Re: Functions computed by Turing Machines MUST apply finite string transformations to inputs

On 5/3/2025 3:45 PM, Richard Heathfield wrote:

 I am conscious that you have already explained to me (twice!) that Mr O's approach is aimed not at overturning the overarching indecidability proof but a mere detail of Linz's proof. Unfortunately, your explanations have not managed to establish a firm root in what passes for my brain. This may be because I'm too dense to grok them, or possibly it's because your explanations are TOAST (see above).
 You have said, I think, that Olcott doesn't need a universal decider in order to prove his point. But a less ambitious decider doesn't contradict Linz's proof, surely? So once more for luck, what exactly would PO be establishing with his non-universal and impatient simulator if he could only get it to work?

The core issue is that PO, despise being nearly 70 and having worked as a programmer, fundamentally doesn't understand proof by contradiction.
He thinks that the H in the Linz proof *is* a halt decider, and therefore whatever result it comes up with *must* be correct.
He then concludes that whatever mapping that H is computing is the "correct" halting function and therefore the *actual* halting function is "wrong".  It is on this basis that he claims HHH(DD)==0 is correct, and therefore *any* halting problem proof is flawed.
His alternate halting criteria, in which he uses simulation, is that H(X,Y) determines what would happen if the code of H was replaced by a pure simulator and H(X,Y) is subsequently run to simulate X(Y).  In cases where X at some point calls H this results in an answer of non-halting but also changes the code being decided on.  This is obviously invalid, but PO then goes through a series of "justifications" (ex. H is the test code, not the code under test) based on the idea that H *must* be correct.