Re: Undecidability based on epistemological antinomies V2 --Tarski Proof--

On 4/22/2024 4:35 AM, Mikko wrote:

On 2024-04-21 14:44:37 +0000, olcott said:
 

On 4/21/2024 2:57 AM, Mikko wrote:

On 2024-04-20 15:20:05 +0000, olcott said:
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On 4/20/2024 2:54 AM, Mikko wrote:

On 2024-04-19 18:04:48 +0000, olcott said:
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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some ordinary proofs of ordinary theorems are no longer valid and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.

 No, it isn't. You introduced youtself as a topic of discussion so
you are a legitimate topic of discussion.
 I didn't claim that there be any reasoning, incorrect or otherwise.
 

If you claim I am a bad teacher you must point out what is wrong with
the lesson otherwise your claim that I am a bad teacher is essentially
an as hominem attack.

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.

 You have not shown that you can determine either semantic or syntactic
correctness.
 

That is more direct ad hominem.
I claim that the error of logic is that it diverges from semantics
and https://plato.stanford.edu/entries/logic-relevance/ proves
that I am correct about this and fixed the problem.

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

 Therefore it were easier if you could easily check whether a particular
string is a proposition or a sequence or propositions.
 

We construe this
Incomplete(F) ≡ ∃x ∈ L ((L ⊬  x) ∧ (L ⊬ ¬x))
As this
Proposition(F, x) ≡ ∃x ∈ F ((F ⊢ x) ∨ (F ⊢ ¬x))
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer