Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!border-4.nntp.ord.giganews.com!border-1.nntp.ord.giganews.com!nntp.giganews.com!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: The key undecidable instance that I know about --- Truth-bearers
 ONLY
Date: Mon, 17 Mar 2025 07:26:40 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <71ee1fe6f1c2b4e16f9250107531b6a43112cb95@i2pn2.org>
References: <vqkib1$r5np$1@dont-email.me> <vqksgr$sf7f$2@dont-email.me>
 <c2a4c70287c029f462d5579a8602746386f546fc@i2pn2.org>
 <vql4mq$uv13$1@dont-email.me>
 <9a2fbcc7a803bc91d320117f8c8e03e03799e9b3@i2pn2.org>
 <vqlmtf$11p4p$2@dont-email.me>
 <95ca0b344ae29f6911a73c655ddbe1c7214f8519@i2pn2.org>
 <vqo4ke$1l6i0$1@dont-email.me>
 <c5b83ef1ae7f77e3ff1fe97dcb557af5380c2ddd@i2pn2.org>
 <vqo7or$1l6i0$3@dont-email.me> <vqo8bf$1lehl$1@dont-email.me>
 <vqoac7$1lvqs$1@dont-email.me> <vqp4h7$1u7ri$1@dont-email.me>
 <vr4cjs$3u6l5$2@dont-email.me>
 <dcea3256423309576ce5cddc21201afbae10ddec@i2pn2.org>
 <vr58ue$m5ov$2@dont-email.me>
 <d17d20f85eba90c7dc80b2ef3f16810947b919c4@i2pn2.org>
 <vr5dh3$q4oj$5@dont-email.me>
 <826c8dc93d6f1449302cf3a2992a0d8d42b317df@i2pn2.org>
 <vr6ne3$1udpn$1@dont-email.me>
 <5b7f8e24bbd9817f74e1f50ee3c3c6def714314b@i2pn2.org>
 <vr7q0i$2o5t3$7@dont-email.me>
 <bcd51c2d82fd26c6ca32651b2a646bbdcc8a00b8@i2pn2.org>
 <vr88rt$3bidi$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 17 Mar 2025 11:26:41 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="560995"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
In-Reply-To: <vr88rt$3bidi$2@dont-email.me>
X-Spam-Checker-Version: SpamAssassin 4.0.0
Content-Language: en-US
Lines: 223

On 3/17/25 12:36 AM, olcott wrote:
> On 3/16/2025 9:52 PM, Richard Damon wrote:
>> On 3/16/25 8:22 PM, olcott wrote:
>>> On 3/16/2025 5:50 PM, Richard Damon wrote:
>>>> On 3/16/25 10:32 AM, olcott wrote:
>>>>> On 3/16/2025 6:33 AM, Richard Damon wrote:
>>>>>> On 3/15/25 10:37 PM, olcott wrote:
>>>>>>> On 3/15/2025 9:12 PM, Richard Damon wrote:
>>>>>>>> On 3/15/25 9:19 PM, olcott wrote:
>>>>>>>>> On 3/15/2025 3:44 PM, Richard Damon wrote:
>>>>>>>>>> On 3/15/25 1:15 PM, olcott wrote:
>>>>>>>>>>> On 3/11/2025 5:50 AM, Mikko wrote:
>>>>>>>>>>>> On 2025-03-11 03:23:51 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 3/10/2025 9:49 PM, dbush wrote:
>>>>>>>>>>>>>> On 3/10/2025 10:39 PM, olcott wrote:
>>>>>>>>>>>>>>> On 3/10/2025 9:21 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 3/10/25 9:45 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 3/10/2025 5:45 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 3/9/25 11:39 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> LP := ~True(LP)  DOES SPECIFY INFINITE RECURSION.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> WHich is irrelevent, as that isn't the statement in 
>>>>>>>>>>>>>>>>>> view, only what could be shown to be a meaning of the 
>>>>>>>>>>>>>>>>>> actual statement.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> The Liar Paradox PROPERLY FORMALIZED <is> Infinitely 
>>>>>>>>>>>>>>>>> recursive
>>>>>>>>>>>>>>>>> thus semantically incorrect.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> But is irrelevent to your arguement.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> "It would then be possible to reconstruct the antinomy 
>>>>>>>>>>>>>>>>> of the liar
>>>>>>>>>>>>>>>>>   in the metalanguage, by forming in the language 
>>>>>>>>>>>>>>>>> itself a sentence"
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Right, the "Liar" is in the METALANGUAGE, not the 
>>>>>>>>>>>>>>>> LANGUAGE where the predicate is defined.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You are just showing you don't understand the concept of 
>>>>>>>>>>>>>>>> Metalanguage.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Thus anchoring his whole proof in the Liar Paradox even if
>>>>>>>>>>>>>>>>> you do not understand the term "metalanguage" well enough
>>>>>>>>>>>>>>>>> to know this.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Yes, there is a connection to the liar's paradox, and 
>>>>>>>>>>>>>>>> that is that he shows that the presumed existance of a 
>>>>>>>>>>>>>>>> Truth Predicate forces the logic system to have to 
>>>>>>>>>>>>>>>> resolve the liar's paradox.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> bool True(X)
>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>    if (~unify_with_occurs_check(X))
>>>>>>>>>>>>>>>      return false;
>>>>>>>>>>>>>>>    else if (~Truth_Bearer(X))
>>>>>>>>>>>>>>>     return false;
>>>>>>>>>>>>>>>    else
>>>>>>>>>>>>>>>     return IsTrue(X);
>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> LP := ~True(LP)
>>>>>>>>>>>>>>> True(LP) resolves to false.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> ~True(LP) resolves to true
>>>>>>>>>>>>>
>>>>>>>>>>>>> It may seem that way if you fail to understand
>>>>>>>>>>>>> Clocksin & Mellish explanation of
>>>>>>>>>>>>>
>>>>>>>>>>>>> Most Prolog systems will allow you to
>>>>>>>>>>>>> satisfy goals like:
>>>>>>>>>>>>>    equal(X, X).
>>>>>>>>>>>>>    ?- equal(foo(Y), Y).
>>>>>>>>>>>>>
>>>>>>>>>>>>> that is, they will allow you to match a
>>>>>>>>>>>>> term against an uninstantiated subterm of itself.
>>>>>>>>>>>>>
>>>>>>>>>>>>> ON PAGE 3
>>>>>>>>>>>>> https://www.researchgate.net/ 
>>>>>>>>>>>>> publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>>>>>>>>>>
>>>>>>>>>>>> That you can quote some text but don't say anything about it 
>>>>>>>>>>>> supports the
>>>>>>>>>>>> hypthesis that you don't understand the text you quoted.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> I said that unify_with_occurs_check() detects
>>>>>>>>>>> cycles in the directed graph of the evaluation
>>>>>>>>>>> sequence of an expression that does explain
>>>>>>>>>>> everything even if it seems like I said
>>>>>>>>>>> blah, blah, blah to everyone not knowing the
>>>>>>>>>>> meaning of these words: "cycle", directed graph"
>>>>>>>>>>> "evaluation sequence".
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Except for the fact that you aren't giving it the actual x 
>>>>>>>>>> that Tarski creates (or the G for Godel) as expressed in the 
>>>>>>>>>> language, in part because it uses logic that can't be 
>>>>>>>>>> expressed in Prolog.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Tarski's Liar Paradox from page 248
>>>>>>>>>     It would then be possible to reconstruct the antinomy of 
>>>>>>>>> the liar
>>>>>>>>>     in the metalanguage, by forming in the language itself a 
>>>>>>>>> sentence
>>>>>>>>>     x such that the sentence of the metalanguage which is 
>>>>>>>>> correlated
>>>>>>>>>     with x asserts that x is not a true sentence.
>>>>>>>>>     https://liarparadox.org/Tarski_247_248.pdf
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Formalized as:
>>>>>>>>
>>>>>>>> NO!!
>>>>>>>>
>>>>>>>> That is what it reduces to in the metalangugae, but not what it 
>>>>>>>> is in the language, which is where it counts.
>>>>>>>>
>>>>>>>>> x ∉ True if and only if p
>>>>>>>>> where the symbol 'p' represents the whole sentence x
>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>>>>>>
>>>>>>>>> Not all all. It is merely that Tarski's somewhat clumsy
>>>>>>>>> syntax does not encode the Liar Paradox where its
>>>>>>>>> pathological self-reference can be directly seen.
>>>>>>>>
>>>>>>>> No, Tarski's syntax
>>>>>>>>
>>>>>>>>>
>>>>>>>>> He does not formalize most important part:
>>>>>>>>> "where the symbol 'p' represents the whole sentence x"
>>>>>>>>>
>>>>>>>>> If he did formalize that most important part it would
>>>>>>>>> be this: x ∉ True if and only if x
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Nope, you are just not understanding that 'x' is a fairly 
>>>>>>>> complecated sentence in the language, for which in the 
>>>>>>>> metalanguge, it can be reduced to the symbol p.
>>>>>>>>
>>>>>>>
>>>>>>> When Tarski formalized the Liar Paradox
>>>>>>> HE DID IT INCORRECTLY.
>>>>>>
>>>>>> We wasn't "Formalizing" the Liar Paradox.
>>>>>>
========== REMAINDER OF ARTICLE TRUNCATED ==========