meekerdb wrote:
> On 8/21/2012 3:26 PM, benjayk wrote:
>> meekerdb wrote:
>>> On 8/21/2012 2:52 PM, benjayk wrote:
>>>> meekerdb wrote:
>>>>> On 8/21/2012 2:24 PM, benjayk wrote:
>>>>>> meekerdb wrote:
>>>>>>> "This sentence cannot be confirmed to be true by a human being."
>>>>>>> The Computer
>>>>>> He might be right in saying that (See my response to Saibal).
>>>>>> But it can't confirm it as well (how could it, since we as humans
>>>>>> can't
>>>>>> confirm it and what he knows about us derives from what we program
>>>>>> into
>>>>>> it?). So still, it is less capable than a human.
>>>>> I know it by simple logic - in which I have observed humans to be
>>>>> relatively slow and
>>>>> error prone.
>>>>> regards, The Computer
>>>>    Well, that is you imagining to be a computer. But program an actual
>>>> computer that concludes this without it being hard-coded into it. All
>>>> it
>>>> could do is repeat the opinion you feed it, or disagree with you,
>>>> depending
>>>> on how you program it.
>>>> There is nothing computational that suggest that the statement is true
>>>> or
>>>> false. Or if it you believe it is, please attempt to show how.
>>>> In fact there is a better formulation of the problem: 'The truth-value
>>>> of
>>>> this statement is not computable.'.
>>>> It is true, but this can't be computed, so obviously no computer can
>>>> reach
>>>> this conclusion without it being fed to it via input (which is
>>>> something
>>>> external to the computer). Yet we can see that it is true.
>>> Not really.  You're equivocating on "computable" as "what can be
>>> computed"
>>> and "what a
>>> computer does".  You're supposing that a computer cannot have the
>>> reflexive inference
>>> capability to "see" that the statement is true.
>> No, I don't supppose that it does. It results from the fact that we get a
>> contradiction if the computer could see that the statement is true (since
>> it
>> had to compute it, which is all it can do).
>> meekerdb wrote:
>>>   Yet you're also supposing that when we
>>> "see" it is true that that is not a computation.
>> No. It can't be a computation, since if it were a computation we couldn't
>> conclude it is true (as this would be a contradiction, as I showed
>> above).
> You avoid the contradiction by saying, "What *I'm* doing is not
> computation." which you 
> can say because you don't know what you're doing - you're just "seeing"
> it's true.  If you 
> knew what you were doing you would know you were computing too and you'd
> be in the same 
> contradiction that you suppose the computer is in because computing "is
> all it can do."  
> You're implicitly *assuming* you can do something that is not computing to
> avoid the 
> contradiction and thereby prove you can do something beyond computing -
> see the circularity
Not really. The fact that I can see its true proves that I can't be only
doing computation, because by only doing computation (and only allowing
binary logic as the answer) we could never arrive at the fact that the
sentence is true.

A computer would derive that it is false, and thus it is true and thus it is
false,... Or it would derive that it is true and thus that its answer must
be wrong (because its own way of arriving there contradicts the sentence),
so it must be false after all, etc... But it would never arrive at the fact
that the statement it is clearly true.
Yet I see that it is clearly true, since a computer could never unambigously
see its true (as the last paragraph shows).

We could only hardcode the statement into the computer, but then it just
states it and doesn't confirm it by itself.

You could say that I am beyond the level of the computer and thus can see
something about the computer that the computer can't.

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