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 --- Ultimate Foundation of Truth Date: Wed, 26 Feb 2025 22:59:56 -0500 Organization: i2pn2 (i2pn.org) Message-ID: References: <0f7cd503773838ad12f124f23106d53552e277b8@i2pn2.org> <7e3e9d35d880cfcad12f505dfb39c5650cdd249e@i2pn2.org> <3cf165ef9793e844dc9d5db82aecbc47f9545367@i2pn2.org> <080bf2b1c322247548c6ec61c9f054359062ccd4@i2pn2.org> <6fc61a762b56308f9919993f29ba3e77f7ba84c7@i2pn2.org> <6320ec8cdc4ab9fc06e5001c0b4069132ce1af58@i2pn2.org> <9c6309a46ca0fdf2ce98f50a09891e143d81ab90@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 27 Feb 2025 03:59:56 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1971976"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US In-Reply-To: Bytes: 4917 Lines: 68 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". This isn't tri-valued logic we are talking about. And even if you tried to make a tri-valued logic, we run into the problem that if we were really talking about a tri-valued logic, we get back to the problem by just defining a simple predicate that operates on logic values and maps: True -> True False -> False Nonsense -> False and we get back to the original problem. You need "Nonsense" to not be a logic value, but something more like a signal-Nan with no way to test it without triggering it, which isn't something logic accepts in the normal domain, and likely just isn't useful.