Le 18-août-06, à 22:59, complexitystudies a écrit :

>>
>
> As 1Z has so nicely put, existence implies causal interaction.
> Numbers cannot causally interact, therefore they do not exist,
> save as thoughts in our brains.

Don(t say this to a logician. there are as many notion of "causality" 
than there are modal logics.
(But I guess you assume a physical world and define "causal" by some 
"interaction").
I don't need that. I need only math "causality", like if p divide 8 
then p divides 24.



>
> Of course I do not believe that 37 could be a non prime number,
> simply because what it means to be "prime" has been exactly
> defined in arithmetic.

You reassure me.



> I just say that these are thought constructs
> with no independent existence (independent of human brains, not of a
> concrete human brain).
>
> You might say, that 37 was prime even in the Jurassic, but I say:
> nobody had invented arithmetic yet, so it's about as true as the
> fact that James Bond was played by Sean Connery was in the Jurassic.
>
> I define a system:
>
> 1 + 1 = 2
> 2 + 1 = 1
> 1 + 2 = 1
>
> That's all. Okay, it doesn't describe much and probably isn't very
> useful, but other than that it is not inferior to peano arithmetic.
> Does my system now exist mind-independtly for all eternity?


Yes, and even Robinson Arithmetic can prove that. It exists because 
among all fortran programs there exist an infinity of programs which 
compute your table. (it is a Wi or a Fi)
Of course "existing" does not mean interesting. Some numbers could be 
(relatively) boring, but that is hardly provably so in general.



>
>
>> I have not yet seen a book on human brain which does not presuppose 
>> the
>> understanding of the natural numbers.
>
> Of course, because it is a useful way to describe reality. But in our
> brains, not numbers operate, but chemicals.


I agree. The question here is what are eventually the chemicals. Comp 
answers: it is necessarily an average of point of views on an infinity 
of possible computational continuations. Put in that way, it even looks 
like some formulation of QM. The details are tricky of course (both 
with comp and with the QM only).


<snip>


>
>
>  I let you
>> discover that, and feel free to ask questions if you have a problem
>> with UDA.
>
> Thank you, I will.
>
>
>>
>> It is really the point of the UDA. It shows that computationalism (the
>> idea that I am a digitalizable machine) is incompatible with "weak
>> materialism" (the idea that there is a primary stuff or matter or
>> aristotelian substances).
> Ok, I'll watch for this in UDA.
>>
>
>> But until now, comp leads only to weirdness, not contradiction. And
>> then that weirdness seems to explain the quantum weirdness ...
>> Intuitively and qualitatively (already by UDA), and then technically
>> through the interview of some universal turing machine.
>
> But wouldn't this universal turing machine need to be composed of
> matter, and then the whole caboodle starts from the beginning?


No. The additive+multiplicative structure of the non negative integers 
(what logician called the natural numbers) is already a video-game rich 
enough to generate coherent and sharable set of computational first 
person plural histories. That *is* the point. Don't take this for 
granted at all. UDA explain why. The lobian interview explain how.
The question is not does Humty-Dumpty "exist"? The question is "does 
not comp entails too much probable Humpty-Dumpty in my neighborhood" 
and "how to test that".
The question is "does comp entails *more*, or *less* white rabbits than 
QM already predicts apparently with some accuracy".

Bruno


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


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