On 30 Dec 2009, at 17:07, benjayk wrote:

>
>
> Bruno Marchal wrote:
>>
>>>
>>
>> They are. Numbers are primitive. The variable x and y represents
>> excusively those numbers. Finite pieces of computation are speical
>> numbers, like prime numbers. To be a (finite piece of a) computation
>> is a property of number, a relation which has to be defined in term  
>> of
>> addition and multiplication of numbers. To be a computation are
>> emergent property (emerging from addition and multiplication).
> Sorry, I just don't get it. Your theory necessarily presumes dreams  
> before
> numbers, because for you numbers appear just in your dreams.

Not at all. Comp presuppose some understanding of consciousness, but  
then, after the uda reasoning we can understand that for the ontology  
we need no mre than a theory like Robinson arithmetic. It does not  
presuppose dreams. Dreams will be defined in term of number relations  
(computations). I think you are confusing the level and the meta-level.
Maxwell electromagnetism does not presuppose consciousness. And this  
has nothing to do that Maxwell presuppose consciousness in his  
colleagues when reading his paper, but that is an assumption at some  
metalevel, not in the theory.





> Additionally,
> the notion of numbers relies on the notion of truth,

Not at all.



> which is a notion that
> fundamentally can't be defined, only known.

This is not correct. Pean Arithmetic can define a notion of truth for  
any formula with a determinate length. Tarski theorem just forbid a  
general notion of truth to be defined in the theory, for formula with  
an finite but not fixed in advance length.



> Without *experiencing* truth
> there is no sense to numbers.

I think you are confusing third person numbers, and the human first  
person experience of numbers.
Arithmetical realism is the explicit assumption that truth of the form  
"17 is a prime number" is not dependent of the existence of humans, or  
even of a physical universe.




> So there are numbers without there being
> "dreaming"/experiencing first.

I guess you meant "so there are no numbers ...".
But this is not the theory I propose. I take Arithmetic as starting  
point. Dreaming/experiencing will be a property of numbers.
It is really NUMBER => CONSCIOUSNESS => MATTER (=> HUMAN CONSCIOUSNESS  
=> HUMAN NUMBER)



>
> It seems to me that you call that "primitive", which relies already  
> on the
> truths ("there are dreams/experiences") of which it gives emergence  
> to. Do
> you see my problem with that?

Not really. And it seems that your remark could apply to any theory.  
We have to agree on some starting point. The starting point I use is  
already used by almost all theories of nature and human. You are  
confusing, I think, a statement like 2+3 = 5, and "I understand that  
2+3 = 5". Those are very different.



>
>
>
> Bruno Marchal wrote:
>>
>>> But since you don't only assume mechanism, but
>>> also conciousness (like all theories)
>>
>> Digitam mechanism (comp) assumes consciousness explicitly (cf the
>> sense of the "yes doctor"). Most theories does not assume
>> "consciousness". The word does not appear in the description of the
>> theories.
> I don't think it's necessary to write that you assume conciousness.  
> All
> theories assume truth and still no one makes this implicit.

By assumption, I mean the assumption present, concretely, in the  
theory. Not the meta-assumption needed to understand that humans can  
understand the theory.




> Because it is
> obivous; you simply can't deny there is truth or that you're  
> conscious.

Right.




> Well,
> actually you can deny it, but then it is clear for me that your use  
> of the
> words "conciousness" or "truth" doesn't point to what I mean.

Sure. And for "mechanism", I assume that consciousness is invariant  
for some functional substitution. So I have to mention "consciousness"  
rather explicitly. That is normal: digital mechanism is a theory of  
consciousness, before being a theory of matter.



>
>
> Bruno Marchal wrote:
>>
>>> and consensual reality (the dreams in
>>> which the representations of numbers appear), I don't see how it
>>> makes sense
>>> to put numbers "before" conciousness and (perceived) reality.
>>
>> Well, it is a bit like "addition" comes before "being prime". You  
>> need
>> addition in Robinson arithmetic to define what a prime number is.  
>> Then
>> you need addition, and prime, before defining when a number represent
>> a finite piece of computation. And you need that to eventually attach
>> consciousness to computations. The "before" is logical, not temporal.
> I need someone making sense of "addition in Robinson arithmetic"  
> before I
> (logically) can refer to addition in Robinson arithmetic (or if you  
> want it
> this way "I need the sense itself in 'addition in Robinson arithmetic'
> before I can refer to addition in Robinson arithmetic").
> It makes sense for me to say that we need numbers in order to link
> conciousness to numbers, but that is already obvious. But you need
> conciousness (the mysterious "senser" or "sensing") in order to make  
> sense
> of anything, including numbers.

Not in the theory. This would lead to an infinite regress. Just open  
any book of math, you will not see any assumption on consciousness.  
The assumption will be "0 is a number". If x is a number then s(x) is  
a number", if s(x) = s(y) then x = y", 0 ≠ s(x), etc.
Addition is defined by x + 0 = x and x + s(y) = s(x+y).

This makes it possible to a machine to prove elementary addition to be  
correct. If we assume consciousness at that level, then we will not  
explain consciousness.



> Numbers just come before any *notion* of conciousness that is  
> reflected in
> the numbers, but they can't come before conciousness itself.

They can't come, in any sense. A number does not come. A number is  
even or odd, or little than an other number, etc.
I use the number like a physicist or any scientist. You will not  
criticize Einstein's relativity, because he use numbers without  
mentioning consciousness. There is no reason to do this here.


>
>
> Bruno Marchal wrote:
>>
>>>> But this is just insulting the machines, and nothing else.
>>> My point is not to insult machines. A machine is identified by what
>>> it does,
>>> because feelings can not be uniquely linked with a machine.
>>
>> Why? We can, for all practical purpose, attach a mind to a machine.
>> What we cannot do is to attach a machine to a mind, but "only" an
>> infinity of machine to a mind.
> How can we attach a mind to a machine? If you have the description  
> of a
> machine, you know what it feels? You are a machine lover indeed ;).


If I have a  description of the machine, I still cannot *known* if it  
feels. But if the 3-description of the machine and its behavior, is  
enough similar to me, then I can believe, or guess, that it feelms  
something relatrively similar to me. This is what I do with *you*  
right now. Progress in neurophysiology could help to make me better  
guesses, but attributing consciousness to an other is always a sort of  
guess.



>
>
> Bruno Marchal wrote:
>>
>>> Conciousness is already attached to an
>>> infinity of machines and from our perspective we are at least
>>> conciousness;
>>> that which is always sure here and now. So every observer, just by
>>> virtue of
>>> observing *anything*, already feels the truth about an infinity of
>>> machines.
>>> But *are* we machines then? If we always are or "could be"
>>> infinitely many
>>> machines, if we always feel some truth about *every machine*, it is
>>> not a
>>> bit of an understatement to say we are a machine or even machines?
>>
>> You are right, and that is why sometimes I sum up the reversal by
>> saying that
>> 3-we being a 3-machine entails that the 1-we are not machine.
>> There is a sense to say that first person, from the first person  
>> view,
>> are not machine. This is already true for the third (and seventh and
>> eigth) hypostases. the machine already tell us that they are not
>> machine, from their point of view. But G*, the "theologian of the
>> machine" knows that 1-we = 3-we. The machine cannot know that.
> This is not clear for me. "3-we being a 3-machine entails that the 1- 
> we are
> not machine.", but "1-we = 3-we"...? How could this possibly be?

Yes, that is subtle. This is alas clear only at the AUDA level. We  
have that G* proves (1-we = 3-we), but G does not prove it. It means  
that the statement "(1-we = 3-we)" is true but not provable (like self- 
consistency). All those true but non provable statement belongs to the  
corona G* \  G. It is true (for the machine) but unprovable (by the  
machine). It is the sort of sentences that Gödel, Löb etc. have  
discovered.
My feeling is that you lack a bit of mathematical logic, which makes  
you confuse level of theories, and which makes you lack the important  
distinction between syntactical truth and semantical truth.  
Mathematical logic has such distinction as main subject matter,  
including results linking the two notions.



> It seems to
> be possible only if it is wrong that 3-we is a machine, but assuming  
> it
> leads to the right conclusion it is not a machine. But this would  
> mean COMP
> is self-refuting.

Not really. G does not prove 1 = 3. This does NOT mean that G proves  
NOT(1 = 3). You are confusing, I think: G does not prove p, with G  
proves NOT p.     (~Bp is not equivalent with B~p)

I really suggest to you to buy the book by Mendelson on logic. It  
would provide you a big help.

Bruno

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



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