Re: ROADMAP (well, not yet really...

From: complexitystudies <complexitystudies.domain.name.hidden>
Date: Tue, 15 Aug 2006 20:52:47 +0200

Hello to the List :-)

The deductions made via UDA are impressing,
but I would like to seriously question the Platonic
Assumptions underlying all this reasoning.

Arguments like the perfectness of 6 seem sensible at
first sight, but only because we look at this with human
eyes.

1) Mathematical thought only exists in human (or alien intelligent)
   brains. It thus has neural correlates.

2) These neural correlates are strongly coupled to our sensory
   experiences, how we experience the world in an embodied way.

3) No brains, no neural correlates, no mathematics.
   It doesn't make sense to argue about the perfectness of 6 when there
   is nobody around to argue, when nobody thinks about "sixness".
   These concepts are ways of organizing the world around us, not
   platonic entities existing - indeed - where?

4) Why do we acknowledge some math as correct, other as not? It is only
   our grounding in reality, in our sensory experience, which let's us
   say: this mathematics describe reality sensibly.
   When we place one rock on another, then have two rocks, it is indeed
   not astounding that 1 + 1 = 2 in our symbol space. But, again, this
   is not a "description" of even an effect of math on reality, rather
             it is us getting back that what we have inferred beforehand.

5) Indeed, in advanced mathematics, one is often astounded that some
math seems to perfectly fit reality, without us having thought of this
application before. But in truth, this results from a selection effect
of perception.
The major body of mathematics is highly aesthetic but has no relevance
to physical structures in the real world. Only the mathematics which
"fits" (and getting this fit sometimes is not astounding, see point 4,
because we laid it into the system by our experience of the sensory
world) inspires some people to wonder why this works.

Example: in many equations, we throw away negative solutions because
"they don't make sense".

This illustrates that math doesn't fit by itself, we make it fit.

6) When we have accepted that mathematics does not exist in a platonic
realm, but arises from our embodied experience of the world, we should
humbly return to hypothesis, theory, validation, falsification, and a
constant construction of a world around us which makes sense to
_our specific human brains_, no more, no less.

---
I think "Quantum Weirdness", Gödels Incompleteness Theorem etc. are
only consequences of our embodied mathematics, which has evolved on
our macroscopical scale, and this granularity and method of reasoning
is not adequate for dimensions which transend our immediate sensory
experience.
As such, I also find MWI and other extravagancies and erroneous way
of approaching our current body of knowledge. This path leads astray.
Science is successful because we stay connected with "reality" (our
sensory, and enhanced - with machines - sensory experiences).
We cannot hope for more, at least at our level of understanding.
Interesting Literature:
- 	Where Mathematics Comes from: How the Embodied Mind Brings 		
Mathematics Into Being; George Lakoff and Rafael Nunez, 2001
- 	Metaphors We Live; George Lakoff, Mark Johnson 2003
-	Chasing Reality. Strife Over Realism; Mario Bunge, 2006
(I can recommend nearly everything by Bunge, who excels at clear
reasoning, and is committed to an unspeculative view on nature)
Best Regards,
Günther
Bruno Marchal wrote:
> 
> Le 14-août-06, à 19:21, Brent Meeker a écrit :
> 
>> But how must the perfect number exist or not exist?  You say you only 
>> mean
>> it must be true that there is a number equal to the sum of its divsors
>> independent of you.  Do you mean independent only in the sense that 
>> others
>> will know 6 is perfect after you're gone, or do you mean 6 is perfect
>> independent of all humans, all intelligent beings, the whole world?
> 
> 
> In the second sense.
> The perfectness of 6 is what would make any sufficiently clever entity 
> from any possible (consistent) worlds, existing or not,  to know that. 
> In that sense it has to be a primitive truth.
> 
> You can see this through a sequence of  stronger and stronger modesty 
> principles:
> 1) Bruno is not so important that 6 would loose its "perfection" after 
> Bruno is gone;
> 2) The Belgian are not so important that 6 would loose its perfectness 
> after the Belgian are gone;
> 3) The European are not so important that 6 would loose ...
> 4) The Humans are not so ...
> 5) The Mammals are not so ...
> 6) The creature of Earth are not so ...
> 7) the creature of the Solar system are not so ...
> 8) the creature of the Milky way are not so ...
> 9) the creature of the local universe are not so ...
> 10) the creature of the multiverse are not so ...
> 11) the creature of the multi multi verse are not so
> 11) the possible creatures are not so ...
> 
> Yes, I think (and assume in the Arithmetical realist part of comp) that 
> the fact that 6 is equal to its proper divisors sum, is a truth beyond 
> time, space, whatever ...
> I have the feeling I would lie to myself to think the contrary. I am 
> frankly more sure about that than about the presence of coffee in my 
> cup right now. I cannot imagine that the numbers themselves could go 
> away. They are not eternal, because they are not even in the category 
> of things capable of lasting or not with respect to any form of 
> observable or not reality.
> 
> Bruno
> 
> http://iridia.ulb.ac.be/~marchal/
> 
> 
> > 
> 
> 
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Received on Tue Aug 15 2006 - 14:54:36 PDT