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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Re: Undecidability based on epistemological antinomies V2 --Tarski
 Proof--
Date: Sun, 21 Apr 2024 09:44:37 -0500
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On 4/21/2024 2:57 AM, Mikko wrote:
> On 2024-04-20 15:20:05 +0000, olcott said:
> 
>> On 4/20/2024 2:54 AM, Mikko wrote:
>>> On 2024-04-19 18:04:48 +0000, olcott said:
>>>
>>>> When we create a three-valued logic system that has these
>>>> three values: {True, False, Nonsense}
>>>> https://en.wikipedia.org/wiki/Three-valued_logic
>>>
>>> Such three valued logic has the problem that a tautology of the
>>> ordinary propositional logic cannot be trusted to be true. For
>>> example, in ordinary logic A ∨ ¬A is always true. This means that
>>> some ordinary proofs of ordinary theorems are no longer valid and
>>> you need to accept the possibility that a theory that is complete
>>> in ordinary logic is incomplete in your logic.
>>>
>>
>> I only used three-valued logic as a teaching device. Whenever an
>> expression of language has the value of {Nonsense} then it is
>> rejected and not allowed to be used in any logical operations. It
>> is basically invalid input.
> 
> You cannot teach because you lack necessary skills. Therefore you
> don't need any teaching device.
> 

That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error
in my reasoning. Saying that in your opinion I am a bad teacher
is too close to ad hominem because it refers to your opinion of
me and utterly bypasses any of my reasoning.

> As you make the syntax of your language dependent on semantics
> you lose one of the greatest advantage of formal languages:
> the simplicity of determination whether a string is a well formed
> formula.
> 

Not at all. By combining them together we can simultaneously determine
syntactic and semantic correctness. By keeping them separate we have
misconstrued expressions that are not even propositions as propositions
that prove incompleteness and undecidability.

A proposition is a central concept in the philosophy of language,
semantics, logic, and related fields, often characterized as the primary
bearer of truth or falsity. Propositions are also often characterized as
being the kind of thing that declarative sentences denote.
https://en.wikipedia.org/wiki/Proposition

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