complexitystudies 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?
I agree. Mathematics and logic are ways of constraining our propositions so
we don't assert contradictions; contradictions of our own rules. But that
doesn't mean they are strong enough to keep us from asserting absurdities.
>
> 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
I'll take a look at Lakoff. You might like William S. Cooper's "The
Evolution of Reason" which argues that logic and mathematics are produced by
evolution. Hence they would be common in any intelligent species that arose
by evolution.
Brent Meeker
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Received on Tue Aug 15 2006 - 21:41:31 PDT