On 10/23/24 9:20 AM, olcott wrote:
On 10/22/2024 10:02 PM, Richard Damon wrote:
On 10/22/24 10:56 AM, olcott wrote:
On 10/22/2024 6:22 AM, Richard Damon wrote:
On 10/21/24 11:17 PM, olcott wrote:
On 10/21/2024 9:48 PM, Richard Damon wrote:
On 10/21/24 10:04 PM, olcott wrote:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the >>>>>>>>> fact that
some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that >>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>> theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there >>>>>>>> is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
Only if "can not be determined" means that there isn't an actual
answer to it,
Not that we don't know the answer to it.
For instance, the Twin Primes conjecture is either True, or it is
False, it can't be a non-truth-bearer, as either there is or there >>>>>> isn't a highest pair of primes that differs by two.
Sure.
So, you agree your definition is wrong
The fact we don't know, and maybe can never know, doesn't make the >>>>>> question incorrect.
Some truth is just unknowable.
Sure.
And again.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
Right, and a question that we don't know (or maybe can't know) but >>>>>> is either true or false, is not an incorrect question.
Sure.
So you argee again that you proposition is wrong.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Does D halt, is not an incorrect question, as it will halt or not. >>>>>>
Tarski is a simpler example for this case.
His theory rightfully cannot determine whether
the following sentence is true or false:
"This sentence is not true".
Because that sentence is not a truth bearer.
No, that isn't his statement, but of course your problem is you
can't understand his actual statement so need to paraphrase it, and
that loses some critical properties.
Haskell Curry species expressions of theory {T} that are
stipulated to be true:
Thus, given {T}, an elementary theorem is an
elementary statement which is true.
https://www.liarparadox.org/Haskell_Curry_45.pdf
When we start with the foundation that True(L,x) is defined
as applying a set of truth preserving operations to a set
of expressions of language stipulated to be true Tarski's
proof fails.
We overcome Tarski Undefinability the same way that ZFC
overcame Russell's Paradox. We replace the prior foundation
with a new one.
https://liarparadox.org/Tarski_275_276.pdf
So, DO THAT then, and show what you get.
So, just as Z and F did, and went through ALL the logical proofs to
show what you could do with there rules, write up your complete set of
rules and then show what can be done with it.
They could have accomplished the same thing by merely
adding the rule that no set can be a member of itself.
This by itself eliminates Russell's Paradox.
You have been told this for years, but don't seem to understand,
perhaps because you don't understand the basics well enough to
actually do that.
Note, it isn't just the summary you will find on the informal sites
that you need to do, but the FORMAL PROOF that is in their academic
papers.
Papers you probably can't understand.
And not, that since you are moving to a more basic level, of changing
the fundamental rules of the logic, you can't just assume any of the
existing logic principles still work.
What would stop working in Naive Set theory if we simply
added the axiom that no set can be a member of itself?
That wouldn't affect it at all, since the use of axioms is always voluntary.
When you are doing logic, are you checking at each step against every
"rule" to see if you are violating any?
No, because that isn't how logic works.
This seens to be a common problem with you, showing your total lack of understanding on how logic works.
The is not "interrupt" in logic that catches you if you try to put a bad assumption into the system, it just blows the system up.
Now, if you want to try to see how a logic system would work with a rule
like that, go ahead and try.
My first thought would be that suddenly your system will have "memory"
and the truth of some statments might bepend on the order you have done
things before, determining which gate gets closed by your "interrupt" rule.
This may well be the sort of thing where it takes 20 pages to show
that 2 + 3 = 5 at the fundamental level of defining what + means.
Not when the algorithm for doing first-grade arithmetic
on ASCII digit strings is provided.
But "First Grade arithmetic" isn't able to PROVE its answers.
But then, it seems your logic can\'t do that either and it seems you
don't understand that problem.
I still remember the difficulties I gave my elementary school teachers
when I would ask them "Why?" for some of the things they were teaching,
when the methods commonly used were just rote memorization.
Fortunately, there was some "New Math" available that had some of the
answers about Why?
That does not mean that True(L,x) cannot be defined.
It only means that some expression ore not truth bearers.
His proof does, the fact that you don't undetstand what he is
talking about doesn't make him wrong.
You asserting he is wrong becuase you don't understand his proof
makes you wrong, and STUPID.
That the H that it was built from won't give the right answer is
irrelevent.
You just don't understand what the terms mean, because you CHOSE
to make youself ignorant, and thus INTENTIONALY made yourself into >>>>>> a pathetic ignorant pathological lying idiot.
Sorry, but that is the facts.
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