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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --Tarski
 Proof--
Date: Sat, 20 Apr 2024 08:56:10 -0400
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On 4/20/24 2:05 AM, olcott wrote:
> On 4/19/2024 6:20 PM, Richard Damon wrote:
>> On 4/19/24 2:04 PM, olcott wrote:
>>> On 4/18/2024 8:58 PM, Richard Damon wrote:
>>>> On 4/18/24 9:11 PM, olcott wrote:
>>>>> On 4/18/2024 5:31 PM, Richard Damon wrote:
>>>>>> On 4/18/24 10:50 AM, olcott wrote:
>>>>>>> On 4/17/2024 10:13 PM, Richard Damon wrote:
>>>>>>>> On 4/17/24 10:34 PM, olcott wrote:
>>>>>>>>> ...14 Every epistemological antinomy can likewise be used for a 
>>>>>>>>> similar
>>>>>>>>> undecidability proof...(Gödel 1931:43-44)
>>>>>>>>>
>>>>>>>>> *Parphrased as*
>>>>>>>>> Every expression X that cannot possibly be true or false proves 
>>>>>>>>> that the
>>>>>>>>> formal system F cannot correctly determine whether X is true or 
>>>>>>>>> false.
>>>>>>>>> Which shows that X is undecidable in F.
>>>>>>>>
>>>>>>>> Nope.
>>>>>>>>
>>>>>>>> Just more of your LIES and STUPIDITY.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Which shows that F is incomplete, even though X cannot possibly 
>>>>>>>>> be a
>>>>>>>>> proposition in F because propositions must be true or false.
>>>>>>>>
>>>>>>>> But that ISN'T the definition of "Incomplete", so you are just 
>>>>>>>> LYING.
>>>>>>>>
>>>>>>>> Godel showed that a statment, THAT WAS TRUE, couldn't be proven 
>>>>>>>> in F.
>>>>>>>>
>>>>>>>> You don't even seem to understand what the statement G actually 
>>>>>>>> is, because all you look at are the "clift notes" versions, and 
>>>>>>>> don't even understand that.
>>>>>>>>
>>>>>>>> Remember, G is a statement about the non-existance of a number 
>>>>>>>> that has a specific property. Until you understand that, your 
>>>>>>>> continued talking about this is just more LIES and DECIET, 
>>>>>>>> proving your absoulute STUPIDITY.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> A proposition is a central concept in the philosophy of language,
>>>>>>>>> semantics, logic, and related fields, often characterized as 
>>>>>>>>> the primary
>>>>>>>>> bearer of truth or falsity.
>>>>>>>>> https://en.wikipedia.org/wiki/Proposition
>>>>>>>>>
>>>>>>>>
>>>>>>>> Right, and if you don't know what the proposition is that you 
>>>>>>>> are arguing about, you are just proven to be a stupid liar.
>>>>>>>>
>>>>>>>
>>>>>>> If you are going to continue to be mean and call me names I will 
>>>>>>> stop
>>>>>>> talking to you. Even if you stop being mean and stop calling me 
>>>>>>> names
>>>>>>> if you continue to dogmatically say that I am wrong without pointing
>>>>>>> out all of the details of my error, I will stop talking to you.
>>>>>>>
>>>>>>> This is either a civil debate and an honest dialogue or you will
>>>>>>> hear nothing form me.
>>>>>>>
>>>>>>
>>>>>> I say you are WRONG, because you ARE.
>>>>>>
>>>>>> You say Godel's statement that is unprovable, is unprovable 
>>>>>> because it is an epistimalogical antinomy, when it isn't.
>>>>>>
>>>>>> It is a statement about the non-existance of a number that 
>>>>>> satisfies a particular property, which will be a truth bearing 
>>>>>> statement (The number must either exist or it doesn't)
>>>>>>
>>>>>> THAT MAKES YOU A LIAR.
>>>>>>
>>>>>
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>> *That is NOT how undecidability generically works and you know it*
>>>>
>>>> Well, Godel wasn't talking about "undecidability", but 
>>>> incompletenwss, which is what the WORDS you used talked about. (Read 
>>>> what you said above).
>>>>
>>>> INCOMPLETENESS is EXACTLY about the inability to prove statements 
>>>> that are true.
>>>
>>> *That is an excellent and correct foundation for what I am saying*
>>>
>>> When we create a three-valued logic system that has these
>>> three values: {True, False, Nonsense}
>>> https://en.wikipedia.org/wiki/Three-valued_logic
>>
>> IF you want to work with a Three Value logic system, then DO SO.
>>
>> But, remember, once you make you system 3-values, you immediately 
>> loose the ability to reference to anything proved in the classical 
>> two-value
>>
>>>
>>> Then "This sentence is not true" has the semantic value of {Nonsense}
>>> This sentence is not true: "This sentence is not true" has the semantic
>>> value of {True}.
>>>
>>> Although it may be difficult to understand that is exactly the
>>> difference between Tarski's "theory" and "metatheory" simplified
>>> as much as possible.
>>
>> And, once you add that third value to logic, you can't USE Tarski, or 
>> even talk about what he did, as it is OUTSIDE your frame of logic.
>>
> 
> For teaching purposes it is easier to think of it as
> a third semantic value. In actuality it would be
> rejected as invalid input.
> 

So make up your mind!!!

The problem is that the DEFINITION of a Halt Decider, or a Truth 
Predicate is that NO INPUT is "invalid". For a Halt Decider, IT IS 
DEFINED that if the input doesn't represent a Halting Computation, the 
answer is NO, and for a Truth Predicate, if the statement is not True, 
then the Truth Predicate says No, be it a false statement, or a 
statement that is not a Truth Bearer.

Thus there is not option to "reject".

>>>
>>> This is Tarski's Liar Paradox basis
>>> https://liarparadox.org/Tarski_247_248.pdf
>>>
>>> That he refers to in this paragraph of his actual proof
>>>    "In accordance with the first part of Th. I we can obtain
>>>     the negation of one of the sentences in condition (α) of
>>>     convention T of § 3 as a consequence of the definition of
>>>     the symbol 'Pr' (provided we replace 'Tr' in this convention
>>>     by 'Pr')." https://liarparadox.org/Tarski_275_276.pdf
>>>
>>> Allows his original formalized Liar Paradox:
>>>
>>> x ∉ True if and only if p
>>> where the symbol 'p' represents the whole sentence x
>>
>> Right, He shows that this statement is EXPRESSABLE in the meta-theory 
>> (something I don't think you understand)
>>
> 
> I do. I understand it better than most.
> This sentence is not true: "This sentence is not true" is true.

SO, the truth predicate could s

> 
>>>
>>> to be reverse-engineered from Line(1) of his actual proof:
>>> (I changed his abbreviations of "Pr" and "Tr" into words)
>>
>> Note, "Th I" was established without reference to the meaning of the 
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