On 12 Sep 2012, at 15:28, Platonist Guitar Cowboy wrote:

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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 and assume >> I 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 settle oreven>> adress 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 the rightto> be 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 just>> introduce new metas because their proof is not written inarithmetic).> > But they are. I think sincerely that you miss Gödel's proof. There> will be opportunity I say more on this, here, or on the FOAR list.It> is hard to sum up on few lines. May just buy the book by Davis (now> print by Dover) "The undecidable", it contains all original papersby> Gödel, 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 Iunderstandthe main idea quite well. If Gödels proof was written purely in arithmetic, than it could not beunambigous, and thus not really a proof. The embedding is notunique, andthus by looking at the arithmetic alone you can't have a unambigousproof.Some embeddings that could be represented by this number relationscould"prove" utter nonsense. For example, if you interpret 166568 to mean"!=" or"^6" instead of "=>", the whole proof is nonsense. Thus Gödel's proof necessarily needs a meta-level, or alternatively alevel-transcendent intelligence (I forgot that in my prior post) tobe true,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 they somehowmagically "know" what they are "really" representing. But this isjust abelief and you can't show that this is true, nor take it to begranted thatothers share this assumption.Problem of pinning down "real representation" in itself aside. Can"human" prove to impartial observer that they "magically know whatthey are really representing" or "that they really understand"?

`The idea is that you can understand what they prove as much as you`

`understand what they assume, and this independently of what is the`

`understanding.`

`If *you* agree with the elementary axioms, and inference rule, then`

`you agree, or show a flaw, with the deduction presented to you.`

`The actual interpretation or belief (or disbelief), in the axiom is`

`private and the scientist is mute on this.`

`A scientist will never say "I know", in its field of competence, or`

`even outside (but for some reason that is rare: very often scientist`

`forget the scientific attitude in the field of colleagues, apparently).`

Bruno

How would we prove this? Why should I take for granted that humansdo this, other than legitimacy through naturalized social norms,which really don't have that great a track record?The consequences of differing leaps of faith on axioms andontological bets shouldn't be taboo, if scientific search is toremain sincere somehow, why restrict ourselves to the habitual ones?Fruitful discussion from both of you, so thanks for sharing. m --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.

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