# Re: Simple proof that our intelligence transcends that of computers

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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:
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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"
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>> arguments, while I am precisely showing how these don't settle or even
```>> 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 elementary arithmetic,
```> no need of meta for that.
> You might confuse the simple truth "1+1=2", and the complex truth
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> "Paul understood that 1+1=2". Those are very different, but with comp, > both can be explained *entirely* in arithmetic. You have the right to
```> 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
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>> introduce new metas because their proof is not written in arithmetic).
```>
> But they are. I think sincerely that you miss Gödel's proof. There
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> 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 papers by
```> Gödel, Post, Turing, Church, Kleene, and Rosser.
>
```
Sorry, but this shows that you miss my point. It is not about some subtle aspect 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 could not be
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unambigous, and thus not really a proof. The embedding is not unique, and thus by looking at the arithmetic alone you can't have a unambigous proof. Some embeddings that could be represented by this number relations could "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 a
```
level-transcendent intelligence (I forgot that in my prior post) to be true,
```because only then can we fix the meaning of the Gödel numbers.
```
You can, of course *believe* that the numbers really exists beyond their
```axioms and posses this transcendent intelligence, so that they somehow
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magically "know" what they are "really" representing. But this is just a belief and you can't show that this is true, nor take it to be granted that
```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 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).
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Bruno

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

m

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http://iridia.ulb.ac.be/~marchal/

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