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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Tarski
Date: Mon, 3 Mar 2025 21:24:06 -0600
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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 because it 
>>>>>> specifies “some kind of infinite structure.”
>>>>>
>>>>> Wrong. You above said that the unification LP = not(true(LP)) did not
>>>>> fail. It may fail on another implementation but that is not required.
>>>>>
>>>>>> Go back and read the Clocksin and Mellish example and quote on
>>>>>> the same page until you totally understand it. You only need
>>>>>> example the yellow highlighted text.
>>>>>
>>>>> The supreme authority is not Clocksin and Mellish but ISO/IEC 13211.
>>>>
>>>> Clocksin and Mellish concretely show the result of the
>>>> infinitely recursive structure of their concrete example.
>>>
>>> Irrelevant.
>>>
>>
>> Your above replies prove that you do not understand this
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