Bruno Marchal wrote:
> 
> 
> On 03 Oct 2011, at 21:00, benjayk wrote:
> 
>>
>>
>> Bruno Marchal wrote:
>>>
>>> Just a little correction. I wrote (on 30 Sep 2011) :
>>>
>>>>
>>>> On 30 Sep 2011, at 17:26, benjayk wrote:
>>>>>
> <snip>
>>>>> The only thing that COMP does is to propose a complicated thought
>>>>> construct
>>>>> which essentially reveals its own emptiness. What can COMP possibly
>>>>> mean?
>>>>> For it to have any use we have to make a bet grounded on pure
>>>>> faith... So we
>>>>> could just as well believe in God,
>>>>
>>>> Why not if you make it enough precise so that people can see the
>>>> scientific problem. usually God is used as an empty (indeed) answer.
>>>> But with comp, both comp and God is a question, not an answer.
>>>>
>>>>
>>>>
>>>>> or  - better  -just take the stance of
>>>>> observing whatever happens! Maybe that we have to bet on an
>>>>> substitution
>>>>> level for COMP to have any meaning, and our inability to know any
>>>>> substitution level should lead us to conclude that there probably
>>>>> is no
>>>>> substitution level, or it is undefined, which would just make
>>>>> sense, given
>>>>> that apparently COMP is undefined in its very foundations.
>>>>
>>>> So how would react if your daughter want to say yes to a digitalist
>>>> doctor? Or what if your doctor says that this is the only chance for
>>>> her to survive some disease?
>>>>
>>>> You are using a machine to send this post, which would not even
>>>> exist if comp did not make sense.
>>>
>>> I mean " ... if comp did not make sense for the reason you gave  
>>> above".
>>>
>>> Obviously computer makes sense even if comp is false. But computer
>>> would not have appeared if we did not grasp the elementary
>>> arithmetical ideas.
>> But we did grasp the elementary ideas. My point is just that it  
>> makes no
>> sense to treat arithmetics as something that is meaningful without  
>> concrete
>> objects.
> 
> 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? 



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. 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.
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, whereas the "actual" thing
they rely on (what numbers, or 0 and succesor actually are), remains totally
undefined. So whatever we derive from it is just as mysterious as
consciousness, or matter, or whatever else, since the basis is totally
undefined.



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 ".".
Of course concrete is relative. It's concreteness is not really relevant,
the point is that numbers just apply to countable or measurable things.
Without being countable natural numbers don't even make sense.
In order for COMP to be applicable to reality, reality had to be countable,
but it doesn't seem to me to be countable.
Abstract machines might exist, but just as ideas. 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.




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. 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.


Bruno Marchal wrote:
> 
> But comp needs only that you belief that the elementary arithmetical  
> truth does not depend on you or us (little ego).
> Are you thinking that if an asteroid rips of humanity from the cosmos,  
> the number 17 would get a non trivial divisor?
> 
> That does not make sense, I think.
Of course an asteroid won't influence that the number 17 has no non-trivial
divisor, because we defined the numbers in a way so that the number 17 is
prime, which is true regardless what happens.
The point is that a definition doesn't say anything beyond it's definition.
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. Who says that your
conception of natural numbers is right, and mine is wrong? You are just
asserting the truth of you own axioms when you say that number 17 is prime,
which is as good as saying my axiom is "everything goes" and I derive from
that that you are in reality living inside the belly of an invisible pink
unicorn.

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.

benjayk

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