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: Sat, 1 Mar 2025 19:17:08 -0600 Organization: A noiseless patient Spider Lines: 94 Message-ID: References: <0f7cd503773838ad12f124f23106d53552e277b8@i2pn2.org> <7e3e9d35d880cfcad12f505dfb39c5650cdd249e@i2pn2.org> <3cf165ef9793e844dc9d5db82aecbc47f9545367@i2pn2.org> <080bf2b1c322247548c6ec61c9f054359062ccd4@i2pn2.org> <6fc61a762b56308f9919993f29ba3e77f7ba84c7@i2pn2.org> <41ca355a1f535e767e17d3f4df3d404eb1e61cef@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 02:17:10 +0100 (CET) Injection-Info: dont-email.me; posting-host="0a4c634d78a3c572e27d924fefebd45f"; logging-data="495235"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+gtvlk0DaRV98Qr8D4WbIO" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:eVsHy2GKmGf+vzVWhlOE7eA1hTU= X-Antivirus: Norton (VPS 250301-6, 3/1/2025), Outbound message Content-Language: en-US X-Antivirus-Status: Clean In-Reply-To: Bytes: 6141 On 3/1/2025 3:58 PM, Richard Damon wrote: > On 3/1/25 2:58 PM, olcott wrote: >> On 3/1/2025 2:45 AM, Mikko wrote: >>> On 2025-02-28 22:04:31 +0000, olcott said: >>> >>>> On 2/28/2025 4:04 AM, Mikko wrote: >>>>> On 2025-02-26 01:33:48 +0000, olcott said: >>>>> >>>>>> On 2/25/2025 5:58 PM, Richard Damon wrote: >>>>>>> On 2/25/25 1:40 PM, olcott wrote: >>>>>>>> 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: >>>>>>>>>>>>>>>> On 2/22/2025 9:56 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>> On 2/22/25 1:42 PM, olcott wrote: >>>>>>>>>>>>>>>>>> On 2/22/2025 3:25 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>> On 2025-02-22 04:44:35 +0000, olcott said: >>>>>>>>>>>>>>>>>>>> On 2/21/2025 7:05 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>> On 2/21/25 6:19 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 2/20/2025 2:54 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 2025-02-18 03:59:08 +0000, olcott said: >>>>>>>>> >>>>>>>>>>>>> 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. >>>>>>>> >>>>>>> >>>>>>> No, only in your faulty logic. >>>>>>> >>>>>>> Incomplete means that there are some truths that can't be proven >>>>>>> in the system. >>>>>>> >>>>>> >>>>>> That comes from stupidly failing to require {true in the system} >>>>>> to require {proven in the system}. Fix this one stupid mistake >>>>>> and all of incompleteness goes away. >>>>> >>>>> No, that merely means that "true in the system" is incomplete in some >>>>> systems (e.g., natural numbers). There are sentences that are true in >>>>> practical applications of the system but not in the system itself. >>>>> That is not a defect as it does not prevent useful practical >>>>> aplications. >>>> >>>> The bottom line here is that expressions that do not have >>>> a truth-maker are always untrue. Logic screws this up by >>>> overriding the common meaning of terms with incompatible >>>> meanings. Provable(common) means has a truth-maker. >>> >>> Logic doesn't care about truths and truth makers except in the (usually >>> uninteresting) special cases where truth makers are found in the logic >>> itself. >>> >> >> Incompleteness(math) and Undecidability(logic) are >> artifacts of defining the term provable(math) >> in a way that is inconsistent with provable(common) >> {shown to be definitely true by whatever means}. >> > > Nopw, because shown(common) requires a finite sequence to show to > someone, as people can not see all of an infinite sequence > If the Goldbach conjecture is true and there is only an infinite sequence as its truth-maker then this infinite sequence its proof(common) {shown to be definitely true by whatever means}. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer