Path: ...!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: sci.logic Subject: Re: Mathematical incompleteness has always been a misconception Date: Sat, 1 Feb 2025 08:56:17 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <36192d00aaf301e5c52be81836755df34f81e5a9@i2pn2.org> References: <0a91bd587521969c17e88e93eb8b2076b7a3b0f7@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sat, 1 Feb 2025 13:56:17 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2185258"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US Bytes: 4911 Lines: 92 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. > > This is "proof" in the big sense of the term, > not the term-of-the-art thus idiomatic mathematical > meaning. > > And thus, you admit that you LIE. Incompleteness is a term-of-art based on terms-of-art. So, to use another definition is just an admission of LYING. That you have done this lying for decades, is evidence that you are nothing but the damned liar that you like to talk about and accuse other of. It is a natural characteristic of "evil" to just blindly project its own evil on others.