Stathis Papaioannou wrote:
>>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
>>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
>>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,
> Ethics and aesthetics are culture-specific.
> Empirical science is universe-specific:  eg., any culture, no matter how 
> bizarre its psychology compared to ours, would work out that sodium 
> reacts exothermically with water in a universe similar to our own, but 
> not in a universe where physical laws and fundamental constants are 
> very different from what we are familiar with.
> Mathematical and logical truths, on the other hand, are true in all possible 
> worlds. 

But this is really ciruclar because we define "possible" in terms of obeying 
rules of logic and reason.  I don't say we're wrong to do so - it's the best we 
can do.  But it doesn't prove anything.  I think the concept of logic, 
mathematics, and truth are all in our head and only consequently in the world.

>The lack of contingency on cultural, psychological or physical 
> factors makes these truths fundamentally different; whether you call 
> them perfect, analytic or necessary truths is a matter of taste.

If you directly perceived Hilbert space vectors, which QM tells us describe the 
world, would you count different objects?  I think these truths are contingent 
on how we see the world.  I think there's a good argument that any being that 
both intelligent and evolved will have the same mathematics - that's the jist 
Cooper's book.

Brent Meeker

> Stathis Papaioannou
> _________________________________________________________________
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