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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --Tarski
 Proof--
Date: Fri, 19 Apr 2024 13:04:48 -0500
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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

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.

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

to be reverse-engineered from Line(1) of his actual proof:
(I changed his abbreviations of "Pr" and "Tr" into words)

Here is the Tarski Undefinability Theorem proof
(1) x ∉ Provable if and only if p    // assumption
(2) x ∈ True if and only if p        // assumption
(3) x ∉ Provable if and only if x ∈ True. // derived from (1) and (2)
(4) either x ∉ True or x̄ ∉ True;     // axiom: True(x) ∨ ~True(~x)
(5) if x ∈ Provable, then x ∈ True;  // axiom: Provable(x) → True(x)
(6) if x̄ ∈ Provable, then x̄ ∈ True;  // axiom: Provable(~x) → True(~x)
(7) x ∈ True
(8) x ∉ Provable
(9) x̄ ∉ Provable


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer