Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: sci.logic Subject: Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth Date: Sat, 1 Mar 2025 20:27:41 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <83cd07284fba793a0c2865dc5f6c21a9b9788a3e@i2pn2.org> References: <3cf165ef9793e844dc9d5db82aecbc47f9545367@i2pn2.org> <080bf2b1c322247548c6ec61c9f054359062ccd4@i2pn2.org> <6fc61a762b56308f9919993f29ba3e77f7ba84c7@i2pn2.org> <6320ec8cdc4ab9fc06e5001c0b4069132ce1af58@i2pn2.org> <9c6309a46ca0fdf2ce98f50a09891e143d81ab90@i2pn2.org> <0e0c21ec5ccaeec8f341a86ed64c7447c34d162b@i2pn2.org> <8638c66ecc1669437be5a141cfa358c8c6168cde@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 2 Mar 2025 01:27:42 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2425599"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird Content-Language: en-US In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 8138 Lines: 154 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. > > Incompleteness(math) is this same sort of thing. > Nope, just beyond your understanding.