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 > _________________________________________________________________ > Be one of the first to try Windows Live Mail. > http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
