are 
anticipating.




>
>> Well, the UDA can already be seen as a 'grandmother' way of making 
>> this
>> intuitive. What you have to understand is the turing-universality of
>> addition and multiplication, in the first order logic framework. I 
>> will
>> explain this in all detail, but I have to begin with Church thesis. I
>> propose we try to organize ourself through a well defined sequence of
>> posts, which we can from time to time transform into a pdf, so that we
>> can refer to the pages of that pdf, instead of post messages with
>> fragile addresses. OK?
>
> OK indeed.
>
>> Peter was putting too much philosophical weight to the notion of
>> existence. Recall that the "ontic base of reality" will just be te
>> numbers, and that when I say a number exist, I mean it in the usual
>> sense of elementary high school arithmetic. The key point is that a
>> machine which can prove all the true sigma1-sentence is turing
>> universal. this is already well explained in Torkel Franzen's book (in
>> his first appendix).  Again, don't worry I will explain.
>
> Do I need Franzen's book too?


Hmmm The problem with the logicians is that they have a tendency to 
write beautiful books (and often quite expensive).
So yes, buy or find an exemplar of Franzen's book, but honestly I could 
mention some other good book. But in our context Franzen's book could 
be a good if not the best beginning. His other book on inexhaustibility 
is quite interesting too, even as an introduction to PA (the 
Escherichia Coli of the "lobian machine").
OK. Don't buy it if you decide to buy only one book on Godel, and let 
me think which is the best one. But if you are willing to buy/read two 
books, then get it asap.


>
>> Now, to
>> eliminate redundancy in the explanations, I insist we organize 
>> ourself.
>> I have already explain many of those things, but never in a way so 
>> that
>> I can easily refer to the (too many) posts. All right?
>
> Alright!
>
>> The idea is really this: if you are in front of a running (and thus
>> never stopping UD), the seven steps shows that, taking comp seriously,
>> to make any 100% prediction, you have to take into account all the
>> reconstitutions of yourself (which exist by the comp hyp) and their
>> continuations.
>
> OK, again in terms of 'the One', since all the 'reconstitutions'
> exist, they must all indeed play a role in the 'account' (which can be
> synonymous with narrative or story).


Here there is something not quite correct I think. But I must go. The 
idea is that "all the reconsititution exist in many histories" will 
have just a statitistical effect of the first person view of the way 
the OM (re)combine. Again this is a (grandmother) anticipation.



>
>> By the first person indeterminacy, your future will be determined by
>> the most probable comp histories going throug

Re: Observer Moment = Sigma1-Sentences

[David Nyman]

On 09/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> I hope you will not mind if I ask you "stupid" question, like "Do you
> know what mathematicians mean by "function?".
> Sometimes I realize that some people does not grasp what I say because
> they just miss some elementary vocabulary, or they have a problem with
> the notation.
> Of course anyone can ask any questions. Math is something easy (the
> easiest of all sciences) but if you miss a definition then it *looks*
> difficult.

Thank you for asking, it's very important to ensure full understanding
at all points.  My maths are indeed a bit rusty, but fortunately
resources are easily available as needed to refresh the memory.  Would
you be happy with the wikipedia treatment of 'function'?

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

> OK. But for this I need to be sure you grasp well the UD argument, at
> least the seven first step. The steps will always refer to the 8-steps
> presentation of the summary PDF Slides available here:
> http://iridia.ulb.ac.be/~marchal/publications/
> SANE2004MARCHALAbstract.html

How can I best demonstrate this to your satisfaction?  I accept the
validity of the demonstration in the UDA (which I believe that I'd
already intuited as a consequence of the 'solipsism of the One') that
the first person or reflexive OM must be indeterminate with respect to
its third person manifestations.  However, I also wanted to ask
whether it was important in this context to define in detail the
content and informational limits of a given OM (e.g. its temporal
scope or 'duration')?

> Well, the UDA can already be seen as a 'grandmother' way of making this
> intuitive. What you have to understand is the turing-universality of
> addition and multiplication, in the first order logic framework. I will
> explain this in all detail, but I have to begin with Church thesis. I
> propose we try to organize ourself through a well defined sequence of
> posts, which we can from time to time transform into a pdf, so that we
> can refer to the pages of that pdf, instead of post messages with
> fragile addresses. OK?

OK indeed.

> Peter was putting too much philosophical weight to the notion of
> existence. Recall that the "ontic base of reality" will just be te
> numbers, and that when I say a number exist, I mean it in the usual
> sense of elementary high school arithmetic. The key point is that a
> machine which can prove all the true sigma1-sentence is turing
> universal. this is already well explained in Torkel Franzen's book (in
> his first appendix).  Again, don't worry I will explain.

Do I need Franzen's book too?

> Now, to
> eliminate redundancy in the explanations, I insist we organize ourself.
> I have already explain many of those things, but never in a way so that
> I can easily refer to the (too many) posts. All right?

Alright!

> The idea is really this: if you are in front of a running (and thus
> never stopping UD), the seven steps shows that, taking comp seriously,
> to make any 100% prediction, you have to take into account all the
> reconstitutions of yourself (which exist by the comp hyp) and their
> continuations.

OK, again in terms of 'the One', since all the 'reconstitutions'
exist, they must all indeed play a role in the 'account' (which can be
synonymous with narrative or story).

> By the first person indeterminacy, your future will be determined by
> the most probable comp histories going through your actual state.

By 'probable' you refer to the elusive measure?

> The problem then will consist in defining what is a "probable comp
> history". This is a very difficult problem: for example, when can we
> say that two computations are equivalent, etc.

i.e. from the third person pov?

> The trick I have done is to abandon the idea of searching directly a
> measure on the computations, and, instead, to isolate the mathematical
> structure for the "certain-propositions" by using the self-referential
> logics.

IOW you adopt the view from the inside out?  I would like to
understand this securely.  It seems to me that you're saying that
focusing on self-reference relies on the intrinsic self-location of
first person 'pages' within the 'Library of Babel' of the UD's output.
 Given this, how do such pages then 'cohere' into 'narratives through
time'?

> The first person will feel herself restricted 'in time' indeed.
> Somehow, she creates subjective time/consciousness. But from the ontic
> view, with the "block-all-computations" (alias UD*) there is no time.
>  From the material (first person plural view) pov, it is an open problem
> if there is an "objective time".

I think we may have to come back later to this question of subjective
time.  But for now I rely on you to set the agenda of our more
structured modus operandi.

David

>
>
> Le 08-août-07, à 15:26, David Nyman a écrit :
>
> >
> > On 30/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> >
> >> Meanwhile I would suggest you read the book by David
> >> Albert:

Rép : Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 09-août-07, à 11:22, Kim Jones a écrit :

>
> What is "lobian" apart from la machine, Bruno? Are you referring to
> "angels" here?
>
> Aren't angels machines too?


Angels are not machine. Unless you extend the meaning of machine 
'course, but Angels' provability extend the provability of any 
turing-emulable machine. Sometimes people use the term "supermachine" 
for what I call angel, but mathematically, in principle,  angels have 
nothing to do with machine. Angels can prove any sentence having the 
shape AxP(x) with P(x) decidable. (AxP(x) = For all x P(x)). Universal 
machine are Sigma_1 complete. Angels are PI_1 complete. A sigma_1 
sentence asserts something like "It exists a number having such or such 
verifiable (decidable) property". PI_1 sentences asserts something like 
"all numbers have such or such verifiable (decidable) property".
The most famous PI_1 sentences is the *machine* consistency statement: 
it is indeed equivalent with: all number have the (verifiable) property 
of not being the Godel number (or any arithmetical encoding) of a proof 
of f.
(f = any arithmetical contradiction, like (1+1=2 & ~(1+1=2)).
Angels can be shown to be lobian. They obey G and G*, and G and G* 
describe completely their propositional provability logic.
(btw, I call "god" any non turing emulable entity obeying G and G*, but 
for which G and G* are not complete (you need more axioms to 
characterize their provability power; and I call supergods, entities 
extending vastly the gods.
All that is really the subject matter of recursion theory, alias 
computability theory (which should have been called, like someone said 
in Siena, the theory of un-computability). recursion theory is really 
the science of Angels and Gods, well before being the science of 
Machines. But (and this is a consequence of incompleteness), you cannot 
seriously study machines without studying angels too  For example 
the quantifies version of G* (the first order modal logic of 
provability, the one I note qG*) can be shown to be a superangel: it is 
P1-complete *in* Arithmetical Truth (making bigger than the "unnameable 
God of the machine). This means that the divine intellect, or the 
Plato's "NOUS"  is bigger, in some sense than "God" (Plotinus' ONE). 
Plato would have appreciate, and perhaps Plotinus too because he wants 
the ONE to be simple , but yes the divine intellect is much more 
powerful than the "God" (accepting the arithmetical interpretation of 
the hypostases: see my Plotinus papert).

I will certainly come back on all definitions. But roughly speaking, a 
machine is (Turing)-universal (Sigma_1 complete) if it proves all true 
Sigma_1 sentences. A machine is lobian if not only the machine proves 
all true Sigma_1 sentences, but actually proves, for each Sigma_1 
sentence, that if that sentence is true then she can prove it. Put in 
another way, a machine is universal if, for any Sigma_1 sentence S, it 
is true that S->BS (B = beweisbar, provable). A machine is lobian if 
she proves, for any Sigma_1 sentence S, S->BS. For a universal machine 
(talking a bit of classical logic) S->BS is true about the machine. For 
a lobian machine S->BS is not only true, but provable (again with S 
representing Sigma_1 sentence).

But all this is a theorem. My "abstract" definition of lobianity is: 
any entity proving B(Bp->p)->Bp where B is her provability predicate.
A machine is weakly lobian if B(Bp->p)->Bp is true about the machine 
(not necessarily provable). A typical weakly lobian system which is not 
lobian is the modal logic K, I have talk about sometimes ago. 
B(Bp->p)->Bp is the Lob formula (Loeb, or better Löb; better if well 
printed!).

Don't panic with all that vocabulary and formula, I will try, perhaps 
with the help of people in the list, like David (if everything goes 
well), to be more systematic. Please, indulge the fact that I could 
change a definition in the course of the explanation, for a matter of 
making things easier.

But of course, ask any question, even if I decide to postpone the 
comment, it can help me to figure out where are the difficulties.


Bruno


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


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Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 08-août-07, à 15:26, David Nyman a écrit :

>
> On 30/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> Meanwhile I would suggest you read the book by David
>> Albert: "Quantum Mechanics and Experience"
>
> OK, I've ordered it.


Good.




>
>> I can compare only the "logic of probability/credibility one" of  
>> nature
>> (more or less quantum logic) and the logic of "probability/credibility
>> one" extracts from the discourse of the self-observing machine. It  
>> *is*
>> technical. It cannot be a starting point, I think.
>> In my opinion, the starting point is Church thesis. Once you are back,
>> tell me and I can do that.
>
> OK


I hope you will not mind if I ask you "stupid" question, like "Do you  
know what mathematicians mean by "function?".
Sometimes I realize that some people does not grasp what I say because  
they just miss some elementary vocabulary, or they have a problem with  
the notation.
Of course anyone can ask any questions. Math is something easy (the  
easiest of all sciences) but if you miss a definition then it *looks*  
difficult.





>
>>> The following may not be
>>> relevant in this context, but I'm particularly interested in  
>>> something
>>> you said elsewhere ('simulation argument') about how comp can relate
>>> OMs (and presumably the multiverse structures associated with them)
>>> geometrically 'through time'.
>>
>>
>> If this is not relevant in this context, I ask what is relevant ... ?
>
> I was referring only to its relevance as a a starting point.  However,
> it appears that you think it is.

OK, it is important, but cannot be used as a starting point. We will  
get it soon after Church thesis.



>
>> Now, as I said some days ago, I think that a way to link more
>> formally my work and the everything discussion can consist in defining
>> a notion of basic atomic third person observer moment.
>
> It would help me if you would define the content of this fundamental
> OM concept rather specifically for the purpose of this discussion.


OK. But for this I need to be sure you grasp well the UD argument, at  
least the seven first step. The steps will always refer to the 8-steps  
presentation of the summary PDF Slides available here:
http://iridia.ulb.ac.be/~marchal/publications/ 
SANE2004MARCHALAbstract.html




>
>> The UDA, plus
>> Church thesis + a theorem proved in Boolos and Jeffrey (but see also
>> and better perhaps just Franzen's appendix A) makes it possible to
>> define the comp third person OMs by the Sigma1 sentences of
>> arithmetical language. Those have the shape ExF(x) with F(x)  
>> decidable.
>> For example ExPrime(x) (a prime number exists), Ex(x = code of
>> triple(a,b,c) and machine a gives c on argument b),
>
> Is there a 'grandmotherly' way of making it intuitively compelling
> what makes it possible for the OM to be defined thus?



Well, the UDA can already be seen as a 'grandmother' way of making this  
intuitive. What you have to understand is the turing-universality of  
addition and multiplication, in the first order logic framework. I will  
explain this in all detail, but I have to begin with Church thesis. I  
propose we try to organize ourself through a well defined sequence of  
posts, which we can from time to time transform into a pdf, so that we  
can refer to the pages of that pdf, instead of post messages with  
fragile addresses. OK?





> In your various
> debates with Peter, I guess I've picked up essentially that such truth
> statements stand here for 'existence'.  Yes?

Peter was putting too much philosophical weight to the notion of  
existence. Recall that the "ontic base of reality" will just be te  
numbers, and that when I say a number exist, I mean it in the usual  
sense of elementary high school arithmetic. The key point is that a  
machine which can prove all the true sigma1-sentence is turing  
universal. this is already well explained in Torkel Franzen's book (in  
his first appendix).  Again, don't worry I will explain. Now, to  
eliminate redundancy in the explanations, I insist we organize ourself.  
I have already explain many of those things, but never in a way so that  
I can easily refer to the (too many) posts. All right?


>
>> ... This last
>> example show that the notion of Sigma1 sentences is rather rich and
>> encompasses full computability. So the very restricted notion of
>> Sigma1-proof (restricted from  the point of view of provability) is
>> already absolutely universal with respect to computability. A machine
>> is universal iff the machine is Sigma1 complete, i.e. is capable of
>> proving all true Sigma1 sentences.
>
> Could you expand more slowly on the particular importance of 'full
> computability' here.  Sorry if I'm being slow, but I want to make sure
> I get the intuitions as you intend them.


I will perhaps begin by that important question. Never apologize for  
being slow. It is a symptom that you try to understand the real thing.  
It is normal to be slow.



>
>> Such  a mac

Re: Observer Moment = Sigma1-Sentences

[David Nyman]

On 30/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> Meanwhile I would suggest you read the book by David
> Albert: "Quantum Mechanics and Experience"

OK, I've ordered it.

> I can compare only the "logic of probability/credibility one" of nature
> (more or less quantum logic) and the logic of "probability/credibility
> one" extracts from the discourse of the self-observing machine. It *is*
> technical. It cannot be a starting point, I think.
> In my opinion, the starting point is Church thesis. Once you are back,
> tell me and I can do that.

OK

> > The following may not be
> > relevant in this context, but I'm particularly interested in something
> > you said elsewhere ('simulation argument') about how comp can relate
> > OMs (and presumably the multiverse structures associated with them)
> > geometrically 'through time'.
>
>
> If this is not relevant in this context, I ask what is relevant ... ?

I was referring only to its relevance as a a starting point.  However,
it appears that you think it is.

> Now, as I said some days ago, I think that a way to link more
> formally my work and the everything discussion can consist in defining
> a notion of basic atomic third person observer moment.

It would help me if you would define the content of this fundamental
OM concept rather specifically for the purpose of this discussion.

> The UDA, plus
> Church thesis + a theorem proved in Boolos and Jeffrey (but see also
> and better perhaps just Franzen's appendix A) makes it possible to
> define the comp third person OMs by the Sigma1 sentences of
> arithmetical language. Those have the shape ExF(x) with F(x) decidable.
> For example ExPrime(x) (a prime number exists), Ex(x = code of
> triple(a,b,c) and machine a gives c on argument b),

Is there a 'grandmotherly' way of making it intuitively compelling
what makes it possible for the OM to be defined thus?  In your various
debates with Peter, I guess I've picked up essentially that such truth
statements stand here for 'existence'.  Yes?

> ... This last
> example show that the notion of Sigma1 sentences is rather rich and
> encompasses full computability. So the very restricted notion of
> Sigma1-proof (restricted from  the point of view of provability) is
> already absolutely universal with respect to computability. A machine
> is universal iff the machine is Sigma1 complete, i.e. is capable of
> proving all true Sigma1 sentences.

Could you expand more slowly on the particular importance of 'full
computability' here.  Sorry if I'm being slow, but I want to make sure
I get the intuitions as you intend them.

> Such  a machine codes automatically
> a Universal Dovetailer: to be a UD accessible state is Sigma1.
> So the measure we are searching can be put on the set of Sigma1
> sentences. Intuitively, from UDA, the weight for each Sigma1 sentences
> should be given by the "number" of proof going trough those sentences
> (including the many infinite proofs of some false sigma1 sentences).
> Now we can search for some equivalence relation on those proofs, but
> this is known to be very hard, and that is why I prefer to interview
> the universal lobian machine directly, and content myself with the
> corresponding logic of "certainty".

Is a more 'grandmotherly' form of all this possible to begin with?
I'm remembering the idea of the roadmap, in terms of which the
destination, and the journey towards it, could first be set out in
more general terms, in order to make the problems and their possible
solutions as intuitively compelling as possible at the outset.  It
seems to me often that I get the general drift, and some of the main
ideas, but there's still some confusion as to the whole picture.
Could there be a sort of master 'storybook' version - a narrative of
the key points into which the emerging formal detail could be fitted?

> Yes and No.
> Yes for two reasons: 1) if we assume comp, the UDA shows we have to
> recover knowledge from infinities of computations in the UD* (the
> "block" universal dovetailing. And FOR does presuppose comp.  2) in the
> arithmetization of the UDA, the notion of knowledge coherent with the
> UD thought experience is just given by the older definition of
> knowledge as true justified opinion (in platonism, but also in a lot of
> east and west rational account of mystical experiences). It is a gift
> that we arrive formally here at temporal-like logic of evolving first
> person knowledge.

Do you mean that first person knowledge by definition can emerge only
in an 'evolutionary' way - i.e. that it must necessarily be restricted
'in time', as opposed to some all-encompassing atemporal form (e.g.
the 'knowledge' of the One, if it had a pov)?

David

>
>
> Le 27-juil.-07, à 16:54, David Nyman a écrit :
>
> >
> > On 27/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> >
> >> What are your knowledge of quantum mechanics?
> >
> > Not very deep - only what I've gleaned in a largely non-mathematical
> > way from incessantly reading and

Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 31-juil.-07, à 14:47, Russell Standish a écrit :

>
> On Tue, Jul 31, 2007 at 04:06:10PM +0200, Bruno Marchal wrote:
>>
>>
>> Le 31-juil.-07, à 00:08, Russell Standish a écrit :
>>
>>>
>>> On Mon, Jul 30, 2007 at 11:47:48AM +0200, Bruno Marchal wrote:

 If this is not relevant in this context, I ask what is relevant ... 
 ?
 The problem you mention is at the cross of my work and the 
 everything
 list. Now, as I said some days ago, I think that a way to link more
 formally my work and the everything discussion can consist in 
 defining
 a notion of basic atomic third person observer moment. The UDA, plus
 Church thesis + a theorem proved in Boolos and Jeffrey (but see also
 and better perhaps just Franzen's appendix A) makes it possible to
 define the comp third person OMs by the Sigma1 sentences of
 arithmetical language. Those have the shape ExF(x) with F(x)
 decidable.
 For example ExPrime(x) (a prime number exists), Ex(x = code of
 triple(a,b,c) and machine a gives c on argument b), ... This last
 example show that the notion of Sigma1 sentences is rather rich and
 encompasses full computability. So the very restricted notion of
>>>
>>> Interesting. Since an observer moment contains all information that 
>>> is
>>> known about the universe,
>>
>>
>> ? I guess you mean ... about the observer.
>>
>
> No, I mean all information known by the observer (including, but not
> exclusively information know by the observer about erself).


OK, but then adding "about the universe" is confusing at this stage. 
You interpret the quantum state as describing knowledge. (And then I am 
not sure I follow what you mean by quantum state: you are supposing the 
quantum hyp. here, aren't you (or perhaps your linearity hyp. only? 
Again where would that linearity come from?).


>
>>
>>
>>> this led me to identify the observer moment
>>> and the quantum state vector.
>>
>>
>> ... and the partial relative quantum state vector corresponding to the
>> observer. OK, but at this stage this would be cheating. We can not yet
>> explain why the quantum histories wins over the comp/number relations.
>>
>
> Well I have my own reasons, considering knowledge acquisition as an
> evolutionary process. But I disagree about it being cheating, because
> I don't a priori assume quantum states are elements of a Hilbert
> space. That is a derived property.


So, how do you define quantum state?


>
>>
>>
>>> This is not incompatible with with your
>>> notion of the OM being a Sigma1 sentence, but it places severe
>>> restrictions on the form of the quantum state vector.
>>
>>
>> The OM are the Sigma1 sentences, when they are considered as third
>> person constructs.
>
> Third person is that which is accessible to all observers.


? (This correspond more to the first person plural notion as I have 
defined it in most of my papers: observers appeared in the fourth and 
fifth hypostases, and perhaps already a part of it appears in the third 
one; but there are no observer in the second or first hypostases).

cf:
1  p  (truth, 0-person)
2 Bp (provable, 3-person)
3 Bp & p  (knowable, 1-person)
4 Bp & Dp (observable, measurable; 1-plural-person)
5 Bp & Dp & p (sensationalisable, feelable, personally 
observable/measurable, 1 person again)



> Do you mean
> 0th person perhaps?


? (actually with comp this is defensible, but then you take the risk to 
give a name to the unnameable, indeed you could call Him/Her/It, 
FORTRAN, or JAVA, etc.). It is risky and I prefer not, even if with the 
comp hyp, that moves could be consistent (but could be eventually false 
although irrefutable). Risky.



>
>> Those are really the states accessible by the UD. To
>> get the quantum we have to reconsider those OMs from the points of
>> view. In the arithmetical comp setting this corresponds to looking to
>> the views expressed by the intensional variants of the logic of
>> prpvability (p, Bp, Bp & p, Bp & Dp, Bp & Dp & p, ...) with p
>> restricted to the (arithmetical) Sigma1 sentences. This gives the
>> second row of the 16 hypostases described in your book, page ? (my
>> exemplar is at home!).
>>
>>
>>
>>
>>> There can only
>>> be aleph_0 of them for instance.
>>
>>
>> Not really because the Sigma1 sentences are (a priori) weighted by the
>> computations going through, including those who does not terminate, if
>> only because they dovetail on the reals, and this is enough to suspect
>> that there could be  a continuum (aleph1). Of course it could be less
>> by the existence of some yet unknown equivalence relations (which I
>> succeeded not using thanks to the lobian interview). More on this when
>> David is back.
>>
>
> Alright, but it would be nice to know. There are only a countable
> number of machines, so I thought there'd only be a countable no. of
> Sigma1 sentences.


You are right, but they have different weight (and different relative 
weight) due to their belonging to different 

Re: Observer Moment = Sigma1-Sentences

[Russell Standish]

On Tue, Jul 31, 2007 at 04:06:10PM +0200, Bruno Marchal wrote:
> 
> 
> Le 31-juil.-07, à 00:08, Russell Standish a écrit :
> 
> >
> > On Mon, Jul 30, 2007 at 11:47:48AM +0200, Bruno Marchal wrote:
> >>
> >> If this is not relevant in this context, I ask what is relevant ... ?
> >> The problem you mention is at the cross of my work and the everything
> >> list. Now, as I said some days ago, I think that a way to link more
> >> formally my work and the everything discussion can consist in defining
> >> a notion of basic atomic third person observer moment. The UDA, plus
> >> Church thesis + a theorem proved in Boolos and Jeffrey (but see also
> >> and better perhaps just Franzen's appendix A) makes it possible to
> >> define the comp third person OMs by the Sigma1 sentences of
> >> arithmetical language. Those have the shape ExF(x) with F(x) 
> >> decidable.
> >> For example ExPrime(x) (a prime number exists), Ex(x = code of
> >> triple(a,b,c) and machine a gives c on argument b), ... This last
> >> example show that the notion of Sigma1 sentences is rather rich and
> >> encompasses full computability. So the very restricted notion of
> >
> > Interesting. Since an observer moment contains all information that is
> > known about the universe,
> 
> 
> ? I guess you mean ... about the observer.
> 

No, I mean all information known by the observer (including, but not
exclusively information know by the observer about erself).

> 
> 
> > this led me to identify the observer moment
> > and the quantum state vector.
> 
> 
> ... and the partial relative quantum state vector corresponding to the 
> observer. OK, but at this stage this would be cheating. We can not yet 
> explain why the quantum histories wins over the comp/number relations.
> 

Well I have my own reasons, considering knowledge acquisition as an
evolutionary process. But I disagree about it being cheating, because
I don't a priori assume quantum states are elements of a Hilbert
space. That is a derived property.

> 
> 
> > This is not incompatible with with your
> > notion of the OM being a Sigma1 sentence, but it places severe
> > restrictions on the form of the quantum state vector.
> 
> 
> The OM are the Sigma1 sentences, when they are considered as third 
> person constructs. 

Third person is that which is accessible to all observers. Do you mean
0th person perhaps?

> Those are really the states accessible by the UD. To 
> get the quantum we have to reconsider those OMs from the points of 
> view. In the arithmetical comp setting this corresponds to looking to 
> the views expressed by the intensional variants of the logic of 
> prpvability (p, Bp, Bp & p, Bp & Dp, Bp & Dp & p, ...) with p 
> restricted to the (arithmetical) Sigma1 sentences. This gives the 
> second row of the 16 hypostases described in your book, page ? (my 
> exemplar is at home!).
> 
> 
> 
> 
> > There can only
> > be aleph_0 of them for instance.
> 
> 
> Not really because the Sigma1 sentences are (a priori) weighted by the 
> computations going through, including those who does not terminate, if 
> only because they dovetail on the reals, and this is enough to suspect 
> that there could be  a continuum (aleph1). Of course it could be less 
> by the existence of some yet unknown equivalence relations (which I 
> succeeded not using thanks to the lobian interview). More on this when 
> David is back.
> 

Alright, but it would be nice to know. There are only a countable
number of machines, so I thought there'd only be a countable no. of
Sigma1 sentences.

> 
> 
> 
> > Perhaps these restrictions are
> > testable? Perhaps there is something wrong with identifying the state
> > vector with the OM?
> 
> 
> Comp is really "I am a machine", and not at all "the universe is a 
> machine". The UDA shows that, unless "I am the universe", the 
> proposistion "I am a machine" and "the physical universe is a machine" 
> are incompatible. Indeed the UDA forces the physical laws to emerge 
> locally from *all computations"? A priori again this makes the universe 
> a non computational  object, it seems to me (by UDA).
> 

But the OM is actually the "universe", or at least a snapshot
thereof. So we would expect it to be uncomputable. Is that also the
case of the Sigma1 sentences?

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


A/Prof Russell Standish  Phone 0425 253119 (mobile)
Mathematics  
UNSW SYDNEY 2052 [EMAIL PROTECTED]
Australiahttp://www.hpcoders.com.au


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Re: Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 31-juil.-07, à 00:08, Russell Standish a écrit :

>
> On Mon, Jul 30, 2007 at 11:47:48AM +0200, Bruno Marchal wrote:
>>
>> If this is not relevant in this context, I ask what is relevant ... ?
>> The problem you mention is at the cross of my work and the everything
>> list. Now, as I said some days ago, I think that a way to link more
>> formally my work and the everything discussion can consist in defining
>> a notion of basic atomic third person observer moment. The UDA, plus
>> Church thesis + a theorem proved in Boolos and Jeffrey (but see also
>> and better perhaps just Franzen's appendix A) makes it possible to
>> define the comp third person OMs by the Sigma1 sentences of
>> arithmetical language. Those have the shape ExF(x) with F(x) 
>> decidable.
>> For example ExPrime(x) (a prime number exists), Ex(x = code of
>> triple(a,b,c) and machine a gives c on argument b), ... This last
>> example show that the notion of Sigma1 sentences is rather rich and
>> encompasses full computability. So the very restricted notion of
>
> Interesting. Since an observer moment contains all information that is
> known about the universe,


? I guess you mean ... about the observer.



> this led me to identify the observer moment
> and the quantum state vector.


... and the partial relative quantum state vector corresponding to the 
observer. OK, but at this stage this would be cheating. We can not yet 
explain why the quantum histories wins over the comp/number relations.



> This is not incompatible with with your
> notion of the OM being a Sigma1 sentence, but it places severe
> restrictions on the form of the quantum state vector.


The OM are the Sigma1 sentences, when they are considered as third 
person constructs. Those are really the states accessible by the UD. To 
get the quantum we have to reconsider those OMs from the points of 
view. In the arithmetical comp setting this corresponds to looking to 
the views expressed by the intensional variants of the logic of 
prpvability (p, Bp, Bp & p, Bp & Dp, Bp & Dp & p, ...) with p 
restricted to the (arithmetical) Sigma1 sentences. This gives the 
second row of the 16 hypostases described in your book, page ? (my 
exemplar is at home!).




> There can only
> be aleph_0 of them for instance.


Not really because the Sigma1 sentences are (a priori) weighted by the 
computations going through, including those who does not terminate, if 
only because they dovetail on the reals, and this is enough to suspect 
that there could be  a continuum (aleph1). Of course it could be less 
by the existence of some yet unknown equivalence relations (which I 
succeeded not using thanks to the lobian interview). More on this when 
David is back.




> Perhaps these restrictions are
> testable? Perhaps there is something wrong with identifying the state
> vector with the OM?


Comp is really "I am a machine", and not at all "the universe is a 
machine". The UDA shows that, unless "I am the universe", the 
proposistion "I am a machine" and "the physical universe is a machine" 
are incompatible. Indeed the UDA forces the physical laws to emerge 
locally from *all computations"? A priori again this makes the universe 
a non computational  object, it seems to me (by UDA).


Bruno

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


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Re: Observer Moment = Sigma1-Sentences

[Russell Standish]

On Mon, Jul 30, 2007 at 11:47:48AM +0200, Bruno Marchal wrote:
> 
> If this is not relevant in this context, I ask what is relevant ... ?
> The problem you mention is at the cross of my work and the everything  
> list. Now, as I said some days ago, I think that a way to link more  
> formally my work and the everything discussion can consist in defining  
> a notion of basic atomic third person observer moment. The UDA, plus  
> Church thesis + a theorem proved in Boolos and Jeffrey (but see also  
> and better perhaps just Franzen's appendix A) makes it possible to  
> define the comp third person OMs by the Sigma1 sentences of  
> arithmetical language. Those have the shape ExF(x) with F(x) decidable.  
> For example ExPrime(x) (a prime number exists), Ex(x = code of  
> triple(a,b,c) and machine a gives c on argument b), ... This last  
> example show that the notion of Sigma1 sentences is rather rich and  
> encompasses full computability. So the very restricted notion of  

Interesting. Since an observer moment contains all information that is
known about the universe, this led me to identify the observer moment
and the quantum state vector. This is not incompatible with with your
notion of the OM being a Sigma1 sentence, but it places severe
restrictions on the form of the quantum state vector. There can only
be aleph_0 of them for instance. Perhaps these restrictions are
testable? Perhaps there is something wrong with identifying the state
vector with the OM?



A/Prof Russell Standish  Phone 0425 253119 (mobile)
Mathematics  
UNSW SYDNEY 2052 [EMAIL PROTECTED]
Australiahttp://www.hpcoders.com.au


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Observer Moment = Sigma1-Sentences

[Bruno Marchal]

Le 27-juil.-07, à 16:54, David Nyman a écrit :

>
> On 27/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> What are your knowledge of quantum mechanics?
>
> Not very deep - only what I've gleaned in a largely non-mathematical
> way from incessantly reading and musing about the topic for years.
> But I think I'm sufficiently orientated in the basic ideas and
> alternative interpretations to have a chance at following up at least
> some specific topics, that you might suggest, in more detail.  But
> this can wait if you feel it's premature.



It can wait, and from a purely logical point of view it is necessary  
only at the last step when we will compare the comp-physics and the  
empirical physics. Meanwhile I would suggest you read the book by David  
Albert: "Quantum Mechanics and Experience"
http://www.amazon.com/Quantum-Mechanics-Experience-David-Albert/dp/ 
0674741137
That book even reminds you the elementary linear algebra, and it gives  
the keys for serious study of the conceptual problems. You will not  
been able to solve any physical (implementations) problems, but you  
will be able to understand the conceptual issues of quantum  
information/computing science, which are all we need.





>
>> The empirical
>> test consists in comparing those multiverse strurctures atatched to
>> entitiess-points of view and what we observe ... indirectly
>> (observation is always indirect, ok?).
>
> Definitely OK.  Perhaps an example of a specific comparison of this
> kind would be a good starting point?


I can compare only the "logic of probability/credibility one" of nature  
(more or less quantum logic) and the logic of "probability/credibility  
one" extracts from the discourse of the self-observing machine. It *is*  
technical. It cannot be a starting point, I think.
In my opinion, the starting point is Church thesis. Once you are back,  
tell me and I can do that.




> The following may not be
> relevant in this context, but I'm particularly interested in something
> you said elsewhere ('simulation argument') about how comp can relate
> OMs (and presumably the multiverse structures associated with them)
> geometrically 'through time'.


If this is not relevant in this context, I ask what is relevant ... ?
The problem you mention is at the cross of my work and the everything  
list. Now, as I said some days ago, I think that a way to link more  
formally my work and the everything discussion can consist in defining  
a notion of basic atomic third person observer moment. The UDA, plus  
Church thesis + a theorem proved in Boolos and Jeffrey (but see also  
and better perhaps just Franzen's appendix A) makes it possible to  
define the comp third person OMs by the Sigma1 sentences of  
arithmetical language. Those have the shape ExF(x) with F(x) decidable.  
For example ExPrime(x) (a prime number exists), Ex(x = code of  
triple(a,b,c) and machine a gives c on argument b), ... This last  
example show that the notion of Sigma1 sentences is rather rich and  
encompasses full computability. So the very restricted notion of  
Sigma1-proof (restricted from  the point of view of provability) is  
already absolutely universal with respect to computability. A machine  
is universal iff the machine is Sigma1 complete, i.e. is capable of  
proving all true Sigma1 sentences. Such  a machine codes automatically  
a Universal Dovetailer: to be a UD accessible state is Sigma1.
So the measure we are searching can be put on the set of Sigma1  
sentences. Intuitively, from UDA, the weight for each Sigma1 sentences  
should be given by the "number" of proof going trough those sentences  
(including the many infinite proofs of some false sigma1 sentences).  
Now we can search for some equivalence relation on those proofs, but  
this is known to be very hard, and that is why I prefer to interview  
the universal lobian machine directly, and content myself with the  
corresponding logic of "certainty".



>  Is this is an area where comp
> consequently can recover 'dynamically experienced' observer histories
> within a block or static context more satisfactorily than e.g. the
> Deutsch 'disconnected slice' view as propounded in FOR?


Yes and No.
Yes for two reasons: 1) if we assume comp, the UDA shows we have to  
recover knowledge from infinities of computations in the UD* (the  
"block" universal dovetailing. And FOR does presuppose comp.  2) in the  
arithmetization of the UDA, the notion of knowledge coherent with the  
UD thought experience is just given by the older definition of  
knowledge as true justified opinion (in platonism, but also in a lot of  
east and west rational account of mystical experiences). It is a gift  
that we arrive formally here at temporal-like logic of evolving first  
person knowledge.
No, because today, obviously, the quantum hyp is much more efficacious  
than the comp hyp (except that this really comes from Everett, which is  
SWE-without-collapse+comp, and the UDA shows that comp