Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!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 [CORRECTION] Date: Mon, 3 Feb 2025 14:41:19 -0600 Organization: A noiseless patient Spider Lines: 134 Message-ID: References: <0a91bd587521969c17e88e93eb8b2076b7a3b0f7@i2pn2.org> <36192d00aaf301e5c52be81836755df34f81e5a9@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Mon, 03 Feb 2025 21:41:20 +0100 (CET) Injection-Info: dont-email.me; posting-host="acd5597f2faaf24a7b8ac9a26cbba261"; logging-data="1538274"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18C9V+YRVEkPZ11MynkuZ5W" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:H7ozdoGT4YMSNX3YR/mHatiNV60= Content-Language: en-US X-Antivirus: Norton (VPS 250203-4, 2/3/2025), Outbound message X-Antivirus-Status: Clean In-Reply-To: Bytes: 7453 On 2/1/2025 12:23 PM, Richard Damon wrote: > On 2/1/25 1:10 PM, olcott wrote: >> On 2/1/2025 7:56 AM, Richard Damon wrote: >>> On 1/31/25 10:43 PM, olcott wrote: >>>> On 1/31/2025 7:52 PM, Richard Damon wrote: >>>>> On 1/31/25 12:42 PM, olcott wrote: >>>>>> On 1/31/2025 10:08 AM, Richard Damon wrote: >>>>>>> On 1/31/25 10:20 AM, olcott wrote: >>>>>>>> On 1/31/2025 8:49 AM, Richard Damon wrote: >>>>>>>>> On 1/30/25 8:24 PM, olcott wrote: >>>>>>>>>> On 1/30/2025 7:06 PM, Richard Damon wrote: >>>>>>>>>>> On 1/30/25 6:10 PM, olcott wrote: >>>>>>>>>>>> Within the entire body of analytical truth any expression of >>>>>>>>>>>> language that has no sequence of formalized semantic >>>>>>>>>>>> deductive inference steps from the formalized semantic >>>>>>>>>>>> foundational truths of this system are simply untrue in this >>>>>>>>>>>> system. (Isomorphic to provable from axioms). >>>>>>>>>>>> >>>>>>>>>>>> In other words when any expression of language of any system >>>>>>>>>>>> (formal or informal) has no semantic connection to its >>>>>>>>>>>> semantic meaning in this system then this expression is >>>>>>>>>>>> simply nonsense in this system. "This sentence is untrue" is >>>>>>>>>>>> Boolean nonsense. >>>>>>>>>>>> >>>>>>>>>>>> Copyright PL Olcott 2016 through 2025. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Except that isn't what incompleteness says. >>>>>>>>>>> >>>>>>>>>>> Incompleteness is about the existance of statements which are >>>>>>>>>>> TRUE, because there is a sequence of formal semantic >>>>>>>>>>> deduction that reaches the statement, abet an infinite one, >>>>>>>>>>> but there is no finite sequnce of formal semantic deduction >>>>>>>>>>> to form a proof. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> That might be correct. If it is correct then all then >>>>>>>>>> all that it is really saying is that math is incomplete >>>>>>>>>> because some key pieces were intentionally left out. >>>>>>>>> >>>>>>>>> What was left out? >>>>>>>>> >>>>>>>> >>>>>>>> If there exists no contiguous sequence of semantic deductive >>>>>>>> inference >>>>>>>> steps from the basic facts of a system establishing that the >>>>>>>> semantic meaning of this expression has a value of Boolean true >>>>>>>> in this system then this expression is simply not true in this >>>>>>>> system even if it may be >>>>>>>> true in other more expressive systems. >>>>>>>> >>>>>>>> The system is incomplete in the artificially contrivance way of >>>>>>>> deliberately defined system to be insufficiently expressive. >>>>>>>> >>>>>>> >>>>>>> And what about the fact that ther *IS* a contiguos sequence, >>>>>>> infinite in length, that makes the statement true that you don't >>>>>>> understand. >>>>>>> >>>>>> >>>>>> "Incomplete" means that there is no contiguous sequence of inference >>>>>> steps within the expressiveness of this specific formal system. >>>>>> >>>>> >>>>> No, "Incomplete" means that there is some true statement that can >>>>> not be proven. >>>>> >>>> >>>> Within empirical truth this is possible. >>>> Within analytical truth this is impossible. >>> >>> No, you only think it is impossible, becuase you don't know what you >>> are talking about. >>> >>>> >>>> Unless there is a semantic connection with >>>> a truthmaker to what makes the expression >>>> true IS IS NOT TRUE. >>> >>> Right, and that can be an INFINITE series of connection, which thus >>> don't form a proof. >>> >> >> It does make a {proof} within the foundational base meaning >> of the term {proof} even though it may not meet the idiomatic >> term-of-the-art meaning from math. The generic notion of {Truth} >> itself is only defined in terms of base meanings. When math >> diverges from this it is no longer talking about actual truth. >> >> > > The "foundational base meaning" of a proof in Formal Logic is a FINITE > series. > True[0] cannot possibly exist for any expression of language that is only made true by a semantic connection to its truthmaker WITHOUT SUCH A CONNECTION. This makes the notion of provable[math] essentially a misnomer because it attempts to override and supersede the most basic foundation of the notion of truth itself. > I know of no standard theory of logic that admits an infinite series of > steps as a "proof", as we can not do an infinite series of steps, and a > proof is normally about knowledge, and thus needs to be about something > that we can actually do. > > We can do a finite series of steps to show that an infinite series of > steps exist in another system by the properties of meta-logic, but that > is not a "proof" in that other system, only in the meta-system, again > something that seems to be beyond your understanding. > > And, you are wrong that "truth" only has a single base meaning, as Truth > is established by several different meanings each given a different > "class" of Truth. > > I'm sorry, but you are just showing that you don't really understand the > terms you are using, and tha that you don't even have enough of a basis > to understand that you don't understand the terms. > > You HAVE been shown this, and your repeatedly repeating the same proven > false claims just shows that you are totally ignorant of what you talk > about, and have no concern about the actual meaning of Truth. This shows > that you native tounge is that of your "father", the tounge of lies, > which you try your best to sprea. > > Sorry that you are sealing your fate, which you are likely going to see > sooner than you want. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer