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.".
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.

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.

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. This
doesn't mean that the answer describes an independently existent entity.
I agree that our definitions make sense and describe something, but they are
not a thing in and of themselves. In my view numbers are valid descriptions
of a certain aspect of reality, but this doesn't mean they have any
independent aspect. 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. 

Bruno Marchal wrote:
>> Of course
>> we can say 1+2=3 is 3 just because we defined numbers in the way  
>> that this
>> is true, without resorting to any concreteness.
> Yes. Mathematical realism stems from the intuition that abstract  
> entities can have theor own life (relations with other abstract or  
> concrete entities).
OK, but why would one believe in mathematical realism? It seems more
plausible to me that abstract entities seem to have their own life because
they mirror the life of the non-abstract enitities; but they have no life of
their own. I've never seen evidence of a number apart from countable things
and measurements. The axioms of numbers are just non-sensical (or mere
symbols, open to all interpretation) if not interpreted with respect to
measurements, or countable objects. What does 1+1=2 describe, if not that
one thing and another thing, which are concrete objects that do not
interact, give two things of the same kind.
I treat numbers as a locally (not in terms of space obviously) valid theory
of our world - OR as symbols being capable of representing everything (just
as all other things like apples) -, and I haven't yet seen evidence that
it's more than that.

Bruno Marchal wrote:
>> My point is that we can't derive something about the fundamental  
>> nature of
>> things just by adhering to our own definitions of what numbers are,  
>> since
>> these ultimately are just a bunch of definitions,
> You are right. We need some philosophical principles (like comp) to  
> understand that eventually we don't need those philosophical  
> principle. In the case of comp, we can understand why some (relative)  
> numbers will bet on it, and why some other numbers will not. In fine,  
> it is like with the south american, we can feel them enough close to  
> us to listen to them.
The funny thing is that if you don't give any plausible meaning to numbers
as thing in and of themselves, apart from countability or measurements, you
are just pulling things out of your imagination. Of course you can derive
everything from something that can represent everything (of course it is
possible to represent whatever you wish with the symbols of mathematics).
I have nothing against imaginative use of symbols, but please don't pretend
it has a solid foundation other than that, if you can't even give a
plausible meaning to your axioms.

Bruno Marchal wrote:
>> whereas the "actual" thing
>> they rely on (what numbers, or 0 and succesor actually are), remains  
>> totally
>> undefined.
> Not with comp. An apple becomes something very complex when defined in  
> pure number theory. It will involve infinite sets of long  
> computations, complex group of symmetries, etc. But it is definable  
> (in principle) from numbers (some including LUM observers).
You didn't see my point. The actual thing I was referring to was not an
concrete physical object, but the object of your theory, the supposed
"numbers". As long as you don't give a explanation of what they are, apart
from mere definitions that could mean anything, of course you can derive
everything from that unexplained mystical thing.

Bruno Marchal wrote:
>> So whatever we derive from it is just as mysterious as
>> consciousness, or matter, or whatever else, since the basis is totally
>> undefined.
> The problem does not consist in finding the ultimate definitions, but  
> to agree on elementary propositions, and to explain the rest, of as  
> much as possible from them.
It doesn't help to agree on elementary propositions if they could mean
anything. Or it does, but than we should acknowledge that we just interpret
whatever we wish into something that is so vague as to mean anything. Of
course I am willing to accept 1+1=2, it sounds good. But if you derive
something precise from that, you should be able to say what exactly that
means, otherwise you just showed your ability to interpret symbols that are
so broad as to mean anything in abitrary ways.

Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>>> If it isn't, the whole idea of an abstract machine as an
>>>> independent existing entity goes down the drain, and with it the
>>>> consequences of COMP.
>>> Yes. But this too me seems senseless. It like saying that we cannot
>>> prove that 17 is really prime, we have just prove that the fiollowing
>>> line
>>> .................
>>> cannot be broken in equal non trivial parts (the trivial parts being
>>> the tiny . and the big ................. itself).
>>> But we have no yet verify this for each of the following:
>>> .................
>>> .................
>>> .................
>>> .................
>>> .................
>>> .................
>>> .................
>>> .................
>>> .................
>>> .................
>>> .................
>>> etc.
>>> On the contrary: to understand arithmetic, is quasi-equivalent with
>>> the understanding that a statement like 17 is prime, is independent  
>>> of
>>> all concrete situation, in which 17 might be represented.
>> Lol, the funny thing is that in your explantion you used concrete  
>> things,
>> namely ".".
> Is that a problem?
No, but it doesn't help your point that they exist apart from (relatively)
concrete things. If they do, you wouldn't need to resort to concrete things
to show what they mean.

Bruno Marchal wrote:
>> It's concreteness is not really relevant,
>> the point is that numbers just apply to countable or measurable  
>> things.
> Yes. The natural numbers are somehow the type of the finite discrete  
> or discernible entities.
But then they make no sense as the basis of a TOE, which includes
non-discrete, non-countable, non-measureable, non-comparable,... things.
You need to use Gödel to make sense of it, by using numbers to represent
things beyond them. But then you use numbers as representations, which is
"cheating", as representations can represent anything, which somehow makes
the use of numbers totally empty. It is not even wrong to do, though it
seems to go beyond the axioms of the numbers. Where is the axiom that
numbers can represent things (for example mathematical symbols?).

Bruno Marchal wrote:
>> Without being countable natural numbers don't even make sense.
>> In order for COMP to be applicable to reality, reality had to be  
>> countable,
> Raaah.... Not really. The big 3-thing *can* be countable, because from  
> inside it will be non countable. The important reality is not the big  
> 3-thing seen from outside, because no one can go there. The "real"  
> reality with comp is epistemological. It is the living ideas from  
> *inside*.
I am just seriously doubting that there is a 3-thing. What is the evidence
that numbers are a 3-thing that exists apart from the 1-perspective?
I agree with your conclusion that "The "real"  reality with comp is
epistemological". But I think that ulitmately ontology=epistemology, if we
define knowledge broad enough. The only thing in existence is
self-knowledge, or better (self)-awareness.

Bruno Marchal wrote:
>> but it doesn't seem to me to be countable.
> Because you are inside. (assuming comp, ...).
You are, too, so how do you know of an "outside"? I think it is WAY more
plausible (or rather the only plausible alternative) that there is none,
because I (We), are the only thing that exists, without an outside view.
Outside view exist relative to persons (objects within consciousness), not
relative to consciousness (which is I, or we).

Bruno Marchal wrote:
>> Abstract machines might exist, but just as ideas.
> The point of platonism is that ideas, despite being epistemological  
> does exist, and are somehow more real than the big intellectual  
> construction, which in fine is shown to not really matter, and can be  
> very simple.
I can accept that, but they exists secondarily to existence itself, which is
not an intellectual construction at all. They are a particular view on
existence, and they don't exist on their own. And therefore COMP does not
make sense, or rather is misleading, because it pretends to "just" use
numbers (or other equivalent constructs), where really it just uses numbers
to talk what is beyond them. 

Bruno Marchal wrote:
>> Show that they exist
>> beyond that, and then the further reasoning can be taken more  
>> seriously. If
>> numbers, and abstract machines exist just as ideas, everything  
>> derived from
>> them will be further ideas. You can't unambigously conclude from  
>> some idea
>> something about reality.
> Reality is an idea itself.
Of course, everything we can speak of is an idea. I am not speaking of
reality as an idea, but reality as reality itself.

Bruno Marchal wrote:
>> Bruno Marchal wrote:
>>>> 1, 2, 3,... make only sense in terms of one of something, two of
>>>> something,... OK, we could say it makes sense to have one of
>>>> nothing, two of
>>>> nothing, etc, but in this case numbers are superfluous, and all
>>>> numbers, and
>>>> all computations are equivalent.
>>> I think that 0, 1, 2, and many others are far more simple  
>>> conceptually
>>> than any something you can multiply them by.
>> No. Otherwise we would understand 0, 1, 2, before we understood "one  
>> of
>> something", which clearly is not true.
> This does not follows.
But it seems natural to me.

Bruno Marchal wrote:
>> We understand 1 through "one apple",
>> etc...
>> It is only simpler in terms of being simpler to write down, because we
>> simply eliminate the mention of the "something" that is counted. But  
>> it is
>> more complex to understand, because we mentally have to add the  
>> something in
>> order for the numbers to have meaning beyond intellectual  
>> mastrubation.
> What do you propose as an alternative theory?
None. Or "What is is what is". Existence is self-existent, and
self-revealing as awareness. There is no theory for it, as it is an absolute
creative singularity which escapes all theories in a way that every new
theory creates even more things to explain. It has to be that way, because
theories itself are just a representation appearing within awareness, and
therefore cannot capture awareness (which I treat as the ultimate reality,
as it is the only thing which undoubtably exists).

Bruno Marchal wrote:
> My point is just that if we say "yes" to the doctor, then we have  
> literally no choice on this matter.
Yes, and my point is that this is just your interpretation of what COMP
means. We could just as well say that saying "yes" is just a bet with no
further consequences. Your reasoning depends on vague and quesitonable
assumptions, and therefore is not necessarily valid.
"Yes, doctor" itself is vague. What is "me"? What is an "experiential
change", and what constitutes awareness of an experiential change - it seems
to me that experiential change always occurs, making it already impossible
to substitute without an experiential change. Also I am critical of AR, as I
explained above.

Bruno Marchal wrote:
>> The point is that a definition doesn't say anything beyond it's  
>> definition.
> This is deeply false. Look at the Mandelbrot set, you can intuit that  
> is much more than its definition. That is the base of Gödel's  
> discovery: the arithmetical reality is FAR beyond ANY attempt to  
> define it.
No. The mandelbrot set as a meaningful entity is not made of definitions,
but of geometrical interpretation of the definitions, which are of course
possible and very meaningful.
And Gödel's discover is in my opinion better expressed with "The
arithmetical reality is FAR beyond ANY attempt to define it, as soon as we
use arithmetics to point to the transcendent reality, which of course is
beyond definitions". But this has *nothing* to do with arithmetics in
particular. It is just as true that the kööpül reality is FAR beyond ANY
attempt to define it, for just the same reason. Nothing can ultimately fixed
by any definition, even the simplest logic can't define it's own basis, as
it is not even clear what true, or false means. Every definition relies on
something that is beyond definitions, and thus no definition is meaningful
on its own.

Bruno Marchal wrote:
>> So, the number 17 is always prime because we defined numbers in the  
>> way. If
>> I define some other number system of natural numbers where I just  
>> declare
>> that number 17 shall not be prime, then it is not prime.
> No. You are just deciding to talk about something else.
OK, the point is that it is just a definition, and as such doesn't mean
anything without our interpretation.

Bruno Marchal wrote:
>> Who says that your
>> conception of natural numbers is right, and mine is wrong?
> Then you have to tell me what axioms you want me to make a change. But  
> you will only propose something else universal, and I have already  
> said that I am not sanguine about numbers in particular. I would  
> prefer to use the combinators, or the lambda expression, but natural  
> numbers are well known, and that is why I use them in this list. The  
> laws of mind and matter are independent of the initial theory, once  
> that theory verify the condition of being sigma_1 complete =  
> sufficiently strong to represent the partial computable functions, and  
> to emulate the UD.
It doesn't matter. You get the same problems I described above with other
universal systems (they are just other bunchs of definitions).

Bruno Marchal wrote:
>> Yes, my proposal of declaring 17 to not be prime is ridiculous,  
>> because it
>> doesn't fit with our conceptions of what properties numbers ought to  
>> have,
>> or ought to be able to have. But these conceptions come from our sense
>> perceptions, and imagination, were we can count and measure things.  
>> So when
>> you want to apply numbers to the fundamental realtiy, which as such
>> obviously is not countable, nor measurable, your natural numbers are  
>> as
>> weird as mine, because they both miss the point that reality is not
>> countable.
>> Of course we can do a lot of interpretation to rescue our theory, for
>> example by interpreting something beyond numbers into numbers via  
>> Gödel, but
>> then we could as well just use our capability of interpretation and  
>> skip the
>> number magic.
> The numbers are just more pedagogical. When you say "yes" to the  
> doctor he can put a java program on a disk, or a combinators, but  
> usually people will see only 0 and 1, and still call that a numbers.  
> We assume DIGITAL mechanism, and my goal is just to show that this  
> leads to a reversal physics/machine psychology making the hypothesis  
> testable. The question of using numbers or java programs is a question  
> of  implementation and engineering, like using a mac or a PC.
This is all nice and well, but I am precisely questioning your goal.
Actually many of your conclusion sound good and right to me, but it doesn't
have to do anything with digital mechanism in particular. You are just using
the fact that universal systems are useful for representing EVERYTHING. I am
only critizing your claim that this has to do anything with (abstract)
universal systems in particular.

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