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

From olcott <polcott333@gmail.com>
Newsgroups sci.logic
Subject Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable
Date 2025-05-05 10:39 -0500
Organization A noiseless patient Spider
Message-ID <vvam4d$o6v5$3@dont-email.me> (permalink)
References <vv97ft$3fg66$1@dont-email.me> <vva1ls$6uhv$1@dont-email.me>

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On 5/5/2025 4:50 AM, Mikko wrote:
> On 2025-05-05 02:23:56 +0000, olcott said:
> 
>> 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.
> 
> A formal system has a formal language. Unless the language is too
> restricted for most interesting purposes the negation of every
> sentence is another sentence. In a consistent system some sentence
> is unprovable. If the negation of that system is also unprovable
> then the system is incomplete.
> 

My system skips merely "provable" and goes directly to "provably true".
Expressions such as "This sentence is not true" and its negation
are not provably true, thus rejected as semantically unsound.

> None of the features of specified above prevents an expressible unprovable
> sentence that has an unprovable negation. While adding one of the pair
> to the basic facts there is nothing to prevent an infinite set of such
> pairs.
> 

Basic facts are stipulated to be a finite set
of general knowledge of the world.


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

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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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