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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: True on the basis of meaning --- Good job Richard ! ---Socratic
 method MTT
Date: Mon, 3 Jun 2024 07:56:35 -0500
Organization: A noiseless patient Spider
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On 6/3/2024 2:19 AM, Mikko wrote:
> On 2024-06-02 13:01:15 +0000, olcott said:
> 
>> On 6/2/2024 2:29 AM, Mikko wrote:
>>> On 2024-06-01 15:41:46 +0000, olcott said:
>>>
>>>> On 6/1/2024 2:32 AM, Mikko wrote:
>>>>> On 2024-05-31 15:47:31 +0000, olcott said:
>>>>>
>>>>>> On 5/31/2024 2:17 AM, Mikko wrote:
>>>>>>> On 2024-05-30 13:43:11 +0000, olcott said:
>>>>>>>
>>>>>>>> On 5/30/2024 1:52 AM, Mikko wrote:
>>>>>>>>> On 2024-05-29 13:31:31 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 5/29/2024 3:25 AM, Mikko wrote:
>>>>>>>>>>> On 2024-05-28 14:59:30 +0000, olcott said:
>>>>>>>>>>>
>>>>>>>>>>>> On 5/28/2024 1:59 AM, Mikko wrote:
>>>>>>>>>>>>> On 2024-05-27 14:34:14 +0000, olcott said:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> ?- LP = not(true(LP)).
>>>>>>>>>>>>>> LP = not(true(LP)).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>>>>>>>>>>> false.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> In other words Prolog has detected a cycle in the directed 
>>>>>>>>>>>>>> graph of the
>>>>>>>>>>>>>> evaluation sequence of the structure of the Liar Paradox. 
>>>>>>>>>>>>>> Experts seem
>>>>>>>>>>>>>> to think that Prolog is taking "not" and "true" as 
>>>>>>>>>>>>>> meaningless and is
>>>>>>>>>>>>>> only evaluating the structure of the expression.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The words "not" and "true" of Prolog are meaningful in some 
>>>>>>>>>>>>> contexts
>>>>>>>>>>>>> but not above. The word "true" is meaningful only when it 
>>>>>>>>>>>>> has no arguments.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> That Prolog construes any expression having the same 
>>>>>>>>>>>> structure as the
>>>>>>>>>>>> Liar Paradox as having a cycle in the directed graph of its 
>>>>>>>>>>>> evaluation
>>>>>>>>>>>> sequence already completely proves my point. In other words 
>>>>>>>>>>>> Prolog
>>>>>>>>>>>> is saying that there is something wrong with the expression 
>>>>>>>>>>>> and it must
>>>>>>>>>>>> be rejected.
>>>>>>>>>>>>
>>>>>>>>>>>>> You could try
>>>>>>>>>>>>> ?- LP = not(true(LP), true(LP).
>>>>>>>>>>>>>
>>>>>>>>>>>>> or
>>>>>>>>>>>>> ?- LP = not(true(LP), not(true(LP)).
>>>>>>>>>>>>>
>>>>>>>>>>>>> The predicate unify_with_occurs_check checks whether the 
>>>>>>>>>>>>> resulting
>>>>>>>>>>>>> sructure is acyclic because that is its purpose. Whether a 
>>>>>>>>>>>>> simple
>>>>>>>>>>>>
>>>>>>>>>>>> Yes exactly. If I knew that Prolog did this then I would not 
>>>>>>>>>>>> have
>>>>>>>>>>>> created Minimal Type Theory that does this same thing. That 
>>>>>>>>>>>> I did
>>>>>>>>>>>> create MTT that does do this same thing makes my 
>>>>>>>>>>>> understanding much
>>>>>>>>>>>> deeper.
>>>>>>>>>>>
>>>>>>>>>>> Prolog does not reject LP = not(true(LP)). It can accept it as
>>>>>>>>>>> syntactically valid. Thaat unify_with_occurs_check(LP, 
>>>>>>>>>>> not(true(LP))
>>>>>>>>>>> fails does not mean anything except when it is used, and then it
>>>>>>>>>>> does not reject but simplu evaluates to false, just like 1 = 2
>>>>>>>>>>> is false but not erroneous.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It correctly determines that there is a cycle in the directed 
>>>>>>>>>> graph
>>>>>>>>>> of the evaluation sequence of the expression, which is like an
>>>>>>>>>> infinite loop in a program.
>>>>>>>>>>
>>>>>>>>>> You can understand this or fail to understand this, 
>>>>>>>>>> disagreement is
>>>>>>>>>> incorrect. If you have any disagreement then please back up your
>>>>>>>>>> claims with proof.
>>>>>>>>>>
>>>>>>>>>>>>> unification like LP = not(true(LP)) does same is 
>>>>>>>>>>>>> implementation
>>>>>>>>>>>>> dependent as Prolog rules permit but do not require that. In a
>>>>>>>>>>>>> typical implementation a simple unification does not check for
>>>>>>>>>>>>> cycles.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> ISO Prolog implementations have the built-in predicate
>>>>>>>>>>>> unify_with_occurs_check/2 for sound unification
>>>>>>>>>>>> https://en.wikipedia.org/wiki/Occurs_check#Sound_unification
>>>>>>>>>>>>
>>>>>>>>>>>> Alternatively such expressions crash or remain stuck in 
>>>>>>>>>>>> infinite loops.
>>>>>>>>>>>
>>>>>>>>>>> Not necessarily. What happes depends on the implementation 
>>>>>>>>>>> and on what
>>>>>>>>>>> you do with such structures. You already saw that your
>>>>>>>>>>>
>>>>>>>>>>> ?- LP = not(true(LP)).
>>>>>>>>>>>
>>>>>>>>>>> does not crash and does not remain stuck in infinite loop.
>>>>>>>>>>>
>>>>>>>>>>>>> Anyway, none of this is relevant to the topic of this 
>>>>>>>>>>>>> thread or
>>>>>>>>>>>>> topics of sci.logic.
>>>>>>>>>>>
>>>>>>>>>>> If you want to talk nore about Prolog do it in comp.lang.prolog.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It is relevant to sci.logic in that it exposes fundamental flaws
>>>>>>>>>> with classical logic.
>>>>>>>>>
>>>>>>>>> It does not expose any flaw in classical logic. Flaws in your
>>>>>>>>> understanding of calssical logics are already sufficiently known.
>>>>>>>>
>>>>>>>>     What has now been shown is that L is true if, and only if, 
>>>>>>>> it is
>>>>>>>>     false. Since L must be one or the other, it is both.
>>>>>>>
>>>>>>> No, that has not been shown. Classical logic shows that no sentence
>>>>>>> is true if and only if it is false. If you assumoe otherwise then
>>>>>>> your assumption is false.
>>>>>>>
>>>>>>
>>>>>>     *You removed the relevant context that the principle of 
>>>>>> explosion*
>>>>>>     *of classical logic is shown to be the source of the issue*
>>>>>
>>>>> Principle of exposion is empirically true. It is not a problem of
>>>>> classical logic. You have not shown that any paraconsistent system,
>>>>> where principle of exposion does not apply, is any better.
>>>>>
>>>>
>>>> The ONLY THING that can ever be correctly derived from a contradiction
>>>> is FALSE. People taking classical logic as infallible by simply 
>>>> ignoring
>>>> its inconsistencies are inherently incorrect.
>>>
>>> The inconsistencies are not inconsistencies of logic. No logic can
>>> prevent you from assuming an inconsistency but then it is your
>>> inconsistency.
>>>
>>> People taking classical logic as infallible do so because no situation
>>> where it is wrong has been observed.
>>
>> *Three laws of logic apply to all propositions*
>> ¬(p ∧ ¬p) Law of non-contradiction
>>   (p ∨ ¬p) Law of excluded middle
>>    p = p   Law of identity
> 
> Those laws don't prevent from assuming p. Those laws don't prevent
> from assuming ¬p. Assuming both is assuming something false.


(1) We know that "Not all lemons are yellow", as it has been assumed to 
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