On 11 Mar 2011, at 03:39, Stephen Paul King wrote:


From: Bruno Marchal
Sent: Thursday, March 10, 2011 12:48 PM
To: everything-list@googlegroups.com
Subject: Re: Movie cannot think
Dear Stephen,


On 10 Mar 2011, at 16:27, Stephen Paul King wrote:

-----Original Message-----
From: Bruno Marchal
Sent: Thursday, March 10, 2011 9:10 AM
To: everything-list@googlegroups.com
Subject: Re: Movie cannot think


On 10 Mar 2011, at 13:47, Andrew Soltau wrote:

> All the moments exist, and as Deutsch points out, as you summarise,
> 'The appearance of change is already explained by the fact that
> there are different frames that have an implicit sequence and in
> which the observers state is different', but for change to actually
> happen, the magic finger must move. Otherwise reality would be like
> a movie film sitting in the can in storage.


The change in the "working program" is brought by the "universal
machine" which interprets it. All you need is an initial universal
"machine". It happens that addition and multiplication, with first
order logic is enough to define such an initial universal system, and
the UDA+MGA shows that the laws of mind, including the laws of matter,
does not depend on the choice of the initial universal system.

So elementary arithmetic does emulate, in the mathematical sense,
computations. Arithmetic does not just describe all those
computations: it literally emulate them. This is not trivial to show,
although computer science gives the insight. Computations in
arithmetic are not like movie, they are like a observer line universe
in a block universe.

To add an external time reintroduces a mystery where it is not needed.
That use of time is like the use of "God" as gap explanation by the
pseudo-religious (authoritative) people. You will end up with a
primitive time, a primitive matter, and why not a primitive "god"
responsible for all this.

That is, in my opinion, the correct insight of Deutsch. Except that he
mentions an "implicit sequence", which is typically made explicit by
the universal machine which emulates, albeit statically or
arithmetically-realistically, the computation. All computations in
that setting are ultimately based on the explicit sequence 0, s(0),
s(s(0)), ... (or the equivalent in the combinators, etc.).

Bruno


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

**
Dear Bruno,

I only really have one difficulty with this thought: What choose that particular "initial universal 'machine'"?


[BM]
Addition+multiplication?  (RA, Robinson Arithmetic)

Because it is shown that it is enough to derive mind and matter from it.

Because it is shown that, if we accept the comp bet, it *has to* be enough. And adding anything more betrays the solution of the 1-3 person relations.

Because it is taught in high school, and with few exception accepted and used by everybody.

Because it can be shown to be necessary, in the sense that any weaker theory cannot derive it.

***
[SPK] But how does this address my question? I must have misunderstood you but the word “initial” appears three times in the following:

“The change in the "working program" is brought by the "universal
machine" which interprets it. All you need is an initial universal
"machine". It happens that addition and multiplication, with first
order logic is enough to define such an initial universal system, and
the UDA+MGA shows that the laws of mind, including the laws of matter,
does not depend on the choice of the initial universal system.”

Why does the word “initial” appear here, if there is no sense of a sequence of machine of which there is a least machine? So you are saying that the fact that a “weaker theory” cannot derive it determines its minimality in the sequence?

Words have to be interpreted in their context. here by initial universal machine I was just meaning that I need to postulate the existence of at least one universal system, or a theory having the sigma_1 completeness property. And elementary arithmetic is enough.




Why is it necessary to assume a form of the well founded axiom?

Because the phenomenology of non well foundedness is simple to derive.


It appears to me that you are otherwise there would not necessarily be a minimal machine!

Things like that can be true from some person perspective. So we don't have to assume it, because we can explain it with less assumption.


Even then we have no phenomenological interview of the so defined Löbian Machine to at least give us the appearance that we have found a derivation of mind and matter that can be analytically continued to any person’s experience of what it is like to have a mind in a physical world! I concede that within your argument there is something that seems to be like a mind in an abstract 3-p sense, but you have not shown how such a “mind” interacts with other similarly defined minds except in a reasoning that involves taking the plural case, but mere plurality is not sufficient for yield a general result for concurrency.
***
If it cannot be shown to be unique in contrast to all possible machines, what makes it special?
[BM]
I insist that any first order logical specification of a universal system will do. I have tried to introduce the combinators instead of numbers, but people were a bit uneasy with it, so I take the numbers, which are equivalent with respect to our goal.

What makes it special is Church thesis, in the comp motivation. The closure of the set of partial computable function for the diagonalization procedure.
**
[SPK] OK, but again, I have tried to explain that the Church thesis is not above suspicion as a back-door way of injecting the properties of physicality into your result in my discussion of the Maudlin paper. I even sketched how the Yes Doctor fully assumes physical properties in that there has to be a prior measure of persistence of state to define a substitution level, did you not see this?

I refuted this. And 'yes doctor' is not Church thesis. Indeed comp is 'yes doctor' + Church thesis. You might (re)study sane04.


I can easily be dismissed as lacking the sophisticated wording that you have acquired, but is that not just ab hominem? I do not wish to rubbish your argument or your result, I want to be sure that you understand that there seem to be holes in its logical reasoning, gaps which allow tacit assumptions and pre-analytic thoughts to slip into the reasoning such that it seems that one has obtained a model, but one that only obtains if we all ignore certain features and difficulties.
My goal is to make clear what those problems are, and to formulate them mathematically. This is made possible by the comp hypothesis.




**

We may be blinded by the sophistication and brilliance of our logics but can we really be sure that there is not a deeper level at which this Löbian machine is just another in a vast infinitude?


[BM]
RA is not Löbian. RA is the TOE. RA is equivalent with the UD, and it generates the histories which contains the much more complex Löbian machines. I interview the Löbian machine because they have the maximal introspective power possible.

RA is the TOE, the Löbian machine are the internal observer. They are much clever than RA. I think as clever as you and me.

Also, in science, we are NEVER sure. Comp might be false.

[SPK] RA is a belief that may not be justified. It cannot be considered to be a Theory of Everything if it excludes some aspect of existence that is necessary for its specification!

Assuming comp, RA is enough, almost by connstruction. You are just arguing implicitly against comp, and as far I know you might be right.



Is Robinson Arithmetic Gödel Complete for any expression that can be derived and coded by any number or is it only complete with in the class of statements that it can make?

It is sigma_1 complete, and thus Turing universal. But it is not Löbian, and thus cannot prove its own sigma_1 completeness. Both RA and PA are incomplete, like all theories capable of adding and multiplying.



It obviously is not complete in a non-Gödel sense since we need the Löbian Machine to examine RA so in a sense the Löbian machine is “outside” of RA.

No it is "in". You are doing the "Searle's error". RA emulates all Löbian machine. But RA don't have to believe (prove) what the ¨Lobian" machines talk about. You can imagine that RA is like the SWE. And PA is a physicist (supposed to obey the SWE).




How is this separation possible if RA is the minimal initial system? A minimal initial system would have to be RA + some extra structures and relations such that a Löbian machine can be specified co- existing with the RA,

No RA proves their existence and emulates their computations.



but even then this fails because we need the assumption of eternally existing (thus causeless) numbers or combinators or equivalent to act as a support for RA and the extra structure and relations.

You need to accept the truth of the elementary arithmetical axioms.



Please stop stating that “I interview the Löbian machine...” when you obviously do not. The word “interview” requires the assumption that you as an entity that appears to have a physical manifestation to many other 'observers’ is interacting somehow with an abstract entity that has no physical form. How can we distinguish this verbiage from that of the person that claims to “channel alien intelligences”? It is unseemly!

See my annexe in "conscience et mécanisme" where I provide theorem prover for the arithmetical hypostases. It is an interview, in the sense that you can build a machine, ask questions, get the answers, etc. But the interviex is done mathematically since Gödel's 1931.






    Consider G. Chiatin's Omega! 
http://en.wikipedia.org/wiki/Chaitin%27s_constant


OK.



I question the entire premise of a "special initial conditions"! Why must we believe that there really is a singularity that 'causes' it at all?


[BM]
What initial conditions?

I think you are confusing "initial condition" and the theory we might choose.

***
[SPK] I did not use the word “initial" first but I did try to reason that to state that
“It happens that addition and multiplication, with first
order logic is enough to define such an initial universal system, and
the UDA+MGA shows that the laws of mind, including the laws of matter,
does not depend on the choice of the initial universal system.”
implies something like special initial conditions because such a claim is equivalent to saying that the prior existence of RA

There is not really prior existence of RA, nor is there prior existence of QM. There is atemporal existence of numbers, in the snese that truth like "24 is not prime" are beyond time and space (Arithmetical realism). But then RA reappears as a special universal number *in* RA. (Introducing already a weak form of non well foundedness, BTW).



and first order logic is the uncaused cause of our common reality! How is this different in kind from the argument of ab initio condidit de nihilo in theologies??

Because I assume the elementary arithmetical truth to be independent of me, and of time. If you think that "24 is not prime" depends on something, you have to elaborate on that dependence, and to make clear what are your assumptions.



***

[BM]
I give a theory, quite simple and already known by everybody. And I provide its internal intensional epistemologies/theologies, in the most classical way (Aristotle's logic, Plato Tarski's semantic, George Boole's law of thought, Gödel, Löb, ... Solovay, or simpler George Boolos' laws of mind, Plotinus' theology... and Pythagorus' ontology).

Church Post Kleene Turing Markov thesis resurrects Pythagorus' ontology, with someone no one expected: the universal machine. That's a recurring creative bomb on this planet and it is a typical event in the modern (post Gödel) arithmetical Platonia as seen by its inhabitant.

In UDA i provide a formulation of the mind body problem in the comp frame, understandable by good willing humans. In AUDA i show we can already ask the question to the universal numbers, and get some answers, and some silence too.



Why must we recycle that old theological idea? Are there no viable alternatives?

Yes. Just say say "no" to the digital mechanist surgeon, and this for all levels. You are free to study those alternatives. G and G* will still apply on a large initial segment of the classical theory of self-reference, though.

I am a modest scientist (and this should be an oxymoron).
I mean that I have no clue of the truth.


Bruno

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

[SPK] I know you better than this Bruno! You are humble but still willing to bet that you are correct.

That is a private question which concerns only me and my doctor.



I admire that, I just want to see that your estimation of the odds are correct.
Even if comp is not correct, it remains intersting to compare the physics of the machine and the physics inferred by observations.

Bruno

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



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