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

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On 12 Sep 2012, at 21:48, benjayk wrote:```
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Platonist Guitar Cowboy wrote:
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On Wed, Sep 12, 2012 at 2:05 PM, benjayk

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Bruno Marchal wrote:
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On 11 Sep 2012, at 12:39, benjayk wrote:

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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 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.

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```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 in arithmetic).
```
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 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.

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If Gödels proof was written purely in arithmetic, than it could not be 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.
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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 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

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```

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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"?

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?

```
Can we even literally prove anything apart from axiomatic systems at all? I don't think so. What would we base the claim that something really is a
```proof on?
```
The notion of proving seems to be a quite narrow and restricted one to me.
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```
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:

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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

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Apart from that, it seems human "understanding" is just delusion in many cases, and the rest is very limited at best. Especially when we think we
```really understand fundamental issues we are the most deluded.

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

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