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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability --- incorrect question
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Date: Wed, 23 Oct 2024 08:20:25 -0500
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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?

> 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.

>>
>>>>
>>>> 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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