Re: Why Peter Olcott is both right and wrong

On 5/15/25 9:03 AM, Mr Flibble wrote:

On Thu, 15 May 2025 11:07:48 +0300, Mikko wrote:
 

On 2025-05-15 06:27:13 +0000, Mr Flibble said:
>

Peter is right to say that the halting problem as defined is flawed: he
agrees with me that there is category error at the heart of the problem
definition whereby the decider is conflated with the program being
analysed in an ill-formed self-referential dependency that manifests in
his simulating halt decider as "aborted" infinite recursion.

>
No, he is not right about that. There is no flaw about the problem. The
problem is to create a halt decider. Every Turing machine either is or
is not a halt decider. In order to demonstrate that a Turing machine is
not a halt decider it is sufficient to show one example that it does not
determine correctly.

 False -- the pathologial input cannot be determined correctly because it
is ill-posed.

What is "ill-posed" about it. Remember, The decide is a specific and determined deterministic program, and thus we can compute the answer it WILL give for any input. The "pathological" is also precisely built on that decider, and also is fully deterministic. It begins by using its copy of the algorithm of the decider to get the answer it will give for itself (in the standard proof, from the representation of itself given to it as its input) and then do the opposite.
Which action of that is impossible?
If the decider doesn't process that particular string, it just failed to be4 the required decider. If it does, then the pathological program can just act on the answer it got.

 

>
That a problem is too hard to you does not mean that it be ill-posed.

 It isn't the case that problem is too hard to me, it is the case that it
is ill-posed.
 /Flibble

Nope, just your brain is ill-processing.