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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory,sci.logic Subject: Re: Analytic Truth-makers Date: Wed, 24 Jul 2024 19:57:03 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <4b85633014d21d53e9494bc7dcfbdb15afc24edf@i2pn2.org> References: <3fb77583036a3c8b0db4b77610fb4bf4214c9c23@i2pn2.org> <5406ed035cafb6c47d3b89e92dac58f0b9c67fe8@i2pn2.org> <994febb86b9367c19b35fc184522efc3f562ab04@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 24 Jul 2024 23:57:03 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="245891"; 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: 8016 Lines: 170 On 7/24/24 10:20 AM, olcott wrote: > On 7/24/2024 6:28 AM, Richard Damon wrote: >> On 7/24/24 12:09 AM, olcott wrote: >>> On 7/23/2024 10:27 PM, Richard Damon wrote: >>>> On 7/23/24 11:17 PM, olcott wrote: >>>>> On 7/23/2024 10:03 PM, Richard Damon wrote: >>>>>> On 7/23/24 10:45 PM, olcott wrote: >>>>>>> On 7/23/2024 9:15 PM, Richard Damon wrote: >>>>>>>> On 7/23/24 12:26 PM, olcott wrote: >>>>>>>>> On 7/23/2024 9:51 AM, Wasell wrote: >>>>>>>>>> On Mon, 22 Jul 2024 20:17:15 -0400, in article >>>>>>>>>> <3fb77583036a3c8b0db4b77610fb4bf4214c9c23@i2pn2.org>, Richard >>>>>>>>>> Damon wrote: >>>>>>>>>>> >>>>>>>>>>> On 7/22/24 8:11 PM, olcott wrote: >>>>>>>>>> >>>>>>>>>> [...] >>>>>>>>>> >>>>>>>>>>>> *No stupid I have never been saying anything like that* If g >>>>>>>>>>>> and >>>>>>>>>>>> ~g is not provable in PA then g is not a truth-bearer in PA. >>>>>>>>>>> >>>>>>>>>>> What makes it different fron Goldbach's conjecture? >>>>>>>>>> >>>>>>>>>> I think a better example might be Goodstein's theorem [1]. >>>>>>>>>> >>>>>>>>>> * It is expressible in the same language as PA. >>>>>>>>>> >>>>>>>>>> * It is neither provable, nor disprovable, in PA. >>>>>>>>>> >>>>>>>>>> * We know that it is true in the standard model of arithmetic. >>>>>>>>>> >>>>>>>>>> * We know that it is false in some (necessarily non-standard) >>>>>>>>>> models >>>>>>>>>>    of arithmetic. >>>>>>>>>> >>>>>>>>>> * It was discovered and proved long before it was shown to be >>>>>>>>>>    undecidable in PA. >>>>>>>>>> >>>>>>>>>> The only drawback is that the theorem is somewhat more >>>>>>>>>> complicated >>>>>>>>>> than Goldbach's conjecture -- not a lot, but a bit. >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> [1] >>>>>>>>> >>>>>>>>> >>>>>>>>> I am establishing a new meaning for >>>>>>>>> {true on the basis of meaning expressed in language} >>>>>>>>> Formerly known as {analytic truth}. >>>>>>>>> This makes True(L,x) computable and definable. >>>>>>>> >>>>>>>> You may say that, but you then refuse to do the work to actually >>>>>>>> do that. >>>>>>>> >>>>>>>> The problem is that if you try to redefine the foundation, you >>>>>>>> need to build the whole building all over again, but you just >>>>>>>> don't understand what you need to do that. >>>>>>>> >>>>>>>>> >>>>>>>>> L is the language of a formal mathematical system. >>>>>>>>> x is an expression of that language. >>>>>>>>> >>>>>>>>> When we understand that True(L,x) means that there is a finite >>>>>>>>> sequence of truth preserving operations in L from the semantic >>>>>>>>> meaning of x to x in L, then mathematical incompleteness is >>>>>>>>> abolished. >>>>>>>> >>>>>>>> Except you just defined that this isn't true, as you admit that >>>>>>>> the Goldbach conjecgture COULD be an analytic truth even if it >>>>>>>> doesn't have a finte sequence of truth perserving operations, >>>>>>> >>>>>>> I redefined analytic truth to account for that. Things >>>>>>> like the Goldbach conjecture are in the different class >>>>>>> of currently unknowable. >>>>>> >>>>>> In other words, NOTHING you are talking about apply to the logic >>>>>> that anyone else is using. >>>>>> >>>>>> Note, Godel's G can't be put into that category, as it is KNOWN to >>>>>> be true in PA, because of a proof in MM >>>>> >>>>> You ONLY construe it to be true in PA because that is >>>>> the answer that you memorized. >>>> >>>> No, it is True in PA, because it is LITERALLY True by the words it >>>> uses. >>>> >>>>> >>>>> When you understand that true requires a sequence of >>>>> truth preserving operations and they do not exist in >>>>> PA then it is not true in PA. >>>> >>>> But they DO exist in PA, I guess you just don't understand how math >>>> works. >>>> >>>> The sequence of steps is: >>>> >>>> Check the number 0 to see if it satisfies the PRR. Answer = No. >>>> Check the number 1 to see if it satisfies the PRR. Answer = No. >>>> Check the number 2 to see if it satisfies the PRR. Answer = No. >>>> >>>> keep repeating counting up through all the Natural Numbers. >>>>  From the trick in MM, we can see that the math in PA will say no to >>>> all of them. >>>> >>>> Thus, after an infinite number of steps of truth preserving >>>> operations, we reach the conclusion that NO natural numbers actually >>>> exist that meet that PRR, just like G claimed, so it is correct. >>>> >>> >>> The lack of a proof means untruth. >> >> Nope, lack of a proof means unknown, as you have agreed. > > If an infinite number of steps fail to show that G is > provable in PA then G is untrue in PA. But the infinte number of steps DO show that G is true in PA, because is shows that EVERY Natural Number fails to meet the requirment. YOu don't seem to be understanding the English, I think your brainwashed filter is just clogged. > >> After all, you admitted that if the Goldbach conjecture would be an >> Analytic TRUTH if it was only established by an infinite sequence of >> truth preserving operations. >> > > If an infinite number of steps do show that Goldbach is > provable in PA then Goldbach is true in PA. Right, Just like they showed that G is true. > >> Since you don't know the meaning of the words, you just prove yourself >> unqualified to talk about such things. >> > > Any proof requiring an infinite number of steps never resolved > to a truth value thus its truth value remains unknown. No, "Proofs" can not have an infinite number of steps, proofs are ALWAYS finite in conventional logic. > > An alternative finite proof in MM only shows that the expression > is true in MM. Nope, since the rules of math are the same, it must also be true in PA. I guess you think that just because 2+3 = 5 in one system with normal mathematics, in another system with the exact same rules for mathematics then 2 + 3 might be 6. > > Truthmakers cannot cross system boundaries. -- > Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius > hits a target no one else can see." Arthur Schopenhauer > But the base truthmakers for G in MM and PA are the same items, there is ========== REMAINDER OF ARTICLE TRUNCATED ==========