On 12/7/22 4:46 PM, olcott wrote:
> On 12/7/2022 5:19 PM, Richard Damon wrote:
>> On 12/7/22 2:49 PM, olcott wrote:
>>> On 12/7/2022 4:38 PM, Richard Damon wrote:
>>>> On 12/7/22 2:15 PM, olcott wrote:
>>>>> On 12/7/2022 3:18 PM, Richard Damon wrote:
>>>>>> On 12/7/22 12:13 PM, olcott wrote:
>>>>>>> On 12/7/2022 1:59 PM, Richard Damon wrote:
>>>>>>>> On 12/7/22 11:35 AM, olcott wrote:
>>>>>>>>> On 12/7/2022 1:28 PM, Richard Damon wrote:
>>>>>>>>>> On 12/7/22 10:43 AM, olcott wrote:
>>>>>>>>>>> On 12/7/2022 12:22 PM, Skep Dick wrote:
>>>>>>>>>>>> On Wednesday, 7 December 2022 at 20:05:31 UTC+2, olcott wrote:
>>>>>>>>>>>>> On 12/7/2022 11:28 AM, Jeff Barnett wrote:
>>>>>>>>>>>>>> On 12/7/2022 9:37 AM, Skep Dick wrote:
>>>>>>>>>>>>>>> On Wednesday, 7 December 2022 at 18:30:09 UTC+2, olcott
>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>> On 12/7/2022 10:18 AM, Skep Dick wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> <SIP> <SNIP>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> What did your parents do to you that you've spent your
>>>>>>>>>>>>>>>>> entire life
>>>>>>>>>>>>>>>>> trying to "be right" ?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> If humanity is going to survive we must overturn the Tarski
>>>>>>>>>>>>>>>> undefinabilty theorem to derive an objective criterion
>>>>>>>>>>>>>>>> measure that
>>>>>>>>>>>>>>>> divides truth from lies.
>>>>>>>>>>>>>>> 🤣🤣🤣🤣🤣🤣🤣🤣
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Messiah_complex
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I'm trying to understand whether you think the same aura
>>>>>>>>>>>>>> emanates from
>>>>>>>>>>>>>> you as PO from. For example, the above indicates that you
>>>>>>>>>>>>>> are trying to
>>>>>>>>>>>>>> save him. As one that has watched these threads off an on
>>>>>>>>>>>>>> for a while, I
>>>>>>>>>>>>>> want to warn you that you will not succeed. He's a troll
>>>>>>>>>>>>>> within a nut
>>>>>>>>>>>>>> case within a troll. If he believes himself a savior, that
>>>>>>>>>>>>>> is merely
>>>>>>>>>>>>>> another misconception.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Moving on, tell us about you; you seem to have a good dose
>>>>>>>>>>>>>> of PO in you.
>>>>>>>>>>>>>> On the surface it seems to be a case "of takes one to know
>>>>>>>>>>>>>> one" but we
>>>>>>>>>>>>>> all seek a deeper understanding of the contestants. N.B.
>>>>>>>>>>>>>> I'm not
>>>>>>>>>>>>>> questioning the veracity of your comments about PO - it's
>>>>>>>>>>>>>> almost
>>>>>>>>>>>>>> impossible to attribute too many negatives to him.
>>>>>>>>>>>>>> However, in your
>>>>>>>>>>>>>> capacity as his savior you must demonstrate success,
>>>>>>>>>>>>>> compassion, and a
>>>>>>>>>>>>>> deep understanding of his errors and omissions. I'm not
>>>>>>>>>>>>>> sure you've met
>>>>>>>>>>>>>> that burden yet.
>>>>>>>>>>>>> Severe anthropogenic climate change proven entirely with
>>>>>>>>>>>>> verifiable facts
>>>>>>>>>>>>> https://www.researchgate.net/publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
>>>>>>>>>>>>>
>>>>>>>>>>>>> It is an objectively verifiable fact that climate change
>>>>>>>>>>>>> disinformation
>>>>>>>>>>>>> is effectively preventing sufficient climate change
>>>>>>>>>>>>> mitigation. That
>>>>>>>>>>>>> heat waves are beginning to cause mass deaths is also
>>>>>>>>>>>>> objectively proven:
>>>>>>>>>>>>>
>>>>>>>>>>>>> How one heatwave killed 'a third' of a bat species in
>>>>>>>>>>>>> Australia
>>>>>>>>>>>>> https://www.bbc.com/news/world-australia-46859000
>>>>>>>>>>>>
>>>>>>>>>>>> All of that is completely unrelated to anything you are doing.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> It would seem that way to anyone that only glances at my
>>>>>>>>>>> words before forming a rebuttal.
>>>>>>>>>>>
>>>>>>>>>>> The Tarski Undefinability theorem that "proves" the notion of
>>>>>>>>>>> truth cannot be formalized is directly related to its
>>>>>>>>>>> isomorphism of the 1931 Gödel incompleteness theorem.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You don't understand what Tarski was saying. He is talking
>>>>>>>>>> about formalization WITHIN the system can not define what is
>>>>>>>>>> true in that system.
>>>>>>>>>>
>>>>>>>>>> This is really just a expansion on the incompleteness theorem,
>>>>>>>>>> that there exists within any sufficiently prowerful system of
>>>>>>>>>> logic, statements which can not be proved to be true (or false).
>>>>>>>>> The conventional definition of incompleteness:
>>>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>
>>>>>>>>> The fundamental problem is that the conventional
>>>>>>>>> definition of incompleteness is not actually proof
>>>>>>>>> that T is Incomplete, it is merely proof that φ
>>>>>>>>> in T is not a truth bearer.
>>>>>>>>>
>>>>>>>>> Copyright PL Olcott 2018
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Except the φ from the Godel Proof IS a Truth bearer as all
>>>>>>>> statements of the form 'X is Provable' or 'X is not Provable'
>>>>>>>> are by necessity truth bearers, since a given statement will
>>>>>>>> either be Provable or it will not.
>>>>>>>>
>>>>>>>
>>>>>>> As Ludwig Wittgenstein pointed out:
>>>>>>>    'True in Russell's system' means, as was said:
>>>>>>>     proved in Russell's system; and 'false in Russell's system'
>>>>>>>     means:the opposite has been proved in Russell's system
>>>>>>>     https://www.liarparadox.org/Wittgenstein.pdf
>>>>>>>
>>>>>>> therefore: φ in T is not a truth bearer in T
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> But Wittgenstein is WRONG that True means PROVABLE. That fails the
>>>>>> definition of True used in the field.
>>>>>>
>>>>>
>>>>> It does not mean that Wittgenstein is wrong, he knows these things on
>>>>> the much deeper basis of their philosophical foundation as opposed to
>>>>> and contrast with memorizing a set of rules dogmatically and never
>>>>> bothering to question their foundational basis.
>>>>
>>>> No, HE IS WRONG about the Formal Logic systme of Mathemeatics.
>>>>
>>>> This has been proven.
>>>>
>>>>
>>>>>
>>>>> The only correct way to determine that an analytical expression of
>>>>> formal or natural language is true is:
>>>>
>>>> Note, you are talking about KNOWING it is true, not what makes it true.
>>>>
>>>>>
>>>>> (a) Expressions of language that are stipulated to be true such as
>>>>> Haskell Curry elementary theorems:
>>>>>
>>>>> Thus, given T, an elementary theorem is an elementary statement
>>>>> which is true. https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>
>>>>> encoded in Mendelson as ⊢C, thus provable on the basis that it
>>>>> is a theorem.
>>>>>
>>>>> (b) the application of truth preserving operations to (a) and/or
>>>>> the results of (b).
>>>>>
>>>>> Thus showing that φ is true in T requires φ is provable in T.
>>>>
>>>> It may be needed to SHOW that it is True, but not to BE True.
>>>>
>>>>>
>>>>>> Simple matter of fact.
>>>>>>
>>>>>> FAIL.
>>>>>>
>>>>>> Note, the assumptiion of Asserting True is Provable is that it
>>>>>> means we can not use the law of the excluded middle, which breaks
>>>>>> a lot of the logic the system is built on.
>>>>>>
>>>>>> In fact, from other proofs we have, it shows that the logic system
>>>>>> can not handle systems above a certain level of complexity without
>>>>>> going inconsistent.
>>>>>>
>>>>>
>>>>
>>>> Since you confuse Truth with Knowledge, you are condemned to not to
>>>> be able to actually know the truth.
>>>>
>>>> One problem is that Mathematics is not a "purely analyitcal" field,
>>>> but allows for "empirical" truths to exist that arise out of the
>>>> interactions of the axioms of the field.
>>>>
>>>> For instance, even if we can never find a proof of the answer for
>>>> the Collatz conjecture, what ever is the correct answer, is True.
>>>>
>>>> The Collatz Conjecture by its nature is a Truth Bearer, it allows
>>>> for no middle ground, either there does exist a number that when put
>>>> throuth the 3x+1 or /2 operation never reduces to 1, or there doesn't.
>>>>
>>>> The provability of the statement doesn't matter, becuase the answer
>>>> just IS.
>>>>
>>>
>>> That no proof is currently known to exist is not at all the same thing
>>> as no proof can possibly exist because the expression of language is
>>> self-contradictory.
>>
>> ??? What is the self-contraction? Are you denying that Reality
>> actually exists?
>
> This sentence is not true.
> This sentence cannot be proven.

So?

THe first Sentence is not a Truth Bearer, that is true.

The Second Sentence is True, as The truth value of "This Sentence Can
not be Proven" has to be TRUE, as if it was false, it would meen it wqs
provable, and all provable sentences are True.

Where is the self-contradiction in the statement about proof?

You are just showing you don't know what you are talking about.

SOmething either IS or IS NOT provable, there is an excluded middle for
that sort of statement, as it deals with the EXISTANCE of a proof. A
things either DO or DO NOT exist.
>
>>>
>>> Every element of the entire set of analytical truth is only true because
>>> (as explained above) it is a part of a mutually self-defining
>>> interlocking semantic tautology.
>>>
>>
>> Right, but the field of Mathematics goes BEYOND just "analytic" truth.
>>
>
> Mathematics ⊂ "analytic" truth, thus cannot possibly go beyond
> "analytic" truth.

Nope. Where do you get that?

>
>>> The former is a truth bearer with an unknown truth value and the latter
>>> is not a truth bearer at all.
>>>
>>
>> So, what do you call a statement that MUST be True of False, because
>> it is a sttement of Empirical Fact, but can not be proven?
>>
>
> Not empirical at all. An empirical fact requires sense data from the
> sense organs: I see a television in my living room right now.

No, empirical relats to testing with a reality. The axioms of
mathemematic define a reality that can be tested to determine emperical
fact. The "Mind" can be consider a valid sense organ.

Note, if you want to restrict Emperical to only senses, then you can't
limit analytical to only proven or your analytical systems either can't
express the properties of Mathematics or become inconsistent.

You are about a half a century behind in your understanding of logic.

You are just repeating the errors of history because you refused to
learn from it.

>
>> That is what statements like "X is Provable" or "X is not Provable" are.
>>
>> Since it MUST be either True or False that a proof can exist, "X is
>> Provable" and "X is Not Provable" are Truth Bearers.
>>
>> Thus, Godel sentence is a Truth Bearer, and shown to be unprovable.
>
> Every sentence that meets the following definition is simply not a truth
> bearer in T and thus does not show that T is incomplete.

Source of this claim?

You are just proving your stupidity.

>
> The conventional definition of incompleteness:
> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>
> Every self-contradictory sentence in T meets the above definition.
>

So you have your logic backwards.

No, because self-contradictiory statement fail to meet the requirement
of φ, which must be a truth bearer.

Note, you haven't explained how Provable(x) can ever be a non-truth bearer.