XPost: comp.theory, sci.logic, comp.ai.philosophy
From: flibble@red-dwarf.jmc.corp
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.
---
Would you like me to reconstruct this reasoning as a formal proof or
counter-proof, suitable for inclusion in a debate or publication?
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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