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 Date: Fri, 31 Jan 2025 11:42:57 -0600 Organization: A noiseless patient Spider Lines: 55 Message-ID: References: <0a91bd587521969c17e88e93eb8b2076b7a3b0f7@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 18:42:58 +0100 (CET) Injection-Info: dont-email.me; posting-host="c8ea502332c1ce874eeb9f2ef1eb0fea"; logging-data="3800293"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+mXN1X0FvQRR5aVcVsxhTg" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:5fYFn6PvbarP52wjJt+xz3SNKuQ= X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 250131-10, 1/31/2025), Outbound message Content-Language: en-US In-Reply-To: Bytes: 3789 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. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer