Path: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise --- Olcott doesn't
 understand about formal systems and meta
Date: Mon, 8 Jul 2024 23:39:39 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <8fe08ea4af72f421ed298cf0151929f216797266@i2pn2.org>
References: <v67685$6fr5$1@solani.org> <v6cpnc$1b3m$2@dont-email.me>
 <9e59212316a9b258e95a1de7f5cca46fee37861e@i2pn2.org>
 <v6csla$1otr$2@dont-email.me>
 <3f12eb90be522441c8b95d17d25767fcaf72ed2d@i2pn2.org>
 <v6cvqs$5vir$2@dont-email.me>
 <efced1648cf7ddc1c257d7c4369add3b391dd005@i2pn2.org>
 <v6d2r0$6cgn$2@dont-email.me>
 <931fe5b1e73d204bf20a268dd025489e3040371d@i2pn2.org>
 <v6e5ho$bbcb$2@dont-email.me>
 <0f3e40caf51b61ebb05c4ec2ae44042bff632017@i2pn2.org>
 <v6el1u$e6tb$1@dont-email.me>
 <3c9ef913b1fbbca50c1a4acd02401906646327ed@i2pn2.org>
 <RpKdnUjg8sjx0Bb7nZ2dnZfqlJydnZ2d@giganews.com>
 <2d0b6260615af8afac79ee8de57bcd45c2f2056f@i2pn2.org>
 <v6fk9p$mr5k$1@dont-email.me>
 <8bd5f2159853ff17ef81b27a85141bccc324e7d9@i2pn2.org>
 <v6fkrb$mr5k$2@dont-email.me> <v6fl9a$mr5k$3@dont-email.me>
 <v6huj5$12ktu$2@dont-email.me>
 <7387a77d06e4b00a1c27a447e2744a4f10b25e49@i2pn2.org>
 <v6i08a$12ktu$4@dont-email.me>
 <c81e1794259853dfd7724900ebfab484679615be@i2pn2.org>
 <v6ib0e$185d2$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 9 Jul 2024 03:39:40 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="2644019"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
X-Spam-Checker-Version: SpamAssassin 4.0.0
In-Reply-To: <v6ib0e$185d2$1@dont-email.me>
Content-Language: en-US
Bytes: 6087
Lines: 119

On 7/8/24 11:32 PM, olcott wrote:
> On 7/8/2024 7:37 PM, Richard Damon wrote:
>> On 7/8/24 8:28 PM, olcott wrote:
>>> On 7/8/2024 7:07 PM, Richard Damon wrote:
>>>> On 7/8/24 8:00 PM, olcott wrote:
>>>>> On 7/7/2024 10:09 PM, olcott wrote:
>>>>>> On 7/7/2024 10:02 PM, olcott wrote:
>>>>>>>
>>>>>>> Formal logic is a subset of this.
>>>>>>> Not-a-logic-sentence(PA,g) ≡ (~True(PA,g) ∧ ~True(PA,~g))
>>>>>>> There are no truth preserving operations in PA to g or to ~g
>>>>>>>
>>>>>>
>>>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>>>
>>>>>> Within my analytical framework this Tarski sentence is merely
>>>>>> self-contradictory
>>>>>>
>>>>>> (3) x ∉ Provable if and only if x ∈ True. // (1) and (2) combined
>>>>>>
>>>>>> There are no truth preserving operations in Tarski's
>>>>>> theory to x if and only if There are truth preserving
>>>>>> operations in Tarski's theory to x
>>>>>>
>>>>>
>>>>> There cannot possibly be an infinite proof that proves
>>>>> that there is no finite proof of Tarski x in Tarski's theory
>>>>
>>>> Who says there needs to be a infinite proof, since there is no such 
>>>> thing.
>>>>
>>>> As I said, one example of such an x is Godel's G.
>>>>
>>>>>
>>>>> The infinite proof of the Goldbach conjecture
>>>>> (if it is true) continues to find more true
>>>>> cases than it had before, thus makes progress
>>>>> towards its never ending goal (if its true).
>>>>
>>>> or, it continue to show that there is no counter examples.
>>>>
>>>> "Progress" on an infinite path isn't really measurable.
>>>>
>>>>>
>>>>> The cycles in the following two cases never make any progress
>>>>> towards any goal they are merely stuck in infinite loops.
>>>>
>>>> Which just means you are on the wrong path. One wrong path doesn't 
>>>> me that there is no path.
>>>>
>>>>>
>>>>> The Prolog unify_with_occurs_check test means that
>>>>> LP is stuck in an infinite loop that makes no progress
>>>>> towards resolution. I invented Minimal Type Theory to
>>>>> see this, then I noticed that Prolog does the same thing.
>>>>
>>>> Which is irrelevent, since Prolog can't handle the basics of the 
>>>> field that Traski assumes.
>>>>
>>>>>
>>>>> ?- LP = not(true(LP)).
>>>>> LP = not(true(LP)).
>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>> false.
>>>>>
>>>>> LP := ~(L ⊢ LP)
>>>>> 00 ~ 01
>>>>> 01 ⊢ 01, 00
>>>>> 02 L
>>>>>
>>>>> The cycle in the direct graph of LP is
>>>>> an infinite loop that make no progress
>>>>> towards the goal of evaluating LP as
>>>>> true or false.
>>>>>
>>>>>
>>>>
>>>> So?
>>>>
>>>> Failure to prove by example doesn't show something isn't true.
>>>>
>>>> You are just proving you are stupid and don't know what you are 
>>>> talking about.
>>>
>>> Every expression of language that cannot be proven
>>> or refuted by any finite or infinite sequence of
>>> truth preserving operations connecting it to its
>>> meaning specified as a finite expression of language
>>> is rejected.
>>>
>>
>> So?
>>
>> Tarski's x like Godel's G are know to be true by an infinite sequence 
>> of truth preserving operations.
>>
> 
> "are *know to be true* by an infinite sequence"
> "are *know to be true* by an infinite sequence"
> "are *know to be true* by an infinite sequence"
> "are *know to be true* by an infinite sequence"
> "are *know to be true* by an infinite sequence"
> 
> On 7/8/2024 9:59 PM, Richard Damon wrote:
>  > No, infinite "proofs" determine TRUTH, not knowledge.
> 

Right, G is known (by meta-F) that it is true (in F) because of an 
infinite sequence of truth preserving steps IN F.

By meta-system we can know something about a system that in that system 
it can only be know with an infinite chain.

This idea seems to be beyound your understanding, I think because you 
just don't understand how formal system work, and thus how meta-systems 
work.

These proof you have so much troble with all are dealing with systems 
and meta-systems, and I think you loose track of what is said about each 
and in what system shows it.