Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct Date: Mon, 11 Nov 2024 08:51:20 -0600 Organization: A noiseless patient Spider Lines: 129 Message-ID: References:

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MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 11 Nov 2024 15:51:23 +0100 (CET) Injection-Info: dont-email.me; posting-host="caa393ed49c937630dd8ea795c5bbe8f"; logging-data="1095850"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/6m4qpjEI3wnJ6WbzP3Boo" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:u8OOIwMqFU96pmb2lsQFrw17tUI= In-Reply-To: Content-Language: en-US X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 241111-0, 11/10/2024), Outbound message Bytes: 7133 On 11/11/2024 4:33 AM, Mikko wrote: > On 2024-11-11 04:41:24 +0000, olcott said: > >> On 11/10/2024 10:03 PM, Richard Damon wrote: >>> On 11/10/24 10:08 PM, olcott wrote: >>>> On 11/10/2024 3:52 AM, Mikko wrote: >>>>> On 2024-11-09 18:05:38 +0000, olcott said: >>>>> >>>>>> On 11/9/2024 11:58 AM, Alan Mackenzie wrote: >>>>>>> olcott wrote: >>>>>>>> On 11/9/2024 10:03 AM, Alan Mackenzie wrote: >>>>>>>>> olcott wrote: >>>>>>>>>> On 11/9/2024 5:01 AM, joes wrote: >>>>>>>>>>>>>>>>>>> On 11/8/24 12:25 PM, olcott wrote: >>>>>>> >>>>>>>>>>>>>>>>>>>> That formal systems that only apply truth preserving >>>>>>>>>>>>>>>>>>>> operations >>>>>>>>>>>>>>>>>>>> to expressions of their formal language that have been >>>>>>>>>>>>>>>>>>>> stipulated to be true cannot possibly be undecidable >>>>>>>>>>>>>>>>>>>> is proven >>>>>>>>>>>>>>>>>>>> to be over-your-head on the basis that you have no >>>>>>>>>>>>>>>>>>>> actual >>>>>>>>>>>>>>>>>>>> reasoning as a rebuttal. >>>>>>>>>>> Gödel showed otherwise. >>>>>>> >>>>>>>>>> That is counter-factual within my precise specification. >>>>>>> >>>>>>>>> That's untrue - you don't have a precise specification. And >>>>>>>>> even if you >>>>>>>>> did, Gödel's theorem would still hold. >>>>>>> >>>>>>>>>> When truth is only derived by starting with >>>>>>>>>> truth and applying truth preserving operations >>>>>>>>>> then unprovable in PA becomes untrue in PA. >>>>>>> >>>>>>>>> No. Unprovable will remain. >>>>>>> >>>>>>>> *Like I said you don't pay f-cking attention* >>>>>>> >>>>>>> Stop swearing. I don't pay much attention to your provably false >>>>>>> utterances, no. Life is too short. >>>>>>> >>>>>> >>>>>> That you denigrate what I say without paying attention to what >>>>>> I say the definition of reckless disregard for the truth >>>>>> that loses defamation cases. >>>>>> >>>>>>> Hint: Gödel's theorem applies in any sufficiently powerful logical >>>>>>> system, and the bar for "sufficiently powerful" is not high. >>>>>>> >>>>>> >>>>>> Unless it is stipulated at the foundation of the notion of >>>>>> formal systems that ~Provable(PA, g) simply means ~True(PA, g). >>>>>> >>>>>>>> Unprovable(L,x) means Untrue(L,x) >>>>>>>> Unprovable(L,~x) means Unfalse(L,x) >>>>>>>> ~True(L,x) ^ ~True(L, ~x) means ~Truth-Bearer(L,x) >>>>>>> >>>>>>> If you're going to change the standard meaning of standard words, >>>>>>> you'll >>>>>>> find communicating with other people somewhat strained and >>>>>>> difficult. >>>>>>> >>>>>> >>>>>> ZFC did the same thing and that was the ONLY way >>>>>> that Russell's Paradox was resolved. >>>>>> >>>>>> When ~Provable(PA,g) means ~True(PA,g) then >>>>>> incompleteness cannot exist. >>>>> >>>>> But it doesn't. "Provable(PA,g)" means that there is a proof on g >>>>> in PA >>>>> and "~Provable(PA,g)" means that there is not. These meanings are >>>>> don't >>>>> involve your "True" in any way. You may define "True" as a synonym to >>>>> "Provable" but formal synonyms are not useful. >>>>> >>>> >>>> We can ALWAYS prove that any expression of language is true or >>>> not on the basis of other expressions of language when we have a >>>> coherent definition of True(L,x). >>>> >>> >>> No, we can't. >>> >> >> Proof(Olcott) means a sequence of truth preserving operations >> that many not be finite. > > With a hyperfinite sequnce it is possible to prove a false claim. > It will always be possible to merely prove a false claim. What ceases to be possible is proving that a false claim is true. Within the premise that "elephants are dead mice" it can be proved that {elephants are dead mice} the non-truth of that expression is preserved. Let {T} be such a theory. Then the elementary statements which belong to {T} we shall call the elementary theorems of {T}; we also say that these elementary statements are true for {T}. Thus, given {T}, an elementary theorem is an elementary statement which is true. https://www.liarparadox.org/Haskell_Curry_45.pdf Haskell Curry is referring to a set of expressions that are stipulated to be true in T. We define True(L, x) to mean x is a necessary consequence of the Haskell Curry elementary theorems of L. (Haskell_Curry_Elementary_Theorems(L) □ x) ≡ True(L, x) > The most obvious truth preserving operation is the identity operation. > Its result is the same as its premise, so the truth valure of the > result must be the same as the truth value of the premise. So we > can form a hyperfinite sequence > > 1 = 1, 1 = 1, 1 = 1, ... , 1 = 2, 1 = 2, 1 = 2 > > where ... denotes infinitely manu intermedate steps. The first equation > is true, every other equation is as ture as the one before it and the > last equation is false. > -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer