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 <mikko.levanto@iki.fi>
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: <vgpvp7$as09$1@dont-email.me>
References: <vfli1h$fj8s$1@dont-email.me> <vgakbd$vlda$1@dont-email.me> <vgbm5r$sgg9$1@dont-email.me> <vgg6fh$2s61$1@news.muc.de> <vgg7tk$26klj$1@dont-email.me> <vggjtb$1f3u$1@news.muc.de> <vggund$2am72$1@dont-email.me> <vgkudf$1lrm$1@news.muc.de> <vgl78d$37h38$2@dont-email.me> <vgl9cm$6e3$1@news.muc.de> <vgl9uh$37h38$9@dont-email.me> <vglcnh$agb$1@news.muc.de> <vgldr3$38uph$1@dont-email.me> <vglfui$agb$2@news.muc.de> <vglhij$39mg2$1@dont-email.me> <8c2cbbe343934d211ad8c820c963702e70351a27@i2pn2.org> <vglk31$3a6hn$1@dont-email.me> <19d0838dd000cc4f67c8c64ac6005d5405cf2bd6@i2pn2.org> <vglv58$3bn2s$3@dont-email.me> <cd6cbe7d70fcc282da94aea2107e48ad4b3f44b5@i2pn2.org> <vgm79v$3d9gu$1@dont-email.me> <4b24331953934da921cb7547b6ee2058ac9e7254@i2pn2.org> <vgmb06$3e37h$1@dont-email.me> <2a5107f331836f388ad259bf310311a393c00602@i2pn2.org> <vgnsho$3qq7s$2@dont-email.me> <vgo157$n00$1@news.muc.de> <vgo4ia$3sfle$1@dont-email.me> <vgo7ri$30iv$1@news.muc.de> <vgo89i$3t6n8$1@dont-email.me>
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 <polcott333@gmail.com> wrote:
>>> On 11/9/2024 10:03 AM, Alan Mackenzie wrote:
>>>> olcott <polcott333@gmail.com> 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 <is> 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