Re: Why Peter Olcott is both right and wrong

On 5/15/25 2:27 AM, Mr Flibble wrote:

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.
 Peter however is wrong to say that aborting his infinite recursion is
equivalant to a halting state of non-halting: the truth is pathlogical
input is undecidable: that part Turing et al got right.
 /Flibble

There is nothing wrong with the Halting Problem as actually defined.
There is a lot wrong with how he interprests the Problem, because he doesn't understand the meaning of the basic terms.
First, H needs to be a fully defined program, and its input the representatio of another fully defined program.
When he talks about an infinite set of them pairs, they each are totally different problems, as the input is diffferent for each case, and thus his "induciton" isn't valid. That fact that none of his versions of H can correctly get to the end of their version of D is meaningless, and doesn't show that it is non-halting, when the truth is that for every H that does abort and return 0, the actual behavior of the program its input represents (which calls that H that returns 0) is to halt.
Yes, the Hs that never abort and return 0 will create a D that will never return, but those are different inputs than above, and none of those Hs ever give an answer and thus fail to be the decider asked for.
So, Peter's attempt to refute the problem proof, just recreates a step of the proof showing that no H created by his method ever gvies the right answer, CONFIRMING (not refuting) the proof.
The only world where Peter is correct, would be in some alternate POOPS theory with his totally strange set of rules, which is why no one will every want to use his POOPS if he ever does try to fomralize it.