Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Sat, 9 Nov 2024 18:35:34 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <6ac375cdb6e76add46f57afd23342155d4579b9e@i2pn2.org>
References: <vfli1h$fj8s$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>
	<aef6ebd4fa217f82361fe0117963a949dba66d90@i2pn2.org>
	<vgo4ve$3sfle$2@dont-email.me>
	<fd204ca3ebbad724d3b34ff1775891ccd4f87d04@i2pn2.org>
	<vgo762$3t0tb$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
Injection-Date: Sat, 9 Nov 2024 18:35:34 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="1661163"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="nS1KMHaUuWOnF/ukOJzx6Ssd8y16q9UPs1GZ+I3D0CM";
User-Agent: Pan/0.145 (Duplicitous mercenary valetism; d7e168a
 git.gnome.org/pan2)
X-Spam-Checker-Version: SpamAssassin 4.0.0
Bytes: 5628
Lines: 81

Am Sat, 09 Nov 2024 11:46:42 -0600 schrieb olcott:
> On 11/9/2024 11:27 AM, joes wrote:
>> Am Sat, 09 Nov 2024 11:09:02 -0600 schrieb olcott:
>>> On 11/9/2024 10:04 AM, joes wrote:
>>>> Am Sat, 09 Nov 2024 08:45:12 -0600 schrieb olcott:
>>>>> On 11/9/2024 5:01 AM, joes wrote:
>>>>>> Am Fri, 08 Nov 2024 18:39:34 -0600 schrieb olcott:
>>>>>>> On 11/8/2024 6:33 PM, Richard Damon wrote:
>>>>>>>> On 11/8/24 6:36 PM, olcott wrote:
>>>>>>>>> On 11/8/2024 3:59 PM, Richard Damon wrote:
>>>>>>>>>> On 11/8/24 4:17 PM, olcott wrote:
>>>>>>>>>>> On 11/8/2024 12:31 PM, Richard Damon wrote:
>>>>>>>>>>>> On 11/8/24 1:08 PM, olcott wrote:
>>>>>>>>>>>>> On 11/8/2024 12:02 PM, Richard Damon 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.
>>> Gödel had a different f-cking basis.
>> Where is the difference?
> True is only provable from axioms thus ~Provable(PA, G) == ~True(PA, G)
The metatheory proves otherwise. If G were not true, ~G would need to
be provable.

>>>>> When truth is only derived by starting with truth and applying truth
>>>>> preserving operations then unprovable in PA becomes untrue in PA.
>>>> No, unless your system is less powerful than PA.
>>>> Untrue means the negation is true, but ~G is also unprovable.
>>> It is not any less powerful than PA in the same f-cking way that ZFC
>>> is not less powerful than naive set theory.

Then it is incomplete or inconsistent.


>>>>>>>>>> But, as I pointed out, the way Meta-Math is derived from PA,
>>>>>>>>> Meta-math <IS NOT> PA.
>>>>>>>>> True in meta-math <IS NOT> True in PA.
>>>>>> Yes it is. If MM proves that a sentence is true in PA, that
>>>>>> sentence is true in PA.
>>>>> Within my model: Only PA can prove what is true in PA.

PA can’t prove anything about itself.

>>>>>>>> But MM has exactly the same axioms and rules as PA, so anything
>>>>>>>> established by that set of axioms and rules in MM is established
>>>>>>>> in PA too.
>>>>>>>> There are additional axioms in MM, but the rules are built
>>>>>>>> specifically
>>>>>>> One single level of indirect reference CHANGES EVERYTHING. PA
>>>>>>> speaks PA. Meta-math speaks ABOUT PA.
>>>>>>> The liar paradox is nonsense gibberish except when applied to
>>>>>>> itself, then it becomes true.

What is "the liar paradox applied to itself"?

>>>>> Can yo please add a newline so that you comments are no buried in my
>>>>> comments?
>>>> How does your newsreader mark quotes?
>>> Instead of replying immediately after my comment, skip a line. Leave a
>>> freaking blank line inbetween.
>> Does your reader not mark quotes?
Are you reading in plaintext?

>>>>> This sentence is not true: "This sentence is not true" is true
>>>>> because the inner sentence is nonsense gibberish.
>>>> I think you missed some quotation marks there. The outer sentence is
>>>> true, but the inner is perfectly wellformed and syntactically
>>>> correct.
>>> https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously is
>>> also syntactically well formed and semantic gibberish.
>> "This sentence is not true" however has a welldefined meaning.
> No it does f-cking not. WTF is it true about?

Itself?

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.