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.

A is the set of (even whole numbers greater than 2)
P means {Provably meet the Goldbach criteria}
x ∈ (even whole numbers greater than 2)

This proof is defined as the sequence of steps required to verify that x
is the sum of two primes.

¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math

Math correctly transforms it into this
Goldbach ⇔ ∀x ∈ A, P(x)

⇔ if and only if;
https://en.wikipedia.org/wiki/List_of_logic_symbols

Goldbach if and only if
all elements of the set of
(even whole numbers greater than 2)
Provably meet the Goldbach criteria

If it is impossible to prove that any element of the set of (even whole
numbers greater than 2) does not meet the Goldbach criteria then the
Goldbach conjecture is false translates into

Unless every element of the set of (even whole numbers greater than 2)
provably meets the Goldbach criteria then the Goldbach conjecture is false.

translates into
Unless the Goldbach conjecture is provable it is not true.

--
Copyright 2021 Pete Olcott

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

In sci.math olcott <NoOne@nowhere.com> 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.

So you're a spammer as well as a crank. You posted the same garbage in
the same groups only yesterday. Your identity and your Usenet connection
are known, and it may well be that your provider might withdraw your
posting privileges if you spam too much.

[ .... ]

> Unless the Goldbach conjecture is provable it is not true.

What you posted above is false. See yesterday's thread for details. In
short, truth is not the same thing as provability. That's been proven.
The Earth is _not_ flat.

So stop posting the same garbage again and again and again. It's a bad
habit you need to get out of.

> --
> Copyright 2021 Pete Olcott

--
Alan Mackenzie (Nuremberg, Germany).

On 3/7/2022 11:41 AM, Alan Mackenzie wrote:
> In sci.math olcott <NoOne@nowhere.com> 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.
>
> So you're a spammer as well as a crank. You posted the same garbage in
> the same groups only yesterday. Your identity and your Usenet connection
> are known, and it may well be that your provider might withdraw your
> posting privileges if you spam too much.
>
> [ .... ]
>
>> Unless the Goldbach conjecture is provable it is not true.
>
> What you posted above is false. See yesterday's thread for details. In
> short, truth is not the same thing as provability. That's been proven.
> The Earth is _not_ flat.
>

I proved that your rebuttal is incorrect and you simply ignored my proof.

> So stop posting the same garbage again and again and again. It's a bad
> habit you need to get out of.
>
>> --
>> Copyright 2021 Pete Olcott
>

--
Copyright 2021 Pete Olcott

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

In sci.math olcott <NoOne@nowhere.com> wrote:
> On 3/7/2022 11:41 AM, Alan Mackenzie wrote:
>> In sci.math olcott <NoOne@nowhere.com> 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.

>> So you're a spammer as well as a crank. You posted the same garbage
>> in the same groups only yesterday. Your identity and your Usenet
>> connection are known, and it may well be that your provider might
>> withdraw your posting privileges if you spam too much.

>> [ .... ]

>>> Unless the Goldbach conjecture is provable it is not true.

>> What you posted above is false. See yesterday's thread for details.
>> In short, truth is not the same thing as provability. That's been
>> proven. The Earth is _not_ flat.

> I proved that your rebuttal is incorrect and you simply ignored my
> proof.

You did no such thing. How can you, you don't understand the concept of
a mathematical proof? I skipped over your alleged "proof", yes, partly
because the symbols don't display correctly on my terminal, and partly
because you don't understand what they mean anyway, so the extra effort
to decypher them would just be wasted effort.

>> So stop posting the same garbage again and again and again. It's a
>> bad habit you need to get out of.

> --
> Copyright 2021 Pete Olcott

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

--
Alan Mackenzie (Nuremberg, Germany).

On 3/8/2022 8:54 AM, Alan Mackenzie wrote:
> In sci.math olcott <NoOne@nowhere.com> wrote:
>> On 3/7/2022 11:41 AM, Alan Mackenzie wrote:
>>> In sci.math olcott <NoOne@nowhere.com> 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.
>
>>> So you're a spammer as well as a crank. You posted the same garbage
>>> in the same groups only yesterday. Your identity and your Usenet
>>> connection are known, and it may well be that your provider might
>>> withdraw your posting privileges if you spam too much.
>
>>> [ .... ]
>
>>>> Unless the Goldbach conjecture is provable it is not true.
>
>>> What you posted above is false. See yesterday's thread for details.
>>> In short, truth is not the same thing as provability. That's been
>>> proven. The Earth is _not_ flat.
>
>> I proved that your rebuttal is incorrect and you simply ignored my
>> proof.
>
> You did no such thing. How can you, you don't understand the concept of
> a mathematical proof? I skipped over your alleged "proof", yes, partly

What a nitwit thing to say.
You simply made the assumption that I am wrong.

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.

A is the set of (even whole numbers greater than 2)
P means {Provably meet the Goldbach criteria}
x ∈ (even whole numbers greater than 2)

This proof is defined as the sequence of steps required to verify that x
is the sum of two primes.

¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math

Math correctly transforms it into this
Goldbach ⇔ ∀x ∈ A, P(x)

⇔ if and only if;
https://en.wikipedia.org/wiki/List_of_logic_symbols

Goldbach if and only if
all elements of the set of
(even whole numbers greater than 2)
Provably meet the Goldbach criteria

If it is impossible to prove that any element of the set of (even whole
numbers greater than 2) does not meet the Goldbach criteria then the
Goldbach conjecture is false translates into

Unless every element of the set of (even whole numbers greater than 2)
provably meets the Goldbach criteria then the Goldbach conjecture is false.

translates into
Unless the Goldbach conjecture is provable it is not true.

> because the symbols don't display correctly on my terminal, and partly
> because you don't understand what they mean anyway, so the extra effort
> to decypher them would just be wasted effort.
>
>>> So stop posting the same garbage again and again and again. It's a
>>> bad habit you need to get out of.
>
>> --
>> Copyright 2021 Pete Olcott
>
>> Talent hits a target no one else can hit;
>> Genius hits a target no one else can see.
>> Arthur Schopenhauer
>

--
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 3/7/2022 6:00 PM, Richard Damon wrote:
> On 3/7/22 10:58 AM, 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.
>>
>> A is the set of (even whole numbers greater than 2)
>> P means {Provably meet the Goldbach criteria}
>> x ∈ (even whole numbers greater than 2)
>>
>> This proof is defined as the sequence of steps required to verify that
>> x is the sum of two primes.
>>
>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>>
>> Math correctly transforms it into this
>> Goldbach ⇔ ∀x ∈ A, P(x)
>>
>> ⇔ if and only if;
>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>
>> Goldbach if and only if
>> all elements of the set of
>> (even whole numbers greater than 2)
>> Provably meet the Goldbach criteria
>>
>> If it is impossible to prove that any element of the set of (even
>> whole numbers greater than 2) does not meet the Goldbach criteria then
>> the Goldbach conjecture is false translates into
>
> And how do you PROVE that it is impossible to prove that any element of
> that set doesn't meet the Goldbach criteria?

Every element (even integers > 2)
is either the sum of two primes or it is not.

Goldbach(N) ⇔
N ∈ (even integers > 2)
∃X ∈ prime_number
∃Y ∈ prime_number
| (X + Y = N)

>
>>
>> Unless every element of the set of (even whole numbers greater than 2)
>> provably meets the Goldbach criteria then the Goldbach conjecture is
>> false.
>>
>> translates into
>> Unless the Goldbach conjecture is provable it is not true.
>
> Nope. FAIL.
>
> Having to prove an infinite number of propositions is NOT a proof.
>

Goldbach(N) ⇔
N ∈ (even integers > 2)
∃X ∈ prime_number
∃Y ∈ prime_number
| (X + Y = N)

The sequence of steps required to confirm that N is the sum or two
primes is its proof that N has the Goldbach property.

https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence

If for any reason these steps cannot be performed or fail to confirm
that N is the sum of two primes then the Goldbach conjecture fails.

This logically entails that Goldbach is not true unless every N ∈ (even
integers > 2) is provable, thus true cannot exist apart from provable.

> You really have shown that you don't understand even the basics of Logic
> 101.
>
>
>

--
Copyright 2021 Pete Olcott

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

olcott <NoOne@nowhere.com> wrote:
> On 3/8/2022 8:54 AM, Alan Mackenzie wrote:
>> In sci.math olcott <NoOne@nowhere.com> wrote:
>>> On 3/7/2022 11:41 AM, Alan Mackenzie wrote:
>>>> In sci.math olcott <NoOne@nowhere.com> wrote:

[ .... ]

>>>> What you posted above is false. See yesterday's thread for details.
>>>> In short, truth is not the same thing as provability. That's been
>>>> proven. The Earth is _not_ flat.

>>> I proved that your rebuttal is incorrect and you simply ignored my
>>> proof.

>> You did no such thing. How can you, you don't understand the concept of
>> a mathematical proof? I skipped over your alleged "proof", ....

> What a nitwit thing to say.
> You simply made the assumption that I am wrong.

You said the Earth was flat, or something equivalent. There's no
assumption involved, you are simply and unequivocally wrong.

> 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.

Yes.

> A is the set of (even whole numbers greater than 2)
> P means {Provably meet the Goldbach criteria}
> x ∈ (even whole numbers greater than 2)

> This proof is defined as the sequence of steps required to verify that x
> is the sum of two primes.

You should stop trying to use big words like "proof" that you don't
understand. You are wrong in the above paragraph. A correction might
look something like "This proof as defined as the sequence of steps
required to verify that EVERY x in the set is the sum of two primes.".

> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math

> Math correctly transforms it into this
> Goldbach ⇔ ∀x ∈ A, P(x)

I can't read that, but it's either trivial or wrong or both.

> ⇔ if and only if;
> https://en.wikipedia.org/wiki/List_of_logic_symbols

That you think it necessary to explain "iff" shows how lacking in
mathematical sophistication you are.

> Goldbach if and only if
> all elements of the set of
> (even whole numbers greater than 2)
> Provably meet the Goldbach criteria

You pulled that out of your arse, and it's wrong. It doesn't follow from
anything you've previously shown.

> If it is impossible to prove that any element of the set of (even whole
> numbers greater than 2) does not meet the Goldbach criteria then the
> Goldbach conjecture is false ....

Another product of Peter Olcott's arse. Confused writing, with too many
negatives. If it's impossible to prove whatever all that mess is, then
it says nothing about the truth or falsehood of Goldbach's Conjecture,
unless, perhaps, that impossibility is proven. That level of abstraction
is beyond PO.

> .... translates into

[ Delete repeated falsehood ].

> translates into
> Unless the Goldbach conjecture is provable it is not true.

You just made that up. However you reached that conclusion, you're
unequivocally wrong. You'd do far better getting into something your
mental make up is aligned to. Abstract mathematics is not it.

[ .... ]

> --
> Copyright 2021 Pete Olcott

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

--
Alan Mackenzie (Nuremberg, Germany).

On 3/8/2022 12:38 PM, Alan Mackenzie wrote:
> olcott <NoOne@nowhere.com> wrote:
>> On 3/8/2022 8:54 AM, Alan Mackenzie wrote:
>>> In sci.math olcott <NoOne@nowhere.com> wrote:
>>>> On 3/7/2022 11:41 AM, Alan Mackenzie wrote:
>>>>> In sci.math olcott <NoOne@nowhere.com> wrote:
>
> [ .... ]
>
>>>>> What you posted above is false. See yesterday's thread for details.
>>>>> In short, truth is not the same thing as provability. That's been
>>>>> proven. The Earth is _not_ flat.
>
>>>> I proved that your rebuttal is incorrect and you simply ignored my
>>>> proof.
>
>>> You did no such thing. How can you, you don't understand the concept of
>>> a mathematical proof? I skipped over your alleged "proof", ....
>
>> What a nitwit thing to say.
>> You simply made the assumption that I am wrong.
>
> You said the Earth was flat, or something equivalent. There's no
> assumption involved, you are simply and unequivocally wrong.
>
>> 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.
>
> Yes.
>
>> A is the set of (even whole numbers greater than 2)
>> P means {Provably meet the Goldbach criteria}
>> x ∈ (even whole numbers greater than 2)
>
>> This proof is defined as the sequence of steps required to verify that x
>> is the sum of two primes.
>
> You should stop trying to use big words like "proof" that you don't
> understand.

Most generically a proof applies a sequence of finite string
transformation rules to a set of one or more input finite strings to
determine whether or not another finite string can be derived as a
consequence from these input strings.

> You are wrong in the above paragraph. A correction might
> look something like "This proof as defined as the sequence of steps
> required to verify that EVERY x in the set is the sum of two primes.".
>

I am composing the proof of two separate steps, one is finite and the
other is infinite.

Goldbach(N) ⇔
N ∈ (even integers > 2)
∃X ∈ prime_numbers
∃Y ∈ prime_numbers
(N = X + Y)

If that is unsatisfiable for any N ∈ (even integers > 2) this refutes
Goldbach therefore satisfiability requires provability for every N ∈
(even integers > 2) or Goldbach is untrue.

--
Copyright 2021 Pete Olcott

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

It happens that olcott formulated :
> 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.
>
> A is the set of (even whole numbers greater than 2)
> P means {Provably meet the Goldbach criteria}
> x ∈ (even whole numbers greater than 2)
>
> This proof is defined as the sequence of steps required to verify that x is
> the sum of two primes.
>
> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>
> Math correctly transforms it into this
> Goldbach ⇔ ∀x ∈ A, P(x)
>
> ⇔ if and only if;
> https://en.wikipedia.org/wiki/List_of_logic_symbols
>
> Goldbach if and only if
> all elements of the set of
> (even whole numbers greater than 2)
> Provably meet the Goldbach criteria
>
> If it is impossible to prove that any element of the set of (even whole
> numbers greater than 2) does not meet the Goldbach criteria then the Goldbach
> conjecture is false translates into
>
> Unless every element of the set of (even whole numbers greater than 2)
> provably meets the Goldbach criteria then the Goldbach conjecture is false.
>
> translates into
> Unless the Goldbach conjecture is provable it is not true.

You seem to be saying that all systems now or in the future will have
this particular question as unprovable within that system. Every
system, if I'm not mistaken, *will have* true things which are not
provable from within that system.

How are you proving things about *all* systems including those which we
haven't invented or discoverted yet?

On 3/8/2022 2:19 PM, FromTheRafters wrote:
> It happens that olcott formulated :
>> 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.
>>
>> A is the set of (even whole numbers greater than 2)
>> P means {Provably meet the Goldbach criteria}
>> x ∈ (even whole numbers greater than 2)
>>
>> This proof is defined as the sequence of steps required to verify that
>> x is the sum of two primes.
>>
>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>>
>> Math correctly transforms it into this
>> Goldbach ⇔ ∀x ∈ A, P(x)
>>
>> ⇔ if and only if;
>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>
>> Goldbach if and only if
>> all elements of the set of
>> (even whole numbers greater than 2)
>> Provably meet the Goldbach criteria
>>
>> If it is impossible to prove that any element of the set of (even
>> whole numbers greater than 2) does not meet the Goldbach criteria then
>> the Goldbach conjecture is false translates into
>>
>> Unless every element of the set of (even whole numbers greater than 2)
>> provably meets the Goldbach criteria then the Goldbach conjecture is
>> false.
>>
>> translates into
>> Unless the Goldbach conjecture is provable it is not true.
>
> You seem to be saying that all systems now or in the future will have
> this particular question as unprovable within that system. Every system,
> if I'm not mistaken, *will have* true things which are not provable from
> within that system.
>
> How are you proving things about *all* systems including those which we
> haven't invented or discoverted yet?

I divided up the provability as a finite sequence of steps for each
integer > 2. Then I concluded that unless each element of this set can
be proven to meet the Goldbach criteria that the GoldBach conjecture is
false. This proves that the truth of the Goldbach conjecture cannot
exist apart from its provability.

--
Copyright 2021 Pete Olcott

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

In sci.math olcott <NoOne@nowhere.com> wrote:
> On 3/8/2022 2:19 PM, FromTheRafters wrote:

[ .... ]

>> You seem to be saying that all systems now or in the future will have
>> this particular question as unprovable within that system. Every system,
>> if I'm not mistaken, *will have* true things which are not provable from
>> within that system.

>> How are you proving things about *all* systems including those which we
>> haven't invented or discoverted yet?

> I divided up the provability as a finite sequence of steps for each [
> even ] integer > 2. Then I concluded that unless each element of this
> set can be proven to meet the Goldbach criteria that the GoldBach
> conjecture is false.

As has been explained to you so many times, you are simply wrong, here.
To get anywhere, you need to learn how to deal with infinite sets.

> This proves that the truth of the Goldbach conjecture cannot exist
> apart from its provability.

You cannot base a proof on anything "concluded" by Peter Olcott. PO
lacks the mathematical background and competence reliably to "conclude"
anything involving abstract mathematics.

> --
> Copyright 2021 Pete Olcott

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

--
Alan Mackenzie (Nuremberg, Germany).

On 3/8/2022 3:40 PM, Alan Mackenzie wrote:
> In sci.math olcott <NoOne@nowhere.com> wrote:
>> On 3/8/2022 2:19 PM, FromTheRafters wrote:
>
> [ .... ]
>
>>> You seem to be saying that all systems now or in the future will have
>>> this particular question as unprovable within that system. Every system,
>>> if I'm not mistaken, *will have* true things which are not provable from
>>> within that system.
>
>>> How are you proving things about *all* systems including those which we
>>> haven't invented or discoverted yet?
>
>> I divided up the provability as a finite sequence of steps for each [
>> even ] integer > 2. Then I concluded that unless each element of this
>> set can be proven to meet the Goldbach criteria that the GoldBach
>> conjecture is false.
>
> As has been explained to you so many times, you are simply wrong, here.
> To get anywhere, you need to learn how to deal with infinite sets.
>

You are simply translating between existential quantification and
universal quantification incorrectly.

A is the set of all even integers > 2
P(x) Means that x has been proved to be the sum of two primes.

¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // Proves Goldbach is false
Math correctly transforms it into this
Goldbach ⇔ ∀x ∈ A, P(x) // Proves Goldbach is true

>> This proves that the truth of the Goldbach conjecture cannot exist
>> apart from its provability.
>
> You cannot base a proof on anything "concluded" by Peter Olcott. PO
> lacks the mathematical background and competence reliably to "conclude"
> anything involving abstract mathematics.
>
>> --
>> Copyright 2021 Pete Olcott
>
>> Talent hits a target no one else can hit;
>> Genius hits a target no one else can see.
>> Arthur Schopenhauer
>

--
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 08/03/2022 20:19, FromTheRafters wrote:
> It happens that olcott formulated :
>> 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.
>>
>> A is the set of (even whole numbers greater than 2)
>> P means {Provably meet the Goldbach criteria}
>> x ∈ (even whole numbers greater than 2)
>>
>> This proof is defined as the sequence of steps required to verify that x is the sum of two primes.
>>
>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>>
>> Math correctly transforms it into this
>> Goldbach ⇔ ∀x ∈ A, P(x)
>>
>> ⇔ if and only if;
>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>
>> Goldbach if and only if
>> all elements of the set of
>> (even whole numbers greater than 2)
>> Provably meet the Goldbach criteria
>>
>> If it is impossible to prove that any element of the set of (even whole numbers greater than 2)
>> does not meet the Goldbach criteria then the Goldbach conjecture is false translates into
>>
>> Unless every element of the set of (even whole numbers greater than 2) provably meets the Goldbach
>> criteria then the Goldbach conjecture is false.
>>
>> translates into
>> Unless the Goldbach conjecture is provable it is not true.
>
> You seem to be saying that all systems now or in the future will have this particular question as
> unprovable within that system. Every system, if I'm not mistaken, *will have* true things which are
> not provable from within that system.

PO is not really (capable of) saying any of that. Of course, you must judge PO as /you/ find him -
but much time can be wasted assuming that if he uses a technical word he must have /some/
understanding of the field he's talking about. (WRONG - always challenge any phrase he uses, and
never assume he genuinely understands a word he uses until he proves it to you! And never be put
off if he uses some tecnical word he's come across online that you're a bit shaky on - PO won't
properly understand what he's saying in any case!).

In the current case, I'll float the suggestion that there's no way PO understands "logical system"
or "proof within that system", or even "proof" in a more general sense. And he doesn't understand
what people mean by "true but unprovable" as he conflates true and provable (and doesn't understand
the role of the logical system involved etc. etc. etc. etc...).

When PO doesn't understand what's being said to him, he just cuts and pastes some generic repetition
of previous claims, which becomes a dead give-away once the pattern is recognised. You'll be left
wondering "why are you posting /that/ again? It's not a response to anything I just said..."

Mike.

>
> How are you proving things about *all* systems including those which we haven't invented or
> discoverted yet?

That's just too abstract for PO. It's really /not/ what he's thinking. :)

On 3/8/2022 5:44 PM, Mike Terry wrote:
> On 08/03/2022 20:19, FromTheRafters wrote:
>> It happens that olcott formulated :
>>> 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.
>>>
>>> A is the set of (even whole numbers greater than 2)
>>> P means {Provably meet the Goldbach criteria}
>>> x ∈ (even whole numbers greater than 2)
>>>
>>> This proof is defined as the sequence of steps required to verify
>>> that x is the sum of two primes.
>>>
>>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>>>
>>> Math correctly transforms it into this
>>> Goldbach ⇔ ∀x ∈ A, P(x)
>>>
>>> ⇔ if and only if;
>>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>>
>>> Goldbach if and only if
>>> all elements of the set of
>>> (even whole numbers greater than 2)
>>> Provably meet the Goldbach criteria
>>>
>>> If it is impossible to prove that any element of the set of (even
>>> whole numbers greater than 2) does not meet the Goldbach criteria
>>> then the Goldbach conjecture is false translates into
>>>
>>> Unless every element of the set of (even whole numbers greater than
>>> 2) provably meets the Goldbach criteria then the Goldbach conjecture
>>> is false.
>>>
>>> translates into
>>> Unless the Goldbach conjecture is provable it is not true.
>>
>> You seem to be saying that all systems now or in the future will have
>> this particular question as unprovable within that system. Every
>> system, if I'm not mistaken, *will have* true things which are not
>> provable from within that system.
>
> PO is not really (capable of) saying any of that.  Of course, you must
> judge PO as /you/ find him - but much time can be wasted assuming that
> if he uses a technical word he must have /some/ understanding of the
> field he's talking about.  (WRONG - always challenge any phrase he uses,
> and never assume he genuinely understands a word he uses until he proves
> it to you!  And never be put off if he uses some tecnical word he's come
> across online that you're a bit shaky on - PO won't properly understand
> what he's saying in any case!).
>
> In the current case, I'll float the suggestion that there's no way PO
> understands "logical system" or "proof within that system", or even
> "proof" in a more general sense.

What I am doing is reformulating everything from the ground up such that
a consistent and coherent system of correct reasoning is derived.

I am doing these things at the highest level of philosophical
abstraction above the upper ontology of the tree of analytical knowledge.

https://en.wikipedia.org/wiki/Ontology_(information_science)#Upper_ontology

In this case a proof applies truth preserving operations to expressions
of formal or natural language to derive an expression of language that
is a necessary consequence of the initial expressions of language.

To the extent that logic systems do not conform to this generic model
these logic system diverge from correct reasoning.

It is self-evident that when one applies other than truth preserving
operations to expressions of language that are not known to be true that
untrue expressions of language could result.

The converse is also self-evident: when one ONLY applies truth
preserving operations to expressions of language that known to be true
only true expressions of language can result.

> And he doesn't understand what people
> mean by "true but unprovable" as he conflates true and provable (and
> doesn't understand the role of the logical system involved etc. etc.
> etc. etc...).
>

Once you understand this context of the generic highest level of
abstraction of provability you might understand that an analytical
expression of language can only be determined to be true one of two
possible ways:
(1) It is stipulated to be true, the same idea as Haskell Curry's
"elementary theorem" of theory:
https://www.liarparadox.org/Haskell_Curry_45.pdf

(2) Derived on the basis of "elementary theorems", more precisely as I
add only by applying truth preserving operations to "elementary theorem"
or other expression derived from "elementary theorems".

> When PO doesn't understand what's being said to him, he just cuts and
> pastes some generic repetition of previous claims, which becomes a dead
> give-away once the pattern is recognised.  You'll be left wondering "why
> are you posting /that/ again?  It's not a response to anything I just
> said..."
>
>
> Mike.
>
>>
>> How are you proving things about *all* systems including those which
>> we haven't invented or discoverted yet?
>
> That's just too abstract for PO.  It's really /not/ what he's thinking. :)

--
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 09/03/2022 00:46, olcott wrote:
> On 3/8/2022 5:44 PM, Mike Terry wrote:
>> On 08/03/2022 20:19, FromTheRafters wrote:
>>> It happens that olcott formulated :
>>>> 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.
>>>>
>>>> A is the set of (even whole numbers greater than 2)
>>>> P means {Provably meet the Goldbach criteria}
>>>> x ∈ (even whole numbers greater than 2)
>>>>
>>>> This proof is defined as the sequence of steps required to verify that x is the sum of two primes.
>>>>
>>>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>>>>
>>>> Math correctly transforms it into this
>>>> Goldbach ⇔ ∀x ∈ A, P(x)
>>>>
>>>> ⇔ if and only if;
>>>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>>>
>>>> Goldbach if and only if
>>>> all elements of the set of
>>>> (even whole numbers greater than 2)
>>>> Provably meet the Goldbach criteria
>>>>
>>>> If it is impossible to prove that any element of the set of (even whole numbers greater than 2)
>>>> does not meet the Goldbach criteria then the Goldbach conjecture is false translates into
>>>>
>>>> Unless every element of the set of (even whole numbers greater than 2) provably meets the
>>>> Goldbach criteria then the Goldbach conjecture is false.
>>>>
>>>> translates into
>>>> Unless the Goldbach conjecture is provable it is not true.
>>>
>>> You seem to be saying that all systems now or in the future will have this particular question as
>>> unprovable within that system. Every system, if I'm not mistaken, *will have* true things which
>>> are not provable from within that system.
>>
>> PO is not really (capable of) saying any of that.  Of course, you must judge PO as /you/ find him
>> - but much time can be wasted assuming that if he uses a technical word he must have /some/
>> understanding of the field he's talking about.  (WRONG - always challenge any phrase he uses, and
>> never assume he genuinely understands a word he uses until he proves it to you!  And never be put
>> off if he uses some tecnical word he's come across online that you're a bit shaky on - PO won't
>> properly understand what he's saying in any case!).
>>
>> In the current case, I'll float the suggestion that there's no way PO understands "logical system"
>> or "proof within that system", or even "proof" in a more general sense.
>
> What I am doing is reformulating everything from the ground up such that a consistent and coherent
> system of correct reasoning is derived.
>
> I am doing these things at the highest level of philosophical abstraction above the upper ontology
> of the tree of analytical knowledge.
>
> https://en.wikipedia.org/wiki/Ontology_(information_science)#Upper_ontology
>

Within your delusional framework, perhaps you really do believe what you just said.

To other people it's nothing more than a pretentious boast.

Mike.

On 3/8/2022 7:18 PM, Mike Terry wrote:
> On 09/03/2022 00:46, olcott wrote:
>> On 3/8/2022 5:44 PM, Mike Terry wrote:
>>> On 08/03/2022 20:19, FromTheRafters wrote:
>>>> It happens that olcott formulated :
>>>>> 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.
>>>>>
>>>>> A is the set of (even whole numbers greater than 2)
>>>>> P means {Provably meet the Goldbach criteria}
>>>>> x ∈ (even whole numbers greater than 2)
>>>>>
>>>>> This proof is defined as the sequence of steps required to verify
>>>>> that x is the sum of two primes.
>>>>>
>>>>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>>>>>
>>>>> Math correctly transforms it into this
>>>>> Goldbach ⇔ ∀x ∈ A, P(x)
>>>>>
>>>>> ⇔ if and only if;
>>>>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>>>>
>>>>> Goldbach if and only if
>>>>> all elements of the set of
>>>>> (even whole numbers greater than 2)
>>>>> Provably meet the Goldbach criteria
>>>>>
>>>>> If it is impossible to prove that any element of the set of (even
>>>>> whole numbers greater than 2) does not meet the Goldbach criteria
>>>>> then the Goldbach conjecture is false translates into
>>>>>
>>>>> Unless every element of the set of (even whole numbers greater than
>>>>> 2) provably meets the Goldbach criteria then the Goldbach
>>>>> conjecture is false.
>>>>>
>>>>> translates into
>>>>> Unless the Goldbach conjecture is provable it is not true.
>>>>
>>>> You seem to be saying that all systems now or in the future will
>>>> have this particular question as unprovable within that system.
>>>> Every system, if I'm not mistaken, *will have* true things which are
>>>> not provable from within that system.
>>>
>>> PO is not really (capable of) saying any of that.  Of course, you
>>> must judge PO as /you/ find him - but much time can be wasted
>>> assuming that if he uses a technical word he must have /some/
>>> understanding of the field he's talking about.  (WRONG - always
>>> challenge any phrase he uses, and never assume he genuinely
>>> understands a word he uses until he proves it to you!  And never be
>>> put off if he uses some tecnical word he's come across online that
>>> you're a bit shaky on - PO won't properly understand what he's saying
>>> in any case!).
>>>
>>> In the current case, I'll float the suggestion that there's no way PO
>>> understands "logical system" or "proof within that system", or even
>>> "proof" in a more general sense.
>>
>> What I am doing is reformulating everything from the ground up such
>> that a consistent and coherent system of correct reasoning is derived.
>>
>> I am doing these things at the highest level of philosophical
>> abstraction above the upper ontology of the tree of analytical knowledge.
>>
>> https://en.wikipedia.org/wiki/Ontology_(information_science)#Upper_ontology
>>
>>
>
> Within your delusional framework, perhaps you really do believe what you
> just said.
>

It is self-evident that when one applies other than truth preserving
operations to expressions of language that are not known to be true that
untrue expressions of language could result.

The converse is also self-evident: when one ONLY applies truth
preserving operations to expressions of language that known to be true
only true expressions of language can result.

> To other people it's nothing more than a pretentious boast.
>
> Mike.

--
Copyright 2021 Pete Olcott

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