Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception --- Tarski
Date: Wed, 26 Feb 2025 11:12:37 +0200
Organization: -
Lines: 69
Message-ID: <vpmlu5$2gca0$1@dont-email.me>
References: <vnh0sq$35mcm$1@dont-email.me> <vnqsbh$1c5sq$1@dont-email.me> <vnsm90$1pr86$1@dont-email.me> <vnte6s$1tra8$1@dont-email.me> <vnv4tf$2a43e$1@dont-email.me> <vo0249$2eqdl$1@dont-email.me> <vo1qae$2s4cr$1@dont-email.me> <vo2i10$302f0$1@dont-email.me> <vo4nj4$3f6so$1@dont-email.me> <vo5btf$3ipo2$1@dont-email.me> <vo7ckh$q2p$1@dont-email.me> <vo7tdg$36ra$6@dont-email.me> <voa09t$idij$1@dont-email.me> <7e532aaf77653daac5ca2b70bf26d0a3bc515abf@i2pn2.org> <voceuj$14r1q$1@dont-email.me> <vocp21$16c4e$1@dont-email.me> <vof6hb$1nh1f$1@dont-email.me> <voflif$1q1mh$2@dont-email.me> <vohsmu$29krm$1@dont-email.me> <vp10ic$1e7iv$2@dont-email.me> <f249a1ab72772fbbd2fd8785493f9b91e3bb58b0@i2pn2.org> <vp236u$1n991$4@dont-email.me> <vp6r16$2p1if$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>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 26 Feb 2025 10:12:38 +0100 (CET)
Injection-Info: dont-email.me; posting-host="4125783ded271e1b1bd8769efb7241cf";
	logging-data="2634048"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18r1gKB4w4LrFFVVtZv7/ps"
User-Agent: Unison/2.2
Cancel-Lock: sha1:sY1GkXhQnDGtiPb16/wCxRJMvHQ=
Bytes: 4339

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.

-- 
Mikko