Path: ...!news.misty.com!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 Date: Wed, 5 Feb 2025 10:05:16 -0600 Organization: A noiseless patient Spider Lines: 143 Message-ID: References: <0a91bd587521969c17e88e93eb8b2076b7a3b0f7@i2pn2.org> <36192d00aaf301e5c52be81836755df34f81e5a9@i2pn2.org> <4147f656ab66e4e46f1eab853cc6793efea6ce6e@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Wed, 05 Feb 2025 17:05:17 +0100 (CET) Injection-Info: dont-email.me; posting-host="d482ff4fa4aff5c1ec39fbb15be7cf0c"; logging-data="2582965"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/MNb3DADK6u8scJRVeVatX" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:LXGgVFDkP8M0Kx37d2nH3QvoK9U= In-Reply-To: Content-Language: en-US X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 250205-4, 2/5/2025), Outbound message Bytes: 8038 On 2/5/2025 6:08 AM, Richard Damon wrote: > On 2/4/25 11:30 PM, olcott wrote: >> On 2/3/2025 6:39 PM, Richard Damon wrote: >>> On 2/3/25 12:00 PM, olcott wrote: >>>> 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. >>> >>> Which can be a connection of infinite length. >>> >>>> >>>> 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. >>> >>> But provable is a statment about the existance of a FINITE sequence >>> of connection >>> >> >> That IS NOT what Proof[0] means. >> Proof[0] means that a connection to a truth-maker exists. >> > > Show me an actual formal system defined that allows "Proof" to be an > infinite connection to the truth-maker. All you are doing ios proving > that you are just making up everything you say, > Math is not allowed to change the base meaning of terms. When-so-ever any expression of formal or natural language X lacks a connection to its truthmaker X remains untrue. > I think part of the problem is you just don't understand what a Formal > System is, and since Incompleteness is a property of Formal System (not > just general philosophy) that is an important part. > > Of course, your big part for not understanding Formal Systens is you > don't believe you need to follow the rules, and that is fundamental to > Formal Logic, so its concepts are just foreign to you. > > Sorry, you are just proving your total ignorance of what you talk about, > and so ignorant that you can't see your ignorance. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer