Deutsch   English   Français   Italiano  
<1036q7i$16lpk$1@dont-email.me>

View for Bookmarking (what is this?)
Look up another Usenet article

Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re: HP counter-example INPUT cannot possibly exist --- Peter Linz HP
 Proof
Date: Sat, 21 Jun 2025 12:30:25 -0500
Organization: A noiseless patient Spider
Lines: 83
Message-ID: <1036q7i$16lpk$1@dont-email.me>
References: <YpG1Q.1572310$4AM6.1293015@fx17.ams4>
 <ab53329d43e0587e58fe949b7a8f1dce83bb580f@i2pn2.org>
 <1027uhs$r7bj$2@dont-email.me>
 <6f1855be769b3afc319d871c0d451f381803ba5e@i2pn2.org>
 <1029hvm$1ah2f$1@dont-email.me> <102bhn6$1t2a1$1@dont-email.me>
 <102c462$20jl4$10@dont-email.me> <102e2p4$2iugr$1@dont-email.me>
 <102er47$2ohps$3@dont-email.me> <102gv1s$3cscf$1@dont-email.me>
 <102hgcp$3gqbm$3@dont-email.me> <102m36e$qohc$1@dont-email.me>
 <102mm8v$uef9$8@dont-email.me> <102ok6o$1gto6$1@dont-email.me>
 <102uj28$369b2$1@dont-email.me> <1030gop$3p2jt$1@dont-email.me>
 <10342se$4ms9$1@dont-email.me> <1035qea$vbnq$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sat, 21 Jun 2025 19:30:27 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="c33a34d5810729869e79acc5a916ae39";
	logging-data="1267508"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/+TIyPMAq3yOVGn+Yjk0OQ"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:8zPVjfiCpUBu09VLbtPOES0YGuQ=
Content-Language: en-US
X-Antivirus-Status: Clean
X-Antivirus: Norton (VPS 250621-6, 6/21/2025), Outbound message
In-Reply-To: <1035qea$vbnq$1@dont-email.me>

On 6/21/2025 3:27 AM, Mikko wrote:
> On 2025-06-20 16:39:40 +0000, olcott said:
> 
>> On 6/19/2025 3:12 AM, Mikko wrote:
>>>
>>> But this is not. A proof starts with assumptions that may be true of
>>> false. Each statement that is not a definition, axiom, postulate,
>>> hypthesis or other assumption follows from some previous statements
>>> by an inference rule. The conclusion of a proof is the last statement
>>> of the sequence.
>>
>> Some proofs begin with definitions instead of assumptions.
> 
> Definitions often enable a clearer presentation of the assumptions
> and of the proof.
> 

Some proofs begin with "assumptions" that are defined to be
true, thus are not really mere assumptions at all.

<snip>>>>
>>> Depending on the style of the proof one can ither prove that
>>> the counter example exists or that if a halting decider exists
>>> then the caunter example exists, too, and otherwise none is
>>> needed.
>>
>> No this is counter-factual.
>> It has never been possible for *AN ACTUAL INPUT* to do
>> the opposite of whatever value that it decider decides.
>> *For 90 years no one ever bothered to notice this*
> 
> There is nothing impossible in Linz' construction of the
> counter example. If you think there is you could tell us
> the page, paragraph, and sentence in Linz' book that says
> someting impossible.
> 
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
When M is applied to WM
q0 WM ⊢* Ĥ q0 WM WM ⊢* Ĥ∞
    if M applied to WM halts, and
q0 WM ⊢* Ĥ q0 Wm WM ⊢* Ĥ y1 qn y2
    if M applied to WM does not halt.

*From the bottom of page 319 has been adapted to this*
When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞
   if Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
   if Ĥ applied to ⟨Ĥ⟩ does not halt

This does not have embedded_H reporting on the
behavior specified by its input it has embedded_H
reporting on its own behavior.

When embedded_H is a simulating partial halt decider
then its transition to Ĥ.qn does correctly report that
⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly
reach its own simulated final halt state of ⟨Ĥ.qn⟩.

*It does this even though embedded_H itself halts. embedded_H*
*is not allowed to report on its own behavior. It is only*
*allowed to report on the behavior that its input specifies*

When Ĥ is applied to ⟨Ĥ⟩ and embedded_H is a
simulating partial halt decider
(a) Ĥ copies its input ⟨Ĥ⟩
(b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
(e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(g) goto (d) with one more level of simulation until
embedded_H sees the repeating pattern and transitions to Ĥ.qn.

⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly
reach its own simulated final halt state of ⟨Ĥ.qn⟩ thus can
never do the opposite of whatever embedded_H decides.
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer