Re: Undecidability based on epistemological antinomies V2 --Tarski Proof--

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)
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*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.

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Nope.
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Just more of your LIES and STUPIDITY.
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Which shows that F is incomplete, even though X cannot possibly be a
proposition in F because propositions must be true or false.

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But that ISN'T the definition of "Incomplete", so you are just LYING.
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Godel showed that a statment, THAT WAS TRUE, couldn't be proven in F.
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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.
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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.
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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
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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.
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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.
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This is either a civil debate and an honest dialogue or you will
hear nothing form me.
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I say you are WRONG, because you ARE.
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You say Godel's statement that is unprovable, is unprovable because it is an epistimalogical antinomy, when it isn't.
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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)
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THAT MAKES YOU A LIAR.
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*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*

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Well, Godel wasn't talking about "undecidability", but incompletenwss, which is what the WORDS you used talked about. (Read what you said above).
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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.

 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)

 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 class.

 Here is the Tarski Undefinability Theorem proof
(1) x ∉ Provable if and only if p    // assumption

NOT ASSUMPTION, he has shown that such an x must exist in the theory (if it meets the requirements)

(2) x ∈ True if and only if p        // assumption

NOT ASSUMPTION, but from the DEFINITION of what Truth is, the statement x is true if and only if it is true (since p is the whole statement x)

(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
 

Right.
Thus proving that there exists and x where x must be true, and x must be unprovable.
You just don't understand what an "assumption" is and what is an application of a proven statement.