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.

>>
>> 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.

>> 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.

> 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.

The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

Every self-contradictory sentence in T meets the above definition.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer