On 12 Dec 2009, at 19:11, benjayk wrote:

> Bruno Marchal wrote:
>> On 10 Dec 2009, at 03:23, benjayk wrote:
>>> For me numbers don't make independent sense of the appearance (!) of
>>> matter,
>>> too. Since I cannot conceive of any meaning of the number 2 without
>>> reffering to some "real" (in the sense of every day usage) object.
>> Then all physical theories are circular, and explains nothing. All
>> theories in physics presuppose arithmetical truth (and even  
>> analytical
>> truth, but this is just to simplify the derivations).
> Well every theory is circular in that there are always axiom(s) that  
> are
> presumed to be true (and meaningful), and in that the theory is just  
> correct
> if the reasoning is correct, which can never be proven.
> Basically it just comes down to whether you like or accept the  
> reasoning and
> the axioms.
> Theories and science are just a tool.

I agree. And then computer science, thanks to Kleene and others,  
managed very well the circularity.

> You may feel that some "too circular" theories don't explain  
> anything, but
> you can only say they don't explain anything to you.

I was using using "circular" in its sense of "viciously circular".

> Honestly I think you are a bit dishonest to yourself here, since you  
> already
> presume the appearance of matter,

I assume nowhere primitive matter. I do assume "consensual reality".  
If not, I would not post message on a list.

> unless you can make theories about numbers
> without perceiving anything, which I doubt.

Humans cannot do that, but this is independent which are simùpler  
concept. All scientists agrees on numbers, and to day we can explain  
in a precise sense why numbers is the least we have to assume.

> When you do abstract math you
> nevertheless work with matter, that is, word written on paper or on a
> computer screen. So either you can indeed make sense of a circular  
> theory

Indeed. That is the case. Circularity is fundamental. I will soon  
explain this through the second recursion theorem of Kleene. The whole  
AUDA things is based almost exclusively based on that handling of  
circularity, which makes the self-reference possible, for machine, and  
relatively to universal machine(s).

> or
> you have to agree that no theory explains anything (or you manage to
> manipulate numbers without having the experience of perceiving  
> matter). Or I
> missed your point.

Explaining consists in reducing what I understand badly into what I  
have a better understanding.

Also, my point in not a new theory, a new theorem. If we are machine,  
then matter becomes a complete mystery which has to be explained from  
the numbers (UDA). The theorem is in the "has to". Then it happens to  
the derivation has been partially done (AUDA).

> Bruno Marchal wrote:
>> Of course, the human conception of the numbers depends on the human
>> conception of his neighborhood and life, but when searching a TOE we
>> have to agree on the simplest objects (ontology) from which we derive
>> the others (phenomenology).
> For me this is not meaningful. What kind of phenomology could be  
> derived
> from the "fundamental" numbers?

You may read Plotinus, for having an informal idea. The  
phenomenologies corresponds to the hypostases, + intelligible and  
sensible matter.
from the numbers (+ comp) we can explain the non communicability of  
consciousness, its local undoubtability, how "primitive matter"  
emerges and leads to first plural quantum-like indeterminacies, etc.

> Basically just that they need to be
> phenomena and that they are not expressible in terms of something  
> else. But
> this for me has little to do with what the phenomena *are*.

I don't understand this.

> It's like a
> theory saying: "There is something, but don't aks me what it is."

You should study the theory, and makes specific remark. The theory  
explains what exists, and how the rest emerges from it. All this in a  
way which is sufficiently detailed as to be tested experimentally.

Strictly speaking it is not my theory, it is the universal machines'  

It is a theology because it makes clear the part of the phenomenology  
which is sharable, and the part which is unsharable, except by  
projections, betting, hoping, fearing, praying, etc.

The trick is that a Löbian machine can study the theology of the  
correct machine without knowing if itself is correct, and so without  
knowing if the theology (toy theology if you want) apply to iself.

> And I don't see what's especially simple about numbers. For me they  
> are more
> complex than many everyday
> objects, because they rely on dualistic notions like classical logic  
> and an
> absolute inequality of something (1 is absolutely not 2).

It requires the ability of distinguishing two things, indeed, and the  
ability to repeat action, like taking the successor. Empirically, this  
is grasped by children, and elementary arithmetic is virtually a  
subtheory of all scientific theories, and explictly so for theories  
which happens to be Turing universal.

> Indeed the theory of natural numbers may be the simplest formal  
> system, but
> I am reluctant to see formal systems as "real" objects.

You are confusing arithmetical truth (a non effective concept) with a  
formal theory of elementary arithmetic.
After Gödel, we know that our theories, be it PA or ZF, only scratch  
the surface of Arithmetical truth.

> Bruno Marchal wrote:
>>> So numbers don't give rise to arithmetical truth,
>> You need addition, multiplication and classical logic.
> But this only works because you presume it leads to some kind of truth

Yes. Truth like "2 + 2 = 4", "17 is a prime number", "the machine x  
relatively to the universal machine z output r", etc.

> and
> that addition and multiplication are meaningful (you presume classical
> logic).
> So if anything numbers give rise to an expression of truth in terms  
> of your
> systematization of it. Not too suprising.
> This only works if you like numbers especially much and they help you
> understand truth.

Any first order specification of a universal system/language/machine  
can be used in the place of elementary arithmetic. I use elementary  
arithmetic because it is taught in elementary schools, and no one have  
any serious definition problems with them. It belongs also to the  
common part of the intuitionists and the classical logicians.

> One could as well deny that addition is meaningful without
> context (eg because two rainddrops melt into one: 1+1=1)...

This is another subject. By numbers we mean the natural numbers (or  
integers, real numbers, according to the context, but we make this  
precise at times). In the comp context, can replace number by "java  
program", or "fortran program", or "combinators". It is possible (even  
highly plausible) that some universal systems "reappear locally" more  
often than others. Numbers seems to be both simplest, and to have rich  
extensional properties. No doubt that I like them. But as logicians  
interested in what is a computation, combinators are more useful.

> Bruno Marchal wrote:
>>> but truth gives rise to
>>> (expresses as) numbers.
>> Which truth. What do you mean by 'truth' here?
> I don't know (well I do know in some ways, but expressing them  
> adequatly
> would probably be impossible). What is arithmetical truth? According  
> to
> tarski you can't tell me, either.


Tarski theorem does not make sense without logic and elementary  
arithmetic. So this is part of your theory too?

But then Tarski theorem just shows this. No theory or machine can  
express its truth predicate. But a theory like ZF can easily express  
the truth predicate (indeed the whole theology) of a smaller machine  
(smaller in term of provability ability) like PA.

Arithmetical truth is the simplest notion of truth in the whole field  
of mathematical logic.

> Bruno Marchal wrote:
>>> Maybe "what really exists" is not a meaningful thing to ask in first
>>> place,
>>> because if something "really" exists, it certainly cannot be
>>> expressed with
>>> words.
>> Why? This is like asserting there is no TOE, before searching.
> I cannot search a theory of everything, because it is a meaningless  
> notion
> for me.

I can understand. Already the set of all sets cannot be a set, and to  
"understand everything" makes no sense, but then an hypothesis like  
"we are machine" appears to explain in a more precise sense than usual  
why indeed the search of a t"theory of everything" leads to  
interesting, partially sharable, experience. Universal machine do have  
interesting relation with many non effective (non machine entities),  
including truth indeed.
Personally,  by TOE I mean a theory which unifies all the forces of  
nature, if that exists, with an explanation of the subjective data (No  
elimination of consciousness). And my point is a logician's point: "if  
you belief in mechanism and are a bot rational (or self-honest) , then  
you will belief that physics is a branch of computer science/number  

> Searching it for me feels like searching something that is not there  
> (it
> feels *bad*).

You are right, in the sense that we already know there is no complete  
theory of what universal machines, or numbers, can do and not do.
But that is the reason to become aware that about numbers and machine,  
we know nothing, and the hypothesis that we are machine, makes physics  
a concrete sum on all computations and this has observable consequences.

We are just trying to understand what happens. don't confuse the  
search of a theory of everything, with any normative or authoritative  

If you don't search for a theory of everything, you will adopt the  
current one. A brain is already a (failed) attempt toward a theory of  
everything. Searching *that* is what universal machines do. There is  
no problem with admitting that the word "everything" can have an  
evolving meaning in most terrestrial or effective context.

> Though in another way I think we already have a theory of everything a
> theory can explain *ultimately* (which is *not even remotely* close to
> everything, since the more you trascend a theory the "bigger" the
> possibilities get):
> The theory is that all theories are either contradictory or  
> incomplete (we
> have to go beyond theories to access truth). I think Gödel already  
> made the
> quest for the "complete" theory meaningless.

Gödel showed that all theories on *numbers* are contradictory of  
And it is a direct consequence of Church thesis. Once you grasp the  
concept of universal number or machine, you understand that truth,  
even on just machines and numbers, is not completely axiomatisable.

But that is a reason to be humble  in front of arithmetical truth. Not  
a reason to dismiss it. It kicks back a lot.

Also, if you mention Gödel, it means you accept elementary arithmetic.  
My logical point is that if you believe you (can) surivive with a  
digital *body*, then elementary arithmetic has to be enough. WE have  
too extract the SWE, and other appearances from that. It is a point in  
(applied) logic, if you want.

> Bruno Marchal wrote:
>> But
>> elementary arithmetics does explain both consciousness, including its
>> non definability
> That's funny, because this is little more than empty words for me.

Read the papers. Or ask questions.

> If your
> theory explains something, it needs an definition of it, or it only  
> explains
> that it doesn't explain that which it doesn't defines, except *that*.


> Bruno Marchal wrote:
>> , and matter, including both its computational and non
>> computational aspects.
> For me matter is explained by the fact that it is touchable,  
> seeable, and so
> forth. Elementary arithmetics cannot do that. So no, it doesn't  
> explain
> matter for me.

Hmm... Not yet read UDA I see.

> Maybe it does explain that you cannot reduce experience of matter  
> and maybe
> it can explain measurable features about it; I don't know. But it  
> certainly
> doesn't explain the (for me) fundamental thing about matter, namely  
> that it
> feels how it feels to interact with it.

This is more the problem of consciousness than matter. The expert in  
matter (physicists) are known to put the "feeling" aspect under the  
rug. The rationalist put it under the rug of mechanism, and then I  
explain why this does not work.

> Bruno Marchal wrote:
>> If you have a better explanation, I can listen, but why not study the
>> existing explanation?
> My "explanation" is that every explanation in words is suboptimal/ 
> incomplete
> and you need to trascend words in order to get a better explanation.

But this is a "theorem" in "my theory/conjecture/hypothesis" (that we  
are machine). On the five hypostases, three of them are duplicated  
into the prouvable/non prouvable but true parts, and two of them  
separates the expressible from the non expressible.
This is AUDA, and is part of mathematical logic and computer science.

> You
> could say as well: The best explanation of anything is to experience  
> (and if
> you want to, try to understand it or to explain it in terms of another
> experience), not to reduce the experience to anything else.

reducing = explaining in terms of another experience (always, in my  

> Another try: The only ultimate explanation for everything is that  
> everything
> is the ultimate explanation. Or that there is no divorce between  
> explanation
> for reality/everything and reality itself - they are the same! After  
> all,
> *what could* explain everything, except itself :D? It's  
> acknowledging that
> circularity is valid, though not useful in all expressions and  
> contexts.

That's cute, but we are trying to do a bit of science here. And I  
don't like your religion which seems to imply our quest is vain, right  
at the start; which is ridiculous compared to what we a have already  

You are a bit dogmatic. Humans cannot fly, so all attempts to do so is  
necessarily ridiculous.

> Bruno Marchal wrote:
>>> So why aks a question that can't be answered with words at all?
>> It is up to you to show the question cannot answered at all, and for
>> this you need a theory.
> No I don't. You already see in front of you that the answer to any  
> ultimate
> question (ultimate *for you*) is not to be found in words (since  
> words only
> appear *in* your experience, which I take as meaning that experience  
> is more
> ultimate than words) so any theory is superfluous in that matter.

I have no clue what you are saying, and what you mean by explaining  
through words. The nice point with the computational hypothesis is  
that itv explains exactly that, why, if we are machine, we are  
confronted to the non expressible, the non provable, the non  
computable, necessarily. I explain why universal machine get both  
mystical and rational at the same time.

> Bruno Marchal wrote:
>>> Probably we generally should take words less serious (especially  
>>> with
>>> regards to fundamental questions) and expect no satisfying answers
>>> from
>>> them.
>> This is giving up research. Of course, you can always do that.
> It is very unfortunate that you think you can only research in terms  
> of
> words.

Not only I don't believe that. I pretend it is the contrary already  
for the machines.
And my craving for consciousness has made me studying all the possible  
consciousness state we can get through medication, sleep and drugs,  
which provides perspective on consciousness, but most of the time of  
the "beyond words" type. Note that consciousness itself, although not  
doubtable, is already "beyond word". I just bet you know what I mean  
(that is , that you are not a zombie).

> Personally I think research always starts in experience and words  
> are for
> conveying some part of what you experienced to someone else.

Sure. The theory I study, and the methodology I am using, is based on  
some acknowledgment on that fact.

Do you think it is possible that we are machine, (that we can survive  
with an artificial brain) and if so, have you understand that it  
entails a reversal between physics and number theory (or combinator, C+ 
+; whatever).

You may, just for he fun, try to find an error. It is a deductive  
thought experience (a proof in applied logic).

> But since we
> don't know what our words exactly mean to someone else we better  
> don't take
> them too serious.

In science we have to take our ideas (words) seriously, and make them  
the most precise as possible. Only then are we able to discover the  
inconsistency of our ideas, and progress.

You can also be happy in the contemplation, and each one has some  
favorite path. In my job, and on this list I have chosen the  
"scientific" path, by which I mean clear hypotheses, clear  
consequences, clear testing, and things like that.

The subject matter is difficult and interdisciplinary. And apparently  
we may be wrong on the most fundamental theory of everything  
"theology" since 1500 years. So, no doubt all this asks for work.

To defend the idea that we cannot proceed with the scientific attitude  
in theology or TOE researchs, consists to abandon theology to those  
who does not apply the scientific attitude (the non rationalist).

(I define theology as the quest for truth, like Plato. Then science,  
in the comp frame, can be shown to be the main tool of theology).

> Bruno Marchal wrote:
>> Nevertheless, to invoke a vague theory or philosophy to dismiss
>> automatically the theories bring by others will not help to progress.
> I disagree. An openly vague theory at least doesn't claim to be  
> precise,
> which I think is better than a vague theory that claims to be precise.

Sure. But we are talking on a precise theory/hypothesis here. Digital  

> And
> on fundamental matters, all theories are vague for us, otherwise we  
> would be
> able to comprehend everything at once -


> I have yet to meet a person who
> understands everything. COMP is very vague for me, because in order  
> for it
> to be clear, you would need to understand what numbers are. But this  
> is
> probably impossible, since they are already infinitely complex.

But it is simple to agree on their elementary properties.
That is how physicists succeed in building their theories, they does  
not tergiversate on elementary arithmetical truth.
Then numbers theorists and computer scientist, for different but  
related reasons, shows that numbers can have very complex behavior,  
but that is a quality for explaining new things.

> I think your way of thinking (in this paragraph, not neccesarily in  
> general
> ;-)) is somewhat dangerous, because it leads to pseuodo-precision and
> pseudo-control.

I would have prefered: partial precision and partial control. "Pseudo"  
seems only insulting.
The partialness is guarantied for infinity! It is the key vaccine  
against authoritative arguments.

> From wanting to be clearer than you can (or others can
> understand), dangerous things like authorative religion and states  
> (in the
> form of various repressive systems / ...cracys like democracy) emerge.

Well democracy, imo, is the less repressive systems, although  
obviously democracies are not immune against many form of "humans  
taste of authoritative argument weakness" in many democratic sub- 
institution (Democracies can be rotten, like the human body can have  
I think you have not read well my posts or papers, because I show that  
computationalism prevents the authoritative argument everywhere in  
science, and this including theology (and that is new, since at least  
1500 years).

> I am *not* against making clear theories. I'm against acting like  
> having a
> clear theory, when actually the theory makes nothing clear for most  
> people.

What is unclear? Don't confuse the reasoning, which is long and rather  
very new for some Aristotelian, and the theory, which is the clearest  
of all theories (and actually believed by most rationalist,  
unfortunately in company of a less clearer theory (materialism).

But if you really think that comp is unclear, just ask precision. It  
is the usual manner to proceed.

> And all theories regarding fundamental things make very little  
> clear, which
> shows itself in the theory making no realistically testable  
> predictions and
> in having no practical application (like string theory).

Comp, including the Theaetetus's definition,  makes utterly clear  
experimental predictions. The case of "String theory" is another topic.

It seems to me you have not yet understood the argument, nor seem  
really interested in doing so. Try to be more cautious in the  
expressions when you talk about something you have (clearly) not  

Bruno Marchal



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