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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Tarski
Date: Thu, 6 Mar 2025 07:36:15 -0500
Organization: i2pn2 (i2pn.org)
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In-Reply-To: <vqaqm1$2lgq7$4@dont-email.me>

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
>>>>>>>>>>>>>> the operation must fail.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Because the Prolog Liar Paradox has an “uninstantiated 
>>>>>>>>>>>>>>> subterm of itself” we can know that unification will fail 
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