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 --- Ultimate Foundation of Truth Date: Thu, 27 Feb 2025 22:02:00 -0600 Organization: A noiseless patient Spider Lines: 97 Message-ID: References: <0f7cd503773838ad12f124f23106d53552e277b8@i2pn2.org> <7e3e9d35d880cfcad12f505dfb39c5650cdd249e@i2pn2.org> <3cf165ef9793e844dc9d5db82aecbc47f9545367@i2pn2.org> <080bf2b1c322247548c6ec61c9f054359062ccd4@i2pn2.org> <6fc61a762b56308f9919993f29ba3e77f7ba84c7@i2pn2.org> <6320ec8cdc4ab9fc06e5001c0b4069132ce1af58@i2pn2.org> <9c6309a46ca0fdf2ce98f50a09891e143d81ab90@i2pn2.org> <0e0c21ec5ccaeec8f341a86ed64c7447c34d162b@i2pn2.org> <8638c66ecc1669437be5a141cfa358c8c6168cde@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 28 Feb 2025 05:02:04 +0100 (CET) Injection-Info: dont-email.me; posting-host="de9c75e0e594a6c6f2c98c0fd19b8497"; logging-data="3697451"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX183JbjBE5TSluFbudABABkP" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:J5INOSsmUrFl6mVXOnT3epuGo0Y= Content-Language: en-US X-Antivirus-Status: Clean In-Reply-To: <8638c66ecc1669437be5a141cfa358c8c6168cde@i2pn2.org> X-Antivirus: Norton (VPS 250227-10, 2/27/2025), Outbound message Bytes: 5947 On 2/27/2025 7:00 PM, Richard Damon wrote: > On 2/27/25 9:46 AM, olcott wrote: >> On 2/27/2025 6:45 AM, Richard Damon wrote: >>> On 2/26/25 11:24 PM, olcott wrote: >>>> On 2/26/2025 9:59 PM, Richard Damon wrote: >>>>> On 2/26/25 8:39 PM, olcott wrote: >>>>>> On 2/26/2025 10:03 AM, joes wrote: >>>>>>> Am Wed, 26 Feb 2025 08:34:47 -0600 schrieb olcott: >>>>>>>> On 2/26/2025 6:18 AM, joes wrote: >>>>>>>>> Am Tue, 25 Feb 2025 12:40:04 -0600 schrieb olcott: >>>>>>>>>> On 2/25/2025 12:15 PM, joes wrote: >>>>>>>>>>> Am Mon, 24 Feb 2025 20:02:49 -0600 schrieb olcott: >>>>>>>>>>>> On 2/24/2025 6:12 PM, Richard Damon wrote: >>>>>>>>>>>>> On 2/24/25 6:11 PM, olcott wrote: >>>>>>>>>>>>>> On 2/24/2025 6:27 AM, Richard Damon wrote: >>>>>>>>>>>>>>> On 2/23/25 11:39 PM, olcott wrote: >>>>>>>>>>>>>>>> On 2/23/2025 8:50 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>> On 2/23/25 1:08 PM, olcott wrote: >>>>>>>>> >>>>>>>>>>>>>>> Sure I do. >>>>>>>>>>>>>>> A Systems is semantically sound if every statement that >>>>>>>>>>>>>>> can be >>>>>>>>>>>>>>> proven is actually true by the systems semantics, >>>>>>>>>>>>>> That is very good. >>>>>>>>>>>>>> >>>>>>>>>>>>>>> in other words, the system doesn't allow the proving of a >>>>>>>>>>>>>>> false >>>>>>>>>>>>>>> statement. >>>>>>>>>>>>>> That is not too bad yet ignores that some expressions >>>>>>>>>>>>>> might not >>>>>>>>>>>>>> have any truth value. >>>>>>>>>>>>> Which has nothing to do with "soundness". >>>>>>>>>>>> When any system assumes that every expression is true or >>>>>>>>>>>> false and >>>>>>>>>>>> is capable of encoding expressions that are neither IT IS >>>>>>>>>>>> STUPIDLY >>>>>>>>>>>> WRONG. >>>>>>>>>>> In honour of Gödel this is usually called "incomplete". >>>>>>>>>> Where "incomplete" has always been an idiom for stupid wrong. >>>>>>>>> Your understanding of logic is incomplete. >>>>>>> Which is to say, stupidly wrong. >>>>>>> >>>>>>>> The screwed up notion of "incomplete" is anchored in the stupid >>>>>>>> idea >>>>>>>> that {true in the system} is not required to be {provable in the >>>>>>>> system}. >>>>>>> You are about a century behind on the foundations of mathematics. >>>>>>> >>>>>>>> Any expression of language that can only be verified as true on the >>>>>>>> basis of other expressions of language either has a semantic >>>>>>>> connection >>>>>>>> truthmaker to these other expressions or IT IS SIMPLY NOT TRUE. >>>>>>> I.e. its negation is true. >>>>>>> >>>>>> >>>>>> WTF is the truth value of the negation of nonsense? >>>>>> The Liar Paradox has ALWAYS simply been nonsense. >>>>>> >>>>> >>>>> But we aren't negating "nonsense", we are negating the actual valid >>>>> truth value out of the Truth Primative. >>>>> >>>>> You don't seem to understand that the DEFINITION of what a truth >>>>> primative is requires that True(Nonsense) be false, not "nonsense". >>>>> >>>> >>>>   True("lkekngnkerkn") == false >>>> False("lkekngnkerkn") == false >>>> >>> >>> But ~True("lkekngnkerkn") == true. >>> >> >> Yes >> >>> so if we can define that lkekngnkerkn is ~True(lkekngnkerkn) then we >>> have a problem. >>> f >> >> We are not defining gibberish as anything. >> Gibberish evaluates as ~True because it is gibberish. > > But you are trying to define LP := !True(LP) as gibberish. > Prolog already knows that it gibberish. It has an infinite cycle in the directed graph of its evaluation sequence. See Page 3 for Prolog https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer