benjayk wrote:
> Is the following statement true?
> 'This statement can't be confirmed to be true solely by utilizing a
> computer'
> Imagine a computer trying to solve this problem:
> If it says yes, it leads to a contradiction, since a computer has been
> trying to confirm it, so its answer is wrong.
> If it says no, that is, it claims that it CAN be confirmed by a computer,
> again leading to a contradiction.
> But from this we can derive that a computer cannot correctly answer the
> statement, and so cannot solve the problem in question! So the solution to
> the problem is YES, yet no computer can really confirm the truth of the
> sentence.

There is even a much stronger variant of the sentence.
'This statement can't be confirmed to be true solely by utilizing a computer
and XYZ also can't be confirmed solely using a computer'

Again, the computer has the same problem.

We can't answer no (because this would mean that the computer can confirm
it, which we know to be wrong), but we can answer yes, so it appears that it
has to be true.

Which means that nothing can be ultimately confirmed by a computer. 

Actually the reason for this is simple: The computer can only confirm things
based on what we program into it, but it can't confirm whether what we
program into it is correct (since it needs to assume it, we force it to). So
ultimately it can't confirm anything. Not even that 1+1=2 (since it would
have to confirm the axioms first, which it can't) - yet we can confirm it
empiricially. The computer can only reflect what we confirmed first.
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