Re: Asifism revisited.

[Torgny Tholerus]

Brent Meeker skrev:

> Torgny Tholerus wrote:
>>
>> That is exactly what I wanted to say.  You don't need to have a complete
>> description of arithmetic.  Our universe can be described by doing a
>> number of computations from a finite set of rules.  (To get to the
>> current view of our universe you have to do about 10**60 computations
>> for every point of space...)
>
> How did you arrive at that number?
>
It is the number of Planck times since the birth of Universe.  The age of
Universe is 13,7 billion years, number of seconds in a year is 31 million,
and the Planck time is 5,4 * 10**-44 seconds.  That gives 13,7*10**9 *
31*10**6 / (5,4*10**-44) = 8*10**60.

-- 
Torgny


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A Natural Axiomatization of Church's Thesis

[Jef Allbright]

Apropos much discussion on this list, a new paper is available at


Abstract:
The Abstract State Machine Thesis asserts that every classical
algorithm is behaviorally equivalent to an abstract state machine.
This thesis has been shown to follow from three natural postulates
about algorithmic computation. Here, we prove that augmenting those
postulates with an additional requirement regarding basic operations
implies Church's Thesis, namely, that the only numeric functions that
can be calculated by effective means are the recursive ones (which are
the same, extensionally, as the Turing-computable numeric functions).
In particular, this gives a natural axiomatization of Church's Thesis,
as Gödel and others suggested may be possible.

- Jef

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Re: Some thoughts from Grandma

[Brent Meeker]

Bruno Marchal wrote:
> 
> Le 12-juil.-07, à 16:27, David Nyman a écrit :
> 
>> On 12/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>>
>>> I try to avoid the words like "reflexive" or "reflection" in informal
>>> talk, because it is a tricky technical terms
>>> I tend to agree with what Brent said.
>> Yes, I ended up more or less agreeing with him myself.  But I
>> nevertheless feel, from their posts, that this is *not* what some
>> people have in mind when they use the term 'exists'.
> 
> 
> "existence" is a very very tricky notion. In the theory I am proposing 
> (actually I derived it from the comp principle) the most basic notion 
> of "exists" is remarkably well formalize by first order arithmetical 
> logic, like in Ex(prime(x)):   it exists a prime number.

But isn't this just an elaboration that obscures the prior assumption that 
numbers exist?  If numbers don't exist then Ex(prime(x)) is false, or requires 
a different interpretation of "E".  

Brent Meeker


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Re: Asifism revisited.

[Brent Meeker]

Bruno Marchal wrote:
> 
> Le 12-juil.-07, à 18:43, Brent Meeker a écrit :
> 
>> Bruno Marchal wrote:
>>>
>>> Le 09-juil.-07, à 17:41, Torgny Tholerus a écrit :
>> ...
>>> Our universe is the result of some set of rules. The interesting
>>> thing is to discover the specific rules that span our universe.
>>>
>>>
>>>
>>>
>>> Assuming comp, I don't find plausible that "our universe" can be the
>>> result of some set of rules. Even without comp the "arithmetical
>>> universe" or arithmetical truth (the "ONE" attached to the little 
>>> Peano
>>> Arithmetic Lobian machine) cannot be described by finite set of rules.
>> But it can be "the result of" a finite set of rules. Arithmetic 
>> results from Peano's axioms, but a complete description of arithmetic 
>> is impossible.
> 
> 
> I don't understand.
> 
> Let us define ARITHMETIC (big case) by the set of true (first order 
> logical) arithmetical sentences. (like "prime number exist",
> Let us define arithmetic (lower case) by the set of provable (first 
> order logical) arithmetical sentences, where "provable" means provable 
> by some sound lobian machine.
> By incompleteness, whatever sound machine you consisder the 
> corresponding "arithmetic" is always a proper subset of ARITHMETIC.
> 
> So arithmetical truth (alias ARITHMETIC) cannot be described by any 
> finite set of rules. Finite sets or rules can never generate the whole 
> of arithmetical truth.
> 
> OK?
> 
> Bruno

Yes, I understand.  But ARITHMETIC is generated by or results from Peano's 
axioms - right?

Brent Meeker  

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Re: Asifism revisited.

[Brent Meeker]

Torgny Tholerus wrote:
> Brent Meeker skrev:
>> Bruno Marchal wrote:
>>   
>>> Le 09-juil.-07, à 17:41, Torgny Tholerus a écrit :
>>> 
>> ...
>>   
>>> Our universe is the result of some set of rules. The interesting
>>> thing is to discover the specific rules that span our universe.
>>>
>>>
>>>
>>>
>>> Assuming comp, I don't find plausible that "our universe" can be the 
>>> result of some set of rules. Even without comp the "arithmetical 
>>> universe" or arithmetical truth (the "ONE" attached to the little Peano 
>>> Arithmetic Lobian machine) cannot be described by finite set of rules.
>>> 
>>
>> But it can be "the result of" a finite set of rules. Arithmetic results from 
>> Peano's axioms, but a complete description of arithmetic is impossible.
>>   
> That is exactly what I wanted to say.  You don't need to have a complete 
> description of arithmetic.  Our universe can be described by doing a 
> number of computations from a finite set of rules.  (To get to the 
> current view of our universe you have to do about 10**60 computations 
> for every point of space...)

How did you arrive at that number?

Brent Meeker

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Re: Some thoughts from Grandma

[David Nyman]

Is this better?

"One may say neither that the one mind is prior and all dharmas
posterior nor that all dharmas are prior and the one mind
posterior If one derives all dharmas from the one mind, this is a
vertical relationship. If the mind all at once contains all dharmas,
this is a horizontal relationship. Neither vertical nor horizontal
will do. All one can say is that the mind is all dharmas, and all
dharmas are the mind. Therefore the relationship is neither vertical
nor horizontal, neither the same nor different. It is obscure, subtle
and profound in the extreme. Knowledge cannot know it, nor can words
speak it. Herein lies the reason for its being called "the realm of
the inconceivable."

Chih-i (or Zhiyi, 538-597), founder of Chinese T'ien-t'ai Buddhism,
quoted by Jacqueline I. Stone, Original Enlightenment and the
Transformation of Medieval Japanese Buddhism, Kuroda Institute,
University of Hawai'i Press, 1999, p. 179

(Excerpted from http://www.friesian.com/undecd-1.htm)

David

On 13/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>
> Le 13-juil.-07, à 17:02, David Nyman a écrit :
>
> >  But since the One is not
> > what most people would consider a person (let alone a god), another
> > term would be better.  I wonder what?
>
>
> I think you are trying to give a name to what is unnameable (unless you
> are not lobian;  even lobian non-machine cannot name it).
>
> Bruno
>
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
> >
>

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Re: Some thoughts from Grandma

[David Nyman]

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

> I think you are trying to give a name to what is unnameable (unless you
> are not lobian;  even lobian non-machine cannot name it).

Perish the thought.  But I was referring to 'first person primacy',
not 'the One'.  Maybe something like the 'primacy of the unnameable'?
On the other hand

"Wovon man nicht sprechen kann, darüber muß man schweigen"

It doesn't seem to keep us quiet for long though :-)

David

>
>
> Le 13-juil.-07, à 17:02, David Nyman a écrit :
>
> >  But since the One is not
> > what most people would consider a person (let alone a god), another
> > term would be better.  I wonder what?
>
>
> I think you are trying to give a name to what is unnameable (unless you
> are not lobian;  even lobian non-machine cannot name it).
>
> Bruno
>
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
> >
>

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Re: Some thoughts from Grandma

[Bruno Marchal]

Le 13-juil.-07, à 17:02, David Nyman a écrit :

>  But since the One is not
> what most people would consider a person (let alone a god), another
> term would be better.  I wonder what?


I think you are trying to give a name to what is unnameable (unless you 
are not lobian;  even lobian non-machine cannot name it).

Bruno




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


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Re: Some thoughts from Grandma

[David Nyman]

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

> > I said in an earlier post that this amounted to a kind of solipsism of
> > the One: IOW, the One would be justified in the view (if it had one!)
> > that it was all that existed, and that everything was simply an aspect
> > of itself.
>
> Yes, and this is where Aristotle and Plotinus differs the most (even
> more than Aristotle/Plato). Would the ONE have a pov, He/She/It would
> be solispsist. A sad thing for a "God" 

Sad indeed.  Perhaps the One just has to differentiate to get some company.

Anyway, the notion of the solipsism of the One essentially
encapsulates the view I was trying to put forward from the inception
of our dialogues on "first person primacy".  But since the One is not
what most people would consider a person (let alone a god), another
term would be better.  I wonder what?

David

>
>
> Le 12-juil.-07, à 16:27, David Nyman a écrit :
>
> >
> > On 12/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> >
> >> I try to avoid the words like "reflexive" or "reflection" in informal
> >> talk, because it is a tricky technical terms
> >> I tend to agree with what Brent said.
> >
> > Yes, I ended up more or less agreeing with him myself.  But I
> > nevertheless feel, from their posts, that this is *not* what some
> > people have in mind when they use the term 'exists'.
>
>
> "existence" is a very very tricky notion. In the theory I am proposing
> (actually I derived it from the comp principle) the most basic notion
> of "exists" is remarkably well formalize by first order arithmetical
> logic, like in Ex(prime(x)):   it exists a prime number.
> All other notion of "existence" are modal variant: like
> B[Ex(prime(x))], or ExB(prime(x)); I believe there is a prime number,
> there is a number such that I believe that that number is prime, etc.
> Of course, in the lobian frame, "B" refers itself to an arithmetical
> predicate (the "Beweisbar of Godel 1931).
>
>
>
>
> >
> >> I'm afraid
> >> that sometimes you are near the 1004 fallacy.
> >
> > That may well be, but unfortunately I tend only to discover specific
> > examples of this by trial and error.  But having done so, I try to
> > hold on to the discovery.
>
>
> OK.
>
>
>
> >
> >> But of course
> >> your intuition grew perhaps from non comp or non lobian origin.
> >
> > That's definitely the case.
>
> OK. (except that you are perhaps lobian, just not knowing it).
>
>
>
> >
> >> (I see now what could be the comp lobian "observer moments", and will
> >> say more in a special purpose post.
> >
> > I look forward to it.
>
>
> Thanks. I will do that in august, if you don't mind; it asks for some
> work. It will be related to the content of my next paper, where I
> currently think I will use the "observer moment" notion (and refer to
> the list). Roughly speaking, I think that we have to consider first
> person and third person notion of OM. Nick Bostrom original one is
> clearly a notion of 1-OM.
> I can show that with comp there is a natural notion of 3-OM, which is
> just the (true) Sigma1 sentence. They correspond to the accessible
> states of the Universal Dovetailer, or to the theorem of a Robinsonian
> machine or universal machine.
> A universal machine (or person) get Lobian when she knows (in a
> technically rather weak sense) that she is universal. This makes it
> possible (well, even necessary) for the machine to distinguish the 3-OM
> with all possible 1-OM notion, and this can accelerate the derivation
> of the physical laws from numbers/machines relations. The new and key
> point is the identification of 3-OM directly with Sigma1 sentences.
>
>
> >
> >> Coming back from Siena, I know now that all my work on Church thesis
> >> is
> >> more original than I thought (meaning: I have to publish more before
> >> even logician grasp the whole thing ...).
> >
> > You have a hard row to plough!
>
>
>
> The difficulty is the interdisciplinary overlap of quantum physics,
> mathematical logic and, perhaps the harder part: philosophy or
> mind/theology.
>
>
>
>
> >
> >> Is "us" = to the lobian machine?
> >
> > I just meant observers in general, using myself as the model.
> >
> >>> and I've been trying to convince Torgny
> >>> that we shouldn't fool ourselves into mistaking such conceptions for
> >>> modes of existing.
> >>
> >>
> >> But each point of view (hypostasis) defines its own "mode of
> >> existence". Now Plotinus restricts the notion of existence for the
> >> ideas (here: the effective objects which provably exist in Platonia).
> >> That is why both God and Matter does not really exist in Plotinus
> >> theory. Of course God and Matter do exist, even for Plotinus, but it
> >> is
> >> a different mode of existence.
> >
> > I'm frustrated that I don't seem to be able to communicate what I mean
> > here (I don't know if this is an example of 1004 or not).  I meant
> > that just because we can imagine something in a gods' eye way doesn't
> > (for me) entail that it exists in any other wa

Re: Some thoughts from Grandma

[Bruno Marchal]

Le 12-juil.-07, à 16:27, David Nyman a écrit :

>
> On 12/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> I try to avoid the words like "reflexive" or "reflection" in informal
>> talk, because it is a tricky technical terms
>> I tend to agree with what Brent said.
>
> Yes, I ended up more or less agreeing with him myself.  But I
> nevertheless feel, from their posts, that this is *not* what some
> people have in mind when they use the term 'exists'.


"existence" is a very very tricky notion. In the theory I am proposing 
(actually I derived it from the comp principle) the most basic notion 
of "exists" is remarkably well formalize by first order arithmetical 
logic, like in Ex(prime(x)):   it exists a prime number.
All other notion of "existence" are modal variant: like 
B[Ex(prime(x))], or ExB(prime(x)); I believe there is a prime number, 
there is a number such that I believe that that number is prime, etc. 
Of course, in the lobian frame, "B" refers itself to an arithmetical 
predicate (the "Beweisbar of Godel 1931).




>
>> I'm afraid
>> that sometimes you are near the 1004 fallacy.
>
> That may well be, but unfortunately I tend only to discover specific
> examples of this by trial and error.  But having done so, I try to
> hold on to the discovery.


OK.



>
>> But of course
>> your intuition grew perhaps from non comp or non lobian origin.
>
> That's definitely the case.

OK. (except that you are perhaps lobian, just not knowing it).



>
>> (I see now what could be the comp lobian "observer moments", and will
>> say more in a special purpose post.
>
> I look forward to it.


Thanks. I will do that in august, if you don't mind; it asks for some 
work. It will be related to the content of my next paper, where I 
currently think I will use the "observer moment" notion (and refer to 
the list). Roughly speaking, I think that we have to consider first 
person and third person notion of OM. Nick Bostrom original one is 
clearly a notion of 1-OM.
I can show that with comp there is a natural notion of 3-OM, which is 
just the (true) Sigma1 sentence. They correspond to the accessible 
states of the Universal Dovetailer, or to the theorem of a Robinsonian 
machine or universal machine.
A universal machine (or person) get Lobian when she knows (in a 
technically rather weak sense) that she is universal. This makes it 
possible (well, even necessary) for the machine to distinguish the 3-OM 
with all possible 1-OM notion, and this can accelerate the derivation 
of the physical laws from numbers/machines relations. The new and key 
point is the identification of 3-OM directly with Sigma1 sentences.


>
>> Coming back from Siena, I know now that all my work on Church thesis 
>> is
>> more original than I thought (meaning: I have to publish more before
>> even logician grasp the whole thing ...).
>
> You have a hard row to plough!



The difficulty is the interdisciplinary overlap of quantum physics, 
mathematical logic and, perhaps the harder part: philosophy or 
mind/theology.




>
>> Is "us" = to the lobian machine?
>
> I just meant observers in general, using myself as the model.
>
>>> and I've been trying to convince Torgny
>>> that we shouldn't fool ourselves into mistaking such conceptions for
>>> modes of existing.
>>
>>
>> But each point of view (hypostasis) defines its own "mode of
>> existence". Now Plotinus restricts the notion of existence for the
>> ideas (here: the effective objects which provably exist in Platonia).
>> That is why both God and Matter does not really exist in Plotinus
>> theory. Of course God and Matter do exist, even for Plotinus, but it 
>> is
>> a different mode of existence.
>
> I'm frustrated that I don't seem to be able to communicate what I mean
> here (I don't know if this is an example of 1004 or not).  I meant
> that just because we can imagine something in a gods' eye way doesn't
> (for me) entail that it exists in any other way - what I called (but
> I'll desist!) 'reflexively' (i.e. with reference to itself, or just:
> for itself), which Brent was content to call existence simpliciter.
> This intuition of course just begins with knowing that *I* exist for
> myself, which implies that others exist for themselves, which
> ultimately implies that everything exists for itself - 'the One' being
> the ultimate expression of this.  I don't mean to equate 'exists for
> itself' with consciousness, but to say that consciousness emerges as a
> complex aspect of such self-relation.  I'm convinced both that you
> know what I mean by this, and also that it can be expressed in the
> Lobian discourse (though not by me).



Perhaps. The problem here is that I should explain technical things 
just to help you to figure out the complexity of the point you single 
out. To translate this in the lobian discourse is less easy than you 
think. More on this in august.





>
>>> 'The One' is also a mode of enquiry (no less tricky, of course): it
>>> seems to suggest that the mode of e

Re: Asifism revisited.

[Bruno Marchal]

Le 12-juil.-07, à 18:43, Brent Meeker a écrit :

>
> Bruno Marchal wrote:
>>
>>
>> Le 09-juil.-07, à 17:41, Torgny Tholerus a écrit :
> ...
>> Our universe is the result of some set of rules. The interesting
>> thing is to discover the specific rules that span our universe.
>>
>>
>>
>>
>> Assuming comp, I don't find plausible that "our universe" can be the
>> result of some set of rules. Even without comp the "arithmetical
>> universe" or arithmetical truth (the "ONE" attached to the little 
>> Peano
>> Arithmetic Lobian machine) cannot be described by finite set of rules.
>
> But it can be "the result of" a finite set of rules. Arithmetic 
> results from Peano's axioms, but a complete description of arithmetic 
> is impossible.


I don't understand.

Let us define ARITHMETIC (big case) by the set of true (first order 
logical) arithmetical sentences. (like "prime number exist",
Let us define arithmetic (lower case) by the set of provable (first 
order logical) arithmetical sentences, where "provable" means provable 
by some sound lobian machine.
By incompleteness, whatever sound machine you consisder the 
corresponding "arithmetic" is always a proper subset of ARITHMETIC.

So arithmetical truth (alias ARITHMETIC) cannot be described by any 
finite set of rules. Finite sets or rules can never generate the whole 
of arithmetical truth.

OK?

Bruno




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Re: Asifism revisited.

[Torgny Tholerus]

Brent Meeker skrev:

  Bruno Marchal wrote:
  
  

Le 09-juil.-07, à 17:41, Torgny Tholerus a écrit :

  
  ...
  
  
Our universe is the result of some set of rules. The interesting
thing is to discover the specific rules that span our universe.




Assuming comp, I don't find plausible that "our universe" can be the 
result of some set of rules. Even without comp the "arithmetical 
universe" or arithmetical truth (the "ONE" attached to the little Peano 
Arithmetic Lobian machine) cannot be described by finite set of rules.

  
  
But it can be "the result of" a finite set of rules. Arithmetic results from Peano's axioms, but a complete description of arithmetic is impossible.
  

That is exactly what I wanted to say.  You don't need to have a
complete description of arithmetic.  Our universe can be described by
doing a number of computations from a finite set of rules.  (To get to
the current view of our universe you have to do about 10**60
computations for every point of space...)

-- 
Torgny

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Re: Some thoughts from Grandma

[David Nyman]

On 13/07/07, Brent Meeker <[EMAIL PROTECTED]> wrote:

> > Brent, all that David is getting at is saying nothing "reflexively
> > exists" without being observed.
>
> Observed in what sense?  Consciously, by a conscious being?  Or decoherred 
> into a quasi-classical state, as in QM?  "Reflexive" would seem to imply it's 
> observed by itself.

No, it's not meant to imply that it's 'observed' by itself: rather
just that it *is* itself, which is what I think you meant by
'existence simpliciter'.  Another term might be instantiation.  In
qualifying existence by the term 'reflexive', my point was just that,
when we originally entertain the idea of something 'existing' or not,
we temporarily *abstract* a more tentative sense of 'existence' from
any possible instantiation.  The abstraction is then 'non-reflexive':
it no longer refers to itself, but rather putatively to a referent
from which it has (or could have) been abstracted.  The danger is that
such abstraction may be the very act that seems to rob it of something
that is in fact the brute characteristic of instantiation.

The argument from 'the One' is that its (and derivatively, any)
self-awareness and consciousness derive ultimately from brute, or
reflexive, self-access, and hence can't be understood independent of
such instantiation.  The 'deletion' of these aspects in the
specification Torgny makes for the B-Universe can then be seen as
precisely characteristic of the abstracted sense of 'existence' - i.e.
the free-standing (i.e. non-reflexive) idea - but as making no sense
in the context of reflexive instantiation.

This doesn't in itself constitute any argument for materialism,
because the 'instantiation' could be in terms of any 'possible' world
from the plenitude of such, all of which, in this formulation, derive
from the One.  But my point is that, if a 'world' is arbitrarily
specified as not possessing the brute 'reflexive' characteristic of
instantiation, then this may just be because such a 'world' is in fact
merely the kind of abstraction that is - by this very token -
incapable of such instantiation, and hence not 'possible' either.

The term I used to attempt to convey the brute characteristic of
instantiation was 'reflexivity', in the sense of primitive
self-reference or self-access.  'Observation' by contrast has the
sense of a complex derivative of this brute characteristic in which
various emergent entities are placed in certain kinds of relation *to
each other*.  Russell's sense of 'reflexive' vis-a-vis observation may
indeed also be a useful one, but it's not in fact the point I was
making.

David

>
> Russell Standish wrote:
> > On Tue, Jul 10, 2007 at 04:28:51PM -0700, Brent Meeker wrote:
> >> I don't see that "relexive" adding anything here.  It's just "existence" 
> >> simpliciter isn't it?
> >>
> >
> > Brent, all that David is getting at is saying nothing "reflexively
> > exists" without being observed.
>
> Observed in what sense?  Consciously, by a conscious being?  Or decoherred 
> into a quasi-classical state, as in QM?  "Reflexive" would seem to imply it's 
> observed by itself.
>
> Brent Meeker
>
> >The tree falling unobserved in the
> > forest does not exist reflexively, but may exist in other senses of
> > the word. It seems quite a useful concept - I may have called it
> > anthropic existence elsewhere, but it doesn't seem to have an accepted
> > name.
> >
> > Cheers
> >
>
>
> >
>

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