Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise Date: Fri, 5 Jul 2024 15:12:54 -0500 Organization: A noiseless patient Spider Lines: 185 Message-ID: References: <4394939716c6c6d2ed1fa9b5a269ed261768914e@i2pn2.org> <5e4fb6d29fbd03c807c9a8d4140f807a44c29cb9@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 05 Jul 2024 22:12:55 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f325a973008a37eaa6ec545239278e3d"; logging-data="3603178"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX194iAZGpI00KFqEguDyd9V+" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:exJpHjkcp0+1+7ICth/SuTi6iqc= In-Reply-To: <5e4fb6d29fbd03c807c9a8d4140f807a44c29cb9@i2pn2.org> Content-Language: en-US Bytes: 9083 On 7/5/2024 2:54 PM, Richard Damon wrote: > On 7/5/24 1:38 PM, olcott wrote: >> On 7/5/2024 11:23 AM, Richard Damon wrote: >>> On 7/4/24 11:19 PM, olcott wrote: >>>> On 7/4/2024 10:00 PM, Richard Damon wrote: >>>>> On 7/4/24 10:38 PM, olcott wrote: >>>>>> On 7/4/2024 8:58 PM, Mild Shock wrote: >>>>>>> >>>>>>> When red means blue, and yellow means >>>>>>> green, then black is white. Thanks for your hint! >>>>>>> >>>>>>> If my Grandmother had wheels she would have been a bike >>>>>>> https://www.youtube.com/watch?v=OplyHCIBmfE >>>>>>> >>>>>> >>>>>> *Here is the same thing more clearly* >>>>>> Every expression of language that is {true on the basis of >>>>>> its verbal meaning} is only made true by a sequence of truth >>>>>> preserving operations to this {verbal meaning}. >>>>>> >>>>>> The only way that we know that puppies are not fifteen >>>>>> story office buildings is that the accurate verbal model >>>>>> of the actual world tells use so. >>>>> >>>>> But, even if we can't find that sequence of truth perserving >>>>> operations, but one exists (which might be infinite) makes the >>>>> statement true, but not known. >>>>> >>>>> This is one of your confusions, You confuse a statment being True, >>>>> with the statement being KNOWN to be True. >>>>> >>>>> There are a number of great problems and conjectures that seem to >>>>> be true, but we can not prove them. They MUST be either True or >>>>> False, as by their nature, there is no middle ground (something >>>>> either exsits or it doesn't, or the count of something is either >>>>> finite or infinite). >>>>> >>>>> The ACTUAL TRUTH  (or falsehood) of such a statement is thus firmly >>>>> established by the system in which the conjeture is embedded, even >>>>> if our knowledge of the value of the truth of the statement is not >>>>> known, or possible even knowable. >>>>> >>>>> The concept of "incompleteness" for a logical system is a >>>>> recognition that the system has grown powerful enough that there >>>>> exist some truths in the system that no finite proof of those >>>>> statements exist, and only infinite chains of inference in the >>>>> system can establish it. >>>>> >>>>> Mathematics is one source for these sorts of truths, as the >>>>> possiblity of problems having NO number that satisfy them, or an >>>>> infinite number that satisfy them show paths that can use in >>>>> infinite number of steps to prove them, and might only be provable >>>>> if some "inductive" shortcut can be found. >>>>> >>>> >>>> Yet my system screens out pathological expressions that >>>> are incorrectly determined to be incompleteness of the >>>> formal system. When we do that then True(L,x) can be defined >>>> for every expression not requiring an infinite sequence >>>> of steps. True(L,x) or True(L,~x) or not a truth bearer in L. >>> >>> No, it dies in self-inconsistency. >>> >>> Note "Every expression BUT ..."  isn't "Every expresion ." >>> >> >> Every expression such that neither X nor ~X is provable in L >> is simply not a truth bearer in L. This does correctly reject >> self-contradictory expressions that wold otherwise be interpreted >> as the incompleteness of L. > > FALSE STATEMENT. > Can't be false it is stipulated. > Some statements are true due to an infinite number of steps to ther > truth-makers of the system. > Already covered that. > You will lead your logic system into contradictions by your definition > (or you just need to treat it as a worthless phrase that doesn't > actually tell you anything, particually what you call non-truth-bearers, > which might actuall be statement that are true or false). > Not at all. Such a system does detect and reject self-contradictory expressions thus does not use this as any basis for incompleteness. >> >> This works correctly for every element of the accurate verbal >> model of the actual world. Since we can see that things like >> the Goldbach conjecture can be proven *OR REFUTED* in an infinite >> sequence then an algorithm can see this too. For everything >> else it is an infallibly correct system of reasoning. >> > > So, you ADMIT that you definition doesn't work for some statements, and > thus is not correct. > It detects expressions that require infinite steps as out of scope and correctly determines all of the rest. > Note, the algorithm can not tell wether the statement like to Goldback > conjecture is true or not, or even if it takes an infinite number of > steps to come to that answer. Thus, you statement is just a FALSEHOOD. > Not at all. Because it is dead obvious to humans that Goldbach can be proved or refuted in an infinite number of steps an algorithm can see this too. > You just don't understand logic well enough to understand that can't > have definitions that just don't work as the basis of a system. > > By your definition, the Goldbach conjecture must currently be consider a > non-truth-bearer, but we KNOW that it must be either true or false, we It would be construed as out-of-scope. Whether or not there was evidence of: (a) Election fraud that could have possibly changed the outcome of the 2020 presidential election or (b) Very harmful climate change caused by humans would be in scope. > just don't know which, so you definition of a truth-bearer is just a lie. > > What you are defining are KNOWLEDGE bearers, statements that there truth > can be known. The key problem that it solves is that it makes True(L,x) computable for all of the most important things that really matter. You are essentially saying that A cure for cancer is totally useless because it only cures 99.99% of cancers. > But we can't even know if the Goldbach conjecture is a > knowledge-bearer or not. If it turns out to be false, then that fact is > knowable, but not yet known (since showing the number, as a simple > finite proof that no pair of primes below it sum to it make it prove > false), but if it is true, there might be a proof, or there might not be. > > So even Knowledge-Bearers as a concept is has limited use. Knowledge, > that which we currently know, is a valid concept, and one that admits > things can be added to it. > > And Truth-Bearers, with the allowance of infinite chains to establish > the truth (or falseness) of the statement can be useful, though we do > need to admit we don't know, and perhaps CAN'T know that truth value, > and need to allow for some statements that we don't yet have the ability > to know if they are truth-bearers or not. > > But your definition of truth-bearers is just worthless for most logic > systems, claiming to be about truth but actually being about knowledge > isn't a good definition, and just shows your fundamental > misunderstanding about what is actually truth and how it differs from > knowledge. > >> >>> So, your logic only works in systems small enough to be somewhat akin >>> to toys. Those that are limited enough not to be able to cause the >>> problems, which means it excludes most systems that support math. >>> >>>> >>>>>> >>>>>>> olcott schrieb: >>>>>>>> When provable means true and false means unprovable >>>>>>>> then (Γ ⊢ X) means X is true in Γ. ========== REMAINDER OF ARTICLE TRUNCATED ==========