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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability --- incorrect question
 --- PROGRESS
Date: Thu, 24 Oct 2024 19:44:41 -0400
Organization: i2pn2 (i2pn.org)
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On 10/24/24 9:14 AM, olcott wrote:
> On 10/23/2024 9:58 PM, Richard Damon wrote:
>> 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.
>>
> 
> So when a first grade student answers the question
> What is the sum of 2 + 3?
> and they answer: "a box of stale donuts"
> they are correct because the use of axioms is always
> voluntary?

No, because they can't show how to get there from the facts (axioms) 
they have been given.

This seems to show the stupidity of your logic.

To show something, you need to build the finite string of operations 
from the given facts (axioms) using the finite set of operations, to get 
to you comclusion.

If there is a fact you didn't need, or an operation you didn't need to 
use, that is fine.

Logic doesn't have rules like "X can not be equal to Y, and any 
operation that might show that X is equal to Y can't be used".

We might have an initial assumption, or even a definition that X was not 
Y. And if we do, then if we can show that X was equal to Y, then that 
just means that either we did a step that was valid, or that the rules 
for the system are just inconsistant.

This idea seems beyound your understanding.
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