Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic knowledge
Date: Sat, 5 Apr 2025 10:44:07 +0300
Organization: -
Lines: 40
Message-ID: <vsqn07$1nmlv$1@dont-email.me>
References: <vrfvbd$256og$2@dont-email.me> <vrh432$39r47$1@dont-email.me> <vrhami$3fbja$2@dont-email.me> <vrj9lu$1791p$1@dont-email.me> <vrjn82$1ilbe$2@dont-email.me> <vrmpc1$bnp3$1@dont-email.me> <vrmteo$cvat$6@dont-email.me> <vru000$33rof$1@dont-email.me> <vrug71$3gia2$6@dont-email.me> <0306c3c2d4a6d05a8bb7441c0b23d325aeac3d7b@i2pn2.org> <vrvnvv$ke3p$1@dont-email.me> <vs0egm$1cl6q$1@dont-email.me> <vs1f7j$296sp$2@dont-email.me> <vs3ad6$2o1a$1@dont-email.me> <vs4sjd$1c1ja$8@dont-email.me> <vs63o2$2nal3$1@dont-email.me> <vs6v2l$39556$17@dont-email.me> <vs8hia$13iam$1@dont-email.me> <vs8uoq$1fccq$2@dont-email.me> <vsb4in$14lqk$1@dont-email.me> <vsb9d5$19ka5$1@dont-email.me> <04aa9edbe77f4e701297d873264511f820d85526@i2pn2.org> <vsbu9j$1vihj$1@dont-email.me> <vsdlso$3shbn$2@dont-email.me> <vsen5l$th5g$5@dont-email.me> <vsg1b2$2ed9k$1@dont-email.me> <vsh9c9$3mdkb$2@dont-email.me> <vsj073$1g8q1$1@dont-email.me> <vsjn4k$26s7s$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sat, 05 Apr 2025 09:44:07 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="f9307d8d2dc3a84618ee3d69a5f67187";
	logging-data="1825471"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/5HdtrONnIe3vQRnukEza/"
User-Agent: Unison/2.2
Cancel-Lock: sha1:OjXGep4IZFMBchaPEv+jVl8DmLM=
Bytes: 3337

On 2025-04-02 16:03:32 +0000, olcott said:

> On 4/2/2025 4:32 AM, Mikko wrote:
>> On 2025-04-01 17:56:25 +0000, olcott said:
>> 
>>> On 4/1/2025 1:33 AM, Mikko wrote:
>>>> On 2025-03-31 18:33:26 +0000, olcott said:
>>>> 
>>>>> 
>>>>> Anything the contradicts basic facts or expressions
>>>>> semantically entailed from these basic facts is proven
>>>>> false.
>>>> 
>>>> Anything that follows from true sentences by a truth preserving
>>>> transformations is true. If you can prove that a true sentence
>>>> is false your system is unsound.
>>> 
>>> Ah so we finally agree on something.
>>> What about the "proof" that detecting inconsistent
>>> axioms is impossible? (I thought that I remebered this).
>> 
>> A method that can always determine whether a set of axioms is inconsistent
>> does not exist. However, there are methods that can correctly determine
>> about some axiom systems that they are inconsistent and fail on others.
>> 
>> The proof is just another proof that some function is not Turing computable.
> 
> A finite set of axioms would seem to always be verifiable
> as consistent or inconsistent.  This may be the same for
> a finite list of axiom schemas.

If ordinary logic is used it is sufficient to prove that there is
a sentence that cannot be proven in order to prove consistency or
to prove two sentences that contradict each other in order to prove 
inconsistency. But if neither proof is known there is no method to
find one.

-- 
Mikko