On 4/15/2023 8:15 PM, Richard Damon wrote:
> On 4/15/23 8:56 PM, olcott wrote:
>> On 4/15/2023 7:45 PM, Richard Damon wrote:
>>> On 4/15/23 8:29 PM, olcott wrote:
>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>>>
>>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>>> True in F, and to be True just requires an infinite sequence of
>>>>>>> inference steps.
>>>>>>>
>>>>>>> The only one trying to prove in F that G is true is you, and that
>>>>>>> operation can easily be proven to be impossible,
>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>
>>>>>
>>>>> Maybe your FAKE G,
>>>>
>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>> Do you understand that it is not satisfiable in F because it is self-
>>>> contradictory in F ?
>>>>
>>>> I will keep asking this until you answer.
>>>>
>>> But that doesn't matter, because it isn't the statement that proves
>>> that all sufficiently powerful systems are inconsistent.
>>>
>>> Note, the fact that it would be impossible to actually prove your
>>> pseudo-G in F doesn't mean that it can't be true.
>>>
>>> Note, it can't be False, but its status of being a Truth Bearer can't
>>> be proven in F.
>>>
>>>
>>> Maybe you need to learn to read, because my answer DOES answer your
>>> question and show that you are wrong.
>>>
>>> Just shows the level of your intelect.
>>>
>>> Another point, you are showing that you don't understand what
>>> "self-contradictory" means.
>>>
>>> "This statement is not Provable" is NOT Self-Contradictory, as it has
>>> a possible set of truth values that makes it satisified, that is
>>> being True but Unprovable.
>>>
>>
>> When G asserts its own unprovability in F is proven in F this requires a
>> sequence of inference steps in F that proves there is no such sequence
>> of inference steps in F.
>>
>> Try and show how you would provide a sequence of inference steps in F
>> that correctly proves that no such set of inference steps exists in F.
>>
>
> But G isn't PROVEN in F, it just is TRUE in F.
>
When G asserts that it is unprovable in F this cannot be proven F ONLY
because this proof requires a sequence of inference steps in F that
proves there is no such sequence of inference steps in F, not because F
is in any way incomplete.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 9:26 PM, olcott wrote:
> On 4/15/2023 8:15 PM, Richard Damon wrote:
>> On 4/15/23 8:56 PM, olcott wrote:
>>> On 4/15/2023 7:45 PM, Richard Damon wrote:
>>>> On 4/15/23 8:29 PM, olcott wrote:
>>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>>>>
>>>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>>>> True in F, and to be True just requires an infinite sequence of
>>>>>>>> inference steps.
>>>>>>>>
>>>>>>>> The only one trying to prove in F that G is true is you, and
>>>>>>>> that operation can easily be proven to be impossible,
>>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>>
>>>>>>
>>>>>> Maybe your FAKE G,
>>>>>
>>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>>> Do you understand that it is not satisfiable in F because it is self-
>>>>> contradictory in F ?
>>>>>
>>>>> I will keep asking this until you answer.
>>>>>
>>>> But that doesn't matter, because it isn't the statement that proves
>>>> that all sufficiently powerful systems are inconsistent.
>>>>
>>>> Note, the fact that it would be impossible to actually prove your
>>>> pseudo-G in F doesn't mean that it can't be true.
>>>>
>>>> Note, it can't be False, but its status of being a Truth Bearer
>>>> can't be proven in F.
>>>>
>>>>
>>>> Maybe you need to learn to read, because my answer DOES answer your
>>>> question and show that you are wrong.
>>>>
>>>> Just shows the level of your intelect.
>>>>
>>>> Another point, you are showing that you don't understand what
>>>> "self-contradictory" means.
>>>>
>>>> "This statement is not Provable" is NOT Self-Contradictory, as it
>>>> has a possible set of truth values that makes it satisified, that is
>>>> being True but Unprovable.
>>>>
>>>
>>> When G asserts its own unprovability in F is proven in F this requires a
>>> sequence of inference steps in F that proves there is no such sequence
>>> of inference steps in F.
>>>
>>> Try and show how you would provide a sequence of inference steps in F
>>> that correctly proves that no such set of inference steps exists in F.
>>>
>>
>> But G isn't PROVEN in F, it just is TRUE in F.
>>
> When G asserts that it is unprovable in F this cannot be proven F ONLY
> because this proof requires a sequence of inference steps in F that
> proves there is no such sequence of inference steps in F, not because F
> is in any way incomplete.
>
>

But G DOESN'T "assert" it is unprovable in F, so that doesn't matter.

It can be DERIVED (in Meta-F) that G is unprovable in F.

Note, the DEFINITION of "Incompleteness" is that a system is Incomplete
if there exists a true statement in the system that can not be proven.

G is such a statement, it is True if F, and it can not be proven in F.

That makes F incomplete.

Your arguing about it just shows you don't understand the meaning of the
words you are using.

What don't you get about the fact that G can not be proven in F, but it
is also established (not proven in F) that G is True in F so, BY
DEFINITION F is Incomplete.

You are just proving your ignorance.

On 4/15/2023 8:35 PM, Richard Damon wrote:
> On 4/15/23 9:26 PM, olcott wrote:
>> On 4/15/2023 8:15 PM, Richard Damon wrote:
>>> On 4/15/23 8:56 PM, olcott wrote:
>>>> On 4/15/2023 7:45 PM, Richard Damon wrote:
>>>>> On 4/15/23 8:29 PM, olcott wrote:
>>>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>>>>>
>>>>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>>>>> True in F, and to be True just requires an infinite sequence of
>>>>>>>>> inference steps.
>>>>>>>>>
>>>>>>>>> The only one trying to prove in F that G is true is you, and
>>>>>>>>> that operation can easily be proven to be impossible,
>>>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>>>
>>>>>>>
>>>>>>> Maybe your FAKE G,
>>>>>>
>>>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>>>> Do you understand that it is not satisfiable in F because it is self-
>>>>>> contradictory in F ?
>>>>>>
>>>>>> I will keep asking this until you answer.
>>>>>>
>>>>> But that doesn't matter, because it isn't the statement that proves
>>>>> that all sufficiently powerful systems are inconsistent.
>>>>>
>>>>> Note, the fact that it would be impossible to actually prove your
>>>>> pseudo-G in F doesn't mean that it can't be true.
>>>>>
>>>>> Note, it can't be False, but its status of being a Truth Bearer
>>>>> can't be proven in F.
>>>>>
>>>>>
>>>>> Maybe you need to learn to read, because my answer DOES answer your
>>>>> question and show that you are wrong.
>>>>>
>>>>> Just shows the level of your intelect.
>>>>>
>>>>> Another point, you are showing that you don't understand what
>>>>> "self-contradictory" means.
>>>>>
>>>>> "This statement is not Provable" is NOT Self-Contradictory, as it
>>>>> has a possible set of truth values that makes it satisified, that
>>>>> is being True but Unprovable.
>>>>>
>>>>
>>>> When G asserts its own unprovability in F is proven in F this
>>>> requires a
>>>> sequence of inference steps in F that proves there is no such sequence
>>>> of inference steps in F.
>>>>
>>>> Try and show how you would provide a sequence of inference steps in F
>>>> that correctly proves that no such set of inference steps exists in F.
>>>>
>>>
>>> But G isn't PROVEN in F, it just is TRUE in F.
>>>
>> When G asserts that it is unprovable in F this cannot be proven F ONLY
>> because this proof requires a sequence of inference steps in F that
>> proves there is no such sequence of inference steps in F, not because F
>> is in any way incomplete.
>>
>>
>
> But G DOESN'T "assert" it is unprovable in F, so that doesn't matter.
>
*I am stipulating that it does. Try and follow my reasoning on this*

When G asserts that it is unprovable in F this cannot be proven F ONLY
because this proof requires a sequence of inference steps in F that
proves there is no such sequence of inference steps in F, not because F
is in any way incomplete.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 9:59 PM, olcott wrote:
> On 4/15/2023 8:35 PM, Richard Damon wrote:
>> On 4/15/23 9:26 PM, olcott wrote:
>>> On 4/15/2023 8:15 PM, Richard Damon wrote:
>>>> On 4/15/23 8:56 PM, olcott wrote:
>>>>> On 4/15/2023 7:45 PM, Richard Damon wrote:
>>>>>> On 4/15/23 8:29 PM, olcott wrote:
>>>>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>>>>>> True in F, and to be True just requires an infinite sequence
>>>>>>>>>> of inference steps.
>>>>>>>>>>
>>>>>>>>>> The only one trying to prove in F that G is true is you, and
>>>>>>>>>> that operation can easily be proven to be impossible,
>>>>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>>>>
>>>>>>>>
>>>>>>>> Maybe your FAKE G,
>>>>>>>
>>>>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>>>>> Do you understand that it is not satisfiable in F because it is
>>>>>>> self-
>>>>>>> contradictory in F ?
>>>>>>>
>>>>>>> I will keep asking this until you answer.
>>>>>>>
>>>>>> But that doesn't matter, because it isn't the statement that
>>>>>> proves that all sufficiently powerful systems are inconsistent.
>>>>>>
>>>>>> Note, the fact that it would be impossible to actually prove your
>>>>>> pseudo-G in F doesn't mean that it can't be true.
>>>>>>
>>>>>> Note, it can't be False, but its status of being a Truth Bearer
>>>>>> can't be proven in F.
>>>>>>
>>>>>>
>>>>>> Maybe you need to learn to read, because my answer DOES answer
>>>>>> your question and show that you are wrong.
>>>>>>
>>>>>> Just shows the level of your intelect.
>>>>>>
>>>>>> Another point, you are showing that you don't understand what
>>>>>> "self-contradictory" means.
>>>>>>
>>>>>> "This statement is not Provable" is NOT Self-Contradictory, as it
>>>>>> has a possible set of truth values that makes it satisified, that
>>>>>> is being True but Unprovable.
>>>>>>
>>>>>
>>>>> When G asserts its own unprovability in F is proven in F this
>>>>> requires a
>>>>> sequence of inference steps in F that proves there is no such sequence
>>>>> of inference steps in F.
>>>>>
>>>>> Try and show how you would provide a sequence of inference steps in F
>>>>> that correctly proves that no such set of inference steps exists in F.
>>>>>
>>>>
>>>> But G isn't PROVEN in F, it just is TRUE in F.
>>>>
>>> When G asserts that it is unprovable in F this cannot be proven F ONLY
>>> because this proof requires a sequence of inference steps in F that
>>> proves there is no such sequence of inference steps in F, not because F
>>> is in any way incomplete.
>>>
>>>
>>
>> But G DOESN'T "assert" it is unprovable in F, so that doesn't matter.
>>
> *I am stipulating that it does. Try and follow my reasoning on this*

So you are stipulating that you aren't working on Godel's Proof?

>
> When G asserts that it is unprovable in F this cannot be proven F ONLY
> because this proof requires a sequence of inference steps in F that
> proves there is no such sequence of inference steps in F, not because F
> is in any way incomplete.
>

So, you admit you don't understand the meaning of Incomplete as applied
to Logic.

Yes, F is incomplete because there is no "Proof" of G in F, even though
G is TRUE in F. That BY DEFINITION makes F Incomplete.

PERIOD.

Yes, if you just stipulate a statement like that but don't make it True,
then that, by itself, doesn't make the Theory incomplete. The Theory
might not be powerful enough to express Godel's proof in it, and thus
might not be powerful enough to be forced to be incomplete.

There ARE simple enough logic systems that can be complete, not all
logic systems are incomplete. The proof just requires that the system be
able to handle certain properties of whole numbers to be incomplete.

You repeating your argument just points out that you don't actually
understand the meaning of the words you have been claiming to be an
expert in all these years.

You have just proven yourself ignorant.

Your repeated reusing of terms from proofs that you try to redefine to
mean something not quite what they meant, is a good sign that you are
trying to be deceptive, as has been pointed out many times in the past.

On 4/15/2023 9:24 PM, Richard Damon wrote:
> On 4/15/23 9:59 PM, olcott wrote:
>> On 4/15/2023 8:35 PM, Richard Damon wrote:
>>> On 4/15/23 9:26 PM, olcott wrote:
>>>> On 4/15/2023 8:15 PM, Richard Damon wrote:
>>>>> On 4/15/23 8:56 PM, olcott wrote:
>>>>>> On 4/15/2023 7:45 PM, Richard Damon wrote:
>>>>>>> On 4/15/23 8:29 PM, olcott wrote:
>>>>>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>>>>>>>
>>>>>>>>>>> So, there is no claim that G is provable in F, just that it
>>>>>>>>>>> is True in F, and to be True just requires an infinite
>>>>>>>>>>> sequence of inference steps.
>>>>>>>>>>>
>>>>>>>>>>> The only one trying to prove in F that G is true is you, and
>>>>>>>>>>> that operation can easily be proven to be impossible,
>>>>>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Maybe your FAKE G,
>>>>>>>>
>>>>>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>>>>>> Do you understand that it is not satisfiable in F because it is
>>>>>>>> self-
>>>>>>>> contradictory in F ?
>>>>>>>>
>>>>>>>> I will keep asking this until you answer.
>>>>>>>>
>>>>>>> But that doesn't matter, because it isn't the statement that
>>>>>>> proves that all sufficiently powerful systems are inconsistent.
>>>>>>>
>>>>>>> Note, the fact that it would be impossible to actually prove your
>>>>>>> pseudo-G in F doesn't mean that it can't be true.
>>>>>>>
>>>>>>> Note, it can't be False, but its status of being a Truth Bearer
>>>>>>> can't be proven in F.
>>>>>>>
>>>>>>>
>>>>>>> Maybe you need to learn to read, because my answer DOES answer
>>>>>>> your question and show that you are wrong.
>>>>>>>
>>>>>>> Just shows the level of your intelect.
>>>>>>>
>>>>>>> Another point, you are showing that you don't understand what
>>>>>>> "self-contradictory" means.
>>>>>>>
>>>>>>> "This statement is not Provable" is NOT Self-Contradictory, as it
>>>>>>> has a possible set of truth values that makes it satisified, that
>>>>>>> is being True but Unprovable.
>>>>>>>
>>>>>>
>>>>>> When G asserts its own unprovability in F is proven in F this
>>>>>> requires a
>>>>>> sequence of inference steps in F that proves there is no such
>>>>>> sequence
>>>>>> of inference steps in F.
>>>>>>
>>>>>> Try and show how you would provide a sequence of inference steps in F
>>>>>> that correctly proves that no such set of inference steps exists
>>>>>> in F.
>>>>>>
>>>>>
>>>>> But G isn't PROVEN in F, it just is TRUE in F.
>>>>>
>>>> When G asserts that it is unprovable in F this cannot be proven F ONLY
>>>> because this proof requires a sequence of inference steps in F that
>>>> proves there is no such sequence of inference steps in F, not because F
>>>> is in any way incomplete.
>>>>
>>>>
>>>
>>> But G DOESN'T "assert" it is unprovable in F, so that doesn't matter.
>>>
>> *I am stipulating that it does. Try and follow my reasoning on this*
>
> So you are stipulating that you aren't working on Godel's Proof?
>
>>
>> When G asserts that it is unprovable in F this cannot be proven F ONLY
>> because this proof requires a sequence of inference steps in F that
>> proves there is no such sequence of inference steps in F, not because F
>> is in any way incomplete.
>>
>
> So, you admit you don't understand the meaning of Incomplete as applied
> to Logic.
>
> Yes, F is incomplete because there is no "Proof" of G in F, even though
> G is TRUE in F. That BY DEFINITION makes F Incomplete.
>
The reason that G is unprovable in F is clearly that there is something
wrong with G and not that there is anything wrong with F.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 10:30 PM, olcott wrote:
> On 4/15/2023 9:24 PM, Richard Damon wrote:
>> On 4/15/23 9:59 PM, olcott wrote:
>>> On 4/15/2023 8:35 PM, Richard Damon wrote:
>>>> On 4/15/23 9:26 PM, olcott wrote:
>>>>> On 4/15/2023 8:15 PM, Richard Damon wrote:
>>>>>> On 4/15/23 8:56 PM, olcott wrote:
>>>>>>> On 4/15/2023 7:45 PM, Richard Damon wrote:
>>>>>>>> On 4/15/23 8:29 PM, olcott wrote:
>>>>>>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>>>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>> So, there is no claim that G is provable in F, just that it
>>>>>>>>>>>> is True in F, and to be True just requires an infinite
>>>>>>>>>>>> sequence of inference steps.
>>>>>>>>>>>>
>>>>>>>>>>>> The only one trying to prove in F that G is true is you, and
>>>>>>>>>>>> that operation can easily be proven to be impossible,
>>>>>>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Maybe your FAKE G,
>>>>>>>>>
>>>>>>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>>>>>>> Do you understand that it is not satisfiable in F because it is
>>>>>>>>> self-
>>>>>>>>> contradictory in F ?
>>>>>>>>>
>>>>>>>>> I will keep asking this until you answer.
>>>>>>>>>
>>>>>>>> But that doesn't matter, because it isn't the statement that
>>>>>>>> proves that all sufficiently powerful systems are inconsistent.
>>>>>>>>
>>>>>>>> Note, the fact that it would be impossible to actually prove
>>>>>>>> your pseudo-G in F doesn't mean that it can't be true.
>>>>>>>>
>>>>>>>> Note, it can't be False, but its status of being a Truth Bearer
>>>>>>>> can't be proven in F.
>>>>>>>>
>>>>>>>>
>>>>>>>> Maybe you need to learn to read, because my answer DOES answer
>>>>>>>> your question and show that you are wrong.
>>>>>>>>
>>>>>>>> Just shows the level of your intelect.
>>>>>>>>
>>>>>>>> Another point, you are showing that you don't understand what
>>>>>>>> "self-contradictory" means.
>>>>>>>>
>>>>>>>> "This statement is not Provable" is NOT Self-Contradictory, as
>>>>>>>> it has a possible set of truth values that makes it satisified,
>>>>>>>> that is being True but Unprovable.
>>>>>>>>
>>>>>>>
>>>>>>> When G asserts its own unprovability in F is proven in F this
>>>>>>> requires a
>>>>>>> sequence of inference steps in F that proves there is no such
>>>>>>> sequence
>>>>>>> of inference steps in F.
>>>>>>>
>>>>>>> Try and show how you would provide a sequence of inference steps
>>>>>>> in F
>>>>>>> that correctly proves that no such set of inference steps exists
>>>>>>> in F.
>>>>>>>
>>>>>>
>>>>>> But G isn't PROVEN in F, it just is TRUE in F.
>>>>>>
>>>>> When G asserts that it is unprovable in F this cannot be proven F ONLY
>>>>> because this proof requires a sequence of inference steps in F that
>>>>> proves there is no such sequence of inference steps in F, not
>>>>> because F
>>>>> is in any way incomplete.
>>>>>
>>>>>
>>>>
>>>> But G DOESN'T "assert" it is unprovable in F, so that doesn't matter.
>>>>
>>> *I am stipulating that it does. Try and follow my reasoning on this*
>>
>> So you are stipulating that you aren't working on Godel's Proof?
>>
>>>
>>> When G asserts that it is unprovable in F this cannot be proven F ONLY
>>> because this proof requires a sequence of inference steps in F that
>>> proves there is no such sequence of inference steps in F, not because F
>>> is in any way incomplete.
>>>
>>
>> So, you admit you don't understand the meaning of Incomplete as
>> applied to Logic.
>>
>> Yes, F is incomplete because there is no "Proof" of G in F, even
>> though G is TRUE in F. That BY DEFINITION makes F Incomplete.
>>
> The reason that G is unprovable in F is clearly that there is something
> wrong with G and not that there is anything wrong with F.
>
>

Nope.

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

Why is a statement that is unprovable have something "wrong" about it.

That just shows your mind has a problem with handling things it doesn't
understand.

You are just proving your ignorance.

Can you actually PROVE what you saying, if not, you are just proving
yourself to b a Hippocrite.

And that means an ACTUAL PROOF, stating the accepted truth-makers you
are starting with, and use actual LOGIC to derive the results.

This is just above your mental ability.

On 4/15/2023 9:46 PM, Richard Damon wrote:
> On 4/15/23 10:30 PM, olcott wrote:
>> On 4/15/2023 9:24 PM, Richard Damon wrote:
>>> On 4/15/23 9:59 PM, olcott wrote:
>>>> On 4/15/2023 8:35 PM, Richard Damon wrote:
>>>>> On 4/15/23 9:26 PM, olcott wrote:
>>>>>> On 4/15/2023 8:15 PM, Richard Damon wrote:
>>>>>>> On 4/15/23 8:56 PM, olcott wrote:
>>>>>>>> On 4/15/2023 7:45 PM, Richard Damon wrote:
>>>>>>>>> On 4/15/23 8:29 PM, olcott wrote:
>>>>>>>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>>>>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>> So, there is no claim that G is provable in F, just that it
>>>>>>>>>>>>> is True in F, and to be True just requires an infinite
>>>>>>>>>>>>> sequence of inference steps.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The only one trying to prove in F that G is true is you,
>>>>>>>>>>>>> and that operation can easily be proven to be impossible,
>>>>>>>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Maybe your FAKE G,
>>>>>>>>>>
>>>>>>>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>>>>>>>> Do you understand that it is not satisfiable in F because it
>>>>>>>>>> is self-
>>>>>>>>>> contradictory in F ?
>>>>>>>>>>
>>>>>>>>>> I will keep asking this until you answer.
>>>>>>>>>>
>>>>>>>>> But that doesn't matter, because it isn't the statement that
>>>>>>>>> proves that all sufficiently powerful systems are inconsistent.
>>>>>>>>>
>>>>>>>>> Note, the fact that it would be impossible to actually prove
>>>>>>>>> your pseudo-G in F doesn't mean that it can't be true.
>>>>>>>>>
>>>>>>>>> Note, it can't be False, but its status of being a Truth Bearer
>>>>>>>>> can't be proven in F.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Maybe you need to learn to read, because my answer DOES answer
>>>>>>>>> your question and show that you are wrong.
>>>>>>>>>
>>>>>>>>> Just shows the level of your intelect.
>>>>>>>>>
>>>>>>>>> Another point, you are showing that you don't understand what
>>>>>>>>> "self-contradictory" means.
>>>>>>>>>
>>>>>>>>> "This statement is not Provable" is NOT Self-Contradictory, as
>>>>>>>>> it has a possible set of truth values that makes it satisified,
>>>>>>>>> that is being True but Unprovable.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When G asserts its own unprovability in F is proven in F this
>>>>>>>> requires a
>>>>>>>> sequence of inference steps in F that proves there is no such
>>>>>>>> sequence
>>>>>>>> of inference steps in F.
>>>>>>>>
>>>>>>>> Try and show how you would provide a sequence of inference steps
>>>>>>>> in F
>>>>>>>> that correctly proves that no such set of inference steps exists
>>>>>>>> in F.
>>>>>>>>
>>>>>>>
>>>>>>> But G isn't PROVEN in F, it just is TRUE in F.
>>>>>>>
>>>>>> When G asserts that it is unprovable in F this cannot be proven F
>>>>>> ONLY
>>>>>> because this proof requires a sequence of inference steps in F that
>>>>>> proves there is no such sequence of inference steps in F, not
>>>>>> because F
>>>>>> is in any way incomplete.
>>>>>>
>>>>>>
>>>>>
>>>>> But G DOESN'T "assert" it is unprovable in F, so that doesn't matter.
>>>>>
>>>> *I am stipulating that it does. Try and follow my reasoning on this*
>>>
>>> So you are stipulating that you aren't working on Godel's Proof?
>>>
>>>>
>>>> When G asserts that it is unprovable in F this cannot be proven F ONLY
>>>> because this proof requires a sequence of inference steps in F that
>>>> proves there is no such sequence of inference steps in F, not because F
>>>> is in any way incomplete.
>>>>
>>>
>>> So, you admit you don't understand the meaning of Incomplete as
>>> applied to Logic.
>>>
>>> Yes, F is incomplete because there is no "Proof" of G in F, even
>>> though G is TRUE in F. That BY DEFINITION makes F Incomplete.
>>>
>> The reason that G is unprovable in F is clearly that there is something
>> wrong with G and not that there is anything wrong with F.
>>
>>
>
> Nope.
>
> You are just showing you don't understand what you are talking about.
>
> Why is a statement that is unprovable have something "wrong" about it.
>

G is unprovable because it is self-contradictory, making it erroneous.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 10:54 PM, olcott wrote:

> G is unprovable because it is self-contradictory, making it erroneous.
>

Since you don't understand the meaning of self-contradictory, that claim
is erroneous.

You are also working with a Strawman, because you can't understand the
actual statement G, so even if you were right about the statement you
are talking about, you would still be wrong about the actual statement.

The ACTUAL G has no "Self-Reference" in it, so can't be
"Self-Contradictory".

You are just proving how ignorant you are of logic.

On Sunday, 16 April 2023 at 13:16:37 UTC+2, Richard Damon wrote:

> You are just proving how ignorant you are of logic.

Even in sci.math??

Richard Damon, if that's your fucking real name,
you are another example of retarded is a compliment.
Not to even mention the amount of crap you spout.

*Plonk*

Julio

On Monday, 24 April 2023 at 17:58:34 UTC+2, olcott wrote:
> On 4/22/2023 7:27 PM, Richard Damon wrote:

> The reason that G cannot be proved in F is that this requires a
> sequence of inference steps in F that proves no such sequence
> of inference steps exists in F.

Wrong. G is proven unprovable at the meta-level.
And it couldn't be otherwise, since it is unprovable.

BTW, I don't know where Damon has read about infinite
proofs, but not only those are in fact irrelevant to GIT,
they are altogether disallowed by the usual paradigm
and necessarily so by any effective paradigm.

Julio

On 4/24/2023 11:19 AM, Julio Di Egidio wrote:
> On Monday, 24 April 2023 at 17:58:34 UTC+2, olcott wrote:
>> On 4/22/2023 7:27 PM, Richard Damon wrote:
>
>> The reason that G cannot be proved in F is that this requires a
>> sequence of inference steps in F that proves no such sequence
>> of inference steps exists in F.
>
> Wrong. G is proven unprovable at the meta-level.

G is proven unprovable at the meta-level. is correct.

> And it couldn't be otherwise, since it is unprovable.
>

You just contradicted yourself. (you forgot to include "in F").

G is provable in Meta-F and unprovable in F BECAUSE a proof of G in F
requires a sequence of inference steps in F that proves that they
themselves do not exist.

> BTW, I don't know where Damon has read about infinite
> proofs, but not only those are in fact irrelevant to GIT,
> they are altogether disallowed by the usual paradigm
> and necessarily so by any effective paradigm.
>
> Julio

Thanks for that. Can you support that with a link or a reference?

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Monday, 24 April 2023 at 21:09:04 UTC+2, olcott wrote:
> On 4/24/2023 11:19 AM, Julio Di Egidio wrote:
> > On Monday, 24 April 2023 at 17:58:34 UTC+2, olcott wrote:
> >> On 4/22/2023 7:27 PM, Richard Damon wrote:
> >
> >> The reason that G cannot be proved in F is that this requires a
> >> sequence of inference steps in F that proves no such sequence
> >> of inference steps exists in F.
> >
> > Wrong. G is proven unprovable at the meta-level.
>
> G is proven unprovable at the meta-level. is correct.
>
> > And it couldn't be otherwise, since it is unprovable.
>
> You just contradicted yourself. (you forgot to include "in F").

I didn't forget nor contradicted anything, you blithering
piece of demented shit, and I can also read English.

> G is provable in Meta-F and unprovable in F BECAUSE a proof of G in F
> requires a sequence of inference steps in F that proves that they
> themselves do not exist.

Thanks but no thanks, for some more of just the same
spamming crap, you other insane spammer and enemy
of humanity ad nauseam.

ESAD, you and the whole unspeakable bandwagon.

*Plonk*

Julio

On 4/24/2023 11:19 AM, Julio Di Egidio wrote:
> On Monday, 24 April 2023 at 17:58:34 UTC+2, olcott wrote:
>> On 4/22/2023 7:27 PM, Richard Damon wrote:
>
>> The reason that G cannot be proved in F is that this requires a
>> sequence of inference steps in F that proves no such sequence
>> of inference steps exists in F.
>
> Wrong. G is proven unprovable at the meta-level.
> And it couldn't be otherwise, since it is unprovable.
>

Not precisely correct, I corrected your imprecision by my [insertions]

> Wrong. G is proven unprovable [in F] at the meta-level [in meta-F]
> And it couldn't be otherwise, since it is unprovable [in F].

> BTW, I don't know where Damon has read about infinite
> proofs, but not only those are in fact irrelevant to GIT,

That is great to know. I agree that you are probably correct.
Can you please document this so that Richard can know he is wrong?

> they are altogether disallowed by the usual paradigm
> and necessarily so by any effective paradigm.
>
> Julio

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/24/2023 11:19 AM, Julio Di Egidio wrote:
> On Monday, 24 April 2023 at 17:58:34 UTC+2, olcott wrote:
>> On 4/22/2023 7:27 PM, Richard Damon wrote:
>
>> The reason that G cannot be proved in F is that this requires a
>> sequence of inference steps in F that proves no such sequence
>> of inference steps exists in F.
>
> Wrong. G is proven unprovable at the meta-level.
> And it couldn't be otherwise, since it is unprovable.
>
> BTW, I don't know where Damon has read about infinite
> proofs, but not only those are in fact irrelevant to GIT,
> they are altogether disallowed by the usual paradigm

This link seems to agree with you:
https://mathoverflow.net/questions/37070/why-cant-proofs-have-infinitely-many-steps

> and necessarily so by any effective paradigm.
>
> Julio

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Tuesday, 25 April 2023 at 01:35:44 UTC+2, Richard Damon wrote:

> Thus, we can prove in Meta-F that G must be true in F.

True in F is nonsense, G is a true arithmetic statement
period: G is true, the proof is meta-theoretical, just G is
in the language of F but/and not provable in F.

Plus, as I have already pointed out to you, there is in fact
no "Meta-F": in GIT the argument is a meta-argument and
meta-proof but is not formal and ultimately cannot be!

Sure, you too keep spamming...

Julio

On 4/24/2023 7:41 PM, Julio Di Egidio wrote:
> On Tuesday, 25 April 2023 at 01:35:44 UTC+2, Richard Damon wrote:
>
>> Thus, we can prove in Meta-F that G must be true in F.
>
> True in F is nonsense, G is a true arithmetic statement
> period: G is true, the proof is meta-theoretical, just G is
> in the language of F but/and not provable in F.
>
> Plus, as I have already pointed out to you, there is in fact
> no "Meta-F": in GIT the argument is a meta-argument and
> meta-proof but is not formal and ultimately cannot be!
>
> Sure, you too keep spamming...
>
> Julio

Gödel’s Theorem, as a simple corollary of Proposition VI (p. 57) is
frequently called, proves that there are arithmetical propositions which
are undecidable (i.e. neither provable nor disprovable) within their
arithmetical system, and the proof proceeds by actually specifying such
a proposition, namely the proposition g expressed by the formula to
which “17 Gen r” refers (p. 58). g is an arithmetical proposition; but
the proposition that g is undecidable within the system is not an
arithmetical proposition, since it is concerned with provability within
an arithmetical system, and this is a meta-arithmetical and not an
arithmetical notion. Gödel’s Theorem is thus a result which belongs not
to mathematics but to metamathematics, the name given by Hilbert to the
study of rigorous proof in mathematics and symbolic logic. (page 6)

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Tuesday, 25 April 2023 at 01:35:44 UTC+2, Richard Damon wrote:

> With a finite number of steps in Meta-F,
> we can prove that the infinite
> number of steps in F exist and are true.

And I had not even noticed this other piece of
utter, plain and adamantly repeated nonsense.

Is there any universe in which that nonsense
somehow makes sense, or are you really a
genius more genius than even Olcott?

Julio

On Tuesday, 25 April 2023 at 02:47:54 UTC+2, olcott wrote:

> Gödel’s Theorem, as a simple corollary of
> Proposition VI (p. 57) is

still ununderstood by you and forever will be.

Fucking pathetic to be charitable.

*Plonk*

Julio

On 4/24/2023 7:51 PM, Julio Di Egidio wrote:
> On Tuesday, 25 April 2023 at 02:47:54 UTC+2, olcott wrote:
>
>> Gödel’s Theorem, as a simple corollary of
>> Proposition VI (p. 57) is
>
> still ununderstood by you and forever will be.
>
> Fucking pathetic to be charitable.
>
> *Plonk*
>
> Julio

The standard notation F ⊢ A is used to express (in the meta-level) that
A is derivable in F, that is, that there is a proof of A in F, or, in
other words, that A is a theorem of F. Accordingly, F ⊬ A means that A
is not derivable in F.

https://plato.stanford.edu/entries/goedel-incompleteness/

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/26/23 2:07 AM, olcott wrote:
> On 4/25/2023 6:56 AM, Richard Damon wrote:
>> On 4/25/23 12:03 AM, olcott wrote:
>>> On 4/24/2023 6:35 PM, Richard Damon wrote:
>>>> On 4/24/23 11:25 AM, olcott wrote:
>>>>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>>>>> On 4/22/23 6:49 PM, olcott wrote:
>>>>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> G is unprovable because it is self-contradictory, making
>>>>>>>>>>>>>>> it erroneous.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Since you don't understand the meaning of
>>>>>>>>>>>>>> self-contradictory, that claim is erroneous.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>>>>
>>>>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Any proof of G in F requires a sequence of inference steps
>>>>>>>>>>>>> in F that
>>>>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>>>>
>>>>>>>>>>>> It is of course impossible to prove in F that a statement is
>>>>>>>>>>>> true but not provable in F.
>>>>>>>>>>>>
>>>>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>>>>
>>>>>>>>>>> To prove G in F you do.
>>>>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>>>>> This sentence is not true: "This sentence is not true" is true.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So, you don't understand how to prove that something is "True
>>>>>>>>>> in F" by doing the steps in Meta-F.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>>>>> expressed in his theory is true in his meta-theory.
>>>>>>>>
>>>>>>>> No, he didn't, he showed that *IF* a certain assuption was true,
>>>>>>>> then the Liar's paradox would be true, thus that assumption can
>>>>>>>> not be true.
>>>>>>>>
>>>>>>>
>>>>>>> When one level of indirect reference is applied to the Liar
>>>>>>> Paradox it
>>>>>>> becomes actually true. There was no "if".
>>>>>>>
>>>>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>>>>
>>>>>>>> Your
>>>>>>>>
>>>>>>>>>
>>>>>>>>> We can do the same thing when G asserts its own unprovability
>>>>>>>>> in F.
>>>>>>>>> G cannot be proved in F because this requires a sequence of
>>>>>>>>> inference
>>>>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>>>>
>>>>>>>> Right, you can't prove, in F, that G is true, but you can prove,
>>>>>>>> in Meta-F, that G is true in F, and that G is unprovable in F,
>>>>>>>> which is what is required.
>>>>>>>>
>>>>>>>
>>>>>>> When G asserts its own unprovability in F it cannot be proved in F
>>>>>>> because this requires a sequence of inference steps in F that
>>>>>>> prove that
>>>>>>> they themselves do not exist.
>>>>>>>
>>>>>>> Meta-F merely removes the self-contradiction the same way
>>>>>>> Tarski's Meta-
>>>>>>> theory removed the self-contradiction.
>>>>>>>
>>>>>>>
>>>>>>>> You are just showing that your mind can't handle the basics of
>>>>>>>> logic, or truth.
>>>>>>>>
>>>>>>>
>>>>>>> It may seem that way to someone that learns things by rote and
>>>>>>> mistakes
>>>>>>> this for actual understanding of exactly how all of the elements
>>>>>>> of a
>>>>>>> proof fit together coherently or fail to do so.
>>>>>>>
>>>>>>>> It sounds like you are too stupid to learn, and that you have
>>>>>>>> intentionaally hamstrung yourself to avoid being "polluted" by
>>>>>>>> "rote-learning" so you are just self-inflicted ignorant.
>>>>>>>>
>>>>>>>> If you won't even try to learn the basics, you have just
>>>>>>>> condemned yourself into being a pathological liar because you
>>>>>>>> just don't any better.
>>>>>>>>
>>>>>>>
>>>>>>> I do at this point need to understand model theory very thoroughly.
>>>>>>>
>>>>>>> Learning the details of these things could have boxed me into a
>>>>>>> corner
>>>>>>> prior to my philosophical investigation of seeing how the key
>>>>>>> elements
>>>>>>> fail to fit together coherently.
>>>>>>>
>>>>>>> It is true that the set of analytical truth is simply a set of
>>>>>>> semantic
>>>>>>> tautologies. It is true that formal systems grounded in this
>>>>>>> foundation
>>>>>>> cannot be incomplete nor have any expressions of language that are
>>>>>>> undecidable. Now that I have this foundation I have a way to see
>>>>>>> exactly
>>>>>>> how the concepts of math diverge from correct reasoning.
>>>>>>>
>>>>>>>>>
>>>>>>>>> You and I can see both THAT G cannot be proved in F and WHY G
>>>>>>>>> cannot be
>>>>>>>>> proved in F. G cannot be proved in F for the same pathological
>>>>>>>>> self-reference(Olcott 2004) reason that the Liar Paradox cannot
>>>>>>>>> be proved in Tarski's theory.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Which he didn't do, but you are too stupid to understand
>>>>>>>> claissic arguement forms.
>>>>>>>>
>>>>>>>
>>>>>>> It is not that I do not understand, it is that I can directly see
>>>>>>> where and how formal mathematical systems diverge from correct
>>>>>>> reasoning.
>>>>>>
>>>>>> But since you are discussing Formal Logic, you need to use the
>>>>>> rules of Formal logic.
>>>>>>
>>>>>> The other way to say it is that your "Correct Reasoning" diverges
>>>>>> from the accepted and proven system of Formal Logic.
>>>>>
>>>>>
>>>>>
>>>>> In classical logic, intuitionistic logic and similar logical
>>>>> systems, the principle of explosion
>>>>>
>>>>> ex falso [sequitur] quodlibet,
>>>>> 'from falsehood, anything [follows]'
>>>>>
>>>>> ex contradictione [sequitur] quodlibet,
>>>>> 'from contradiction, anything [follows]')
>>>>
>>>> Right, if a logic system can prove a contradiction, that out of that
>>>> contradiction you can prove anything
>>>>
>>>>>
>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>
>>>>> ∴ FALSE ⊢ Donald Trump is the Christ
>>>>> ∴ FALSE ⊢ Donald Trump is Satan
>>>>
>>>> Which isn't what was being talked about.
>>>>
>>>> You clearly don't understand how the principle of explosion works,
>>>> which isn't surprising considering how many misconseptions you have
>>>> about how logic works.
>>>>
>>>
>>> ex falso [sequitur] quodlibet,'from falsehood, anything [follows]'
>>> ∴ FALSE ⊢ Donald Trump is the Christ
>>
>> But you are using the wrong symbol
>>
>>
>
> 'from falsehood, anything [follows]'
> FALSE Proves that Donald Trump is the Christ

On 4/26/23 12:38 AM, olcott wrote:
> On 4/25/2023 6:56 AM, Richard Damon wrote:
>> On 4/24/23 11:28 PM, olcott wrote:
>>> On 4/24/2023 6:35 PM, Richard Damon wrote:
>>>> On 4/24/23 12:13 PM, olcott wrote:
>>>>> On 4/24/2023 10:58 AM, olcott wrote:
>>>>>> On 4/22/2023 7:27 PM, Richard Damon wrote:
>>>>>>> On 4/22/23 7:57 PM, olcott wrote:
>>>>>>>> On 4/22/2023 6:19 PM, Richard Damon wrote:
>>>>>>>>> On 4/22/23 6:49 PM, olcott wrote:
>>>>>>>>>> On 4/22/2023 5:22 PM, Richard Damon wrote:
>>>>>>>>>>> On 4/22/23 6:10 PM, olcott wrote:
>>>>>>>>>>>> On 4/22/2023 4:54 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 4/22/23 5:36 PM, olcott wrote:
>>>>>>>>>>>>>> On 4/22/2023 4:27 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 4/22/23 5:08 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> G is unprovable because it is self-contradictory,
>>>>>>>>>>>>>>>>>> making it erroneous.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Since you don't understand the meaning of
>>>>>>>>>>>>>>>>> self-contradictory, that claim is erroneous.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> When G asserts its own unprovability in F:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> But Godel's G doesn't do that.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Any proof of G in F requires a sequence of inference
>>>>>>>>>>>>>>>> steps in F that
>>>>>>>>>>>>>>>> prove that they themselves do not exist in F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It is of course impossible to prove in F that a statement
>>>>>>>>>>>>>>> is true but not provable in F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You don't need to do the proof in F,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> To prove G in F you do.
>>>>>>>>>>>>>> Otherwise you are doing the same cheap trick as Tarski:
>>>>>>>>>>>>>> This sentence is not true: "This sentence is not true" is
>>>>>>>>>>>>>> true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> So, you don't understand how to prove that something is
>>>>>>>>>>>>> "True in F" by doing the steps in Meta-F.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> I just showed you how Tarski proved that the Liar Paradox
>>>>>>>>>>>> expressed in his theory is true in his meta-theory.
>>>>>>>>>>>
>>>>>>>>>>> No, he didn't, he showed that *IF* a certain assuption was
>>>>>>>>>>> true, then the Liar's paradox would be true, thus that
>>>>>>>>>>> assumption can not be true.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> When one level of indirect reference is applied to the Liar
>>>>>>>>>> Paradox it
>>>>>>>>>> becomes actually true. There was no "if".
>>>>>>>>>>
>>>>>>>>>> This sentence is not true: "This sentence is not true" <IS> TRUE.
>>>>>>>>>>
>>>>>>>>>>> Your
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> We can do the same thing when G asserts its own
>>>>>>>>>>>> unprovability in F.
>>>>>>>>>>>> G cannot be proved in F because this requires a sequence of
>>>>>>>>>>>> inference
>>>>>>>>>>>> steps in F that prove that they themselves do not exist in F.
>>>>>>>>>>>
>>>>>>>>>>> Right, you can't prove, in F, that G is true, but you can
>>>>>>>>>>> prove, in Meta-F, that G is true in F, and that G is
>>>>>>>>>>> unprovable in F, which is what is required.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> When G asserts its own unprovability in F it cannot be proved
>>>>>>>>>> in F
>>>>>>>>>> because this requires a sequence of inference steps in F that
>>>>>>>>>> prove that
>>>>>>>>>> they themselves do not exist.
>>>>>>>>>>
>>>>>>>>>> Meta-F merely removes the self-contradiction the same way
>>>>>>>>>> Tarski's Meta-
>>>>>>>>>> theory removed the self-contradiction.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> You are just showing that your mind can't handle the basics
>>>>>>>>>>> of logic, or truth.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It may seem that way to someone that learns things by rote and
>>>>>>>>>> mistakes
>>>>>>>>>> this for actual understanding of exactly how all of the
>>>>>>>>>> elements of a
>>>>>>>>>> proof fit together coherently or fail to do so.
>>>>>>>>>>
>>>>>>>>>>> It sounds like you are too stupid to learn, and that you have
>>>>>>>>>>> intentionaally hamstrung yourself to avoid being "polluted"
>>>>>>>>>>> by "rote-learning" so you are just self-inflicted ignorant.
>>>>>>>>>>>
>>>>>>>>>>> If you won't even try to learn the basics, you have just
>>>>>>>>>>> condemned yourself into being a pathological liar because you
>>>>>>>>>>> just don't any better.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I do at this point need to understand model theory very
>>>>>>>>>> thoroughly.
>>>>>>>>>>
>>>>>>>>>> Learning the details of these things could have boxed me into
>>>>>>>>>> a corner
>>>>>>>>>> prior to my philosophical investigation of seeing how the key
>>>>>>>>>> elements
>>>>>>>>>> fail to fit together coherently.
>>>>>>>>>>
>>>>>>>>>> It is true that the set of analytical truth is simply a set of
>>>>>>>>>> semantic
>>>>>>>>>> tautologies. It is true that formal systems grounded in this
>>>>>>>>>> foundation
>>>>>>>>>> cannot be incomplete nor have any expressions of language that
>>>>>>>>>> are
>>>>>>>>>> undecidable. Now that I have this foundation I have a way to
>>>>>>>>>> see exactly
>>>>>>>>>> how the concepts of math diverge from correct reasoning.
>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> You and I can see both THAT G cannot be proved in F and WHY
>>>>>>>>>>>> G cannot be
>>>>>>>>>>>> proved in F. G cannot be proved in F for the same
>>>>>>>>>>>> pathological self-reference(Olcott 2004) reason that the
>>>>>>>>>>>> Liar Paradox cannot be proved in Tarski's theory.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Which he didn't do, but you are too stupid to understand
>>>>>>>>>>> claissic arguement forms.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It is not that I do not understand, it is that I can directly
>>>>>>>>>> see where and how formal mathematical systems diverge from
>>>>>>>>>> correct reasoning.
>>>>>>>>>
>>>>>>>>> But since you are discussing Formal Logic, you need to use the
>>>>>>>>> rules of Formal logic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I have never been talking about formal logic. I have always been
>>>>>>>> talking
>>>>>>>> about the philosophical foundations of correct reasoning.
>>>>>>>
>>>>>>> No, you have been talking about theorys DEEP in formal logic. You
>>>>>>> can't talk about the "errors" in those theories, with being in
>>>>>>> formal logic.
>>>>>>>
>>>>>>> IF you think you can somehow talk about the foundations, while
>>>>>>> working in the penthouse, you have just confirmed that you do not
>>>>>>> understand how ANY form of logic works.
>>>>>>>
>>>>>>> PERIOD.
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>>>> The other way to say it is that your "Correct Reasoning"
>>>>>>>>> diverges from the accepted and proven system of Formal Logic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It is correct reasoning in the absolute sense that I refer to.
>>>>>>>> If anyone has the opinion that arithmetic does not exist they are
>>>>>>>> incorrect in the absolute sense of the word: "incorrect".
>>>>>>>>
>>>>>>>
>>>>>>> IF you reject the logic that a theory is based on, you need to
>>>>>>> reject the logic system, NOT the theory.
>>>>>>>
>>>>>>> You are just showing that you have wasted your LIFE because you
>>>>>>> don'tunderstnad how to work ligic.
>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Because you are a learned-by-rote person you make sure to
>>>>>>>>>> never examine
>>>>>>>>>> whether or not any aspect of math diverges from correct
>>>>>>>>>> reasoning, you
>>>>>>>>>> simply assume that math is the gospel even when it contradicts
>>>>>>>>>> itself.
>>>>>>>>>
>>>>>>>>> Nope, I know that with logic, if you follow the rules, you will
>>>>>>>>> get the correct answer by the rules.
>>>>>>>>>
>>>>>>>>> If you break the rules, you have no idea where you will go.
>>>>>>>>>
>>>>>>>>
>>>>>>>> In other words you never ever spend any time on making sure that
>>>>>>>> these
>>>>>>>> rules fit together coherently.
>>>>>>>
>>>>>>> The rules work together just fine.
>>>>>>>
>>>>>>> YOU don't like some of the results, but they work just fine for
>>>>>>> most of the field.
>>>>>>>
>>>>>>> You are just PROVING that you have no idea how to actually
>>>>>>> discuss a new foundation for logic, likely because you are
>>>>>>> incapable of actually comeing up with a consistent basis for
>>>>>>> working logic.
>>>>>>>
>>>>>>>>
>>>>>>>>> As I have told you before, if you want to see what your
>>>>>>>>> "Correct > Reasoning" can do as a replaceent logic system, you
>>>>>>>>> need to start at the
>>>>>>>>> BEGINNING, and see wht it gets.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The foundation of correct reasoning is that the entire body of
>>>>>>>> analytical truth is a set of semantic tautologies.
>>>>>>>>
>>>>>>>> This means that all correct inference always requires
>>>>>>>> determining the
>>>>>>>> semantic consequence of expressions of language. This semantic
>>>>>>>> consequence can be specified syntactically, and indeed must be
>>>>>>>> represented syntactically to be computable
>>>>>>> Meaningless gobbledy-good until you actually define what you mean
>>>>>>> and spell out the actual rules that need to be followed.
>>>>>>>
>>>>>>> Note, "Computability" is actually a fairly late in the process
>>>>>>> concept. You first need to show that you logic can actually do
>>>>>>> something useful
>>>>>>>
>>>>>>>>
>>>>>>>>> To just try to change things at the end is just PROOF that your
>>>>>>>>> "Correct Reasoning" has to not be based on any real principles
>>>>>>>>> of logic.
>>>>>>>>>
>>>>>>>>> Since it is clear that you want to change some of the basics of
>>>>>>>>> how logic works, you are not allowed to just use ANY of
>>>>>>>>> classical logic until you actually show what part of it is
>>>>>>>>> still usable under your system and what changes happen.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Whenever an expression of language is derived as the semantic
>>>>>>>> consequence of other expressions of language we have valid
>>>>>>>> inference.
>>>>>>>
>>>>>>> And, are you using the "classical" definition of "semantic"
>>>>>>> (which makes this sentence somewhat cirular) or do you mean
>>>>>>> something based on the concept you sometimes use of  "the meaning
>>>>>>> of the words".
>>>>>>>
>>>>>>
>>>>>> *Principle of explosion*
>>>>>> An alternate argument for the principle stems from model theory. A
>>>>>> sentence P is a semantic consequence of a set of sentences Γ only if
>>>>>> every model of Γ is a model of P. However, there is no model of the
>>>>>> contradictory set (P ∧ ¬P) A fortiori, there is no model of (P ∧ ¬P)
>>>>>> that is not a model of Q. Thus, vacuously, every model of (P ∧ ¬P)
>>>>>> is a
>>>>>> model of Q. Thus, Q is a semantic consequence of (P ∧ ¬P).
>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>
>>>>>> Vacuous truth does not count as truth.
>>>>>> All variables must be quantified
>>>>>>
>>>>>> "all cell phones in the room are turned off" will be true when no
>>>>>> cell phones are in the room.
>>>>>>
>>>>>> ∃cp ∈ cell_phones (in_this_room(cp)) ∧ turned_off(cp))
>>>>>>
>>>>>>
>>>>>>>>
>>>>>>>> The semantic consequence must be specified syntactically so that
>>>>>>>> it can
>>>>>>>> be computed or examined in formal systems.
>>>>>>>>
>>>>>>>> Just like in sound deductive inference when the premises are
>>>>>>>> known to be
>>>>>>>> true, and the reasoning valid (a semantic consequence) then the
>>>>>>>> conclusion is necessarily true.
>>>>>>>
>>>>>>> So, what is the difference in your system from classical Formal
>>>>>>> Logic?
>>>>>>>
>>>>>>
>>>>>> Semantic Necessity operator: ⊨□
>>>>>>
>>>>>>     FALSE ⊨□ FALSE // POE abolished
>>>>>> (P ∧ ¬P) ⊨□ FALSE // POE abolished
>>>>>>
>>>>>> ⇒ and → symbols are replaced by ⊨□
>>>>>>
>>>>>> The sets that the variables range over must be defined
>>>>>> all variables must be quantified
>>>>>>
>>>>>> // x is a semantic consequence of its premises in L
>>>>>> Provable(P,x) ≡ ∃x ∈ L, ∃P ⊆ L (P ⊨□ x)
>>>>>>
>>>>>> // x is a semantic consequence of the axioms of L
>>>>>> True(L,x) ≡ ∃x ∈ L (Axioms(L) ⊨□ x)
>>>>>>
>>>>>> *The above is all that I know right now*
>>>>>>
>>>>>>
>>>>>>>> The most important aspect of the tiny little foundation of a formal
>>>>>>>> system that I already specified immediately above is self-evident:
>>>>>>>> True(L,X) can be defined and incompleteness is impossible.
>>>>>>>
>>>>>>> I don't think your system is anywhere near establish far enough
>>>>>>> for you to say that.
>>>>>>
>>>>>> Try and show exceptions to this rule and I will fill in any gaps that
>>>>>> you find.
>>>>>>
>>>>>> G asserts its own unprovability in F
>>>>>> The reason that G cannot be proved in F is that this requires a
>>>>>> sequence of inference steps in F that proves no such sequence
>>>>>> of inference steps exists in F.
>>>>>>
>>>>>>
>>>>> ∃sequence_of_inference_steps ⊆ F (sequence_of_inference_steps ⊢
>>>>> ∄sequence_of_inference_steps ⊆ F)
>>>>>
>>>>>
>>>>
>>>> So, you don't understand the differnce between the INFINITE set of
>>>> sequence steps that show that G is True, and the FINITE number of
>>>> steps that need to be shown to make G provable.
>>>>
>>>
>>> The experts seem to believe that unless a proof can be transformed into
>>> a finite sequence of steps it is no actual proof at all. Try and cite a
>>> source that says otherwise.
>>
>> WHy? Because I agree with that. A Proof needs to be done in a finite
>> number of steps.
>>
>> The question is why the infinite number of steps in F that makes G
>> true don't count for making it true.
>>
>> Yes, you can't write that out to KNOW it to be true, but that is the
>> differece between knowledge and fact.
>>
>
> Infinite proof are not allowed: Because they can't possibly ever occur.
>
>>>
>>> We can imagine an Oracle machine that can complete these proofs in the
>>> same sort of way that we can imagine a magic fairy that waves a magic
>>> wand.
>>>
>>>> You are just showing you don't understand what you talking about and
>>>> just spouting word (or symbol) salad.
>>>>
>>>> You are oriving you are an IDIOT.
>>>
>>> I am seeing these things at a deeper philosophical level than you
>>> are. I know that is hard to believe.
>>
>> But not according to the rules of the system you are talking about.
>>
>> You don't get to change the rules on a system.
>>
>
> YES I DO !!!
> My whole purpose to provide the *correct reasoning* foundation such that
> formal systems can be defined without undecidability or undefinability,
> or inconsistently.

On 4/16/2023 6:16 AM, Richard Damon wrote:
> On 4/15/23 10:54 PM, olcott wrote:
>
>> G is unprovable because it is self-contradictory, making it erroneous.
>>
>
> Since you don't understand the meaning of self-contradictory, that claim
> is erroneous.
>

When G asserts its own unprovability in F:

Any proof of G in F requires a sequence of inference steps in F that
prove that they themselves do not exist in F.

This is precisely analogous to you proving that you yourself never
existed.

> You are also working with a Strawman, because you can't understand the
> actual statement G, so even if you were right about the statement you
> are talking about, you would still be wrong about the actual statement.
>
> The ACTUAL G has no "Self-Reference" in it, so can't be
> "Self-Contradictory".
>
> You are just proving how ignorant you are of logic.
>

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/22/23 5:08 PM, olcott wrote:
> On 4/16/2023 6:16 AM, Richard Damon wrote:
>> On 4/15/23 10:54 PM, olcott wrote:
>>
>>> G is unprovable because it is self-contradictory, making it erroneous.
>>>
>>
>> Since you don't understand the meaning of self-contradictory, that
>> claim is erroneous.
>>
>
> When G asserts its own unprovability in F:

But Godel's G doesn't do that.

>
> Any proof of G in F requires a sequence of inference steps in F that
> prove that they themselves do not exist in F.

It is of course impossible to prove in F that a statement is true but
not provable in F.

You don't need to do the proof in F, Godel shows how to construct a
Meta-F system from F that allows construction a proof IN META-F that
shows that his G is True in F, and not provable in F.

>
> This is precisely analogous to you proving that you yourself never
> existed.

Nope, you are just proving you can't do your strawman, because you have
straw for brains.

You start from an incorrect assertion, that G actually asserts its own
unprovability, and then continue to make errors in asserting that this
is proven in F itself.

This just shows you fundamentally don't understand how the logic works,
and that you are too stupid to be able to be taught it.

On 4/22/2023 4:27 PM, Richard Damon wrote:
> On 4/22/23 5:08 PM, olcott wrote:
>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>> On 4/15/23 10:54 PM, olcott wrote:
>>>
>>>> G is unprovable because it is self-contradictory, making it erroneous.
>>>>
>>>
>>> Since you don't understand the meaning of self-contradictory, that
>>> claim is erroneous.
>>>
>>
>> When G asserts its own unprovability in F:
>
> But Godel's G doesn't do that.
>
>>
>> Any proof of G in F requires a sequence of inference steps in F that
>> prove that they themselves do not exist in F.
>
> It is of course impossible to prove in F that a statement is true but
> not provable in F.
>
> You don't need to do the proof in F,

To prove G in F you do.
Otherwise you are doing the same cheap trick as Tarski:
This sentence is not true: "This sentence is not true" is true.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/22/23 5:36 PM, olcott wrote:
> On 4/22/2023 4:27 PM, Richard Damon wrote:
>> On 4/22/23 5:08 PM, olcott wrote:
>>> On 4/16/2023 6:16 AM, Richard Damon wrote:
>>>> On 4/15/23 10:54 PM, olcott wrote:
>>>>
>>>>> G is unprovable because it is self-contradictory, making it erroneous.
>>>>>
>>>>
>>>> Since you don't understand the meaning of self-contradictory, that
>>>> claim is erroneous.
>>>>
>>>
>>> When G asserts its own unprovability in F:
>>
>> But Godel's G doesn't do that.
>>
>>>
>>> Any proof of G in F requires a sequence of inference steps in F that
>>> prove that they themselves do not exist in F.
>>
>> It is of course impossible to prove in F that a statement is true but
>> not provable in F.
>>
>> You don't need to do the proof in F,
>
> To prove G in F you do.
> Otherwise you are doing the same cheap trick as Tarski:
> This sentence is not true: "This sentence is not true" is true.
>
>

So, you don't understand how to prove that something is "True in F" by
doing the steps in Meta-F.

Just shows you are ignorant.

Too bad you are going to die in such disgrace.

All you need to do is show that there exist a (possibly infinte) set of
steps from the truth makers in F, using the rules of F, to G. Youy don't
need to actually DO this in F, if you have a system that knowns about F.

Your mind is just too small.