Bruno Marchal wrote:
> On 08 Oct 2011, at 13:14, benjayk wrote:
>> Bruno Marchal wrote:
>>> On 04 Oct 2011, at 21:59, benjayk wrote:
>>>> Bruno Marchal wrote:
>>>>> On 03 Oct 2011, at 21:00, benjayk wrote:
>>>>> I don't see why.
>>>>> Concrete objects can be helpful to grasp elementary ideas about
>>>>> numbers for *some* people, but they might be embarrassing for  
>>>>> others.
>>>> Well, we don't need concrete *physical* objects, necessarily, but
>>>> concrete
>>>> "mental" objects, for example measurement. What do numbers mean
>>>> without any
>>>> concrete object, or measurement? What does 1+1=2 mean if there
>>>> nothing to
>>>> measure or count about the object in question?
>>> It means that when you add the successor of zero with itself you get
>>> the successor of one, or the successor of the successor of zero.
>> But that does this *mean*? These are just a bunch of words. You  
>> could as
>> well write
>> "It means that when you colmüd the pööl of ämpod with itself you  
>> get
>> the pööl of trübda, or the pööl of the pööl of ämpod.".
> Exactly! That is the point of axiomatization.
> Hilbert said this to explain what his axiomatic geometry means: "you  
> can replace the terms 'points', 'lines', and 'planes', by  the term  
> 'elephant', 'table' and 'glass of bear'.
> Now, doing this would not be pedagogical, and we use the most commonly  
> used symbols. That is "+" for colmüd, "s" for pööl, and the symbol  
> "0" for your ämpod. We already have some axioms for logic and  
> equality, and all you need consists in agreeing or not with the  
> following principles:
> 0 ≠ s(x)
> s(x) = s(y) -> x = y
> x+0 = x
> x+s(y) = s(x+y)
> x*0=0
> x*s(y)=(x*y)+x
> The intended meaning being 0 is not a successor of any number, etc.  
> You can say "the ämpod is different from all pööls". No problem, but  
> it is obviously quite unpedagogical, I think.
You don't get the point. Of course I can agree with these principles
concerning countable and measureable things.
The point is that successor and 0 become meaningless, or just mere symbols,
when removed from that context.
I don't agree with these axioms removed from any context, as without it,
they are meaningless. I don't necessarily disagree with them, either, I just
treat them as mere symbols then.
Of course we can still use them in a meta-sense by using .. = "2" as a
representation for, say a nose, and ... = "3" as a representation for a rose
and succesor= "+1" as a representation for smelling, and then 2+1=3 means
that a nose smells a rose. But then we could just as well use any other
symbol, like ß or more meaningfully ":o) o-".

Bruno Marchal wrote:
> Personally, I might prefer to use the combinators. But we have to  
> agree on some principle about some initial universal system to see how  
> they reflect UDA, in such a way that we can explain the quanta and the  
> qualia, with the comp assumption in the background, and in the theory  
> itself.
Yes, you can use any universal system, which is going to be just as
meaningless as numbers.
Let's take a programming language. When the code says "while(i<5) then i++;
print "Nose smells rose" end" then this make sense for the user as he can
read "nose smells rose". But in an abstract context, "nose smells rose" has
no particular meaning and the while loop is just a loop, which also has no
particular meaning (though it has a particular function). No matter what the
programming code says, it only makes sense through a user, or an intelligent
programmer. But you remove it from that context also, leaving no meaning
left, except empty symbol manipulation which could mean anything (which
rescues the meaning by making it possible to interpret everything in it, but
this defeats the purpose of using numbers or other formal systems).
All the (formal) universal systems you can name have the exact same flaw as
numbers. They only make sense in a context, otherwise they just function as
symbols making them as useful as saying
"ÜGFDÖÜGÖGÜÖFGÜFGÄFÄFÄFGÄFG--#-äsd#-ds#-d##" and then explaining that this
means "earth".
This is what COMP&C (this means comp and conlusion) does. It makes a lot of
complicated assumption and long-winded explantions and interpretation of
symbols, just to conclude that the 1-p (which is practically the only
perspective there is) cannot be captured by any rational means anyway. Then
it claims to be a refutable theory, but without making any particular
prediction that is not obvious already.

Bruno Marchal wrote:
>> If you just have a bunch of words without being able to make sense  
>> of them,
>> everything you "derive" from it will just be whatever you happen to
>> interpret in a bunch of non-sensical words.
> The axioms above are used by all scientists everyday, implicitly or  
> explicitly.
Of course they are! I say nothing to the contrary. The axioms are used as
*tools* because they reflect some aspect of reality. But they can only be
used where this is the case, namely comparable measurements and countable
things. COMP claims to explain quanta and qualia, which as such are not
measurable and countable (of course particular quanta can be measured, but
not quanta as such), therefore it uses a tool that is useless in this
endavour (and useless here means meaningless). The result is the same as
just using the axioms p and ~p. You get whatever you manage to interpret
into the axioms, which doesn't mainly depend on the axiom, but rather your
compassity to be creative with your ability of interpretation.

Bruno Marchal wrote:
>  What you say does not make sense.
Then just explain what numbers mean. And no, repeating the axioms does not
constitute an explantion. They just make (obvious) sense with regards to
countable things. Please explain the sense beyond that.

Bruno Marchal wrote:
> What axioms are you disagreeing with?
All. They make little to no sense in the context you use them.

Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>>> Bruno Marchal wrote:
>>>>> The diophantine equation x^2 = 2y^2 has no solution. That fact does
>>>>> not seem to me to depend on any concreteness, and I would say that
>>>>> concreteness is something relative. You seem to admit that naive
>>>>> materialism might be false, so why would little "concrete" pieces  
>>>>> on
>>>>> stuff, or time, helps in understanding that no matter what: there  
>>>>> are
>>>>> no natural numbers, different from 0, capable to satisfy the simple
>>>>> equation x^2 = 2y^2.
>>>> This is just a consequence of using our definitions consistently.
>>> Not really. In this case, we can indeed derived this from our
>>> definitions and axioms, but this is contingent to us. The very idea  
>>> of
>>> being realist about the additive and multiplicative structure of
>>> numbers, is that such a fact might be true independently of our
>>> cognitive abilities.
>> Yeah, so I ask what is the meaning of being realist about it? I  
>> can't see
>> any. The only meaning is when we work with countable objects, or
>> measurements, which indeed follow some rules that mathematics  
>> describe.
> Mathematics is born from the fact that abstract things can have meaning.
Obviously. So what? I am not denying that. Having meaning does not mean
"being realist about". They are real as epistemological constructs, and what
they describe is a part of reality. But real in an ultimate sense is only
reality itself (awareness). This means that persons (including myself!),
objects, physical reality also don't exist as fundamentally real. Just
awareness does, and these things are expressions of it (the more concrete
things just temporary expressions, like my body).

Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>> We don't know if there is an infinity of twin primes, but we can  
>>> still
>>> believe that "God" has a definite idea on that question.
>> We could as well say that our definitions make the answer to that  
>> question
>> well-defined, even if we haven't yet figured out what the answer is.
> So the answer does no more depend on us. That is what I mean by being  
> realist.
The answer depends on us as we invented the numbers (we = rationally
intelligent beings., including all forms of aliens that might exists, I
guess that they are probably humanoid as well). There is no requirement that
we know all the consequences of everything we invent.

Bruno Marchal wrote:
>> This
>> doesn't mean that the answer describes an independently existent  
>> entity.
> It implies that the truth of existential arithmetical proposition does  
> not depend on us.
It doesn't in the way that when the humans on this earth die there will most
probably still be other intelligent beings left that can assert the
But even if they do not depend on us as humans, they may not be true
independently of the context, that is, they only make sense with respect to
some aspects of reality, not all of it  (which would be required for a
meaningful TOE).

Bruno Marchal wrote:
>> but this doesn't mean they have any
>> independent aspect.
> You said yourself that the question is well defined.
So? Why does that entail that they are independent?

Bruno Marchal wrote:
>> That is, I don't think our mathematical formulation of
>> numbers describe numbers as a thing of itself, but rather are a  
>> particular
>> expression of regularity in awareness.
> Most probably. But assuming comp, they give a very good coordinate  
> system to study the computations. The laws of mind and matter does not  
> a priori depends on the initial choice. Numbers (with + and *) are  
> just the simplest and the most well known, even if very few people got  
> the impact of Gödel's discovery, which makes two times more sense with  
> the mechanist assumption.
Bingo, "The laws of mind and matter does not  a priori depends on the
initial choice." (though I don't think that they are any absolute laws, just
local ones, but let's just call the regularities laws, even if they can't be
written down). This choice can be an abitrary thing whatsoever. If I decide
to explain everything with the word "Kartoffelbrei" the universe will still
be the same.
Of course you can use numbers (or other computations), the point is rather
that this is pointless, even if "theoretically possible". Using some
convoluted way of reprenting things beyond numbers with numbers is just
useless, as we can more easily represent these things with concepts in
language (you have to resort to that anyway, as examplified by your  heavy
use of words in critical points).

Bruno Marchal wrote:
> Some universal system can play some more important role to figure out  
> some aspect of reality, but that has to be deduced from a theory  
> independent approach to computation if we want to extract and  
> distinguish the quanta and the qualia (like trough the logics of self- 
> reference).
Why make it so complicated? Ulitamtely, logic can't capture self-reference
anyway, so why not skip that stage and just go to the source of
self-reference, the self itself (yourself).

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