Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: dbush Newsgroups: sci.logic Subject: Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth Date: Sun, 2 Mar 2025 12:00:50 -0500 Organization: A noiseless patient Spider Lines: 199 Message-ID: References: <6fc61a762b56308f9919993f29ba3e77f7ba84c7@i2pn2.org> <6320ec8cdc4ab9fc06e5001c0b4069132ce1af58@i2pn2.org> <9c6309a46ca0fdf2ce98f50a09891e143d81ab90@i2pn2.org> <0e0c21ec5ccaeec8f341a86ed64c7447c34d162b@i2pn2.org> <8638c66ecc1669437be5a141cfa358c8c6168cde@i2pn2.org> <83cd07284fba793a0c2865dc5f6c21a9b9788a3e@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 02 Mar 2025 18:00:49 +0100 (CET) Injection-Info: dont-email.me; posting-host="532f9ff796323674ebd2d76d6a96062e"; logging-data="906311"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/rG1OBYj9UoX9wihNR/3Tl" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:AQuvQHzERRQf5UbAxZTDgXx6CFU= In-Reply-To: Content-Language: en-US Bytes: 10561 On 3/2/2025 11:53 AM, olcott wrote: > On 3/2/2025 10:28 AM, dbush wrote: >> On 3/2/2025 11:02 AM, olcott wrote: >>> On 3/2/2025 9:23 AM, dbush wrote: >>>> On 3/1/2025 11:46 PM, olcott wrote: >>>>> On 3/1/2025 7:27 PM, Richard Damon wrote: >>>>>> On 3/1/25 8:22 PM, olcott wrote: >>>>>>> On 3/1/2025 3:58 PM, Richard Damon wrote: >>>>>>>> On 2/28/25 6:57 PM, olcott wrote: >>>>>>>>> On 2/28/2025 8:30 AM, Richard Damon wrote: >>>>>>>>>> On 2/27/25 11:02 PM, olcott wrote: >>>>>>>>>>> On 2/27/2025 7:00 PM, Richard Damon wrote: >>>>>>>>>>>> On 2/27/25 9:46 AM, olcott wrote: >>>>>>>>>>>>> On 2/27/2025 6:45 AM, Richard Damon wrote: >>>>>>>>>>>>>> On 2/26/25 11:24 PM, olcott wrote: >>>>>>>>>>>>>>> On 2/26/2025 9:59 PM, Richard Damon wrote: >>>>>>>>>>>>>>>> On 2/26/25 8:39 PM, olcott wrote: >>>>>>>>>>>>>>>>> On 2/26/2025 10:03 AM, joes wrote: >>>>>>>>>>>>>>>>>> Am Wed, 26 Feb 2025 08:34:47 -0600 schrieb olcott: >>>>>>>>>>>>>>>>>>> On 2/26/2025 6:18 AM, joes wrote: >>>>>>>>>>>>>>>>>>>> Am Tue, 25 Feb 2025 12:40:04 -0600 schrieb olcott: >>>>>>>>>>>>>>>>>>>>> On 2/25/2025 12:15 PM, joes wrote: >>>>>>>>>>>>>>>>>>>>>> Am Mon, 24 Feb 2025 20:02:49 -0600 schrieb olcott: >>>>>>>>>>>>>>>>>>>>>>> On 2/24/2025 6:12 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2/24/25 6:11 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 2/24/2025 6:27 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2/23/25 11:39 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/23/2025 8:50 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/23/25 1:08 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>> Sure I do. >>>>>>>>>>>>>>>>>>>>>>>>>> A Systems is semantically sound if every >>>>>>>>>>>>>>>>>>>>>>>>>> statement that can be >>>>>>>>>>>>>>>>>>>>>>>>>> proven is actually true by the systems semantics, >>>>>>>>>>>>>>>>>>>>>>>>> That is very good. >>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>> in other words, the system doesn't allow the >>>>>>>>>>>>>>>>>>>>>>>>>> proving of a false >>>>>>>>>>>>>>>>>>>>>>>>>> statement. >>>>>>>>>>>>>>>>>>>>>>>>> That is not too bad yet ignores that some >>>>>>>>>>>>>>>>>>>>>>>>> expressions might not >>>>>>>>>>>>>>>>>>>>>>>>> have any truth value. >>>>>>>>>>>>>>>>>>>>>>>> Which has nothing to do with "soundness". >>>>>>>>>>>>>>>>>>>>>>> When any system assumes that every expression is >>>>>>>>>>>>>>>>>>>>>>> true or false and >>>>>>>>>>>>>>>>>>>>>>> is capable of encoding expressions that are >>>>>>>>>>>>>>>>>>>>>>> neither IT IS STUPIDLY >>>>>>>>>>>>>>>>>>>>>>> WRONG. >>>>>>>>>>>>>>>>>>>>>> In honour of Gödel this is usually called >>>>>>>>>>>>>>>>>>>>>> "incomplete". >>>>>>>>>>>>>>>>>>>>> Where "incomplete" has always been an idiom for >>>>>>>>>>>>>>>>>>>>> stupid wrong. >>>>>>>>>>>>>>>>>>>> Your understanding of logic is incomplete. >>>>>>>>>>>>>>>>>> Which is to say, stupidly wrong. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> The screwed up notion of "incomplete" is anchored in >>>>>>>>>>>>>>>>>>> the stupid idea >>>>>>>>>>>>>>>>>>> that {true in the system} is not required to be >>>>>>>>>>>>>>>>>>> {provable in the >>>>>>>>>>>>>>>>>>> system}. >>>>>>>>>>>>>>>>>> You are about a century behind on the foundations of >>>>>>>>>>>>>>>>>> mathematics. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> Any expression of language that can only be verified >>>>>>>>>>>>>>>>>>> as true on the >>>>>>>>>>>>>>>>>>> basis of other expressions of language either has a >>>>>>>>>>>>>>>>>>> semantic connection >>>>>>>>>>>>>>>>>>> truthmaker to these other expressions or IT IS SIMPLY >>>>>>>>>>>>>>>>>>> NOT TRUE. >>>>>>>>>>>>>>>>>> I.e. its negation is true. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> WTF is the truth value of the negation of nonsense? >>>>>>>>>>>>>>>>> The Liar Paradox has ALWAYS simply been nonsense. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> But we aren't negating "nonsense", we are negating the >>>>>>>>>>>>>>>> actual valid truth value out of the Truth Primative. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> You don't seem to understand that the DEFINITION of what >>>>>>>>>>>>>>>> a truth primative is requires that True(Nonsense) be >>>>>>>>>>>>>>>> false, not "nonsense". >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>   True("lkekngnkerkn") == false >>>>>>>>>>>>>>> False("lkekngnkerkn") == false >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> But ~True("lkekngnkerkn") == true. >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> Yes >>>>>>>>>>>>> >>>>>>>>>>>>>> so if we can define that lkekngnkerkn is >>>>>>>>>>>>>> ~True(lkekngnkerkn) then we have a problem. >>>>>>>>>>>>>> f >>>>>>>>>>>>> >>>>>>>>>>>>> We are not defining gibberish as anything. >>>>>>>>>>>>> Gibberish evaluates as ~True because it is gibberish. >>>>>>>>>>>> >>>>>>>>>>>> But you are trying to define LP := !True(LP) as gibberish. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Prolog already knows that it gibberish. >>>>>>>>>> >>>>>>>>>> Because, like you, Prolog can't handle the needed logic. >>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> It has an infinite cycle in the directed graph of its >>>>>>>>>>> evaluation sequence. >>>>>>>>>> >>>>>>>>>> But infinite cycles are not prohibited in logic systems that >>>>>>>>>> support the properties of the Natural Numbers. The MUST allow >>>>>>>>>> them or you can't HAVE the Natural Numbers. >>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> See Page 3 for Prolog >>>>>>>>>>> https://www.researchgate.net/ >>>>>>>>>>> publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Just shows your stupidity, thinking that all logic is just >>>>>>>>>> primitive, and not understanding what the Godel sentence >>>>>>>>>> actually is. Your mind seems to have blocked out the actual >>>>>>>>>> sentence presented earlier because you know you don't >>>>>>>>>> understand it, so you think it must be gibberisn, but it is >>>>>>>>>> you mind that is gibberish. >>>>>>>>>> >>>>>>>>>> You didn't give it the ACTUAL Godel sentence, just the >>>>>>>>>> simplified interpretation of it. The problem is that the >>>>>>>>>> actual Godel sentence can't be expressed in Prolog, as it uses >>>>>>>>>> 2nd order logic operations, which Prolog doesn't handle. >>>>>>>>>> >>>>>>>>>> Of course, since your mind can't handle them either, you can't >>>>>>>>>> understand that. >>>>>>>>> >>>>>>>>> Carefully study the Clocksin and Mellish on page 3 knucklehead. >>>>>>>>> Read and reread the yellow highlighted text until you totally >>>>>>>>> get it. >>>>>>>>> >>>>>>>> >>>>>>>> Right, Neither G nor ~G are provable in F. >>>>>>>> >>>>>>> >>>>>>> Provable(common) >>>>>>> {shown to be definitely true by whatever means} >>>>>>> is the only relevant notion of provable. >>>>>> >>>>>> And "Shown" requires finite. >>>>>> >>>>>> Please show me an infinite proof. >>>>>> >>>>>> Try to do it. That might be your task if Gehenna. >>>>>> >>>>>>> >>>>>>> We could say that it is totally impossible for anyone >>>>>>> to touch their own head by adding the requirement >>>>>>> that they must touch their own head without ever ========== REMAINDER OF ARTICLE TRUNCATED ==========