Re: ALL undecidability is unmasked

From	olcott <polcott333@gmail.com>
Newsgroups	sci.logic, sci.math, comp.theory
Subject	Re: ALL undecidability is unmasked
Date	2026-07-15 10:14 -0500
Organization	A noiseless patient Spider
Message-ID	<1138849$1925n$1@dont-email.me> (permalink)
References	<1133181$3n00p$1@dont-email.me> <1134uh7$8rn9$1@dont-email.me> <11363cq$la1s$1@dont-email.me> <1137cm5$10g9m$1@dont-email.me>

Cross-posted to 3 groups.

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On 7/15/2026 2:25 AM, Mikko wrote:
> On 14/07/2026 22:41, olcott wrote:
>> On 7/14/2026 4:12 AM, Mikko wrote:
>>> On 13/07/2026 18:46, olcott wrote:
>>>> All undecidability is unmasked as semantic
>>>> incoherence or outside of the body of knowledge.
>>>
>>> Gödel's sentence is true about natural numbers. 
>>
>> That stays the same in my system yet in my system
>> undecidability and incompleteness cannot possibly exist.
> 
> If Gödel's undecidable sentence does not exist in your system then
> you cannot say in that system that it is true about natural numbers.
> 
>> P ⊢ Q means syntactic derivation implements semantic
>> entailment encoded in syntactically the language.
> 
> The exact meaning ⊢ depends on the context. When talking about Gödel's
> sentence it means, unless defined otherwise, that the sentence Q can
> be inferred from P according to the rules of ordinary formal logic.
> 

I am stipulating that it only means
<semantic entailment encoded syntactically>

>> This is the only inference steps allowed.
> 
> THere are equivalent ways to represent ordinary logic. 

My system includes the semantics of Full English.

> Some styles
> use only one inference rule, usually modus ponens,

<semantic entailment encoded syntactically>
is the only inference step allowed.

>  and a large set
> of axioms and axiom rules. Others use a large set of inference
> rules and a small set of axioms and axiom rules or even no axioms
> and axiom rules at all.
> 
>> PA ⊢ G is simply false.
>> (P ∧ ¬P) ⊢ Q is simply false.
> 
> The latter is off-topic per the subject line. But in any context
> people really car or need to care about (P ∧ ¬P) ⊢ Q is true,

Full English semantics thus the meaning of
the words of P forces the meaning of the words
of Q to be true, else not an inference step.

-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).

Thread

ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-13 10:46 -0500
  Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-14 10:11 +0300
    Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-14 13:18 -0500
      Re: ALL undecidability is unmasked "Fred. Zwarts" <F.Zwarts@HetNet.nl> - 2026-07-15 11:11 +0200
        Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-15 09:56 -0500
          Re: ALL undecidability is unmasked "Fred. Zwarts" <F.Zwarts@HetNet.nl> - 2026-07-16 11:01 +0200
            Re: ALL undecidability is unmasked "Fred. Zwarts" <F.Zwarts@HetNet.nl> - 2026-07-18 12:02 +0200
              Re: ALL undecidability is unmasked Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-07-18 20:07 +0100
  Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-14 12:12 +0300
    Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-14 14:41 -0500
      Re: ALL undecidability is unmasked André G. Isaak <agisaak@gm.invalid> - 2026-07-14 13:48 -0600
        Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-14 15:01 -0500
          Re: ALL undecidability is unmasked André G. Isaak <agisaak@gm.invalid> - 2026-07-14 14:30 -0600
            Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-14 15:42 -0500
              Re: ALL undecidability is unmasked André G. Isaak <agisaak@gm.invalid> - 2026-07-14 15:06 -0600
                Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-14 16:14 -0500
                Re: ALL undecidability is unmasked André G. Isaak <agisaak@gm.invalid> - 2026-07-14 15:34 -0600
                Re: ALL undecidability is unmasked Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-18 13:48 +0100
      Re: ALL undecidability is unmasked Alan Mackenzie <acm@muc.de> - 2026-07-14 19:57 +0000
        Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-14 15:16 -0500
          Re: ALL undecidability is unmasked dbush <dbush.mobile@gmail.com> - 2026-07-14 16:18 -0400
          Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-15 10:35 +0300
            Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-15 10:31 -0500
              Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-16 12:16 +0300
          Re: ALL undecidability is unmasked Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-18 14:17 +0100
      Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-15 10:25 +0300
        Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-15 10:14 -0500
          Re: ALL undecidability is unmasked Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-15 20:18 +0100
            Re: ALL undecidability is unmasked olcott <polcott333@gmail.com> - 2026-07-15 14:44 -0500
              Re: ALL undecidability is unmasked Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-18 19:21 +0100
              Re: ALL undecidability is unmasked Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-18 19:21 +0100
            Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-16 09:11 +0300
              Re: ALL undecidability is unmasked Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-18 12:30 +0100
                Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-19 11:55 +0300
                Re: ALL undecidability is unmasked Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-19 10:49 +0100
                Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-20 10:54 +0300
                Re: ALL undecidability is unmasked Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-21 13:31 +0100
                Re: ALL undecidability is unmasked Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-21 08:43 -0700
                Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-22 09:58 +0300
          Re: ALL undecidability is unmasked dbush <dbush.mobile@gmail.com> - 2026-07-15 15:24 -0400
          Re: ALL undecidability is unmasked Mikko <mikko.levanto@iki.fi> - 2026-07-16 12:23 +0300

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