Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>>> Bruno Marchal wrote:
>>>>> Then computer science provides a theory of consciousness, and
>>>>> explains how
>>>>> consciousness emerges from numbers,
>>>> How can consciousness be shown to emerge from numbers when it is
>>>> already
>>>> assumed at the start?
>>> In science we assume at some meta-level what we try to explain at  
>>> some
>>> level. We have to assume the existence of the moon to try theories
>>> about its origin.
>> That's true, but I think this is a different case. The moon seems to  
>> have a
>> past, so it makes sense to say it emerged from its constituent  
>> parts. In the
>> past, it was already there as a possibility.
> OK, I should say that it emerges arithmetically. I thought you did  
> already understand that time is not primitive at all. More on this  
> below.
Yeah, the problem is that "consciousness emerging from arithmetics" means
just that we manage to point to its existence within the theory. We have no
reason to suppose this expresses something more fundamental, that is, that
consciousness literally emerges from arithmetics. Honestly, I don't even
know how to interpret this literally.

Bruno Marchal wrote:
>> But consciousness as such has no past, so what would it mean that it  
>> emerges
>> from numbers? Emerging is something taking place within time.  
>> Otherwise we
>> are just saying we can deduce it from a theory, but this in and of  
>> itself
>> doesn't mean that what is derived is prior to what it is derived from.
>> To the contrary, what we call numbers just emerges after  
>> consciousness has
>> been there for quite a while. You might argue that they were there  
>> before,
>> but I don't see any evidence for it. What the numbers describe was  
>> there
>> before, this is certainly true (or you could say there were implicitly
>> there).
> OK. That would be a real disagreement. I just assume that the  
> arithmetical relations are true independently of anything. For example  
> I consider the truth of Goldbach conjecture as already settled in  
> Platonia. Either it is true that all even number bigger than 2 are the  
> sum of two primes, or that this is not true, and this independently on  
> any consideration on time, spaces, humans, etc.
> Humans can easily verify this for little even numbers: 4 = 2+2, 6 =  
> 3+3, 8 = 3+5, etc. But we don't have found a proof of this, despite  
> many people have searched for it.
> I can see that the expression of such a statement needs humans or some  
> thinking entity, but I don't see how the fact itself would depend on  
> anything (but the definitions).
My point is subtle, I wouldn't necessarily completly disagree with what you
said. The problem is that in some sense everything is already there in some
form, so in this sense 1+1=2 and 2+2=4 is independently, primarily true, but
so is everything else. Consciousness is required for any meaning to exist,
and ultimately is equivalent to it (IMO), so we derive from the meaning in
numbers that meaning exist. It's true, but ultimately trivial.

Either everything is independently true, which doesn't really seem to be the
case, or things are generally interdependent. 1+1=2 is just true because
2+2=4 and I can just be conscious because 1+1=2, but 1+1=2 is just true
because I am conscious, and 1+1=2 is true because my mouse pad is blue,

This view makes sense to me, because it is so simple. One particular
statement true statement is true, only because every particular statement
true statement is true, and because what is true is true. In this sense
every statement is true because of every other statement. If we derive
something, we just explain how we become aware of the truth (of a
statement). There is no objective hierarchy of emergence (but apparently
necessarily a subjective progression, we will first understand some things
and later some other things).
That's why it makes little sense to me to say consciousness as such arises
out of numbers. Subjectively we first need consciousness to make sense of
numbers. But certainly understanding of numbers can lead us to become more

Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>> Yet, consciousness is not assumed as
>>> something primitive in the TOE itself.
>> But this doesn't really matter, as we already assume that it's  
>> primitive,
>> because we use it before we can even formulate anything.
> We already assumed it exists, sure. But why would that imply that it  
> exists primitively? It exist fundamentally: in the sense that once you  
> have all the true arithmetical relation, consciousness exists. So,  
> consciousness is not something which appears or emerges in time or  
> space, but it is not primitive in the sense that its existence is a  
> logical consequence of arithmetical truth (provably so when we assume  
> comp and accept some definition).
> Sometimes I sketch this in the following manner. The arrows are logico- 
> arithmetical deduction:
I accept this deduction. But just because it can deduced does not mean it is
more primary. To me there is no reason to suspect that consciousness does
not exist primitively.

Bruno Marchal wrote:
>> You can't just
>> ignore what you already know, by not making your assumptions  
>> explicit in
>> your theory.
> It is just not an assumption in the theory, but a derived existence.  
> With comp, consciousness is implicit in the arithmetical truth.
Maybe, but it seems arithmetical truth is implicit in consciousness also.

Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>>> In theory, even one symbol can represent every statement in any
>>>> language,
>>> That does not make sense for me. (or it is trivia).
>> Yes, it is trivial. We just encode statements with numbers expressed  
>> with
>> one symbol (eg + is I, 1 is II,...).
> How will you encode with one symbol the statement 1+1=2? I think you  
> will need two symbols, unless you fix a bijection between a language  
> and the natural numbers.
Right, this is what I mean.

Bruno Marchal wrote:
>  But you will need a richer language to  
> describe that bijection.
But as you said below, the same it true for expressing points with natural
numbers. It makes only sense if we encode the points in the numbers and have
an external decoding mechanism.

Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>>> but still it's not as powerful as the language it represents.
>>>> Similarily if you use just natural numbers as a TOE, you won't be
>>>> able to
>>>> directly express important concepts like dimensionality.
>>> Why? If you prove this, I abandon comp immediately.
>> Hm, how do you express the point (3,4) on a two-dimensional plane with
>> natural numbers?
> I might use a Gödel-like coding for the string "(s(s(s(0))),  
> s(s(s(s(0)))))", like coding "(" by 2, "s" by 3, "0" by 4 and ")" by  
> 5, and then the string itself, using the prime numbers, by 2^2 * 3^3 *  
> 5^2 * 7^3 * etc. That is each prime number exponent the code of the  
> particular symbol. Or something like that, where I can code an  
> axiomatic of the plane by a number too, etc.
But then you faild to directly express the concept! You just represented it
in a less rich language.

Bruno Marchal wrote:
>> It seems we have to interpret the numbers in a certain way
>> to do this, and can't express it directly. If we used gaussian  
>> integers we
>> could simply describe the point as 3+4i.
> That's OK, but 3+4i can itself be coded, by 2^(code of 3)*3^(code of  
> +)*5^(code of 4) *7^(code of i).
But that's the point! It can be *coded*. But everything can be coded with
the symbol "I" as well. In both cases we need some intelligent decoding to
retrieve the meaning. 

Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>> From comp you can
>>> derive the whole of physics, and this should be easy to understand if
>>> you get the UDA1-7.
>> Well, I get that if we accept COMP we need to associate sheafs of
>> computations to mind-states, but I have no clue how natural numbers  
>> can be
>> used to derive physics, or even formulate anything related to physics,
>> without using a meta-level of interpretation. It seems we always  
>> need a more
>> powerful language to do that.
> So physics becomes a first person uncertainty calculus associating to  
> each computational state a collection of computations, hopefully with  
> a reasonable measure (which has to be derived by the self-reference  
> logic.
> The meta-level of comprehension can be embedded in the arithmetical  
> truth, in the same way that Gödel discovered that metamathematics can  
> be embedded in (and retrieved from) arithmetic.
It all comes down to the same thing, that we encode statements in
arithmetic. But for this to make sense we need some external thing to make
sense of the encoded statements.

Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>> Comp remains incomplete on God, consciousness and
>>> souls, and can explain why, but physics, including dimensionality is
>>> entirely explained. To be sure comp is still "hesitating" between
>>> dimension 2 and dimension 24 for the shadow of the notion of space,
>>> but this is a very complex mathematical problem, and it assumes that
>>> the Z1* logic (the "divine" third person plural points of view) give
>>> rise to some mathematical structure (Temperley-Lieb algebra, braid
>>> groups).
>> But how can you formulate dimension 2 / 24 or Z1* logic in arithmetic?
> Z1* is the logic of Bp & Dt & p; the p are arithmetic proposition and  
> the B and D are the Beweisbar arithmetical predicate and its dual (D =  
> ~B~). The Gödel-like arithmetization does the remaining work.
But then the result of the arithmetization makes no sense by itself, doesn't
it? So natural numbers are not sufficient after all? It seems to me we have
to know how the arithmetization worked, and what it arithmetized to make
sense out of it.

Bruno Marchal wrote:
> Remember that: I do assume comp, and whatever is your conception of  
> space and dimension, this is already represented in your brain through  
> neuronal relations (say), and those neuronal relations are themselves  
> represented, even emulated, in arithmetic.
So, they are represented? But you can represent anything with anything. This
is just trivial. I can just say that this letter "A" represents the axioms
of peano arithemtic, and that's my TOE. Of course, arithmetic representation
is much more clever and expressive, but that's beside the point.

Bruno Marchal wrote:
>> I
>> mean, you don't have to explain it precisely, but can you give a  
>> hint how
>> this could even be conceived to be possible?
> I hope that what I say above helps a bit. Let me try again.
> We assume comp. So you can imagine that all the "reality" we observe  
> is secondary: we might be dreaming, or, sharing "a video game", or  
> being in a matrix (a giant computer handling the whole game and the  
> software of our minds), OK?

Bruno Marchal wrote:
> Now, and that is not obvious, but is rather well known by logicians,  
> is that such a matrix is emulated by the arithmetical consequences of  
> the laws of addition and multiplication. The step 8 of UDA explains  
> that, assuming we are physical computers, we cannot distinguish a  
> physical computer from its infinitely many arithmetical emulations,  
> and that in fine, by taking into account the first person  
> indeterminacy, whatever we can observe below our substitution level  
> results from a sort of competition among *all* universal machine/ 
> numbers. That set of numbers is not a computable set, and only God  
> knows the winner. Yet, machines can backtrack from observation and  
> introspection to get better and better picture.

Bruno Marchal wrote:
> I am not proposing an explanation of "reality", on the contrary, I  
> show that a very common hypothesis, mechanism (made clear through  
> Church thesis and computer science) makes the mind body problem two  
> times more difficult than it is usually understood.
> It makes the physical laws more mysterious, it leads to a purely  
> arithmetical body problem.
> And at first sight, it does look like a refutation of comp, because if  
> we just look at the computations, we can expect an inflation of  
> possibilities (the white rabbit problem). It looks like even if we  
> were in one winning computation, perhaps physical, we are immediately  
> at first send in a solipsistic mental space, and then get dissolve in  
> white noise. And that, admittedly is not confirmed by the experiments  
> nor experience, except with salvia perhaps :).
OK.... Well everything you said was natural language, not numbers, so in
some sense you unfortunately missed my point (even though it was
interesting) :). It seems to me it is impossible to formulate this in
arithmetic without postulating some more powerful language first, and then
represent it in arithmetic. But in this case arithmetic is hardly
fundamental anymore.
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