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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Formal systems that cannot possibly be incomplete except for
 unknowns and unknowable
Date: Tue, 6 May 2025 12:14:04 -0500
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On 5/6/2025 5:04 AM, joes wrote:
> Am Mon, 05 May 2025 14:22:58 -0500 schrieb olcott:
>> On 5/5/2025 1:52 PM, Alan Mackenzie wrote:
>>> olcott <polcott333@gmail.com> wrote:
>>>> On 5/5/2025 1:19 PM, Alan Mackenzie wrote:
>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>> On 5/5/2025 11:05 AM, Alan Mackenzie wrote:
>>>
>>>>>>> Follow the details of the proof of Gödel's Incompleteness Theorem,
>>>>>>> and apply them to your "system".  That will give you your counter
>>>>>>> example.
>>>
>>>>>> My system does not do "provable" instead it does "provably true".
>>>
>>>>> I don't know anything about your "system" and I don't care.  If it's
>>>>> a formal system with anything above minimal capabilities, Gödel's
>>>>> Theorem applies to it, and the "system" will be incomplete (in
>>>>> Gödel's sense).
>>>
>>>> I reformulate the entire notion of "formal system"
>>>> so that undecidability ceases to be possible.
>>>
>>> Liar.  That is impossible.
>>>
>> When you start with truth and only apply truth preserving operations
>> then you necessarily end up with truth.
> Truth such as Gödel's undecidability theorem, but not all truths.
> 

The entire body of all general knowledge that can be
expressed using language is included in the system
that I propose.

Undecidability cannot possibly occur in any system
that ONLY derives True(x) by applying truth preserving
operations to basic facts that are stipulated to be true.

LP = "This sentence is not true."
True(LP) == FALSE
True(~LP) == FALSE
Proves that LP is not a valid proposition with a truth value.

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