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 --- Tarski Date: Thu, 13 Feb 2025 07:17:40 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <8536ee3d6c6779e9c6dffd843b8559fe1bc43d61@i2pn2.org> References: <7e532aaf77653daac5ca2b70bf26d0a3bc515abf@i2pn2.org> <215f0e70debdc339ff49a081984405aeb8312c3c@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Thu, 13 Feb 2025 12:17:41 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="4036608"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: Content-Language: en-US X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 4058 Lines: 60 On 2/12/25 11:08 PM, olcott wrote: > On 2/11/2025 9:36 PM, Richard Damon wrote: >> On 2/11/25 9:07 AM, olcott wrote: >>> On 2/11/2025 3:50 AM, Mikko wrote: >>>> On 2025-02-10 11:48:16 +0000, olcott said: >>>> >>>>> On 2/10/2025 2:55 AM, Mikko wrote: >>>>>> On 2025-02-09 13:10:37 +0000, Richard Damon said: >>>>>> >>>>>>> On 2/9/25 5:33 AM, Mikko wrote: >>>>>>>> Of course, completness can be achieved if language is sufficiently >>>>>>>> restricted so that sufficiently many arithemtic truths become >>>>>>>> inexpressible. >>>>>>>> >>>>>>>> It is far from clear that a theory of that kind can express all >>>>>>>> arithmetic >>>>>>>> truths that Peano arithmetic can and avoid its incompletness. >>>>>>> >>>>>>> WHich, it seems, are the only type of logic system that Peter can >>>>>>> understand. >>>>>>> >>>>>>> He can only think in primitive logic systems that can't reach the >>>>>>> complexity needed for the proofs he talks about, but can't see >>>>>>> the problem, as he just doesn't understand the needed concepts. >>>>>> >>>>>> That would be OK if he wouldn't try to solve problems that cannot >>>>>> even >>>>>> exist in those systems. >>>>> >>>>> There are no problems than cannot be solved in a system >>>>> that can also reject semantically incorrect expressions. >>>> >>>> The topic of the discussion is completeness. Is there a complete system >>>> that can solve all solvable problems? >>>> >>> >>> When the essence of the change is to simply reject expressions >>> that specify semantic nonsense there is no reduction in the >>> expressive power of such a system. >>> >> >> The problem is your logic rejects its own output as semantic nonsense. >> > > Spouting off nonsense without any actual basis in reasoning... WHat nonsense? I speak a fact. The "result" of True(L, x) must be an output of your logic system. To say that !True(L, x) is a "nonsense", means either you logic doesn't have a well define negation operator, or True(L, x) is itself nonsense. Thus, your "logic" calls itself nonsense. All you are doing is proving that everything you have been saying is just built on nonsense, and that nonsense is your native tongue. >