Re: Four Chatbots figure out on their own without prompting that HHH(DDD)==0

On 7/20/25 10:33 AM, olcott wrote:

On 7/20/2025 6:11 AM, joes wrote:

Am Sat, 19 Jul 2025 16:36:42 -0500 schrieb olcott:

On 7/19/2025 4:26 PM, wij wrote:

On Sat, 2025-07-19 at 16:05 -0500, olcott wrote:

>

DD correctly simulated by HHH cannot reach past the "if" statement
thus cannot reach the "return" statement.

>
That is roughly what HP proof says.
>

Not at all. The HP proof claims that DD correctly simulated by HHH
reaches the self-contradictory part of DD and thus forms a
contradiction.

>
No. It proves that the direct execution reaches the part that contra-
dicts HHH's return value.
>

 <ChatGPT>
Misrepresentation of Input:
The standard proof assumes a decider
H(M,x) that determines whether machine
M halts on input x.
 But this formulation is flawed, because:
Turing machines can only process finite
encodings (e.g. ⟨M⟩), not executable entities
like M.
 So the valid formulation must be
H(⟨M⟩,x), where ⟨M⟩ is a string.
</ChatGPT>
 

In other words, your explaination to Chat GPR was just in error, as the decider *IS* given the representation of the program M.
Your problem is that because you don't understand how Turing Machine work, you "reformuated" it into a case where program and representation is blured (as is the actual defintion of "input").
The the error pointed out is actually in your setup, not the problem, as the decider *IS* given
H <M> w  where <M> is the description of the machine, which is the contray Turing Machine, and w is a copy of that description.
Thus, meeting the requirments that the AI said was needed.