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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott <polcott333@gmail.com> Newsgroups: sci.logic Subject: Re: Mathematical incompleteness has always been a misconception Date: Fri, 31 Jan 2025 09:20:24 -0600 Organization: A noiseless patient Spider Lines: 45 Message-ID: <vnipno$3i9to$1@dont-email.me> References: <vnh0sq$35mcm$1@dont-email.me> <0a91bd587521969c17e88e93eb8b2076b7a3b0f7@i2pn2.org> <vnh8nn$36l6o$1@dont-email.me> <ea5f49681418383d811c8989f031d0376ec4bca0@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Fri, 31 Jan 2025 16:20:25 +0100 (CET) Injection-Info: dont-email.me; posting-host="c8ea502332c1ce874eeb9f2ef1eb0fea"; logging-data="3745720"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+tmjZQsvojRlhrtBQ3Wzay" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:gE3jh7VrUCy+u1MmE+NKfs+zCL8= In-Reply-To: <ea5f49681418383d811c8989f031d0376ec4bca0@i2pn2.org> X-Antivirus-Status: Clean Content-Language: en-US X-Antivirus: Norton (VPS 250131-8, 1/31/2025), Outbound message Bytes: 3235 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. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer