On 3/5/2022 4:20 PM, Richard Damon wrote:
>
> On 3/5/22 4:48 PM, olcott wrote:
>> On 3/5/2022 3:39 PM, Richard Damon wrote:
>>>
>>> On 3/5/22 4:04 PM, olcott wrote:
>>>> On 3/5/2022 1:30 PM, Richard Damon wrote:
>>>>> On 3/5/22 1:53 PM, olcott wrote:
>>>>>> On 3/5/2022 5:07 AM, Richard Damon wrote:
>>>>>>>
>>>>>>> On 3/4/22 11:04 PM, olcott wrote:
>>>>>>>> On 3/4/2022 10:03 PM, Python wrote:
>>>>>>>>> olcott wrote:
>>>>>>>>>> On 3/4/2022 9:44 PM, Python wrote:
>>>>>>>>>>> olcott wrote:
>>>>>>>>>>> ...
>>>>>>>>>>>> True cannot possibly exist apart from provable thus Gödel
>>>>>>>>>>>> could not have possibly found any expression of any language
>>>>>>>>>>>> L that is both true in L and unprovable in L.
>>>>>>>>>>>
>>>>>>>>>>> But still he did.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You might as well have said that Gödel had a dog that was
>>>>>>>>>> three cats.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Nope. I didn't say that. Stop dodging and lying.
>>>>>>>>>
>>>>>>>>> Gödel exhibited an expression can be true in L and unprovable
>>>>>>>>> in L.
>>>>>>>>
>>>>>>>> He did not. This is impossible.
>>>>>>>> It is inherently true at the deepest philosophical level that
>>>>>>>> analytic truth only exists as connections between expressions of
>>>>>>>> language.
>>>>>>>> The proof of this is that no valid counter-examples exist.
>>>>>>>>
>>>>>>>
>>>>>>> Denial of actual Truth is a good sign of insanity.
>>>>>>>
>>>>>>> Please seek Professional Help.
>>>>>>>
>>>>>>> Saying something is wrong just because you disagree with the
>>>>>>> conclusion is NOT the Analytical Logic way.
>>>>>>>
>>>>>>> To Refute a logical argument, you need to show what particular
>>>>>>> step breaks the rules of logic that are enforce in the field that
>>>>>>> the argument is presented in, or which assumed premise that went
>>>>>>> into the argument is not True in that field.
>>>>>>>
>>>>>>> Of course to do this, you need to actually read and understand
>>>>>>> the argument, and not just depend on your own gut feelings.
>>>>>>
>>>>>> I am saying that the only way that we can know that an analytic
>>>>>> expression of language is true is that it is either defined to be
>>>>>> true or it is derived by applying truth preserving operations to
>>>>>> expressions of language that are defined to be true.
>>>>>>
>>>>>> The above statements prove themselves to be true categorically on
>>>>>> the basis of the meaning of their words.
>>>>>>
>>>>>
>>>>> And you are confusing KNOWLEDGE with TRUTH.
>>>>>
>>>>> For something to be a KNOWN TRUTH, it needs some way to 'Prove' it,
>>>>> either an Analytic Proof, or a proper observation for
>>>>> Emperical/Synthetic Proof. But it is True before it was proven, if
>>>>> it was true.
>>>>>
>>>>> Proofs can not change the Truth value of statements (unless they
>>>>> are statements about something having been proven), they just move
>>>>> them from an unproven (and likely unknown, but maybe presumed)
>>>>> statement to being Knowledge and Proven True.
>>>>>
>>>>>
>>>>> It is OBVIOUS that something can be True but not Known.
>>>>>
>>>>
>>>> Goldbach's conjecture is one of the oldest and best-known unsolved
>>>> problems in number theory and all of mathematics. It states that
>>>> every even whole number greater than 2 is the sum of two prime numbers.
>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>
>>>> The truth that we begin with is the proof that the Goldbach criteria
>>>> is met with every element of the sequence even whole numbers greater
>>>> than 2 that has been tested.
>>>>
>>>> Testing an element N of this sequence begins with the element N as
>>>> its premise then testing every pair of primes that are numerically
>>>> less that this element to see if the sum of any pair = N.
>>>>
>>>> ∀N ∈ (even whole numbers greater than 2)
>>>> ∃!x ∈ Prime_Numbers < N
>>>> ∃!y ∈ Prime_Numbers < N
>>>> Sum(x,y) == n
>>>>
>>>> ∀N ∈ (even whole numbers greater than 2)
>>>> Every case where Goldbach's criteria is met is a formal proof from N
>>>> to the satisfaction of the above expression, thus proving its truth.
>>>
>>> So, how do you PROVE that this holds for ALL even numbers? Remember,
>>> THAT is the conjecture, not that it works for 'lots' of values.
>>>
>>> The fact that we haven't found an exception, doesn't mean that an
>>> exception doesn't exist, just that we haven't found it yet.
>>>
>>> Until you show you can test EVERY even number, you can't use that as
>>> your proof, and so your method has failed to actually prove it.
>>>
>>>>
>>>>> Therefore not all Truth needs to be Provable.
>>>>
>>>> If any element N of (even whole numbers greater than 2) cannot be
>>>> proven to satisfy the Goldbach criteria then Goldbach's conjecture
>>>> is false.
>>>>
>>>> For Goldbach true cannot possibly exist apart from provable is proven.
>>>
>>> WRONG
>>>
>>> Goldbach conjecture MUST be either True or it is FALSE.
>> Unless there exists a proof that each (even whole number greater than
>> 2) meets the Goldbach criteria it is not true. If even one of these
>> proofs does not exist then it is not true.
>>
>> True cannot possibly exist apart from provable.
>>
>
> WRONG.
>
> IT is an EMPRICAL FACT, that the Goldbach conjecture must be either true
> of false.
>

It is an analytical fact not an empirical fact.

If there exists a single (even whole number greater than 2) that cannot
possibly be proved to meet the Goldbach criteria then the Goldbach
conjecture is not true.

Otherwise every (even whole number greater than 2) can be proved to meet
the Goldbach criteria, thus True depends on Provable.

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

On 3/5/2022 5:09 PM, Richard Damon wrote:
> On 3/5/22 5:51 PM, olcott wrote:
>> On 3/5/2022 4:20 PM, Richard Damon wrote:
>>>
>>> On 3/5/22 4:48 PM, olcott wrote:
>>>> On 3/5/2022 3:39 PM, Richard Damon wrote:
>>>>>
>>>>> On 3/5/22 4:04 PM, olcott wrote:
>>>>>> On 3/5/2022 1:30 PM, Richard Damon wrote:
>>>>>>> On 3/5/22 1:53 PM, olcott wrote:
>>>>>>>> On 3/5/2022 5:07 AM, Richard Damon wrote:
>>>>>>>>>
>>>>>>>>> On 3/4/22 11:04 PM, olcott wrote:
>>>>>>>>>> On 3/4/2022 10:03 PM, Python wrote:
>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>> On 3/4/2022 9:44 PM, Python wrote:
>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>> ...
>>>>>>>>>>>>>> True cannot possibly exist apart from provable thus Gödel
>>>>>>>>>>>>>> could not have possibly found any expression of any
>>>>>>>>>>>>>> language L that is both true in L and unprovable in L.
>>>>>>>>>>>>>
>>>>>>>>>>>>> But still he did.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> You might as well have said that Gödel had a dog that was
>>>>>>>>>>>> three cats.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Nope. I didn't say that. Stop dodging and lying.
>>>>>>>>>>>
>>>>>>>>>>> Gödel exhibited an expression can be true in L and unprovable
>>>>>>>>>>> in L.
>>>>>>>>>>
>>>>>>>>>> He did not. This is impossible.
>>>>>>>>>> It is inherently true at the deepest philosophical level that
>>>>>>>>>> analytic truth only exists as connections between expressions
>>>>>>>>>> of language.
>>>>>>>>>> The proof of this is that no valid counter-examples exist.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Denial of actual Truth is a good sign of insanity.
>>>>>>>>>
>>>>>>>>> Please seek Professional Help.
>>>>>>>>>
>>>>>>>>> Saying something is wrong just because you disagree with the
>>>>>>>>> conclusion is NOT the Analytical Logic way.
>>>>>>>>>
>>>>>>>>> To Refute a logical argument, you need to show what particular
>>>>>>>>> step breaks the rules of logic that are enforce in the field
>>>>>>>>> that the argument is presented in, or which assumed premise
>>>>>>>>> that went into the argument is not True in that field.
>>>>>>>>>
>>>>>>>>> Of course to do this, you need to actually read and understand
>>>>>>>>> the argument, and not just depend on your own gut feelings.
>>>>>>>>
>>>>>>>> I am saying that the only way that we can know that an analytic
>>>>>>>> expression of language is true is that it is either defined to
>>>>>>>> be true or it is derived by applying truth preserving operations
>>>>>>>> to expressions of language that are defined to be true.
>>>>>>>>
>>>>>>>> The above statements prove themselves to be true categorically
>>>>>>>> on the basis of the meaning of their words.
>>>>>>>>
>>>>>>>
>>>>>>> And you are confusing KNOWLEDGE with TRUTH.
>>>>>>>
>>>>>>> For something to be a KNOWN TRUTH, it needs some way to 'Prove'
>>>>>>> it, either an Analytic Proof, or a proper observation for
>>>>>>> Emperical/Synthetic Proof. But it is True before it was proven,
>>>>>>> if it was true.
>>>>>>>
>>>>>>> Proofs can not change the Truth value of statements (unless they
>>>>>>> are statements about something having been proven), they just
>>>>>>> move them from an unproven (and likely unknown, but maybe
>>>>>>> presumed) statement to being Knowledge and Proven True.
>>>>>>>
>>>>>>>
>>>>>>> It is OBVIOUS that something can be True but not Known.
>>>>>>>
>>>>>>
>>>>>> Goldbach's conjecture is one of the oldest and best-known unsolved
>>>>>> problems in number theory and all of mathematics. It states that
>>>>>> every even whole number greater than 2 is the sum of two prime
>>>>>> numbers.
>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>
>>>>>> The truth that we begin with is the proof that the Goldbach
>>>>>> criteria is met with every element of the sequence even whole
>>>>>> numbers greater than 2 that has been tested.
>>>>>>
>>>>>> Testing an element N of this sequence begins with the element N as
>>>>>> its premise then testing every pair of primes that are numerically
>>>>>> less that this element to see if the sum of any pair = N.
>>>>>>
>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>> ∃!x ∈ Prime_Numbers < N
>>>>>> ∃!y ∈ Prime_Numbers < N
>>>>>> Sum(x,y) == n
>>>>>>
>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>> Every case where Goldbach's criteria is met is a formal proof from
>>>>>> N to the satisfaction of the above expression, thus proving its
>>>>>> truth.
>>>>>
>>>>> So, how do you PROVE that this holds for ALL even numbers?
>>>>> Remember, THAT is the conjecture, not that it works for 'lots' of
>>>>> values.
>>>>>
>>>>> The fact that we haven't found an exception, doesn't mean that an
>>>>> exception doesn't exist, just that we haven't found it yet.
>>>>>
>>>>> Until you show you can test EVERY even number, you can't use that
>>>>> as your proof, and so your method has failed to actually prove it.
>>>>>
>>>>>>
>>>>>>> Therefore not all Truth needs to be Provable.
>>>>>>
>>>>>> If any element N of (even whole numbers greater than 2) cannot be
>>>>>> proven to satisfy the Goldbach criteria then Goldbach's conjecture
>>>>>> is false.
>>>>>>
>>>>>> For Goldbach true cannot possibly exist apart from provable is
>>>>>> proven.
>>>>>
>>>>> WRONG
>>>>>
>>>>> Goldbach conjecture MUST be either True or it is FALSE.
>>>> Unless there exists a proof that each (even whole number greater
>>>> than 2) meets the Goldbach criteria it is not true. If even one of
>>>> these proofs does not exist then it is not true.
>>>>
>>>> True cannot possibly exist apart from provable.
>>>>
>>>
>>> WRONG.
>>>
>>> IT is an EMPRICAL FACT, that the Goldbach conjecture must be either
>>> true of false.
>>>
>>
>> It is an analytical fact not an empirical fact.
>>
>> If there exists a single (even whole number greater than 2) that
>> cannot possibly be proved to meet the Goldbach criteria then the
>> Goldbach conjecture is not true.
>>
>> Otherwise every (even whole number greater than 2) can be proved to
>> meet the Goldbach criteria, thus True depends on Provable.
>>
>
> Right, if one exception exists, the conjecture is not true, but false.
>
> We do not have, and may never have, a proof that no such exception exists.
>
> Thus, by your definition, YOU can not treat the 'Truth' of the
> conjecture as a Truth Bearer, because you don't KNOW if it is actually
> provable, let alone if it is provably true.
>

On 3/5/2022 5:36 PM, Richard Damon wrote:
> On 3/5/22 6:16 PM, olcott wrote:
>> On 3/5/2022 5:09 PM, Richard Damon wrote:
>>> On 3/5/22 5:51 PM, olcott wrote:
>>>> On 3/5/2022 4:20 PM, Richard Damon wrote:
>>>>>
>>>>> On 3/5/22 4:48 PM, olcott wrote:
>>>>>> On 3/5/2022 3:39 PM, Richard Damon wrote:
>>>>>>>
>>>>>>> On 3/5/22 4:04 PM, olcott wrote:
>>>>>>>> On 3/5/2022 1:30 PM, Richard Damon wrote:
>>>>>>>>> On 3/5/22 1:53 PM, olcott wrote:
>>>>>>>>>> On 3/5/2022 5:07 AM, Richard Damon wrote:
>>>>>>>>>>>
>>>>>>>>>>> On 3/4/22 11:04 PM, olcott wrote:
>>>>>>>>>>>> On 3/4/2022 10:03 PM, Python wrote:
>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>> On 3/4/2022 9:44 PM, Python wrote:
>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>> ...
>>>>>>>>>>>>>>>> True cannot possibly exist apart from provable thus
>>>>>>>>>>>>>>>> Gödel could not have possibly found any expression of
>>>>>>>>>>>>>>>> any language L that is both true in L and unprovable in L.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> But still he did.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You might as well have said that Gödel had a dog that was
>>>>>>>>>>>>>> three cats.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Nope. I didn't say that. Stop dodging and lying.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Gödel exhibited an expression can be true in L and unprovable
>>>>>>>>>>>>> in L.
>>>>>>>>>>>>
>>>>>>>>>>>> He did not. This is impossible.
>>>>>>>>>>>> It is inherently true at the deepest philosophical level
>>>>>>>>>>>> that analytic truth only exists as connections between
>>>>>>>>>>>> expressions of language.
>>>>>>>>>>>> The proof of this is that no valid counter-examples exist.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Denial of actual Truth is a good sign of insanity.
>>>>>>>>>>>
>>>>>>>>>>> Please seek Professional Help.
>>>>>>>>>>>
>>>>>>>>>>> Saying something is wrong just because you disagree with the
>>>>>>>>>>> conclusion is NOT the Analytical Logic way.
>>>>>>>>>>>
>>>>>>>>>>> To Refute a logical argument, you need to show what
>>>>>>>>>>> particular step breaks the rules of logic that are enforce in
>>>>>>>>>>> the field that the argument is presented in, or which assumed
>>>>>>>>>>> premise that went into the argument is not True in that field.
>>>>>>>>>>>
>>>>>>>>>>> Of course to do this, you need to actually read and
>>>>>>>>>>> understand the argument, and not just depend on your own gut
>>>>>>>>>>> feelings.
>>>>>>>>>>
>>>>>>>>>> I am saying that the only way that we can know that an
>>>>>>>>>> analytic expression of language is true is that it is either
>>>>>>>>>> defined to be true or it is derived by applying truth
>>>>>>>>>> preserving operations to expressions of language that are
>>>>>>>>>> defined to be true.
>>>>>>>>>>
>>>>>>>>>> The above statements prove themselves to be true categorically
>>>>>>>>>> on the basis of the meaning of their words.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> And you are confusing KNOWLEDGE with TRUTH.
>>>>>>>>>
>>>>>>>>> For something to be a KNOWN TRUTH, it needs some way to 'Prove'
>>>>>>>>> it, either an Analytic Proof, or a proper observation for
>>>>>>>>> Emperical/Synthetic Proof. But it is True before it was proven,
>>>>>>>>> if it was true.
>>>>>>>>>
>>>>>>>>> Proofs can not change the Truth value of statements (unless
>>>>>>>>> they are statements about something having been proven), they
>>>>>>>>> just move them from an unproven (and likely unknown, but maybe
>>>>>>>>> presumed) statement to being Knowledge and Proven True.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> It is OBVIOUS that something can be True but not Known.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Goldbach's conjecture is one of the oldest and best-known
>>>>>>>> unsolved problems in number theory and all of mathematics. It
>>>>>>>> states that every even whole number greater than 2 is the sum of
>>>>>>>> two prime numbers.
>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>
>>>>>>>> The truth that we begin with is the proof that the Goldbach
>>>>>>>> criteria is met with every element of the sequence even whole
>>>>>>>> numbers greater than 2 that has been tested.
>>>>>>>>
>>>>>>>> Testing an element N of this sequence begins with the element N
>>>>>>>> as its premise then testing every pair of primes that are
>>>>>>>> numerically less that this element to see if the sum of any pair
>>>>>>>> = N.
>>>>>>>>
>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>> ∃!x ∈ Prime_Numbers < N
>>>>>>>> ∃!y ∈ Prime_Numbers < N
>>>>>>>> Sum(x,y) == n
>>>>>>>>
>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>> Every case where Goldbach's criteria is met is a formal proof
>>>>>>>> from N to the satisfaction of the above expression, thus proving
>>>>>>>> its truth.
>>>>>>>
>>>>>>> So, how do you PROVE that this holds for ALL even numbers?
>>>>>>> Remember, THAT is the conjecture, not that it works for 'lots' of
>>>>>>> values.
>>>>>>>
>>>>>>> The fact that we haven't found an exception, doesn't mean that an
>>>>>>> exception doesn't exist, just that we haven't found it yet.
>>>>>>>
>>>>>>> Until you show you can test EVERY even number, you can't use that
>>>>>>> as your proof, and so your method has failed to actually prove it.
>>>>>>>
>>>>>>>>
>>>>>>>>> Therefore not all Truth needs to be Provable.
>>>>>>>>
>>>>>>>> If any element N of (even whole numbers greater than 2) cannot
>>>>>>>> be proven to satisfy the Goldbach criteria then Goldbach's
>>>>>>>> conjecture is false.
>>>>>>>>
>>>>>>>> For Goldbach true cannot possibly exist apart from provable is
>>>>>>>> proven.
>>>>>>>
>>>>>>> WRONG
>>>>>>>
>>>>>>> Goldbach conjecture MUST be either True or it is FALSE.
>>>>>> Unless there exists a proof that each (even whole number greater
>>>>>> than 2) meets the Goldbach criteria it is not true. If even one of
>>>>>> these proofs does not exist then it is not true.
>>>>>>
>>>>>> True cannot possibly exist apart from provable.
>>>>>>
>>>>>
>>>>> WRONG.
>>>>>
>>>>> IT is an EMPRICAL FACT, that the Goldbach conjecture must be either
>>>>> true of false.
>>>>>
>>>>
>>>> It is an analytical fact not an empirical fact.
>>>>
>>>> If there exists a single (even whole number greater than 2) that
>>>> cannot possibly be proved to meet the Goldbach criteria then the
>>>> Goldbach conjecture is not true.
>>>>
>>>> Otherwise every (even whole number greater than 2) can be proved to
>>>> meet the Goldbach criteria, thus True depends on Provable.
>>>>
>>>
>>> Right, if one exception exists, the conjecture is not true, but false.
>>>
>>> We do not have, and may never have, a proof that no such exception
>>> exists.
>>>
>>> Thus, by your definition, YOU can not treat the 'Truth' of the
>>> conjecture as a Truth Bearer, because you don't KNOW if it is
>>> actually provable, let alone if it is provably true.
>>>
>>
>> Unless every element of the set of (even whole number greater than 2)
>> provably meets the Goldbach criteria, the Goldbach conjecture is not
>> true, thus proving that its truth depends on its provability.
>>
>
> WRONG.
>
> Repeating your statement doesn't make it True.
>
> I will now DEMAND that you PROVE your statement or be able to just claim
> you are are liar and a Hypocrite.

On 3/5/2022 6:46 PM, Richard Damon wrote:
>
> On 3/5/22 7:12 PM, olcott wrote:
>> On 3/5/2022 5:36 PM, Richard Damon wrote:
>>> On 3/5/22 6:16 PM, olcott wrote:
>>>> On 3/5/2022 5:09 PM, Richard Damon wrote:
>>>>> On 3/5/22 5:51 PM, olcott wrote:
>>>>>> On 3/5/2022 4:20 PM, Richard Damon wrote:
>>>>>>>
>>>>>>> On 3/5/22 4:48 PM, olcott wrote:
>>>>>>>> On 3/5/2022 3:39 PM, Richard Damon wrote:
>>>>>>>>>
>>>>>>>>> On 3/5/22 4:04 PM, olcott wrote:
>>>>>>>>>> On 3/5/2022 1:30 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/5/22 1:53 PM, olcott wrote:
>>>>>>>>>>>> On 3/5/2022 5:07 AM, Richard Damon wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 3/4/22 11:04 PM, olcott wrote:
>>>>>>>>>>>>>> On 3/4/2022 10:03 PM, Python wrote:
>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>> On 3/4/2022 9:44 PM, Python wrote:
>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>> ...
>>>>>>>>>>>>>>>>>> True cannot possibly exist apart from provable thus
>>>>>>>>>>>>>>>>>> Gödel could not have possibly found any expression of
>>>>>>>>>>>>>>>>>> any language L that is both true in L and unprovable
>>>>>>>>>>>>>>>>>> in L.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> But still he did.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You might as well have said that Gödel had a dog that
>>>>>>>>>>>>>>>> was three cats.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Nope. I didn't say that. Stop dodging and lying.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Gödel exhibited an expression can be true in L and
>>>>>>>>>>>>>>> unprovable
>>>>>>>>>>>>>>> in L.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> He did not. This is impossible.
>>>>>>>>>>>>>> It is inherently true at the deepest philosophical level
>>>>>>>>>>>>>> that analytic truth only exists as connections between
>>>>>>>>>>>>>> expressions of language.
>>>>>>>>>>>>>> The proof of this is that no valid counter-examples exist.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Denial of actual Truth is a good sign of insanity.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Please seek Professional Help.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Saying something is wrong just because you disagree with
>>>>>>>>>>>>> the conclusion is NOT the Analytical Logic way.
>>>>>>>>>>>>>
>>>>>>>>>>>>> To Refute a logical argument, you need to show what
>>>>>>>>>>>>> particular step breaks the rules of logic that are enforce
>>>>>>>>>>>>> in the field that the argument is presented in, or which
>>>>>>>>>>>>> assumed premise that went into the argument is not True in
>>>>>>>>>>>>> that field.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Of course to do this, you need to actually read and
>>>>>>>>>>>>> understand the argument, and not just depend on your own
>>>>>>>>>>>>> gut feelings.
>>>>>>>>>>>>
>>>>>>>>>>>> I am saying that the only way that we can know that an
>>>>>>>>>>>> analytic expression of language is true is that it is either
>>>>>>>>>>>> defined to be true or it is derived by applying truth
>>>>>>>>>>>> preserving operations to expressions of language that are
>>>>>>>>>>>> defined to be true.
>>>>>>>>>>>>
>>>>>>>>>>>> The above statements prove themselves to be true
>>>>>>>>>>>> categorically on the basis of the meaning of their words.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> And you are confusing KNOWLEDGE with TRUTH.
>>>>>>>>>>>
>>>>>>>>>>> For something to be a KNOWN TRUTH, it needs some way to
>>>>>>>>>>> 'Prove' it, either an Analytic Proof, or a proper observation
>>>>>>>>>>> for Emperical/Synthetic Proof. But it is True before it was
>>>>>>>>>>> proven, if it was true.
>>>>>>>>>>>
>>>>>>>>>>> Proofs can not change the Truth value of statements (unless
>>>>>>>>>>> they are statements about something having been proven), they
>>>>>>>>>>> just move them from an unproven (and likely unknown, but
>>>>>>>>>>> maybe presumed) statement to being Knowledge and Proven True.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> It is OBVIOUS that something can be True but not Known.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Goldbach's conjecture is one of the oldest and best-known
>>>>>>>>>> unsolved problems in number theory and all of mathematics. It
>>>>>>>>>> states that every even whole number greater than 2 is the sum
>>>>>>>>>> of two prime numbers.
>>>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>>>
>>>>>>>>>> The truth that we begin with is the proof that the Goldbach
>>>>>>>>>> criteria is met with every element of the sequence even whole
>>>>>>>>>> numbers greater than 2 that has been tested.
>>>>>>>>>>
>>>>>>>>>> Testing an element N of this sequence begins with the element
>>>>>>>>>> N as its premise then testing every pair of primes that are
>>>>>>>>>> numerically less that this element to see if the sum of any
>>>>>>>>>> pair = N.
>>>>>>>>>>
>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>> ∃!x ∈ Prime_Numbers < N
>>>>>>>>>> ∃!y ∈ Prime_Numbers < N
>>>>>>>>>> Sum(x,y) == n
>>>>>>>>>>
>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>> Every case where Goldbach's criteria is met is a formal proof
>>>>>>>>>> from N to the satisfaction of the above expression, thus
>>>>>>>>>> proving its truth.
>>>>>>>>>
>>>>>>>>> So, how do you PROVE that this holds for ALL even numbers?
>>>>>>>>> Remember, THAT is the conjecture, not that it works for 'lots'
>>>>>>>>> of values.
>>>>>>>>>
>>>>>>>>> The fact that we haven't found an exception, doesn't mean that
>>>>>>>>> an exception doesn't exist, just that we haven't found it yet.
>>>>>>>>>
>>>>>>>>> Until you show you can test EVERY even number, you can't use
>>>>>>>>> that as your proof, and so your method has failed to actually
>>>>>>>>> prove it.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> Therefore not all Truth needs to be Provable.
>>>>>>>>>>
>>>>>>>>>> If any element N of (even whole numbers greater than 2) cannot
>>>>>>>>>> be proven to satisfy the Goldbach criteria then Goldbach's
>>>>>>>>>> conjecture is false.
>>>>>>>>>>
>>>>>>>>>> For Goldbach true cannot possibly exist apart from provable is
>>>>>>>>>> proven.
>>>>>>>>>
>>>>>>>>> WRONG
>>>>>>>>>
>>>>>>>>> Goldbach conjecture MUST be either True or it is FALSE.
>>>>>>>> Unless there exists a proof that each (even whole number greater
>>>>>>>> than 2) meets the Goldbach criteria it is not true. If even one
>>>>>>>> of these proofs does not exist then it is not true.
>>>>>>>>
>>>>>>>> True cannot possibly exist apart from provable.
>>>>>>>>
>>>>>>>
>>>>>>> WRONG.
>>>>>>>
>>>>>>> IT is an EMPRICAL FACT, that the Goldbach conjecture must be
>>>>>>> either true of false.
>>>>>>>
>>>>>>
>>>>>> It is an analytical fact not an empirical fact.
>>>>>>
>>>>>> If there exists a single (even whole number greater than 2) that
>>>>>> cannot possibly be proved to meet the Goldbach criteria then the
>>>>>> Goldbach conjecture is not true.
>>>>>>
>>>>>> Otherwise every (even whole number greater than 2) can be proved
>>>>>> to meet the Goldbach criteria, thus True depends on Provable.
>>>>>>
>>>>>
>>>>> Right, if one exception exists, the conjecture is not true, but false.
>>>>>
>>>>> We do not have, and may never have, a proof that no such exception
>>>>> exists.
>>>>>
>>>>> Thus, by your definition, YOU can not treat the 'Truth' of the
>>>>> conjecture as a Truth Bearer, because you don't KNOW if it is
>>>>> actually provable, let alone if it is provably true.
>>>>>
>>>>
>>>> Unless every element of the set of (even whole number greater than
>>>> 2) provably meets the Goldbach criteria, the Goldbach conjecture is
>>>> not true, thus proving that its truth depends on its provability.
>>>>
>>>
>>> WRONG.
>>>
>>> Repeating your statement doesn't make it True.
>>>
>>> I will now DEMAND that you PROVE your statement or be able to just
>>> claim you are are liar and a Hypocrite.
>>
>>  >>>> If there exists a single (even whole number greater than 2) that
>>  >>>> cannot possibly be proved to meet the Goldbach criteria then the
>>  >>>> Goldbach conjecture is not true.
>>
>> If >= 1 element is not provable then false entails
>> < 1 elements are not provable entails
>> all elements are provable.
>
> You aren't making sense, because you don't understand the difference
> between True and Provable.
>
> Yes, If we can show >= 1 numbers that fail the requirements we have
> proven that the conjecture is False.

On 3/5/2022 7:24 PM, Richard Damon wrote:
>
> On 3/5/22 8:03 PM, olcott wrote:
>> On 3/5/2022 6:46 PM, Richard Damon wrote:
>>>
>>> On 3/5/22 7:12 PM, olcott wrote:
>>>> On 3/5/2022 5:36 PM, Richard Damon wrote:
>>>>> On 3/5/22 6:16 PM, olcott wrote:
>>>>>> On 3/5/2022 5:09 PM, Richard Damon wrote:
>>>>>>> On 3/5/22 5:51 PM, olcott wrote:
>>>>>>>> On 3/5/2022 4:20 PM, Richard Damon wrote:
>>>>>>>>>
>>>>>>>>> On 3/5/22 4:48 PM, olcott wrote:
>>>>>>>>>> On 3/5/2022 3:39 PM, Richard Damon wrote:
>>>>>>>>>>>
>>>>>>>>>>> On 3/5/22 4:04 PM, olcott wrote:
>>>>>>>>>>>> On 3/5/2022 1:30 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 3/5/22 1:53 PM, olcott wrote:
>>>>>>>>>>>>>> On 3/5/2022 5:07 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 3/4/22 11:04 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 3/4/2022 10:03 PM, Python wrote:
>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>> On 3/4/2022 9:44 PM, Python wrote:
>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>> ...
>>>>>>>>>>>>>>>>>>>> True cannot possibly exist apart from provable thus
>>>>>>>>>>>>>>>>>>>> Gödel could not have possibly found any expression
>>>>>>>>>>>>>>>>>>>> of any language L that is both true in L and
>>>>>>>>>>>>>>>>>>>> unprovable in L.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> But still he did.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> You might as well have said that Gödel had a dog that
>>>>>>>>>>>>>>>>>> was three cats.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Nope. I didn't say that. Stop dodging and lying.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Gödel exhibited an expression can be true in L and
>>>>>>>>>>>>>>>>> unprovable
>>>>>>>>>>>>>>>>> in L.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> He did not. This is impossible.
>>>>>>>>>>>>>>>> It is inherently true at the deepest philosophical level
>>>>>>>>>>>>>>>> that analytic truth only exists as connections between
>>>>>>>>>>>>>>>> expressions of language.
>>>>>>>>>>>>>>>> The proof of this is that no valid counter-examples exist.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Denial of actual Truth is a good sign of insanity.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Please seek Professional Help.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Saying something is wrong just because you disagree with
>>>>>>>>>>>>>>> the conclusion is NOT the Analytical Logic way.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> To Refute a logical argument, you need to show what
>>>>>>>>>>>>>>> particular step breaks the rules of logic that are
>>>>>>>>>>>>>>> enforce in the field that the argument is presented in,
>>>>>>>>>>>>>>> or which assumed premise that went into the argument is
>>>>>>>>>>>>>>> not True in that field.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Of course to do this, you need to actually read and
>>>>>>>>>>>>>>> understand the argument, and not just depend on your own
>>>>>>>>>>>>>>> gut feelings.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I am saying that the only way that we can know that an
>>>>>>>>>>>>>> analytic expression of language is true is that it is
>>>>>>>>>>>>>> either defined to be true or it is derived by applying
>>>>>>>>>>>>>> truth preserving operations to expressions of language
>>>>>>>>>>>>>> that are defined to be true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The above statements prove themselves to be true
>>>>>>>>>>>>>> categorically on the basis of the meaning of their words.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> And you are confusing KNOWLEDGE with TRUTH.
>>>>>>>>>>>>>
>>>>>>>>>>>>> For something to be a KNOWN TRUTH, it needs some way to
>>>>>>>>>>>>> 'Prove' it, either an Analytic Proof, or a proper
>>>>>>>>>>>>> observation for Emperical/Synthetic Proof. But it is True
>>>>>>>>>>>>> before it was proven, if it was true.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Proofs can not change the Truth value of statements (unless
>>>>>>>>>>>>> they are statements about something having been proven),
>>>>>>>>>>>>> they just move them from an unproven (and likely unknown,
>>>>>>>>>>>>> but maybe presumed) statement to being Knowledge and Proven
>>>>>>>>>>>>> True.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> It is OBVIOUS that something can be True but not Known.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Goldbach's conjecture is one of the oldest and best-known
>>>>>>>>>>>> unsolved problems in number theory and all of mathematics.
>>>>>>>>>>>> It states that every even whole number greater than 2 is the
>>>>>>>>>>>> sum of two prime numbers.
>>>>>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>>>>>
>>>>>>>>>>>> The truth that we begin with is the proof that the Goldbach
>>>>>>>>>>>> criteria is met with every element of the sequence even
>>>>>>>>>>>> whole numbers greater than 2 that has been tested.
>>>>>>>>>>>>
>>>>>>>>>>>> Testing an element N of this sequence begins with the
>>>>>>>>>>>> element N as its premise then testing every pair of primes
>>>>>>>>>>>> that are numerically less that this element to see if the
>>>>>>>>>>>> sum of any pair = N.
>>>>>>>>>>>>
>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>> ∃!x ∈ Prime_Numbers < N
>>>>>>>>>>>> ∃!y ∈ Prime_Numbers < N
>>>>>>>>>>>> Sum(x,y) == n
>>>>>>>>>>>>
>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>> Every case where Goldbach's criteria is met is a formal
>>>>>>>>>>>> proof from N to the satisfaction of the above expression,
>>>>>>>>>>>> thus proving its truth.
>>>>>>>>>>>
>>>>>>>>>>> So, how do you PROVE that this holds for ALL even numbers?
>>>>>>>>>>> Remember, THAT is the conjecture, not that it works for
>>>>>>>>>>> 'lots' of values.
>>>>>>>>>>>
>>>>>>>>>>> The fact that we haven't found an exception, doesn't mean
>>>>>>>>>>> that an exception doesn't exist, just that we haven't found
>>>>>>>>>>> it yet.
>>>>>>>>>>>
>>>>>>>>>>> Until you show you can test EVERY even number, you can't use
>>>>>>>>>>> that as your proof, and so your method has failed to actually
>>>>>>>>>>> prove it.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>> Therefore not all Truth needs to be Provable.
>>>>>>>>>>>>
>>>>>>>>>>>> If any element N of (even whole numbers greater than 2)
>>>>>>>>>>>> cannot be proven to satisfy the Goldbach criteria then
>>>>>>>>>>>> Goldbach's conjecture is false.
>>>>>>>>>>>>
>>>>>>>>>>>> For Goldbach true cannot possibly exist apart from provable
>>>>>>>>>>>> is proven.
>>>>>>>>>>>
>>>>>>>>>>> WRONG
>>>>>>>>>>>
>>>>>>>>>>> Goldbach conjecture MUST be either True or it is FALSE.
>>>>>>>>>> Unless there exists a proof that each (even whole number
>>>>>>>>>> greater than 2) meets the Goldbach criteria it is not true. If
>>>>>>>>>> even one of these proofs does not exist then it is not true.
>>>>>>>>>>
>>>>>>>>>> True cannot possibly exist apart from provable.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> WRONG.
>>>>>>>>>
>>>>>>>>> IT is an EMPRICAL FACT, that the Goldbach conjecture must be
>>>>>>>>> either true of false.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It is an analytical fact not an empirical fact.
>>>>>>>>
>>>>>>>> If there exists a single (even whole number greater than 2) that
>>>>>>>> cannot possibly be proved to meet the Goldbach criteria then the
>>>>>>>> Goldbach conjecture is not true.
>>>>>>>>
>>>>>>>> Otherwise every (even whole number greater than 2) can be proved
>>>>>>>> to meet the Goldbach criteria, thus True depends on Provable.
>>>>>>>>
>>>>>>>
>>>>>>> Right, if one exception exists, the conjecture is not true, but
>>>>>>> false.
>>>>>>>
>>>>>>> We do not have, and may never have, a proof that no such
>>>>>>> exception exists.
>>>>>>>
>>>>>>> Thus, by your definition, YOU can not treat the 'Truth' of the
>>>>>>> conjecture as a Truth Bearer, because you don't KNOW if it is
>>>>>>> actually provable, let alone if it is provably true.
>>>>>>>
>>>>>>
>>>>>> Unless every element of the set of (even whole number greater than
>>>>>> 2) provably meets the Goldbach criteria, the Goldbach conjecture
>>>>>> is not true, thus proving that its truth depends on its provability.
>>>>>>
>>>>>
>>>>> WRONG.
>>>>>
>>>>> Repeating your statement doesn't make it True.
>>>>>
>>>>> I will now DEMAND that you PROVE your statement or be able to just
>>>>> claim you are are liar and a Hypocrite.
>>>>
>>>>  >>>> If there exists a single (even whole number greater than 2) that
>>>>  >>>> cannot possibly be proved to meet the Goldbach criteria then the
>>>>  >>>> Goldbach conjecture is not true.
>>>>
>>>> If >= 1 element is not provable then false entails
>>>> < 1 elements are not provable entails
>>>> all elements are provable.
>>>
>>> You aren't making sense, because you don't understand the difference
>>> between True and Provable.
>>>
>>> Yes, If we can show >= 1 numbers that fail the requirements we have
>>> proven that the conjecture is False.
>>
>> If a proof exists (even if we never know it) that >= 1 numbers that
>> fail the requirements then it is false (even if we never know it).
>>
>> Only if no proof exists (even if we never know it) that fail the
>> requirements then it is true.
>>
>> This is simply other other way of saying that unless every element of
>> the set can be proven to meet the requirements (even if we never know
>> it) then the conjecture is False.
>>
>
> You just don't understand about infinitie sets do you. You are not
> guarenteed to be able to make a finite proof that all of an infinite set
> meets the requirements.
>

On 3/5/2022 7:56 PM, Richard Damon wrote:
> On 3/5/22 8:37 PM, olcott wrote:
>> On 3/5/2022 7:24 PM, Richard Damon wrote:
>>>
>>> On 3/5/22 8:03 PM, olcott wrote:
>>>> On 3/5/2022 6:46 PM, Richard Damon wrote:
>>>>>
>>>>> On 3/5/22 7:12 PM, olcott wrote:
>>>>>> On 3/5/2022 5:36 PM, Richard Damon wrote:
>>>>>>> On 3/5/22 6:16 PM, olcott wrote:
>>>>>>>> On 3/5/2022 5:09 PM, Richard Damon wrote:
>>>>>>>>> On 3/5/22 5:51 PM, olcott wrote:
>>>>>>>>>> On 3/5/2022 4:20 PM, Richard Damon wrote:
>>>>>>>>>>>
>>>>>>>>>>> On 3/5/22 4:48 PM, olcott wrote:
>>>>>>>>>>>> On 3/5/2022 3:39 PM, Richard Damon wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 3/5/22 4:04 PM, olcott wrote:
>>>>>>>>>>>>>> On 3/5/2022 1:30 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 3/5/22 1:53 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 3/5/2022 5:07 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> On 3/4/22 11:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 3/4/2022 10:03 PM, Python wrote:
>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 3/4/2022 9:44 PM, Python wrote:
>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>> ...
>>>>>>>>>>>>>>>>>>>>>> True cannot possibly exist apart from provable
>>>>>>>>>>>>>>>>>>>>>> thus Gödel could not have possibly found any
>>>>>>>>>>>>>>>>>>>>>> expression of any language L that is both true in
>>>>>>>>>>>>>>>>>>>>>> L and unprovable in L.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> But still he did.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> You might as well have said that Gödel had a dog
>>>>>>>>>>>>>>>>>>>> that was three cats.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Nope. I didn't say that. Stop dodging and lying.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Gödel exhibited an expression can be true in L and
>>>>>>>>>>>>>>>>>>> unprovable
>>>>>>>>>>>>>>>>>>> in L.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> He did not. This is impossible.
>>>>>>>>>>>>>>>>>> It is inherently true at the deepest philosophical
>>>>>>>>>>>>>>>>>> level that analytic truth only exists as connections
>>>>>>>>>>>>>>>>>> between expressions of language.
>>>>>>>>>>>>>>>>>> The proof of this is that no valid counter-examples
>>>>>>>>>>>>>>>>>> exist.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Denial of actual Truth is a good sign of insanity.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Please seek Professional Help.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Saying something is wrong just because you disagree
>>>>>>>>>>>>>>>>> with the conclusion is NOT the Analytical Logic way.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> To Refute a logical argument, you need to show what
>>>>>>>>>>>>>>>>> particular step breaks the rules of logic that are
>>>>>>>>>>>>>>>>> enforce in the field that the argument is presented in,
>>>>>>>>>>>>>>>>> or which assumed premise that went into the argument is
>>>>>>>>>>>>>>>>> not True in that field.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Of course to do this, you need to actually read and
>>>>>>>>>>>>>>>>> understand the argument, and not just depend on your
>>>>>>>>>>>>>>>>> own gut feelings.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I am saying that the only way that we can know that an
>>>>>>>>>>>>>>>> analytic expression of language is true is that it is
>>>>>>>>>>>>>>>> either defined to be true or it is derived by applying
>>>>>>>>>>>>>>>> truth preserving operations to expressions of language
>>>>>>>>>>>>>>>> that are defined to be true.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The above statements prove themselves to be true
>>>>>>>>>>>>>>>> categorically on the basis of the meaning of their words.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> And you are confusing KNOWLEDGE with TRUTH.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> For something to be a KNOWN TRUTH, it needs some way to
>>>>>>>>>>>>>>> 'Prove' it, either an Analytic Proof, or a proper
>>>>>>>>>>>>>>> observation for Emperical/Synthetic Proof. But it is True
>>>>>>>>>>>>>>> before it was proven, if it was true.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Proofs can not change the Truth value of statements
>>>>>>>>>>>>>>> (unless they are statements about something having been
>>>>>>>>>>>>>>> proven), they just move them from an unproven (and likely
>>>>>>>>>>>>>>> unknown, but maybe presumed) statement to being Knowledge
>>>>>>>>>>>>>>> and Proven True.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It is OBVIOUS that something can be True but not Known.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Goldbach's conjecture is one of the oldest and best-known
>>>>>>>>>>>>>> unsolved problems in number theory and all of mathematics.
>>>>>>>>>>>>>> It states that every even whole number greater than 2 is
>>>>>>>>>>>>>> the sum of two prime numbers.
>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The truth that we begin with is the proof that the
>>>>>>>>>>>>>> Goldbach criteria is met with every element of the
>>>>>>>>>>>>>> sequence even whole numbers greater than 2 that has been
>>>>>>>>>>>>>> tested.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Testing an element N of this sequence begins with the
>>>>>>>>>>>>>> element N as its premise then testing every pair of primes
>>>>>>>>>>>>>> that are numerically less that this element to see if the
>>>>>>>>>>>>>> sum of any pair = N.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>>>> ∃!x ∈ Prime_Numbers < N
>>>>>>>>>>>>>> ∃!y ∈ Prime_Numbers < N
>>>>>>>>>>>>>> Sum(x,y) == n
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>>>> Every case where Goldbach's criteria is met is a formal
>>>>>>>>>>>>>> proof from N to the satisfaction of the above expression,
>>>>>>>>>>>>>> thus proving its truth.
>>>>>>>>>>>>>
>>>>>>>>>>>>> So, how do you PROVE that this holds for ALL even numbers?
>>>>>>>>>>>>> Remember, THAT is the conjecture, not that it works for
>>>>>>>>>>>>> 'lots' of values.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The fact that we haven't found an exception, doesn't mean
>>>>>>>>>>>>> that an exception doesn't exist, just that we haven't found
>>>>>>>>>>>>> it yet.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Until you show you can test EVERY even number, you can't
>>>>>>>>>>>>> use that as your proof, and so your method has failed to
>>>>>>>>>>>>> actually prove it.
>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Therefore not all Truth needs to be Provable.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If any element N of (even whole numbers greater than 2)
>>>>>>>>>>>>>> cannot be proven to satisfy the Goldbach criteria then
>>>>>>>>>>>>>> Goldbach's conjecture is false.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> For Goldbach true cannot possibly exist apart from
>>>>>>>>>>>>>> provable is proven.
>>>>>>>>>>>>>
>>>>>>>>>>>>> WRONG
>>>>>>>>>>>>>
>>>>>>>>>>>>> Goldbach conjecture MUST be either True or it is FALSE.
>>>>>>>>>>>> Unless there exists a proof that each (even whole number
>>>>>>>>>>>> greater than 2) meets the Goldbach criteria it is not true.
>>>>>>>>>>>> If even one of these proofs does not exist then it is not true.
>>>>>>>>>>>>
>>>>>>>>>>>> True cannot possibly exist apart from provable.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> WRONG.
>>>>>>>>>>>
>>>>>>>>>>> IT is an EMPRICAL FACT, that the Goldbach conjecture must be
>>>>>>>>>>> either true of false.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It is an analytical fact not an empirical fact.
>>>>>>>>>>
>>>>>>>>>> If there exists a single (even whole number greater than 2)
>>>>>>>>>> that cannot possibly be proved to meet the Goldbach criteria
>>>>>>>>>> then the Goldbach conjecture is not true.
>>>>>>>>>>
>>>>>>>>>> Otherwise every (even whole number greater than 2) can be
>>>>>>>>>> proved to meet the Goldbach criteria, thus True depends on
>>>>>>>>>> Provable.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Right, if one exception exists, the conjecture is not true, but
>>>>>>>>> false.
>>>>>>>>>
>>>>>>>>> We do not have, and may never have, a proof that no such
>>>>>>>>> exception exists.
>>>>>>>>>
>>>>>>>>> Thus, by your definition, YOU can not treat the 'Truth' of the
>>>>>>>>> conjecture as a Truth Bearer, because you don't KNOW if it is
>>>>>>>>> actually provable, let alone if it is provably true.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Unless every element of the set of (even whole number greater
>>>>>>>> than 2) provably meets the Goldbach criteria, the Goldbach
>>>>>>>> conjecture is not true, thus proving that its truth depends on
>>>>>>>> its provability.
>>>>>>>>
>>>>>>>
>>>>>>> WRONG.
>>>>>>>
>>>>>>> Repeating your statement doesn't make it True.
>>>>>>>
>>>>>>> I will now DEMAND that you PROVE your statement or be able to
>>>>>>> just claim you are are liar and a Hypocrite.
>>>>>>
>>>>>>  >>>> If there exists a single (even whole number greater than 2)
>>>>>> that
>>>>>>  >>>> cannot possibly be proved to meet the Goldbach criteria then
>>>>>> the
>>>>>>  >>>> Goldbach conjecture is not true.
>>>>>>
>>>>>> If >= 1 element is not provable then false entails
>>>>>> < 1 elements are not provable entails
>>>>>> all elements are provable.
>>>>>
>>>>> You aren't making sense, because you don't understand the
>>>>> difference between True and Provable.
>>>>>
>>>>> Yes, If we can show >= 1 numbers that fail the requirements we have
>>>>> proven that the conjecture is False.
>>>>
>>>> If a proof exists (even if we never know it) that >= 1 numbers that
>>>> fail the requirements then it is false (even if we never know it).
>>>>
>>>> Only if no proof exists (even if we never know it) that fail the
>>>> requirements then it is true.
>>>>
>>>> This is simply other other way of saying that unless every element
>>>> of the set can be proven to meet the requirements (even if we never
>>>> know it) then the conjecture is False.
>>>>
>>>
>>> You just don't understand about infinitie sets do you. You are not
>>> guarenteed to be able to make a finite proof that all of an infinite
>>> set meets the requirements.
>>>
>>
>> If there is a single element of the set of (even whole numbers greater
>> than 2) that cannot be proven to meet the requirements then the
>> Goldbach conjecture fails
>>

On 3/5/2022 9:09 PM, Richard Damon wrote:
> On 3/5/22 9:39 PM, olcott wrote:
>> On 3/5/2022 7:56 PM, Richard Damon wrote:
>>> On 3/5/22 8:37 PM, olcott wrote:
>>>> On 3/5/2022 7:24 PM, Richard Damon wrote:
>>>>>
>>>>> On 3/5/22 8:03 PM, olcott wrote:
>>>>>> On 3/5/2022 6:46 PM, Richard Damon wrote:
>>>>>>>
>>>>>>> On 3/5/22 7:12 PM, olcott wrote:
>>>>>>>> On 3/5/2022 5:36 PM, Richard Damon wrote:
>>>>>>>>> On 3/5/22 6:16 PM, olcott wrote:
>>>>>>>>>> On 3/5/2022 5:09 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/5/22 5:51 PM, olcott wrote:
>>>>>>>>>>>> On 3/5/2022 4:20 PM, Richard Damon wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 3/5/22 4:48 PM, olcott wrote:
>>>>>>>>>>>>>> On 3/5/2022 3:39 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 3/5/22 4:04 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 3/5/2022 1:30 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 3/5/22 1:53 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 3/5/2022 5:07 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> On 3/4/22 11:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 3/4/2022 10:03 PM, Python wrote:
>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 3/4/2022 9:44 PM, Python wrote:
>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> ...
>>>>>>>>>>>>>>>>>>>>>>>> True cannot possibly exist apart from provable
>>>>>>>>>>>>>>>>>>>>>>>> thus Gödel could not have possibly found any
>>>>>>>>>>>>>>>>>>>>>>>> expression of any language L that is both true
>>>>>>>>>>>>>>>>>>>>>>>> in L and unprovable in L.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> But still he did.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> You might as well have said that Gödel had a dog
>>>>>>>>>>>>>>>>>>>>>> that was three cats.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Nope. I didn't say that. Stop dodging and lying.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Gödel exhibited an expression can be true in L and
>>>>>>>>>>>>>>>>>>>>> unprovable
>>>>>>>>>>>>>>>>>>>>> in L.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> He did not. This is impossible.
>>>>>>>>>>>>>>>>>>>> It is inherently true at the deepest philosophical
>>>>>>>>>>>>>>>>>>>> level that analytic truth only exists as connections
>>>>>>>>>>>>>>>>>>>> between expressions of language.
>>>>>>>>>>>>>>>>>>>> The proof of this is that no valid counter-examples
>>>>>>>>>>>>>>>>>>>> exist.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Denial of actual Truth is a good sign of insanity.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Please seek Professional Help.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Saying something is wrong just because you disagree
>>>>>>>>>>>>>>>>>>> with the conclusion is NOT the Analytical Logic way.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> To Refute a logical argument, you need to show what
>>>>>>>>>>>>>>>>>>> particular step breaks the rules of logic that are
>>>>>>>>>>>>>>>>>>> enforce in the field that the argument is presented
>>>>>>>>>>>>>>>>>>> in, or which assumed premise that went into the
>>>>>>>>>>>>>>>>>>> argument is not True in that field.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Of course to do this, you need to actually read and
>>>>>>>>>>>>>>>>>>> understand the argument, and not just depend on your
>>>>>>>>>>>>>>>>>>> own gut feelings.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> I am saying that the only way that we can know that an
>>>>>>>>>>>>>>>>>> analytic expression of language is true is that it is
>>>>>>>>>>>>>>>>>> either defined to be true or it is derived by applying
>>>>>>>>>>>>>>>>>> truth preserving operations to expressions of language
>>>>>>>>>>>>>>>>>> that are defined to be true.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> The above statements prove themselves to be true
>>>>>>>>>>>>>>>>>> categorically on the basis of the meaning of their words.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> And you are confusing KNOWLEDGE with TRUTH.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> For something to be a KNOWN TRUTH, it needs some way to
>>>>>>>>>>>>>>>>> 'Prove' it, either an Analytic Proof, or a proper
>>>>>>>>>>>>>>>>> observation for Emperical/Synthetic Proof. But it is
>>>>>>>>>>>>>>>>> True before it was proven, if it was true.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Proofs can not change the Truth value of statements
>>>>>>>>>>>>>>>>> (unless they are statements about something having been
>>>>>>>>>>>>>>>>> proven), they just move them from an unproven (and
>>>>>>>>>>>>>>>>> likely unknown, but maybe presumed) statement to being
>>>>>>>>>>>>>>>>> Knowledge and Proven True.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> It is OBVIOUS that something can be True but not Known.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Goldbach's conjecture is one of the oldest and
>>>>>>>>>>>>>>>> best-known unsolved problems in number theory and all of
>>>>>>>>>>>>>>>> mathematics. It states that every even whole number
>>>>>>>>>>>>>>>> greater than 2 is the sum of two prime numbers.
>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The truth that we begin with is the proof that the
>>>>>>>>>>>>>>>> Goldbach criteria is met with every element of the
>>>>>>>>>>>>>>>> sequence even whole numbers greater than 2 that has been
>>>>>>>>>>>>>>>> tested.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Testing an element N of this sequence begins with the
>>>>>>>>>>>>>>>> element N as its premise then testing every pair of
>>>>>>>>>>>>>>>> primes that are numerically less that this element to
>>>>>>>>>>>>>>>> see if the sum of any pair = N.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>>>>>> ∃!x ∈ Prime_Numbers < N
>>>>>>>>>>>>>>>> ∃!y ∈ Prime_Numbers < N
>>>>>>>>>>>>>>>> Sum(x,y) == n
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>>>>>> Every case where Goldbach's criteria is met is a formal
>>>>>>>>>>>>>>>> proof from N to the satisfaction of the above
>>>>>>>>>>>>>>>> expression, thus proving its truth.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> So, how do you PROVE that this holds for ALL even
>>>>>>>>>>>>>>> numbers? Remember, THAT is the conjecture, not that it
>>>>>>>>>>>>>>> works for 'lots' of values.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The fact that we haven't found an exception, doesn't mean
>>>>>>>>>>>>>>> that an exception doesn't exist, just that we haven't
>>>>>>>>>>>>>>> found it yet.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Until you show you can test EVERY even number, you can't
>>>>>>>>>>>>>>> use that as your proof, and so your method has failed to
>>>>>>>>>>>>>>> actually prove it.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Therefore not all Truth needs to be Provable.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> If any element N of (even whole numbers greater than 2)
>>>>>>>>>>>>>>>> cannot be proven to satisfy the Goldbach criteria then
>>>>>>>>>>>>>>>> Goldbach's conjecture is false.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> For Goldbach true cannot possibly exist apart from
>>>>>>>>>>>>>>>> provable is proven.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> WRONG
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Goldbach conjecture MUST be either True or it is FALSE.
>>>>>>>>>>>>>> Unless there exists a proof that each (even whole number
>>>>>>>>>>>>>> greater than 2) meets the Goldbach criteria it is not
>>>>>>>>>>>>>> true. If even one of these proofs does not exist then it
>>>>>>>>>>>>>> is not true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> True cannot possibly exist apart from provable.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> WRONG.
>>>>>>>>>>>>>
>>>>>>>>>>>>> IT is an EMPRICAL FACT, that the Goldbach conjecture must
>>>>>>>>>>>>> be either true of false.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> It is an analytical fact not an empirical fact.
>>>>>>>>>>>>
>>>>>>>>>>>> If there exists a single (even whole number greater than 2)
>>>>>>>>>>>> that cannot possibly be proved to meet the Goldbach criteria
>>>>>>>>>>>> then the Goldbach conjecture is not true.
>>>>>>>>>>>>
>>>>>>>>>>>> Otherwise every (even whole number greater than 2) can be
>>>>>>>>>>>> proved to meet the Goldbach criteria, thus True depends on
>>>>>>>>>>>> Provable.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Right, if one exception exists, the conjecture is not true,
>>>>>>>>>>> but false.
>>>>>>>>>>>
>>>>>>>>>>> We do not have, and may never have, a proof that no such
>>>>>>>>>>> exception exists.
>>>>>>>>>>>
>>>>>>>>>>> Thus, by your definition, YOU can not treat the 'Truth' of
>>>>>>>>>>> the conjecture as a Truth Bearer, because you don't KNOW if
>>>>>>>>>>> it is actually provable, let alone if it is provably true.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Unless every element of the set of (even whole number greater
>>>>>>>>>> than 2) provably meets the Goldbach criteria, the Goldbach
>>>>>>>>>> conjecture is not true, thus proving that its truth depends on
>>>>>>>>>> its provability.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> WRONG.
>>>>>>>>>
>>>>>>>>> Repeating your statement doesn't make it True.
>>>>>>>>>
>>>>>>>>> I will now DEMAND that you PROVE your statement or be able to
>>>>>>>>> just claim you are are liar and a Hypocrite.
>>>>>>>>
>>>>>>>>  >>>> If there exists a single (even whole number greater than
>>>>>>>> 2) that
>>>>>>>>  >>>> cannot possibly be proved to meet the Goldbach criteria
>>>>>>>> then the
>>>>>>>>  >>>> Goldbach conjecture is not true.
>>>>>>>>
>>>>>>>> If >= 1 element is not provable then false entails
>>>>>>>> < 1 elements are not provable entails
>>>>>>>> all elements are provable.
>>>>>>>
>>>>>>> You aren't making sense, because you don't understand the
>>>>>>> difference between True and Provable.
>>>>>>>
>>>>>>> Yes, If we can show >= 1 numbers that fail the requirements we
>>>>>>> have proven that the conjecture is False.
>>>>>>
>>>>>> If a proof exists (even if we never know it) that >= 1 numbers
>>>>>> that fail the requirements then it is false (even if we never know
>>>>>> it).
>>>>>>
>>>>>> Only if no proof exists (even if we never know it) that fail the
>>>>>> requirements then it is true.
>>>>>>
>>>>>> This is simply other other way of saying that unless every element
>>>>>> of the set can be proven to meet the requirements (even if we
>>>>>> never know it) then the conjecture is False.
>>>>>>
>>>>>
>>>>> You just don't understand about infinitie sets do you. You are not
>>>>> guarenteed to be able to make a finite proof that all of an
>>>>> infinite set meets the requirements.
>>>>>
>>>>
>>>> If there is a single element of the set of (even whole numbers
>>>> greater than 2) that cannot be proven to meet the requirements then
>>>> the Goldbach conjecture fails
>>>>
>>
>> where A is (even whole numbers greater than 2)
>> and P is Provably meets Goldbach criteria
>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x).
>>
>>>> is merely another way of saying that
>>>>
>>>> unless every element of the set of (even whole numbers greater than
>>>> 2) can be proven to meet the requirements then the Goldbach
>>>> conjecture fails.
>>>>
>>>
>>> You still don't get it, do you.
>>
>> You are the one that fails to understand how existential
>> quantification is translated into universal quantification.
>>
>> https://sites.math.washington.edu/~aloveles/Math300Winter2011/m300Quantifiers.pdf
>>
>>
>> (1) ¬[∀x ∈ A, P(x)] ⇔ ∃x ∈ A, ¬P(x). // from the link
>>
>> where A is (even whole numbers greater than 2)
>> and P is Provably meets Goldbach criteria
>>
>> negate both sides of (1)
>> ∀x ∈ A, P(x) ⇔ ¬∃x ∈ A, ¬P(x).
>>
>> Goldbach ⇔ every element of (even whole numbers greater than 2)
>> Provably meets Goldbach criteria.
>>
>> is a correct transformation of: ¬Goldbach ⇔ ∃x ∈ A, ¬P(x).
>>
>
> And where do you get PROVABLE form any of that.
>
> You still have to PROVE an attribute for every member of the infinite
> set of Evens.
>

On 3/5/2022 9:57 PM, Richard Damon wrote:
> On 3/5/22 10:27 PM, olcott wrote:
>> On 3/5/2022 9:09 PM, Richard Damon wrote:
>>> On 3/5/22 9:39 PM, olcott wrote:
>>>> On 3/5/2022 7:56 PM, Richard Damon wrote:
>>>>> On 3/5/22 8:37 PM, olcott wrote:
>>>>>> On 3/5/2022 7:24 PM, Richard Damon wrote:
>>>>>>>
>>>>>>> On 3/5/22 8:03 PM, olcott wrote:
>>>>>>>> On 3/5/2022 6:46 PM, Richard Damon wrote:
>>>>>>>>>
>>>>>>>>> On 3/5/22 7:12 PM, olcott wrote:
>>>>>>>>>> On 3/5/2022 5:36 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/5/22 6:16 PM, olcott wrote:
>>>>>>>>>>>> On 3/5/2022 5:09 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 3/5/22 5:51 PM, olcott wrote:
>>>>>>>>>>>>>> On 3/5/2022 4:20 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 3/5/22 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 3/5/2022 3:39 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> On 3/5/22 4:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 3/5/2022 1:30 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 3/5/22 1:53 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 3/5/2022 5:07 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> On 3/4/22 11:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 3/4/2022 10:03 PM, Python wrote:
>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 3/4/2022 9:44 PM, Python wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> ...
>>>>>>>>>>>>>>>>>>>>>>>>>> True cannot possibly exist apart from provable
>>>>>>>>>>>>>>>>>>>>>>>>>> thus Gödel could not have possibly found any
>>>>>>>>>>>>>>>>>>>>>>>>>> expression of any language L that is both true
>>>>>>>>>>>>>>>>>>>>>>>>>> in L and unprovable in L.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> But still he did.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> You might as well have said that Gödel had a dog
>>>>>>>>>>>>>>>>>>>>>>>> that was three cats.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Nope. I didn't say that. Stop dodging and lying.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Gödel exhibited an expression can be true in L
>>>>>>>>>>>>>>>>>>>>>>> and unprovable
>>>>>>>>>>>>>>>>>>>>>>> in L.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> He did not. This is impossible.
>>>>>>>>>>>>>>>>>>>>>> It is inherently true at the deepest philosophical
>>>>>>>>>>>>>>>>>>>>>> level that analytic truth only exists as
>>>>>>>>>>>>>>>>>>>>>> connections between expressions of language.
>>>>>>>>>>>>>>>>>>>>>> The proof of this is that no valid
>>>>>>>>>>>>>>>>>>>>>> counter-examples exist.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Denial of actual Truth is a good sign of insanity.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Please seek Professional Help.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Saying something is wrong just because you disagree
>>>>>>>>>>>>>>>>>>>>> with the conclusion is NOT the Analytical Logic way.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> To Refute a logical argument, you need to show what
>>>>>>>>>>>>>>>>>>>>> particular step breaks the rules of logic that are
>>>>>>>>>>>>>>>>>>>>> enforce in the field that the argument is presented
>>>>>>>>>>>>>>>>>>>>> in, or which assumed premise that went into the
>>>>>>>>>>>>>>>>>>>>> argument is not True in that field.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Of course to do this, you need to actually read and
>>>>>>>>>>>>>>>>>>>>> understand the argument, and not just depend on
>>>>>>>>>>>>>>>>>>>>> your own gut feelings.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> I am saying that the only way that we can know that
>>>>>>>>>>>>>>>>>>>> an analytic expression of language is true is that
>>>>>>>>>>>>>>>>>>>> it is either defined to be true or it is derived by
>>>>>>>>>>>>>>>>>>>> applying truth preserving operations to expressions
>>>>>>>>>>>>>>>>>>>> of language that are defined to be true.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> The above statements prove themselves to be true
>>>>>>>>>>>>>>>>>>>> categorically on the basis of the meaning of their
>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> And you are confusing KNOWLEDGE with TRUTH.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> For something to be a KNOWN TRUTH, it needs some way
>>>>>>>>>>>>>>>>>>> to 'Prove' it, either an Analytic Proof, or a proper
>>>>>>>>>>>>>>>>>>> observation for Emperical/Synthetic Proof. But it is
>>>>>>>>>>>>>>>>>>> True before it was proven, if it was true.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Proofs can not change the Truth value of statements
>>>>>>>>>>>>>>>>>>> (unless they are statements about something having
>>>>>>>>>>>>>>>>>>> been proven), they just move them from an unproven
>>>>>>>>>>>>>>>>>>> (and likely unknown, but maybe presumed) statement to
>>>>>>>>>>>>>>>>>>> being Knowledge and Proven True.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> It is OBVIOUS that something can be True but not Known.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Goldbach's conjecture is one of the oldest and
>>>>>>>>>>>>>>>>>> best-known unsolved problems in number theory and all
>>>>>>>>>>>>>>>>>> of mathematics. It states that every even whole number
>>>>>>>>>>>>>>>>>> greater than 2 is the sum of two prime numbers.
>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> The truth that we begin with is the proof that the
>>>>>>>>>>>>>>>>>> Goldbach criteria is met with every element of the
>>>>>>>>>>>>>>>>>> sequence even whole numbers greater than 2 that has
>>>>>>>>>>>>>>>>>> been tested.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Testing an element N of this sequence begins with the
>>>>>>>>>>>>>>>>>> element N as its premise then testing every pair of
>>>>>>>>>>>>>>>>>> primes that are numerically less that this element to
>>>>>>>>>>>>>>>>>> see if the sum of any pair = N.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>>>>>>>> ∃!x ∈ Prime_Numbers < N
>>>>>>>>>>>>>>>>>> ∃!y ∈ Prime_Numbers < N
>>>>>>>>>>>>>>>>>> Sum(x,y) == n
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>>>>>>>> Every case where Goldbach's criteria is met is a
>>>>>>>>>>>>>>>>>> formal proof from N to the satisfaction of the above
>>>>>>>>>>>>>>>>>> expression, thus proving its truth.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> So, how do you PROVE that this holds for ALL even
>>>>>>>>>>>>>>>>> numbers? Remember, THAT is the conjecture, not that it
>>>>>>>>>>>>>>>>> works for 'lots' of values.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> The fact that we haven't found an exception, doesn't
>>>>>>>>>>>>>>>>> mean that an exception doesn't exist, just that we
>>>>>>>>>>>>>>>>> haven't found it yet.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Until you show you can test EVERY even number, you
>>>>>>>>>>>>>>>>> can't use that as your proof, and so your method has
>>>>>>>>>>>>>>>>> failed to actually prove it.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Therefore not all Truth needs to be Provable.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> If any element N of (even whole numbers greater than
>>>>>>>>>>>>>>>>>> 2) cannot be proven to satisfy the Goldbach criteria
>>>>>>>>>>>>>>>>>> then Goldbach's conjecture is false.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> For Goldbach true cannot possibly exist apart from
>>>>>>>>>>>>>>>>>> provable is proven.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> WRONG
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Goldbach conjecture MUST be either True or it is FALSE.
>>>>>>>>>>>>>>>> Unless there exists a proof that each (even whole number
>>>>>>>>>>>>>>>> greater than 2) meets the Goldbach criteria it is not
>>>>>>>>>>>>>>>> true. If even one of these proofs does not exist then it
>>>>>>>>>>>>>>>> is not true.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> True cannot possibly exist apart from provable.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> WRONG.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> IT is an EMPRICAL FACT, that the Goldbach conjecture must
>>>>>>>>>>>>>>> be either true of false.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It is an analytical fact not an empirical fact.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If there exists a single (even whole number greater than
>>>>>>>>>>>>>> 2) that cannot possibly be proved to meet the Goldbach
>>>>>>>>>>>>>> criteria then the Goldbach conjecture is not true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Otherwise every (even whole number greater than 2) can be
>>>>>>>>>>>>>> proved to meet the Goldbach criteria, thus True depends on
>>>>>>>>>>>>>> Provable.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Right, if one exception exists, the conjecture is not true,
>>>>>>>>>>>>> but false.
>>>>>>>>>>>>>
>>>>>>>>>>>>> We do not have, and may never have, a proof that no such
>>>>>>>>>>>>> exception exists.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Thus, by your definition, YOU can not treat the 'Truth' of
>>>>>>>>>>>>> the conjecture as a Truth Bearer, because you don't KNOW if
>>>>>>>>>>>>> it is actually provable, let alone if it is provably true.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Unless every element of the set of (even whole number
>>>>>>>>>>>> greater than 2) provably meets the Goldbach criteria, the
>>>>>>>>>>>> Goldbach conjecture is not true, thus proving that its truth
>>>>>>>>>>>> depends on its provability.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> WRONG.
>>>>>>>>>>>
>>>>>>>>>>> Repeating your statement doesn't make it True.
>>>>>>>>>>>
>>>>>>>>>>> I will now DEMAND that you PROVE your statement or be able to
>>>>>>>>>>> just claim you are are liar and a Hypocrite.
>>>>>>>>>>
>>>>>>>>>>  >>>> If there exists a single (even whole number greater than
>>>>>>>>>> 2) that
>>>>>>>>>>  >>>> cannot possibly be proved to meet the Goldbach criteria
>>>>>>>>>> then the
>>>>>>>>>>  >>>> Goldbach conjecture is not true.
>>>>>>>>>>
>>>>>>>>>> If >= 1 element is not provable then false entails
>>>>>>>>>> < 1 elements are not provable entails
>>>>>>>>>> all elements are provable.
>>>>>>>>>
>>>>>>>>> You aren't making sense, because you don't understand the
>>>>>>>>> difference between True and Provable.
>>>>>>>>>
>>>>>>>>> Yes, If we can show >= 1 numbers that fail the requirements we
>>>>>>>>> have proven that the conjecture is False.
>>>>>>>>
>>>>>>>> If a proof exists (even if we never know it) that >= 1 numbers
>>>>>>>> that fail the requirements then it is false (even if we never
>>>>>>>> know it).
>>>>>>>>
>>>>>>>> Only if no proof exists (even if we never know it) that fail the
>>>>>>>> requirements then it is true.
>>>>>>>>
>>>>>>>> This is simply other other way of saying that unless every
>>>>>>>> element of the set can be proven to meet the requirements (even
>>>>>>>> if we never know it) then the conjecture is False.
>>>>>>>>
>>>>>>>
>>>>>>> You just don't understand about infinitie sets do you. You are
>>>>>>> not guarenteed to be able to make a finite proof that all of an
>>>>>>> infinite set meets the requirements.
>>>>>>>
>>>>>>
>>>>>> If there is a single element of the set of (even whole numbers
>>>>>> greater than 2) that cannot be proven to meet the requirements
>>>>>> then the Goldbach conjecture fails
>>>>>>
>>>>
>>>> where A is (even whole numbers greater than 2)
>>>> and P is Provably meets Goldbach criteria
>>>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x).
>>>>
>>>>>> is merely another way of saying that
>>>>>>
>>>>>> unless every element of the set of (even whole numbers greater
>>>>>> than 2) can be proven to meet the requirements then the Goldbach
>>>>>> conjecture fails.
>>>>>>
>>>>>
>>>>> You still don't get it, do you.
>>>>
>>>> You are the one that fails to understand how existential
>>>> quantification is translated into universal quantification.
>>>>
>>>> https://sites.math.washington.edu/~aloveles/Math300Winter2011/m300Quantifiers.pdf
>>>>
>>>>
>>>> (1) ¬[∀x ∈ A, P(x)] ⇔ ∃x ∈ A, ¬P(x). // from the link
>>>>
>>>> where A is (even whole numbers greater than 2)
>>>> and P is Provably meets Goldbach criteria
>>>>
>>>> negate both sides of (1)
>>>> ∀x ∈ A, P(x) ⇔ ¬∃x ∈ A, ¬P(x).
>>>>
>>>> Goldbach ⇔ every element of (even whole numbers greater than 2)
>>>> Provably meets Goldbach criteria.
>>>>
>>>> is a correct transformation of: ¬Goldbach ⇔ ∃x ∈ A, ¬P(x).
>>>>
>>>
>>> And where do you get PROVABLE form any of that.
>>>
>>> You still have to PROVE an attribute for every member of the infinite
>>> set of Evens.
>>>
>>
>> Like I said you simply do not understand existential and universal
>> quantification well enough to translate between them.
>>
>> A is (even whole numbers greater than 2)
>> P is Provably meets Goldbach criteria
>>
>> On 3/5/2022 5:09 PM, Richard Damon wrote:
>>  > On 3/5/22 5:51 PM, olcott wrote:
>>  >> If there exists a single (even whole number greater than 2) that
>>  >> cannot possibly be proved to meet the Goldbach criteria then the
>>  >> Goldbach conjecture is not true.
>>  >
>>  > Right, if one exception exists, the conjecture is not true, but false.
>>
>> My above paragraph translated into math:
>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x).
>>
>> People that do understand the math of it will be able to transform
>> that into this: Goldbach ⇔ ∀x ∈ A, P(x)
>>
>
> Which means that Goldbachs can be proven False if there exists a number
> that is even > 2 that doesn't meet the requirement.
>
> FINE.
>
> That means that IF Goldbachs Conjecture is False, that fact will be
> provable.
>
> How do you get to the fact that if it is True, it must be provable,

On 3/6/2022 5:57 AM, Richard Damon wrote:
> On 3/5/22 11:03 PM, olcott wrote:
>> On 3/5/2022 9:57 PM, Richard Damon wrote:
>>> On 3/5/22 10:27 PM, olcott wrote:
>>>> On 3/5/2022 9:09 PM, Richard Damon wrote:
>>>>> On 3/5/22 9:39 PM, olcott wrote:
>>>>>> On 3/5/2022 7:56 PM, Richard Damon wrote:
>>>>>>> On 3/5/22 8:37 PM, olcott wrote:
>>>>>>>> On 3/5/2022 7:24 PM, Richard Damon wrote:
>>>>>>>>>
>>>>>>>>> On 3/5/22 8:03 PM, olcott wrote:
>>>>>>>>>> On 3/5/2022 6:46 PM, Richard Damon wrote:
>>>>>>>>>>>
>>>>>>>>>>> On 3/5/22 7:12 PM, olcott wrote:
>>>>>>>>>>>> On 3/5/2022 5:36 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 3/5/22 6:16 PM, olcott wrote:
>>>>>>>>>>>>>> On 3/5/2022 5:09 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 3/5/22 5:51 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 3/5/2022 4:20 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> On 3/5/22 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 3/5/2022 3:39 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> On 3/5/22 4:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 3/5/2022 1:30 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 3/5/22 1:53 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 3/5/2022 5:07 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> On 3/4/22 11:04 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 3/4/2022 10:03 PM, Python wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/4/2022 9:44 PM, Python wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> ...
>>>>>>>>>>>>>>>>>>>>>>>>>>>> True cannot possibly exist apart from
>>>>>>>>>>>>>>>>>>>>>>>>>>>> provable thus Gödel could not have possibly
>>>>>>>>>>>>>>>>>>>>>>>>>>>> found any expression of any language L that
>>>>>>>>>>>>>>>>>>>>>>>>>>>> is both true in L and unprovable in L.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> But still he did.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> You might as well have said that Gödel had a
>>>>>>>>>>>>>>>>>>>>>>>>>> dog that was three cats.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Nope. I didn't say that. Stop dodging and lying.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Gödel exhibited an expression can be true in L
>>>>>>>>>>>>>>>>>>>>>>>>> and unprovable
>>>>>>>>>>>>>>>>>>>>>>>>> in L.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> He did not. This is impossible.
>>>>>>>>>>>>>>>>>>>>>>>> It is inherently true at the deepest
>>>>>>>>>>>>>>>>>>>>>>>> philosophical level that analytic truth only
>>>>>>>>>>>>>>>>>>>>>>>> exists as connections between expressions of
>>>>>>>>>>>>>>>>>>>>>>>> language.
>>>>>>>>>>>>>>>>>>>>>>>> The proof of this is that no valid
>>>>>>>>>>>>>>>>>>>>>>>> counter-examples exist.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Denial of actual Truth is a good sign of insanity.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Please seek Professional Help.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Saying something is wrong just because you
>>>>>>>>>>>>>>>>>>>>>>> disagree with the conclusion is NOT the
>>>>>>>>>>>>>>>>>>>>>>> Analytical Logic way.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> To Refute a logical argument, you need to show
>>>>>>>>>>>>>>>>>>>>>>> what particular step breaks the rules of logic
>>>>>>>>>>>>>>>>>>>>>>> that are enforce in the field that the argument
>>>>>>>>>>>>>>>>>>>>>>> is presented in, or which assumed premise that
>>>>>>>>>>>>>>>>>>>>>>> went into the argument is not True in that field.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Of course to do this, you need to actually read
>>>>>>>>>>>>>>>>>>>>>>> and understand the argument, and not just depend
>>>>>>>>>>>>>>>>>>>>>>> on your own gut feelings.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> I am saying that the only way that we can know
>>>>>>>>>>>>>>>>>>>>>> that an analytic expression of language is true is
>>>>>>>>>>>>>>>>>>>>>> that it is either defined to be true or it is
>>>>>>>>>>>>>>>>>>>>>> derived by applying truth preserving operations to
>>>>>>>>>>>>>>>>>>>>>> expressions of language that are defined to be true.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> The above statements prove themselves to be true
>>>>>>>>>>>>>>>>>>>>>> categorically on the basis of the meaning of their
>>>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> And you are confusing KNOWLEDGE with TRUTH.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> For something to be a KNOWN TRUTH, it needs some
>>>>>>>>>>>>>>>>>>>>> way to 'Prove' it, either an Analytic Proof, or a
>>>>>>>>>>>>>>>>>>>>> proper observation for Emperical/Synthetic Proof.
>>>>>>>>>>>>>>>>>>>>> But it is True before it was proven, if it was true.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Proofs can not change the Truth value of statements
>>>>>>>>>>>>>>>>>>>>> (unless they are statements about something having
>>>>>>>>>>>>>>>>>>>>> been proven), they just move them from an unproven
>>>>>>>>>>>>>>>>>>>>> (and likely unknown, but maybe presumed) statement
>>>>>>>>>>>>>>>>>>>>> to being Knowledge and Proven True.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> It is OBVIOUS that something can be True but not
>>>>>>>>>>>>>>>>>>>>> Known.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Goldbach's conjecture is one of the oldest and
>>>>>>>>>>>>>>>>>>>> best-known unsolved problems in number theory and
>>>>>>>>>>>>>>>>>>>> all of mathematics. It states that every even whole
>>>>>>>>>>>>>>>>>>>> number greater than 2 is the sum of two prime numbers.
>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> The truth that we begin with is the proof that the
>>>>>>>>>>>>>>>>>>>> Goldbach criteria is met with every element of the
>>>>>>>>>>>>>>>>>>>> sequence even whole numbers greater than 2 that has
>>>>>>>>>>>>>>>>>>>> been tested.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Testing an element N of this sequence begins with
>>>>>>>>>>>>>>>>>>>> the element N as its premise then testing every pair
>>>>>>>>>>>>>>>>>>>> of primes that are numerically less that this
>>>>>>>>>>>>>>>>>>>> element to see if the sum of any pair = N.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>>>>>>>>>> ∃!x ∈ Prime_Numbers < N
>>>>>>>>>>>>>>>>>>>> ∃!y ∈ Prime_Numbers < N
>>>>>>>>>>>>>>>>>>>> Sum(x,y) == n
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> ∀N ∈ (even whole numbers greater than 2)
>>>>>>>>>>>>>>>>>>>> Every case where Goldbach's criteria is met is a
>>>>>>>>>>>>>>>>>>>> formal proof from N to the satisfaction of the above
>>>>>>>>>>>>>>>>>>>> expression, thus proving its truth.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> So, how do you PROVE that this holds for ALL even
>>>>>>>>>>>>>>>>>>> numbers? Remember, THAT is the conjecture, not that
>>>>>>>>>>>>>>>>>>> it works for 'lots' of values.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> The fact that we haven't found an exception, doesn't
>>>>>>>>>>>>>>>>>>> mean that an exception doesn't exist, just that we
>>>>>>>>>>>>>>>>>>> haven't found it yet.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Until you show you can test EVERY even number, you
>>>>>>>>>>>>>>>>>>> can't use that as your proof, and so your method has
>>>>>>>>>>>>>>>>>>> failed to actually prove it.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Therefore not all Truth needs to be Provable.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> If any element N of (even whole numbers greater than
>>>>>>>>>>>>>>>>>>>> 2) cannot be proven to satisfy the Goldbach criteria
>>>>>>>>>>>>>>>>>>>> then Goldbach's conjecture is false.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> For Goldbach true cannot possibly exist apart from
>>>>>>>>>>>>>>>>>>>> provable is proven.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> WRONG
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Goldbach conjecture MUST be either True or it is FALSE.
>>>>>>>>>>>>>>>>>> Unless there exists a proof that each (even whole
>>>>>>>>>>>>>>>>>> number greater than 2) meets the Goldbach criteria it
>>>>>>>>>>>>>>>>>> is not true. If even one of these proofs does not
>>>>>>>>>>>>>>>>>> exist then it is not true.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> True cannot possibly exist apart from provable.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> WRONG.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> IT is an EMPRICAL FACT, that the Goldbach conjecture
>>>>>>>>>>>>>>>>> must be either true of false.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> It is an analytical fact not an empirical fact.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> If there exists a single (even whole number greater than
>>>>>>>>>>>>>>>> 2) that cannot possibly be proved to meet the Goldbach
>>>>>>>>>>>>>>>> criteria then the Goldbach conjecture is not true.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Otherwise every (even whole number greater than 2) can
>>>>>>>>>>>>>>>> be proved to meet the Goldbach criteria, thus True
>>>>>>>>>>>>>>>> depends on Provable.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Right, if one exception exists, the conjecture is not
>>>>>>>>>>>>>>> true, but false.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> We do not have, and may never have, a proof that no such
>>>>>>>>>>>>>>> exception exists.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Thus, by your definition, YOU can not treat the 'Truth'
>>>>>>>>>>>>>>> of the conjecture as a Truth Bearer, because you don't
>>>>>>>>>>>>>>> KNOW if it is actually provable, let alone if it is
>>>>>>>>>>>>>>> provably true.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Unless every element of the set of (even whole number
>>>>>>>>>>>>>> greater than 2) provably meets the Goldbach criteria, the
>>>>>>>>>>>>>> Goldbach conjecture is not true, thus proving that its
>>>>>>>>>>>>>> truth depends on its provability.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> WRONG.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Repeating your statement doesn't make it True.
>>>>>>>>>>>>>
>>>>>>>>>>>>> I will now DEMAND that you PROVE your statement or be able
>>>>>>>>>>>>> to just claim you are are liar and a Hypocrite.
>>>>>>>>>>>>
>>>>>>>>>>>>  >>>> If there exists a single (even whole number greater
>>>>>>>>>>>> than 2) that
>>>>>>>>>>>>  >>>> cannot possibly be proved to meet the Goldbach
>>>>>>>>>>>> criteria then the
>>>>>>>>>>>>  >>>> Goldbach conjecture is not true.
>>>>>>>>>>>>
>>>>>>>>>>>> If >= 1 element is not provable then false entails
>>>>>>>>>>>> < 1 elements are not provable entails
>>>>>>>>>>>> all elements are provable.
>>>>>>>>>>>
>>>>>>>>>>> You aren't making sense, because you don't understand the
>>>>>>>>>>> difference between True and Provable.
>>>>>>>>>>>
>>>>>>>>>>> Yes, If we can show >= 1 numbers that fail the requirements
>>>>>>>>>>> we have proven that the conjecture is False.
>>>>>>>>>>
>>>>>>>>>> If a proof exists (even if we never know it) that >= 1 numbers
>>>>>>>>>> that fail the requirements then it is false (even if we never
>>>>>>>>>> know it).
>>>>>>>>>>
>>>>>>>>>> Only if no proof exists (even if we never know it) that fail
>>>>>>>>>> the requirements then it is true.
>>>>>>>>>>
>>>>>>>>>> This is simply other other way of saying that unless every
>>>>>>>>>> element of the set can be proven to meet the requirements
>>>>>>>>>> (even if we never know it) then the conjecture is False.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You just don't understand about infinitie sets do you. You are
>>>>>>>>> not guarenteed to be able to make a finite proof that all of an
>>>>>>>>> infinite set meets the requirements.
>>>>>>>>>
>>>>>>>>
>>>>>>>> If there is a single element of the set of (even whole numbers
>>>>>>>> greater than 2) that cannot be proven to meet the requirements
>>>>>>>> then the Goldbach conjecture fails
>>>>>>>>
>>>>>>
>>>>>> where A is (even whole numbers greater than 2)
>>>>>> and P is Provably meets Goldbach criteria
>>>>>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x).
>>>>>>
>>>>>>>> is merely another way of saying that
>>>>>>>>
>>>>>>>> unless every element of the set of (even whole numbers greater
>>>>>>>> than 2) can be proven to meet the requirements then the Goldbach
>>>>>>>> conjecture fails.
>>>>>>>>
>>>>>>>
>>>>>>> You still don't get it, do you.
>>>>>>
>>>>>> You are the one that fails to understand how existential
>>>>>> quantification is translated into universal quantification.
>>>>>>
>>>>>> https://sites.math.washington.edu/~aloveles/Math300Winter2011/m300Quantifiers.pdf
>>>>>>
>>>>>>
>>>>>> (1) ¬[∀x ∈ A, P(x)] ⇔ ∃x ∈ A, ¬P(x). // from the link
>>>>>>
>>>>>> where A is (even whole numbers greater than 2)
>>>>>> and P is Provably meets Goldbach criteria
>>>>>>
>>>>>> negate both sides of (1)
>>>>>> ∀x ∈ A, P(x) ⇔ ¬∃x ∈ A, ¬P(x).
>>>>>>
>>>>>> Goldbach ⇔ every element of (even whole numbers greater than 2)
>>>>>> Provably meets Goldbach criteria.
>>>>>>
>>>>>> is a correct transformation of: ¬Goldbach ⇔ ∃x ∈ A, ¬P(x).
>>>>>>
>>>>>
>>>>> And where do you get PROVABLE form any of that.
>>>>>
>>>>> You still have to PROVE an attribute for every member of the
>>>>> infinite set of Evens.
>>>>>
>>>>
>>>> Like I said you simply do not understand existential and universal
>>>> quantification well enough to translate between them.
>>>>
>>>> A is (even whole numbers greater than 2)
>>>> P is Provably meets Goldbach criteria
>>>>
>>>> On 3/5/2022 5:09 PM, Richard Damon wrote:
>>>>  > On 3/5/22 5:51 PM, olcott wrote:
>>>>  >> If there exists a single (even whole number greater than 2) that
>>>>  >> cannot possibly be proved to meet the Goldbach criteria then the
>>>>  >> Goldbach conjecture is not true.
>>>>  >
>>>>  > Right, if one exception exists, the conjecture is not true, but
>>>> false.
>>>>
>>>> My above paragraph translated into math:
>>>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x).
>>>>
>>>> People that do understand the math of it will be able to transform
>>>> that into this: Goldbach ⇔ ∀x ∈ A, P(x)
>>>>
>>>
>>> Which means that Goldbachs can be proven False if there exists a
>>> number that is even > 2 that doesn't meet the requirement.
>>>
>>> FINE.
>>>
>>> That means that IF Goldbachs Conjecture is False, that fact will be
>>> provable.
>>>
>>> How do you get to the fact that if it is True, it must be provable,
>>
>> It is simply the translation of the existential quantification:
>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x)
>>    into universal quantification:
>> Goldbach ⇔ ∀x ∈ A, P(x)
>>
>
> Which doesn't say what you think it says.
>
where A is (even whole numbers greater than 2)
and P is Provably meet the Goldbach criteria