Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: comp.theory Subject: Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct Date: Sun, 10 Nov 2024 11:52:39 +0200 Organization: - Lines: 66 Message-ID: References:

<8c2cbbe343934d211ad8c820c963702e70351a27@i2pn2.org> <19d0838dd000cc4f67c8c64ac6005d5405cf2bd6@i2pn2.org>

<4b24331953934da921cb7547b6ee2058ac9e7254@i2pn2.org> <2a5107f331836f388ad259bf310311a393c00602@i2pn2.org>

MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 10 Nov 2024 10:52:39 +0100 (CET) Injection-Info: dont-email.me; posting-host="c32afbfa9d2d3187c54a1874aafea3ea"; logging-data="356361"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX192fXInNcvQ94JUj3BZg0y4" User-Agent: Unison/2.2 Cancel-Lock: sha1:8uKOJRO32gWUIpnF/Plrvodc200= Bytes: 4408 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. -- Mikko