Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable ---ELABORATED

From	olcott <polcott333@gmail.com>
Newsgroups	sci.logic, comp.theory
Subject	Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable ---ELABORATED
Date	2025-05-06 12:46 -0500
Organization	A noiseless patient Spider
Message-ID	<vvdhtn$3cbpq$6@dont-email.me> (permalink)
References	<vv97ft$3fg66$1@dont-email.me> <b47c9e70d415c1e5e469aaab846f0bd05e4bcc51@i2pn2.org> <vvall0$o6v5$1@dont-email.me> <vvc33h$25atc$1@dont-email.me> <0d5349e23b0e81271cc1e08acfe90c45524ceb0a@i2pn2.org>

Cross-posted to 2 groups.

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On 5/6/2025 6:20 AM, Richard Damon wrote:
> On 5/6/25 12:27 AM, olcott wrote:
>> On 5/5/2025 10:31 AM, olcott wrote:
>>> On 5/5/2025 6:04 AM, Richard Damon wrote:
>>>> On 5/4/25 10:23 PM, olcott wrote:
>>>>> When we define formal systems as a finite list of basic facts and 
>>>>> allow semantic logical entailment as the only rule of inference we 
>>>>> have systems that can express any truth that can be expressed in 
>>>>> language.
>>>>>
>>>>> Also with such systems Undecidability is impossible. The only 
>>>>> incompleteness are things that are unknown or unknowable.
>>>>
>>>> Can such a system include the mathematics of the natural numbers?
>>>>
>>>> If so, your claim is false, as that is enough to create that 
>>>> undeciability.
>>>>
>>>
>>> It seems to me that the inferences steps that could
>>> otherwise create undecidability cannot exist in the
>>> system that I propose.
>>>
>>
>> The mathematics of natural numbers (as I have already explained)
>> begins with basic facts about natural numbers and only applies
>> truth preserving operations to these basic facts.
>>
>> When we begin with truth and only apply truth preserving
>> operations then WE NECESSARILY MUST END UP WITH TRUTH.
>>
>> When we ALWAYS end up with TRUTH then we NEVER end up with 
>> UNDECIDABILITY.
>>
>> Its not that hard, iff you pay enough attention.
>>
> 
> But we do, because decidability requires finite steps to get the answer, 
> but Trurh can come from an infinite number of steps.
> 

True(x) accepts any x that can be derived by applying truth
preserving operations to the set of Basic Facts that comprise
the entire body of general knowledge that can be expressed
in language and rejects everything else.

True(x) is really Known_to_be_True(x).
True(~x) is really Known_to_be_False(x).

It cannot have any undecidability its is membership
algorithm for the set of all general knowledge that
can be expressed using language.

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

Thread

Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-04 21:23 -0500
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mikko <mikko.levanto@iki.fi> - 2025-05-05 12:50 +0300
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 10:39 -0500
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mikko <mikko.levanto@iki.fi> - 2025-05-06 13:02 +0300
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Alan Mackenzie <acm@muc.de> - 2025-05-05 10:47 +0000
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 16:03 -0500
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Alan Mackenzie <acm@muc.de> - 2025-05-06 08:30 +0000
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mikko <mikko.levanto@iki.fi> - 2025-05-06 13:04 +0300
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-05 07:04 -0400
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mr Flibble <flibble@red-dwarf.jmc.corp> - 2025-05-05 14:46 +0000
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Heathfield <rjh@cpax.org.uk> - 2025-05-05 16:51 +0100
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mr Flibble <flibble@red-dwarf.jmc.corp> - 2025-05-05 16:10 +0000
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Heathfield <rjh@cpax.org.uk> - 2025-05-05 17:59 +0100
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-05 21:08 -0400
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 10:31 -0500
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-05 21:11 -0400
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 21:26 -0500
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-06 07:16 -0400
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 23:27 -0500
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Alan Mackenzie <acm@muc.de> - 2025-05-06 08:17 +0000
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-06 07:20 -0400
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable ---ELABORATED olcott <polcott333@gmail.com> - 2025-05-06 12:46 -0500
            Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable ---ELABORATED Richard Damon <richard@damon-family.org> - 2025-05-06 22:07 -0400
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-15 16:24 +0000
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-11-15 10:55 -0600
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-15 17:30 +0000
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-11-15 11:43 -0600
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-15 16:49 +0000
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-11-15 11:19 -0600
  Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself olcott <polcott333@gmail.com> - 2025-11-16 09:29 -0600
    Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself HAL 9000 <hal@discovery.nasa> - 2025-11-16 16:46 +0000
      Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself olcott <polcott333@gmail.com> - 2025-11-16 11:07 -0600
      DD simulated by HHH cannot possibly terminate normally olcott <polcott333@gmail.com> - 2025-11-16 11:20 -0600
      Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-16 13:18 -0800

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