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Re: ALL undecidability is unmasked

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On 7/15/2026 2:18 PM, Tristan Wibberley wrote:
> On 15/07/2026 16:14, olcott wrote:
>> 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.
> 
> 
> Really, it refers to inferences of a system with statements formed with
> the unary predicate "|-" *or stipulated alternative presentations of the
> predicate*.
> 
> Godel's system P didn't stipulate the predicate so you don't have to be
> very careful just because you're talking about Godel's sentence, you
> have to be careful because there's such a commonly used meaning in logic
> for "|-" which is derived from Frege's system and reformalised to
> 
>    "A, B, C |- D" is short for "|-A & |-B & |-C => |-D".
> 
> When you say "in this chapter I relate two logistic systems, the
> relating system has the '|-' symbol for the usual predicate but to
> distinguish their statements from it they have '!' and '?' in its place
> in their statements, respectively," you are stipulating alternative
> presentations so you can have the union of the statements of the three
> and you can't use P |- Q for inferences that have statements from the
> two inferior systems for P or for Q - you'd have to say things like "!P
> => ?Q" instead. When you reason about a system that doesn't have the |-
> predicate you can use it by the de faqto conventions of the group you're
> posting at.
> 
> 

P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.

The language of Olcott's system includes the full semantics
of natural language embedded directly in this language.
Its "basic fact" axioms are in a type hierarchy /
knowledge ontology.

It is capable of processing this expression pair:
This sentence is not true: "This sentence is not true"

as the outer expression is true on the basis that the
inner expression has no truth value.

-- 
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).

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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 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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