Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth Date: Sun, 2 Mar 2025 10:02:16 -0600 Organization: A noiseless patient Spider Lines: 178 Message-ID: References: <3cf165ef9793e844dc9d5db82aecbc47f9545367@i2pn2.org> <080bf2b1c322247548c6ec61c9f054359062ccd4@i2pn2.org> <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 17:02:17 +0100 (CET) Injection-Info: dont-email.me; posting-host="f1890a324b06dc16a921f95b9719194f"; logging-data="891687"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19dsP9J0iyIuangi8I3sRo5" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:abC5EOdcUeqR8mXD7EfU6nBDyw0= In-Reply-To: Content-Language: en-US X-Antivirus: Norton (VPS 250302-0, 3/1/2025), Outbound message X-Antivirus-Status: Clean Bytes: 9525 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 >>>> touching their own head. ========== REMAINDER OF ARTICLE TRUNCATED ==========