Path: ...!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Tarski
Date: Sat, 22 Feb 2025 22:56:41 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <a8000bfd27cd3a788bda0d5b66407413d276fe75@i2pn2.org>
References: <vnh0sq$35mcm$1@dont-email.me> <vnl9vj$4f8i$1@dont-email.me>
 <vnndqs$kef3$1@dont-email.me> <vnpd96$vl84$1@dont-email.me>
 <vnqm3p$1apip$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$8@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sun, 23 Feb 2025 03:56:41 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="1346175"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
Content-Language: en-US
X-Spam-Checker-Version: SpamAssassin 4.0.0
In-Reply-To: <vpd19c$irt$8@dont-email.me>
Bytes: 3936
Lines: 65

On 2/22/25 12:24 PM, olcott wrote:
> 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
> YOU ARE 100% COMPLETELY WRONG ABOUT THIS

Sure it is, unless your system can't express the properties of the 
Natural Numbers.

> 
> prolog spots and rejects expressions that have the
> "some kind of infinite structure" Liar Paradox
> form of pathological self-reference. See page 3.

And Prologs logic can't express the properties of the Natural Numbers.

> 
> https://www.researchgate.net/ 
> publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
> 
>>> I am not going bother to quote Clocksin and Mellish
>>> proving that you are wrong.
>>
>> You are right, a quote that does not support your claim
>> is not a good idea.
>>
> 
>