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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: Undecidability based on epistemological antinomies V2 --Tarski
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Date: Sat, 20 Apr 2024 11:39:59 -0400
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On 4/20/24 11:20 AM, olcott wrote:
> 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 some ordinary proofs of ordinary theorems are no longer valid and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.
> 

In other words, you admit that you are being inconsistant about what you 
are saying, because your whole logic system is just inconsistant.

You don't seem to understand that predicates, DEFINED to be able to work 
on ALL memebers of the input domain, must IN FACT, work on all members 
of that domain.

For a Halt Decider, that means the decider needs to be able to answer 
about ANY machine given to it as an input, even a machine that uses a 
copy of the decider and acts contrary to its answer.

If you are going to work on a different problem, you need to be honest 
about that and not LIE and say you are working on the Halting Problem.

And, if you are going to talk about a "Truth Predicate", which is 
defined to be able to take ANY "statement" and say if it is True or not, 
with "nonsense" statements (be they self-contradictory statements, or 
just nonsense) being just not-true.

ANY statement means any statement, so if we define this predicate as 
True(F, x) to be true if x is a statement that is true in the field F, 
then we need to be able to give this predicate the statemet:

In F de define s as NOT True(F, s)


If you claim that your logic is ACTUALLY "two-valued" then if True(F,s) 
returns false, because s is a statement without a truth value, then we 
have the problem that the definition of s now says that s has the value 
of NOT false, which is True.

So, the True predicate was WRONG, as True of a statement that IS true, 
must be true.

If True(F,s) is true, then we have that s is not defined as NOT true, 
which is false, so the True predicate is again WRONG.

The predicate isn't ALLOWED to say "I reject this input" as that isn't a 
truth value (since you claimed you are actually useing a two-valued 
logic) and this predicate is defined to ALWAYS return a truth value.

So, it seems you have a two-valued logic system with three logical values.

Which is just A LIE!

You are just proving you are too stupid to understand what you are 
talking about as you don't understand the meaning of the words you are 
using, as you just studied the system by Zero order principles.