Path: ...!2.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability --- incorrect question
Date: Tue, 22 Oct 2024 10:04:37 -0500
Organization: A noiseless patient Spider
Lines: 53
Message-ID: <vf8eu5$1h5mj$2@dont-email.me>
References: <veoift$29dtl$2@dont-email.me> <veoq3j$2aqp2$1@dont-email.me>
 <vf716u$1607j$1@dont-email.me> <vf7ks8$1d1vt$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Tue, 22 Oct 2024 17:04:38 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="0250fa4f333a237bb4a9bec06e6bd0e6";
	logging-data="1611475"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1++Mwrtki7B2Y9TQqUCGYgo"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:AS+dRmwTfRyOI5tIy//jy6T0X0E=
X-Antivirus: Norton (VPS 241022-2, 10/22/2024), Outbound message
In-Reply-To: <vf7ks8$1d1vt$1@dont-email.me>
Content-Language: en-US
X-Antivirus-Status: Clean
Bytes: 3272

On 10/22/2024 2:39 AM, Mikko wrote:
> On 2024-10-22 02:04:14 +0000, olcott said:
> 
>> On 10/16/2024 11:37 AM, Mikko wrote:
>>> On 2024-10-16 14:27:09 +0000, olcott said:
>>>
>>>> The whole notion of undecidability is anchored in ignoring the fact 
>>>> that
>>>> some expressions of language are simply not truth bearers.
>>>
>>> A formal theory is undecidable if there is no Turing machine that
>>> determines whether a formula of that theory is a theorem of that
>>> theory or not. Whether an expression is a truth bearer is not
>>> relevant. Either there is a valid proof of that formula or there
>>> is not. No third possibility.
>>>
>>
>> After being continually interrupted by emergencies
>> interrupting other emergencies...
>>
>> If the answer to the question: Is X a formula of theory Y
>> cannot be determined to be yes or no then the question
>> itself is somehow incorrect.
> 
> There are several possibilities.
> 
> A theory may be intentionally incomplete. For example, group theory
> leaves several important question unanswered. There are infinitely
> may different groups and group axioms must be true in every group.
> 
> Another possibility is that a theory is poorly constructed: the
> author just failed to include an important postulate.
> 
> Then there is the possibility that the purpose of the theory is
> incompatible with decidability, for example arithmetic.
> 
>> An incorrect question is an expression of language that
>> is not a truth bearer translated into question form.
>>
>> When "X a formula of theory Y" is neither true nor false
>> then "X a formula of theory Y" is not a truth bearer.
> 
> Whether AB = BA is not answered by group theory but is alwasy
> true or false about specific A and B and universally true in
> some groups but not all.
> 

See my most recent reply to Richard it sums up
my position most succinctly.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer