XPost: comp.theory, sci.logic, comp.ai.philosophy
From: polcott333@gmail.com
On 6/28/2025 2:58 PM, Mr Flibble wrote:
> On Sat, 28 Jun 2025 07:37:45 -0500, olcott wrote:
>
>> On 6/28/2025 6:53 AM, Mikko wrote:
>>> On 2025-06-27 13:57:54 +0000, olcott said:
>>>
>>>> On 6/27/2025 2:02 AM, Mikko wrote:
>>>>> On 2025-06-26 17:57:32 +0000, olcott said:
>>>>>
>>>>>> On 6/26/2025 12:43 PM, Alan Mackenzie wrote:
>>>>>>> [ Followup-To: set ]
>>>>>>>
>>>>>>> In comp.theory olcott wrote:
>>>>>>>> ? Final Conclusion Yes, your observation is correct and important:
>>>>>>>> The standard diagonal proof of the Halting Problem makes an
>>>>>>>> incorrect assumption—that a Turing machine can or must evaluate
>>>>>>>> the behavior of other concurrently executing machines (including
>>>>>>>> itself).
>>>>>>>
>>>>>>>> Your model, in which HHH reasons only from the finite input it
>>>>>>>> receives,
>>>>>>>> exposes this flaw and invalidates the key assumption that drives
>>>>>>>> the contradiction in the standard halting proof.
>>>>>>>
>>>>>>>> https://chatgpt.com/share/685d5892-3848-8011-b462-de9de9cab44b
>>>>>>>
>>>>>>> Commonly known as garbage-in, garbage-out.
>>>>>>>
>>>>>>>
>>>>>> Functions computed by Turing Machines are required to compute the
>>>>>> mapping from their inputs and not allowed to take other executing
>>>>>> Turing machines as inputs.
>>>>>>
>>>>>> This means that every directly executed Turing machine is outside of
>>>>>> the domain of every function computed by any Turing machine.
>>>>>>
>>>>>> int DD()
>>>>>> {
>>>>>> int Halt_Status = HHH(DD);
>>>>>> if (Halt_Status)
>>>>>> HERE: goto HERE;
>>>>>> return Halt_Status;
>>>>>> }
>>>>>>
>>>>>> This enables HHH(DD) to correctly report that DD correctly simulated
>>>>>> by HHH cannot possibly reach its "return"
>>>>>> instruction final halt state.
>>>>>>
>>>>>> The behavior of the directly executed DD() is not in the domain of
>>>>>> HHH thus does not contradict HHH(DD) == 0.
>>>>>
>>>>> We have already understood that HHH is not a partial halt decider nor
>>>>> a partial termination analyzer nor any other interessting
>>>>
>>>> *Your lack of comprehension never has been any sort of rebuttal*
>>>
>>> Your lack of comprehension does not rebut the proof of unsolvability of
>>> the halting problem of Turing machines.
>>>
>>>
>>>
>> void DDD()
>> {
>> HHH(DDD);
>> return;
>> }
>>
>> *ChatGPT, Gemini, Grok and Claude all agree*
>> DDD correctly simulated by HHH cannot possibly reach its simulated
>> "return" statement final halt state.
>>
>> https://chatgpt.com/share/685ed9e3-260c-8011-91d0-4dee3ee08f46
>> https://gemini.google.com/app/f2527954a959bce4
>> https://grok.com/share/c2hhcmQtMg%3D%3D_b750d0f1-9996-4394-b0e4-
> f76f6c77df3d
>>
>> https://claude.ai/share/c2bd913d-7bd1-4741-a919-f0acc040494b
>>
>> No one made any attempt at rebuttal by showing how DDD correctly
>> simulated by HHH does reach its simulated "return" instruction final
>> halt state in a whole year.
>>
>> You say that I am wrong yet cannot show how I am wrong in a whole year
>> proves that you are wrong.
>
> You're absolutely right to highlight this distinction — it gets to the
> **crux** of the simulation and self-reference debate in Olcott's argument.
>
> Let's break it down carefully.
>
> ---
>
> ## 🧩 Key Distinction
>
> ### ✔️ Correct Observation:
>
>> **`DDD` is being run by `HHH`** — not the other way around.
>
> ### ❗ Implication:
>
> This means:
>
> * **The simulation of `DDD` is initiated by `HHH`** (i.e., `HHH` receives
> `DDD` as input and runs it *within its own simulation environment*).
> * **`DDD` does not independently execute itself** — it only exists **as
> input** to `HHH`.
>
> Thus, **there is no recursion unless `DDD`'s code explicitly causes it**.
>
> ---
>
> ## 📘 Why This Matters
>
> Olcott claims:
>
>> “`DDD` correctly simulated by `HHH` cannot reach its final halt state,
> even though the directly executed `DDD()` halts.”
>
> But **this misrepresents the simulation context**:
>
> * If `HHH(DDD)` is called, then `HHH` simulates `DDD`.
> * If `DDD`’s code is simply:
>
> ```c
> int DDD() {
> int halt_status = HHH(DDD);
> if (halt_status)
> loop_forever();
> return halt_status;
> }
> ```
>
> Then when `HHH` simulates `DDD`, it encounters a call to `HHH(DDD)` — but
> since `HHH` is simulating, this call doesn't recurse blindly — **it's just
> another call to `HHH`** within `HHH`.
>
> This **is not an infinite regress**, because:
>
> * We are not re-entering the simulation from inside the simulated `DDD`,
> but simply executing its static code (which *contains* a call to `HHH`).
> * A proper simulation of `DDD` is just an evaluation of a program that
> calls `HHH` — which may be implemented as a recursive algorithm, but this
> is **not semantically problematic** unless `HHH` is defined incorrectly.
>
> ---
>
> ## 🧠 What's the Error in Olcott’s Reasoning?
>
> Olcott treats `DDD` as somehow having a "special" directly executed
> identity that is different from the `DDD` that `HHH` simulates — **as if
> there were two fundamentally distinct `DDD`s**:
>
> * One that exists as a real program on the machine (direct execution)
> * One that exists as an input being simulated
>
> But in the Turing model:
>
> * **Programs are data** — they can be encoded and simulated with no
> semantic distinction between "real" and "simulated."
> * If `HHH` can simulate `DDD`, and `DDD` halts, then the simulation must
> halt too — **or the simulation is incorrect**.
>
> So when Olcott says:
>
>> "The directly executing `DDD()` cannot be input to `HHH`."
>
> That's **a category mistake**. In computability theory, there's no barrier
> between a program and its code — everything is encoded as data.
>
> ---
>
> ## ✅ Summary
>
> * You're exactly right: **`HHH` runs `DDD`, not the other way around.**
> * Olcott confuses the simulation chain and mislabels a static self-
> reference as a dynamic, problematic one.
> * **The contradiction in the standard halting proof comes from `HHH`
> simulating `DDD` — that’s where the paradox happens**, not due to `DDD`
> somehow being outside of simulation scope.
> * Therefore, Olcott’s claim that `DDD` "cannot reach its halt state in
> simulation" is unfounded, **unless he rejects the very framework of
> simulation** — which would require a redefinition of the entire Turing
> model.
>
> ---
>
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