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
>>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
>
>
> 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 our
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 is
both intelligent and evolved will have the same mathematics - that's the jist of
Cooper's book.
Brent Meeker
>
> Stathis Papaioannou
> _________________________________________________________________
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>
>
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Received on Wed Aug 16 2006 - 23:45:10 PDT