On 12 Sep 2012, at 21:48, benjayk wrote:

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Platonist Guitar Cowboy wrote:On Wed, Sep 12, 2012 at 2:05 PM, benjayk <benjamin.jaku...@googlemail.com>wrote:Bruno Marchal wrote:On 11 Sep 2012, at 12:39, benjayk wrote:Our discussion is going nowhere. You don't see my points andassumeI want to attack you (and thus are defensive and not open to my criticism), and I am obviously frustrated by that, which is not conducive to a good discussion. We are not opertaing on the same level. You argue using rational, "precise"arguments, while I am precisely showing how these don't settleor evenadress the issue. Like with Gödel, sure we can embed all the meta in arithmetic, but then we still need a super-meta (etc...).I don't think so. We need the understanding of elementaryarithmetic,no need of meta for that. You might confuse the simple truth "1+1=2", and the complex truth"Paul understood that 1+1=2". Those are very different, but withcomp,both can be explained *entirely* in arithmetic. You have theright tobe astonished, as this is not obvious at all, and rather counter- intuitive.There is no proof that can change this, and thus it is pointless to study proofs regarding this issue (as they justintroduce new metas because their proof is not written inarithmetic).But they are. I think sincerely that you miss Gödel's proof. Therewill be opportunity I say more on this, here, or on the FOARlist. Itis hard to sum up on few lines. May just buy the book by Davis (nowprint by Dover) "The undecidable", it contains all originalpapers byGödel, Post, Turing, Church, Kleene, and Rosser.Sorry, but this shows that you miss my point. It is not about somesubtleaspect of Gödel's proof, but about the main idea. And I think I understand the main idea quite well.If Gödels proof was written purely in arithmetic, than it couldnot beunambigous, and thus not really a proof. The embedding is notunique, andthus by looking at the arithmetic alone you can't have a unambigous proof.Some embeddings that could be represented by this number relationscould"prove" utter nonsense. For example, if you interpret 166568 tomean "!="or "^6" instead of "=>", the whole proof is nonsense.Thus Gödel's proof necessarily needs a meta-level, oralternatively alevel-transcendent intelligence (I forgot that in my prior post)to betrue, because only then can we fix the meaning of the Gödel numbers.You can, of course *believe* that the numbers really exists beyondtheiraxioms and posses this transcendent intelligence, so that theysomehowmagically "know" what they are "really" representing. But this isjust abelief and you can't show that this is true, nor take it to begrantedthat others share this assumption.Problem of pinning down "real representation" in itself aside. Can"human"prove to impartial observer that they "magically know what they arereallyrepresenting" or "that they really understand"? How would we prove this? Why should I take for granted that humans do this,other than legitimacy through naturalized social norms, whichreally don'thave that great a track record?Can we even literally prove anything apart from axiomatic systems atall? Idon't think so. What would we base the claim that something reallyis aproof on?The notion of proving seems to be a quite narrow and restricted oneto me.

`That is why we have other notion than proof---which is of the type"`

`belief" (no "Bp -> p" in general), like knowledge, feeling,`

`experience, etc.`

Incompleteness makes possible to recover by intensional nuances:

`for a fixed machine B (I identify the machine with her beliefs) all`

`the Bp, Bp & p, Bp & Dt, Bp & Dt & p, etc. concerns exactly the same`

`arithmetical propositions, but obeys quite different logics`

`(classical, intuitionist, quantum-like, etc.).`

Bruno

Apart from that, it seems human "understanding" is just delusion inmanycases, and the rest is very limited at best. Especially when wethink wereally understand fundamental issues we are the most deluded. benjayk -- View this message in context: http://old.nabble.com/Simple-proof-that-our-intelligence-transcends-that-of-computers-tp34330236p34425351.html Sent from the Everything List mailing list archive at Nabble.com. --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

http://iridia.ulb.ac.be/~marchal/ -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.