Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Tarski
Date: Thu, 6 Mar 2025 20:26:54 -0600
Organization: A noiseless patient Spider
Lines: 264
Message-ID: <vqdlhe$371bi$5@dont-email.me>
References: <vnh0sq$35mcm$1@dont-email.me> <vpb1rf$3jct4$14@dont-email.me>
 <vpc4ed$3sn03$1@dont-email.me> <vpd19c$irt$8@dont-email.me>
 <vphbuh$10ia3$1@dont-email.me> <vpioff$1euhp$2@dont-email.me>
 <vpkngh$21tmo$1@dont-email.me> <vplbej$25vp2$3@dont-email.me>
 <vpmlu5$2gca0$1@dont-email.me> <vpn98f$2jkdj$3@dont-email.me>
 <vps17t$3k1co$1@dont-email.me> <vptbia$3rlov$1@dont-email.me>
 <vpuh0e$551p$1@dont-email.me> <vpvnvr$bjn9$4@dont-email.me>
 <vq4gf3$1bub9$1@dont-email.me> <vq5i34$1htc6$2@dont-email.me>
 <401f8c0b49c2ab6bf0e8ac85de35cfb83b085002@i2pn2.org>
 <vq5ron$1j128$4@dont-email.me>
 <1bb723b96c5e9677ec64335325fb72a98d8132e0@i2pn2.org>
 <vq73qu$1tapm$8@dont-email.me>
 <3e18fe1ae9e025227818f0f094245416e72d78bc@i2pn2.org>
 <vq8cm2$24ijh$3@dont-email.me>
 <ca688ffdb960b5894f4b2b34737d5089c426e23f@i2pn2.org>
 <vq9msk$2ei4j$5@dont-email.me>
 <ca3e1fdecb23a3bb1ea84013f7a5c31df3694f86@i2pn2.org>
 <vqaqm1$2lgq7$4@dont-email.me>
 <d45b81bb724e752c014b42188cea572d60ff8c02@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 07 Mar 2025 03:26:55 +0100 (CET)
Injection-Info: dont-email.me; posting-host="37f702c46a2fdca1e959530ddf954f17";
	logging-data="3376498"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18Y+HSFnqZ9u+7M/pES5kCH"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:8POhQpsnkzXAUIW2Uz2JONwqpGU=
X-Antivirus: Norton (VPS 250306-6, 3/6/2025), Outbound message
In-Reply-To: <d45b81bb724e752c014b42188cea572d60ff8c02@i2pn2.org>
Content-Language: en-US
X-Antivirus-Status: Clean

On 3/6/2025 6:36 AM, Richard Damon wrote:
> On 3/5/25 7:36 PM, olcott wrote:
>> On 3/5/2025 5:41 PM, Richard Damon wrote:
>>> On 3/5/25 9:25 AM, olcott wrote:
>>>> On 3/4/2025 10:59 PM, Richard Damon wrote:
>>>>> On 3/4/25 9:25 PM, olcott wrote:
>>>>>> On 3/4/2025 5:45 PM, Richard Damon wrote:
>>>>>>> On 3/4/25 9:47 AM, olcott wrote:
>>>>>>>> On 3/4/2025 6:29 AM, Richard Damon wrote:
>>>>>>>>> On 3/3/25 10:24 PM, olcott wrote:
>>>>>>>>>> On 3/3/2025 7:07 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/3/25 7:38 PM, olcott wrote:
>>>>>>>>>>>> On 3/3/2025 9:05 AM, Mikko wrote:
>>>>>>>>>>>>> On 2025-03-01 19:42:50 +0000, olcott said:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 3/1/2025 2:37 AM, Mikko wrote:
>>>>>>>>>>>>>>> On 2025-02-28 21:58:34 +0000, olcott said:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On 2/28/2025 3:56 AM, Mikko wrote:
>>>>>>>>>>>>>>>>> On 2025-02-26 14:42:23 +0000, olcott said:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> On 2/26/2025 3:12 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>> On 2025-02-25 21:07:31 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> On 2/25/2025 9:27 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>> On 2025-02-24 21:31:26 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> On 2/24/2025 2:51 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2025-02-22 17:24:59 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> On 2/22/2025 3:12 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-02-21 23:22:23 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/20/2025 3:01 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-02-18 13:50:22 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> There is nothing like that in the following 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> concrete example:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> LP := ~True(LP)
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> In other words you are saying the Prolog is 
>>>>>>>>>>>>>>>>>>>>>>>>>>>> incorrect
>>>>>>>>>>>>>>>>>>>>>>>>>>>> to reject the Liar Paradox.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Above translated to Prolog
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> ?- LP = not(true(LP)).
>>>>>>>>>>>>>>>>>>>>>>>>>>>> LP = not(true(LP)).
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> According to Prolog rules LP = not(true(LP)) 
>>>>>>>>>>>>>>>>>>>>>>>>>>> is permitted to fail.
>>>>>>>>>>>>>>>>>>>>>>>>>>> If it succeeds the operations using LP may 
>>>>>>>>>>>>>>>>>>>>>>>>>>> misbehave. A memory
>>>>>>>>>>>>>>>>>>>>>>>>>>> leak is also possible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>>>>>>>>>>>>>>>>>>>>>>>>> false
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> This merely means that the result of 
>>>>>>>>>>>>>>>>>>>>>>>>>>> unification would be that LP conains
>>>>>>>>>>>>>>>>>>>>>>>>>>> itself. It could be a selmantically valid 
>>>>>>>>>>>>>>>>>>>>>>>>>>> result but is not in the scope
>>>>>>>>>>>>>>>>>>>>>>>>>>> of Prolog language.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> It does not mean that. You are wrong.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> It does in the context where it was presented. 
>>>>>>>>>>>>>>>>>>>>>>>>> More generally,
>>>>>>>>>>>>>>>>>>>>>>>>> unify_with_occurs_check also fails if the 
>>>>>>>>>>>>>>>>>>>>>>>>> arguments are not
>>>>>>>>>>>>>>>>>>>>>>>>> unfiable. But this possibility is already 
>>>>>>>>>>>>>>>>>>>>>>>>> excluded by their
>>>>>>>>>>>>>>>>>>>>>>>>> successfull unification.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> IT CANNOT POSSIBLY BE SEMANTICALLY VALID
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Of course it is. Its semantics is well defined by 
>>>>>>>>>>>>>>>>>>>>>>> the Prolog standard.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Go freaking read the Clocksin and Mellish.
>>>>>>>>>>>>>>>>>>>>>> an "infinite term" means NOT SEMANTICALLY VALID.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Prolog does not define any semantics other than the 
>>>>>>>>>>>>>>>>>>>>> execution semantics
>>>>>>>>>>>>>>>>>>>>> of a prolog program. Therefore no data structure 
>>>>>>>>>>>>>>>>>>>>> has any own semantics.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> The result of the exectution of an instruction like 
>>>>>>>>>>>>>>>>>>>>> LP == not(true(LP))
>>>>>>>>>>>>>>>>>>>>> is not fully defined by the standard so we may say 
>>>>>>>>>>>>>>>>>>>>> that that instruction
>>>>>>>>>>>>>>>>>>>>> is semantically invalid.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> When we ask for Prolog to determine whether an 
>>>>>>>>>>>>>>>>>>>> expression
>>>>>>>>>>>>>>>>>>>> in Prolog is true according to its facts and rules 
>>>>>>>>>>>>>>>>>>>> and the
>>>>>>>>>>>>>>>>>>>> evaluation of the expression gets stuck in an 
>>>>>>>>>>>>>>>>>>>> infinite loop
>>>>>>>>>>>>>>>>>>>> then this expression IS SEMANTICALLY INCORRECT.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Which is not done anywhere above.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> In other words you can't remember things that I said
>>>>>>>>>>>>>>>>>> a few messages ago and I have to endlessly repeat 
>>>>>>>>>>>>>>>>>> everything
>>>>>>>>>>>>>>>>>> every time?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Is this just an instance or your favorite sin? If not, 
>>>>>>>>>>>>>>>>> what do you think
>>>>>>>>>>>>>>>>> I didn't remember?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> page 3 has the liar paradox and the Cloksin & Mellish 
>>>>>>>>>>>>>>>>>> Quote
>>>>>>>>>>>>>>>>>> https://www.researchgate.net/ 
>>>>>>>>>>>>>>>>>> publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> It just says that your prolog system is defective as it 
>>>>>>>>>>>>>>>>> does not reject
>>>>>>>>>>>>>>>>> your LP = not(true(LP)). The Prolog standard says that 
>>>>>>>>>>>>>>>>> this operation may
>>>>>>>>>>>>>>>>> but need not fail. It also cortectly says that
>>>>>>>>>>>>>>>>>  LP = not(true(LP)), write(LP)
>>>>>>>>>>>>>>>>> would not work.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> There is no "need not fail" Clocksin and Mellish says
>>>>>>>>>>>>>>>> impossible to succeed (paraphrase).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> No, that is not said. In a footnote they say that the 
>>>>>>>>>>>>>>> behaviour is undefined,
>>>>>>>>>>>>>>> i.e., an implementation may choose what to do. They do 
>>>>>>>>>>>>>>> say that a typical
>>>>>>>>>>>>>>> implementation does not fail, which implies "need not fail".
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> More precisely it says that there is a cycle in the
>>>>>>>>>>>>>>>> directed graph of the evaluation sequence of the 
>>>>>>>>>>>>>>>> expression.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Assuming that the unification does not fail.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> That you fail to understands that the following means this
>>>>>>>>>>>>>>>> is your lack of understanding not my mistake.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> ?- LP = not(true(LP)).
>>>>>>>>>>>>>>>> LP = not(true(LP)).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It means that the pariticular implementation you used 
>>>>>>>>>>>>>>> exploited the
>>>>>>>>>>>>>>> "need not fail" permission, producing a cycle in the data 
>>>>>>>>>>>>>>> structure.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>>>>>>>>>>>>> false.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> For this operation there is no "need not fail". The 
>>>>>>>>>>>>>>> standard specifies that
========== REMAINDER OF ARTICLE TRUNCATED ==========