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

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some ordinary proofs of ordinary theorems are no longer valid and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.
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.
--
Mikko