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,
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
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?


Unless you reject binary logic, but I am sure the problem also arises in
other logics. I might try this later.

meekerdb wrote:
   As Bruno would say, you are just
rejecting COMP and supposing - not demonstrating - that humans can do
I didn't say hypercomputation. Just something beyond computation.

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