On 5/6/23 9:20 PM, olcott wrote:
> On 5/6/2023 8:06 PM, Richard Damon wrote:
>> On 5/6/23 8:49 PM, olcott wrote:
>>> On 5/6/2023 7:31 PM, Richard Damon wrote:
>>>> On 5/6/23 8:11 PM, olcott wrote:
>>>>> On 5/6/2023 6:48 PM, Richard Damon wrote:
>>>>>> On 5/6/23 6:29 PM, olcott wrote:
>>>>>>> On 5/6/2023 3:45 PM, Richard Damon wrote:
>>>>>>>> On 5/6/23 2:36 PM, olcott wrote:
>>>>>>>>> On 4/28/2023 6:40 AM, Richard Damon wrote:
>>>>>>>>>> On 4/28/23 12:23 AM, olcott wrote:
>>>>>>>>>>> On 4/27/2023 9:41 PM, Richard Damon wrote:
>>>>>>>>>>>> On 4/27/23 9:07 PM, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> The standard definition of mathematical incompleteness:
>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>
>>>>>>>>>>>> Remember, that if φ ∈ F then φ has a defined truth value in
>>>>>>>>>>>> F, it is either True of False, and thus can't be the "Liar's
>>>>>>>>>>>> Paradox".
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> How about this one?
>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>
>>>>>>>>>> You use of terms that you do not define doesn't help you.
>>>>>>>>>>
>>>>>>>>>> Incomplete means, in actual words, that there exists a true
>>>>>>>>>> statement in F that can not be proven in F, or similarly a
>>>>>>>>>> False statement in F that can not be disproven (proven to be
>>>>>>>>>> false).
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I don't think that there is any source that says it is a true
>>>>>>>>> statement in F.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Except that Godel has PROVEN (in Meta-F) that G actually IS true
>>>>>>>> in F.
>>>>>>>>
>>>>>>> Please show me where it says that
>>>>>>>
>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>
>>>>>>
>>>>>> Page 41 (marked as 44 of the PDF)
>>>>>>
>>>>>>  From the remark that [R(q); q] asserts its own unprovability, it
>>>>>> follows at once that [R(q); q] is correct, since [R(q); q] is
>>>>>> certainly unprovable (because undecidable). So the proposition
>>>>>> which is undecidable in the system PM yet turns out to be decided
>>>>>> by metamathematical considerations. The close analysis of this
>>>>>> remarkable circumstance leads to surprising results concerning
>>>>>> proofs of consistency of formal systems, which are dealt with in
>>>>>> more detail in Section 4 (Proposition XI).
>>>>>
>>>>> As I suspected it says nothing about being true in PM.
>>>>>
>>>>
>>>> It says it is CORRECT, which mean the assertion is TRUE (in P and in
>>>> the meta).
>>>>
>>>
>>> It says nothing about being correct or true in PM.
>>> In PM it is undecidable, thus not correct, true, false in PM.
>>
>> Nope, you don't understand that while it is undecideable in the system
>> PM (and thus not PROVABLE or REFUTABLE in PM), it IS shown to be true
>> in the metamathematical system, and thus also true in PM,
>
> Epidemiologically that is not the way that truth is derived.

Can you actually quote a RULE that says that?

You can KNOW that something is true because you can prove that it is
true using another system with the right connections to that original
system.

KNOWLEDGE is not constrained by the same rules that proofs are. A proof
"in a system" can only use the truth makers of that system. A proof
ABOUT a system, which can lead to knowledge about that system, can use
other meta-knowledge of the system to show that something is actually
true in the system.

You are just showing your ignorance of tha ACTUAL principles of
Epistemology.

A LOT of "Knowledge" is based on Truth derived from "meta" systems and
not just from proofs within the system.

>
>> due to the rules of the metamathematical system.
>>
>> You just don't understand what a meta system is, and how truth works
>> between systems because you are too stupid.
>>
>>>
>>>> You just don't understand how the words are being used.
>>>>
>>>> Just because they don't use the magic words that you think in,
>>>> doesn't mean that they aren't saying what they are saying.
>>>
>>
>

On 5/6/2023 8:46 PM, Richard Damon wrote:
> On 5/6/23 9:20 PM, olcott wrote:
>> On 5/6/2023 8:06 PM, Richard Damon wrote:
>>> On 5/6/23 8:49 PM, olcott wrote:
>>>> On 5/6/2023 7:31 PM, Richard Damon wrote:
>>>>> On 5/6/23 8:11 PM, olcott wrote:
>>>>>> On 5/6/2023 6:48 PM, Richard Damon wrote:
>>>>>>> On 5/6/23 6:29 PM, olcott wrote:
>>>>>>>> On 5/6/2023 3:45 PM, Richard Damon wrote:
>>>>>>>>> On 5/6/23 2:36 PM, olcott wrote:
>>>>>>>>>> On 4/28/2023 6:40 AM, Richard Damon wrote:
>>>>>>>>>>> On 4/28/23 12:23 AM, olcott wrote:
>>>>>>>>>>>> On 4/27/2023 9:41 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 4/27/23 9:07 PM, olcott wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> The standard definition of mathematical incompleteness:
>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>
>>>>>>>>>>>>> Remember, that if φ ∈ F then φ has a defined truth value in
>>>>>>>>>>>>> F, it is either True of False, and thus can't be the
>>>>>>>>>>>>> "Liar's Paradox".
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> How about this one?
>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>
>>>>>>>>>>> You use of terms that you do not define doesn't help you.
>>>>>>>>>>>
>>>>>>>>>>> Incomplete means, in actual words, that there exists a true
>>>>>>>>>>> statement in F that can not be proven in F, or similarly a
>>>>>>>>>>> False statement in F that can not be disproven (proven to be
>>>>>>>>>>> false).
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I don't think that there is any source that says it is a true
>>>>>>>>>> statement in F.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Except that Godel has PROVEN (in Meta-F) that G actually IS
>>>>>>>>> true in F.
>>>>>>>>>
>>>>>>>> Please show me where it says that
>>>>>>>>
>>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>>
>>>>>>>
>>>>>>> Page 41 (marked as 44 of the PDF)
>>>>>>>
>>>>>>>  From the remark that [R(q); q] asserts its own unprovability, it
>>>>>>> follows at once that [R(q); q] is correct, since [R(q); q] is
>>>>>>> certainly unprovable (because undecidable). So the proposition
>>>>>>> which is undecidable in the system PM yet turns out to be decided
>>>>>>> by metamathematical considerations. The close analysis of this
>>>>>>> remarkable circumstance leads to surprising results concerning
>>>>>>> proofs of consistency of formal systems, which are dealt with in
>>>>>>> more detail in Section 4 (Proposition XI).
>>>>>>
>>>>>> As I suspected it says nothing about being true in PM.
>>>>>>
>>>>>
>>>>> It says it is CORRECT, which mean the assertion is TRUE (in P and
>>>>> in the meta).
>>>>>
>>>>
>>>> It says nothing about being correct or true in PM.
>>>> In PM it is undecidable, thus not correct, true, false in PM.
>>>
>>> Nope, you don't understand that while it is undecideable in the
>>> system PM (and thus not PROVABLE or REFUTABLE in PM), it IS shown to
>>> be true in the metamathematical system, and thus also true in PM,
>>
>> Epidemiologically that is not the way that truth is derived.
>
> Can you actually quote a RULE that says that?
>
> You can KNOW that something is true because you can prove that it is
> true using another system with the right connections to that original
> system.
>
> KNOWLEDGE is not constrained by the same rules that proofs are. A proof
> "in a system" can only use the truth makers of that system.

Hence G is not true in PM.

> A proof
> ABOUT a system, which can lead to knowledge about that system, can use
> other meta-knowledge of the system to show that something is actually
> true in the system.
>
> You are just showing your ignorance of tha ACTUAL principles of
> Epistemology.
>
> A LOT of "Knowledge" is based on Truth derived from "meta" systems and
> not just from proofs within the system.
>
>>
>>> due to the rules of the metamathematical system.
>>>
>>> You just don't understand what a meta system is, and how truth works
>>> between systems because you are too stupid.
>>>
>>>>
>>>>> You just don't understand how the words are being used.
>>>>>
>>>>> Just because they don't use the magic words that you think in,
>>>>> doesn't mean that they aren't saying what they are saying.
>>>>
>>>
>>
>

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

On 5/6/23 10:13 PM, olcott wrote:
> On 5/6/2023 8:46 PM, Richard Damon wrote:
>> On 5/6/23 9:20 PM, olcott wrote:
>>> On 5/6/2023 8:06 PM, Richard Damon wrote:
>>>> On 5/6/23 8:49 PM, olcott wrote:
>>>>> On 5/6/2023 7:31 PM, Richard Damon wrote:
>>>>>> On 5/6/23 8:11 PM, olcott wrote:
>>>>>>> On 5/6/2023 6:48 PM, Richard Damon wrote:
>>>>>>>> On 5/6/23 6:29 PM, olcott wrote:
>>>>>>>>> On 5/6/2023 3:45 PM, Richard Damon wrote:
>>>>>>>>>> On 5/6/23 2:36 PM, olcott wrote:
>>>>>>>>>>> On 4/28/2023 6:40 AM, Richard Damon wrote:
>>>>>>>>>>>> On 4/28/23 12:23 AM, olcott wrote:
>>>>>>>>>>>>> On 4/27/2023 9:41 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 4/27/23 9:07 PM, olcott wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The standard definition of mathematical incompleteness:
>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Remember, that if φ ∈ F then φ has a defined truth value
>>>>>>>>>>>>>> in F, it is either True of False, and thus can't be the
>>>>>>>>>>>>>> "Liar's Paradox".
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> How about this one?
>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>
>>>>>>>>>>>> You use of terms that you do not define doesn't help you.
>>>>>>>>>>>>
>>>>>>>>>>>> Incomplete means, in actual words, that there exists a true
>>>>>>>>>>>> statement in F that can not be proven in F, or similarly a
>>>>>>>>>>>> False statement in F that can not be disproven (proven to be
>>>>>>>>>>>> false).
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> I don't think that there is any source that says it is a true
>>>>>>>>>>> statement in F.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Except that Godel has PROVEN (in Meta-F) that G actually IS
>>>>>>>>>> true in F.
>>>>>>>>>>
>>>>>>>>> Please show me where it says that
>>>>>>>>>
>>>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>>>
>>>>>>>>
>>>>>>>> Page 41 (marked as 44 of the PDF)
>>>>>>>>
>>>>>>>>  From the remark that [R(q); q] asserts its own unprovability,
>>>>>>>> it follows at once that [R(q); q] is correct, since [R(q); q] is
>>>>>>>> certainly unprovable (because undecidable). So the proposition
>>>>>>>> which is undecidable in the system PM yet turns out to be
>>>>>>>> decided by metamathematical considerations. The close analysis
>>>>>>>> of this remarkable circumstance leads to surprising results
>>>>>>>> concerning proofs of consistency of formal systems, which are
>>>>>>>> dealt with in more detail in Section 4 (Proposition XI).
>>>>>>>
>>>>>>> As I suspected it says nothing about being true in PM.
>>>>>>>
>>>>>>
>>>>>> It says it is CORRECT, which mean the assertion is TRUE (in P and
>>>>>> in the meta).
>>>>>>
>>>>>
>>>>> It says nothing about being correct or true in PM.
>>>>> In PM it is undecidable, thus not correct, true, false in PM.
>>>>
>>>> Nope, you don't understand that while it is undecideable in the
>>>> system PM (and thus not PROVABLE or REFUTABLE in PM), it IS shown to
>>>> be true in the metamathematical system, and thus also true in PM,
>>>
>>> Epidemiologically that is not the way that truth is derived.
>>
>> Can you actually quote a RULE that says that?
>>
>> You can KNOW that something is true because you can prove that it is
>> true using another system with the right connections to that original
>> system.
>>
>> KNOWLEDGE is not constrained by the same rules that proofs are. A
>> proof "in a system" can only use the truth makers of that system.
>
> Hence G is not true in PM.

Nope, you are just proving you don't know a thing about what you are
talking about.

I said you couldn't PROVE G in PM, that says NOTHING about it not being
True in PM, or about what we can KNOW about G in PM.

You are just showing how stupid you are.

Since you didn't show the "Rule" you are using to make your statement
(because it is clear you know there isn't one) you are shown to be just
a pathological liar.

You just don't understand what it means for something to be "True", and
how that differs from being able to prove it in a given system.
This just shows that you concept of "Correct Reasoning" is almost
certainly built on a broken foundation, and thus it is dead in the water
from the very start.

NO ONE is going to pick it up when you are gone, because you can't
establish any actual evidence that you have a workable idea, because you
make it so clear you have no idea what you are talkinga about.

YOU HAVE WASTED YOUR LIFE, and are going to be remembered (for how ever
long you are remembered) as the pathalogical lying idiot who didn't know
what he was talking about.

>
>> A proof ABOUT a system, which can lead to knowledge about that system,
>> can use other meta-knowledge of the system to show that something is
>> actually true in the system.
>>
>> You are just showing your ignorance of tha ACTUAL principles of
>> Epistemology.
>>
>> A LOT of "Knowledge" is based on Truth derived from "meta" systems and
>> not just from proofs within the system.
>>
>>>
>>>> due to the rules of the metamathematical system.
>>>>
>>>> You just don't understand what a meta system is, and how truth works
>>>> between systems because you are too stupid.
>>>>
>>>>>
>>>>>> You just don't understand how the words are being used.
>>>>>>
>>>>>> Just because they don't use the magic words that you think in,
>>>>>> doesn't mean that they aren't saying what they are saying.
>>>>>
>>>>
>>>
>>
>

On 5/6/2023 9:28 PM, Richard Damon wrote:
> On 5/6/23 10:13 PM, olcott wrote:
>> On 5/6/2023 8:46 PM, Richard Damon wrote:
>>> On 5/6/23 9:20 PM, olcott wrote:
>>>> On 5/6/2023 8:06 PM, Richard Damon wrote:
>>>>> On 5/6/23 8:49 PM, olcott wrote:
>>>>>> On 5/6/2023 7:31 PM, Richard Damon wrote:
>>>>>>> On 5/6/23 8:11 PM, olcott wrote:
>>>>>>>> On 5/6/2023 6:48 PM, Richard Damon wrote:
>>>>>>>>> On 5/6/23 6:29 PM, olcott wrote:
>>>>>>>>>> On 5/6/2023 3:45 PM, Richard Damon wrote:
>>>>>>>>>>> On 5/6/23 2:36 PM, olcott wrote:
>>>>>>>>>>>> On 4/28/2023 6:40 AM, Richard Damon wrote:
>>>>>>>>>>>>> On 4/28/23 12:23 AM, olcott wrote:
>>>>>>>>>>>>>> On 4/27/2023 9:41 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 4/27/23 9:07 PM, olcott wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The standard definition of mathematical incompleteness:
>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Remember, that if φ ∈ F then φ has a defined truth value
>>>>>>>>>>>>>>> in F, it is either True of False, and thus can't be the
>>>>>>>>>>>>>>> "Liar's Paradox".
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> How about this one?
>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>
>>>>>>>>>>>>> You use of terms that you do not define doesn't help you.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Incomplete means, in actual words, that there exists a true
>>>>>>>>>>>>> statement in F that can not be proven in F, or similarly a
>>>>>>>>>>>>> False statement in F that can not be disproven (proven to
>>>>>>>>>>>>> be false).
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> I don't think that there is any source that says it is a
>>>>>>>>>>>> true statement in F.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Except that Godel has PROVEN (in Meta-F) that G actually IS
>>>>>>>>>>> true in F.
>>>>>>>>>>>
>>>>>>>>>> Please show me where it says that
>>>>>>>>>>
>>>>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Page 41 (marked as 44 of the PDF)
>>>>>>>>>
>>>>>>>>>  From the remark that [R(q); q] asserts its own unprovability,
>>>>>>>>> it follows at once that [R(q); q] is correct, since [R(q); q]
>>>>>>>>> is certainly unprovable (because undecidable). So the
>>>>>>>>> proposition which is undecidable in the system PM yet turns out
>>>>>>>>> to be decided by metamathematical considerations. The close
>>>>>>>>> analysis of this remarkable circumstance leads to surprising
>>>>>>>>> results concerning proofs of consistency of formal systems,
>>>>>>>>> which are dealt with in more detail in Section 4 (Proposition XI).
>>>>>>>>
>>>>>>>> As I suspected it says nothing about being true in PM.
>>>>>>>>
>>>>>>>
>>>>>>> It says it is CORRECT, which mean the assertion is TRUE (in P and
>>>>>>> in the meta).
>>>>>>>
>>>>>>
>>>>>> It says nothing about being correct or true in PM.
>>>>>> In PM it is undecidable, thus not correct, true, false in PM.
>>>>>
>>>>> Nope, you don't understand that while it is undecideable in the
>>>>> system PM (and thus not PROVABLE or REFUTABLE in PM), it IS shown
>>>>> to be true in the metamathematical system, and thus also true in PM,
>>>>
>>>> Epidemiologically that is not the way that truth is derived.
>>>
>>> Can you actually quote a RULE that says that?
>>>
>>> You can KNOW that something is true because you can prove that it is
>>> true using another system with the right connections to that original
>>> system.
>>>
>>> KNOWLEDGE is not constrained by the same rules that proofs are. A
>>> proof "in a system" can only use the truth makers of that system.
>>
>> Hence G is not true in PM.
>
> Nope, you are just proving you don't know a thing about what you are
> talking about.
>
> I said you couldn't PROVE G in PM, that says NOTHING about it not being
> True in PM, or about what we can KNOW about G in PM.

When PM is asked is G true or false PM says I have no idea.

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

On 5/6/23 10:34 PM, olcott wrote:
> On 5/6/2023 9:28 PM, Richard Damon wrote:
>> On 5/6/23 10:13 PM, olcott wrote:
>>> On 5/6/2023 8:46 PM, Richard Damon wrote:
>>>> On 5/6/23 9:20 PM, olcott wrote:
>>>>> On 5/6/2023 8:06 PM, Richard Damon wrote:
>>>>>> On 5/6/23 8:49 PM, olcott wrote:
>>>>>>> On 5/6/2023 7:31 PM, Richard Damon wrote:
>>>>>>>> On 5/6/23 8:11 PM, olcott wrote:
>>>>>>>>> On 5/6/2023 6:48 PM, Richard Damon wrote:
>>>>>>>>>> On 5/6/23 6:29 PM, olcott wrote:
>>>>>>>>>>> On 5/6/2023 3:45 PM, Richard Damon wrote:
>>>>>>>>>>>> On 5/6/23 2:36 PM, olcott wrote:
>>>>>>>>>>>>> On 4/28/2023 6:40 AM, Richard Damon wrote:
>>>>>>>>>>>>>> On 4/28/23 12:23 AM, olcott wrote:
>>>>>>>>>>>>>>> On 4/27/2023 9:41 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 4/27/23 9:07 PM, olcott wrote:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> The standard definition of mathematical incompleteness:
>>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Remember, that if φ ∈ F then φ has a defined truth value
>>>>>>>>>>>>>>>> in F, it is either True of False, and thus can't be the
>>>>>>>>>>>>>>>> "Liar's Paradox".
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> How about this one?
>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You use of terms that you do not define doesn't help you.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Incomplete means, in actual words, that there exists a
>>>>>>>>>>>>>> true statement in F that can not be proven in F, or
>>>>>>>>>>>>>> similarly a False statement in F that can not be disproven
>>>>>>>>>>>>>> (proven to be false).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> I don't think that there is any source that says it is a
>>>>>>>>>>>>> true statement in F.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Except that Godel has PROVEN (in Meta-F) that G actually IS
>>>>>>>>>>>> true in F.
>>>>>>>>>>>>
>>>>>>>>>>> Please show me where it says that
>>>>>>>>>>>
>>>>>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Page 41 (marked as 44 of the PDF)
>>>>>>>>>>
>>>>>>>>>>  From the remark that [R(q); q] asserts its own unprovability,
>>>>>>>>>> it follows at once that [R(q); q] is correct, since [R(q); q]
>>>>>>>>>> is certainly unprovable (because undecidable). So the
>>>>>>>>>> proposition which is undecidable in the system PM yet turns
>>>>>>>>>> out to be decided by metamathematical considerations. The
>>>>>>>>>> close analysis of this remarkable circumstance leads to
>>>>>>>>>> surprising results concerning proofs of consistency of formal
>>>>>>>>>> systems, which are dealt with in more detail in Section 4
>>>>>>>>>> (Proposition XI).
>>>>>>>>>
>>>>>>>>> As I suspected it says nothing about being true in PM.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It says it is CORRECT, which mean the assertion is TRUE (in P
>>>>>>>> and in the meta).
>>>>>>>>
>>>>>>>
>>>>>>> It says nothing about being correct or true in PM.
>>>>>>> In PM it is undecidable, thus not correct, true, false in PM.
>>>>>>
>>>>>> Nope, you don't understand that while it is undecideable in the
>>>>>> system PM (and thus not PROVABLE or REFUTABLE in PM), it IS shown
>>>>>> to be true in the metamathematical system, and thus also true in PM,
>>>>>
>>>>> Epidemiologically that is not the way that truth is derived.
>>>>
>>>> Can you actually quote a RULE that says that?
>>>>
>>>> You can KNOW that something is true because you can prove that it is
>>>> true using another system with the right connections to that
>>>> original system.
>>>>
>>>> KNOWLEDGE is not constrained by the same rules that proofs are. A
>>>> proof "in a system" can only use the truth makers of that system.
>>>
>>> Hence G is not true in PM.
>>
>> Nope, you are just proving you don't know a thing about what you are
>> talking about.
>>
>> I said you couldn't PROVE G in PM, that says NOTHING about it not
>> being True in PM, or about what we can KNOW about G in PM.
>
> When PM is asked is G true or false PM says I have no idea.
>
>

But you don't "Ask" the system for what it knows, that isn't how logic
works. That PM will "say" "I have no idea" just shows that in PM the
problem is undecidable (which deals with PROVALBE in PM, not TRUTH in PM).

You are just PROVING you are a pathological lying idiot reguarding how
logic works.

We can show that G *IS* true in PM, as we can prove that no such number
CAN exist in the mathematics of PM to make G false, that means that G is
true.

There is no such option as "Not a Truth Bearer" when asking if a number
exists that matchs a computable criteria.

You are just proving yourself to be an idiot. You just are stuck on
INCORRECT definition that you have gaslite youself with, making yourself
into that self-made pathological lying idiot.

On 5/6/2023 9:49 PM, Richard Damon wrote:
> On 5/6/23 10:34 PM, olcott wrote:
>> On 5/6/2023 9:28 PM, Richard Damon wrote:
>>> On 5/6/23 10:13 PM, olcott wrote:
>>>> On 5/6/2023 8:46 PM, Richard Damon wrote:
>>>>> On 5/6/23 9:20 PM, olcott wrote:
>>>>>> On 5/6/2023 8:06 PM, Richard Damon wrote:
>>>>>>> On 5/6/23 8:49 PM, olcott wrote:
>>>>>>>> On 5/6/2023 7:31 PM, Richard Damon wrote:
>>>>>>>>> On 5/6/23 8:11 PM, olcott wrote:
>>>>>>>>>> On 5/6/2023 6:48 PM, Richard Damon wrote:
>>>>>>>>>>> On 5/6/23 6:29 PM, olcott wrote:
>>>>>>>>>>>> On 5/6/2023 3:45 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 5/6/23 2:36 PM, olcott wrote:
>>>>>>>>>>>>>> On 4/28/2023 6:40 AM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 4/28/23 12:23 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 4/27/2023 9:41 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 4/27/23 9:07 PM, olcott wrote:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> The standard definition of mathematical incompleteness:
>>>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Remember, that if φ ∈ F then φ has a defined truth
>>>>>>>>>>>>>>>>> value in F, it is either True of False, and thus can't
>>>>>>>>>>>>>>>>> be the "Liar's Paradox".
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> How about this one?
>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You use of terms that you do not define doesn't help you.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Incomplete means, in actual words, that there exists a
>>>>>>>>>>>>>>> true statement in F that can not be proven in F, or
>>>>>>>>>>>>>>> similarly a False statement in F that can not be
>>>>>>>>>>>>>>> disproven (proven to be false).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I don't think that there is any source that says it is a
>>>>>>>>>>>>>> true statement in F.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Except that Godel has PROVEN (in Meta-F) that G actually IS
>>>>>>>>>>>>> true in F.
>>>>>>>>>>>>>
>>>>>>>>>>>> Please show me where it says that
>>>>>>>>>>>>
>>>>>>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Page 41 (marked as 44 of the PDF)
>>>>>>>>>>>
>>>>>>>>>>>  From the remark that [R(q); q] asserts its own
>>>>>>>>>>> unprovability, it follows at once that [R(q); q] is correct,
>>>>>>>>>>> since [R(q); q] is certainly unprovable (because
>>>>>>>>>>> undecidable). So the proposition which is undecidable in the
>>>>>>>>>>> system PM yet turns out to be decided by metamathematical
>>>>>>>>>>> considerations. The close analysis of this remarkable
>>>>>>>>>>> circumstance leads to surprising results concerning proofs of
>>>>>>>>>>> consistency of formal systems, which are dealt with in more
>>>>>>>>>>> detail in Section 4 (Proposition XI).
>>>>>>>>>>
>>>>>>>>>> As I suspected it says nothing about being true in PM.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> It says it is CORRECT, which mean the assertion is TRUE (in P
>>>>>>>>> and in the meta).
>>>>>>>>>
>>>>>>>>
>>>>>>>> It says nothing about being correct or true in PM.
>>>>>>>> In PM it is undecidable, thus not correct, true, false in PM.
>>>>>>>
>>>>>>> Nope, you don't understand that while it is undecideable in the
>>>>>>> system PM (and thus not PROVABLE or REFUTABLE in PM), it IS shown
>>>>>>> to be true in the metamathematical system, and thus also true in PM,
>>>>>>
>>>>>> Epidemiologically that is not the way that truth is derived.
>>>>>
>>>>> Can you actually quote a RULE that says that?
>>>>>
>>>>> You can KNOW that something is true because you can prove that it
>>>>> is true using another system with the right connections to that
>>>>> original system.
>>>>>
>>>>> KNOWLEDGE is not constrained by the same rules that proofs are. A
>>>>> proof "in a system" can only use the truth makers of that system.
>>>>
>>>> Hence G is not true in PM.
>>>
>>> Nope, you are just proving you don't know a thing about what you are
>>> talking about.
>>>
>>> I said you couldn't PROVE G in PM, that says NOTHING about it not
>>> being True in PM, or about what we can KNOW about G in PM.
>>
>> When PM is asked is G true or false PM says I have no idea.
>>
>>
>
> But you don't "Ask" the system for what it knows, that isn't how logic
> works. That PM will "say" "I have no idea" just shows that in PM the
> problem is undecidable (which deals with PROVALBE in PM, not TRUTH in PM).
>

Epistemic closure ... It is the principle that if a subject S knows p,
and S knows that p entails q, then S can thereby come to know q.
https://en.wikipedia.org/wiki/Epistemic_closure

Knowledge is really only truth that we are aware of. In this case the
subject is PM and PM is helpless to entail anything about G.

>
> You are just PROVING you are a pathological lying idiot reguarding how
> logic works.
>
> We can show that G *IS* true in PM, as we can prove that no such number
> CAN exist in the mathematics of PM to make G false, that means that G is
> true.
>

Since PM has no way to derive this, PM has no knowledge of this.

> There is no such option as "Not a Truth Bearer" when asking if a number
> exists that matchs a computable criteria.
>

"[R(q); q] asserts its own unprovability"
The whole numerical aspect is intended to be an isomorphism to that.

> You are just proving yourself to be an idiot. You just are stuck on
> INCORRECT definition that you have gaslite youself with, making yourself
> into that self-made pathological lying idiot.

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

On 5/6/23 11:07 PM, olcott wrote:
> On 5/6/2023 9:49 PM, Richard Damon wrote:
>> On 5/6/23 10:34 PM, olcott wrote:
>>> On 5/6/2023 9:28 PM, Richard Damon wrote:
>>>> On 5/6/23 10:13 PM, olcott wrote:
>>>>> On 5/6/2023 8:46 PM, Richard Damon wrote:
>>>>>> On 5/6/23 9:20 PM, olcott wrote:
>>>>>>> On 5/6/2023 8:06 PM, Richard Damon wrote:
>>>>>>>> On 5/6/23 8:49 PM, olcott wrote:
>>>>>>>>> On 5/6/2023 7:31 PM, Richard Damon wrote:
>>>>>>>>>> On 5/6/23 8:11 PM, olcott wrote:
>>>>>>>>>>> On 5/6/2023 6:48 PM, Richard Damon wrote:
>>>>>>>>>>>> On 5/6/23 6:29 PM, olcott wrote:
>>>>>>>>>>>>> On 5/6/2023 3:45 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 5/6/23 2:36 PM, olcott wrote:
>>>>>>>>>>>>>>> On 4/28/2023 6:40 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 4/28/23 12:23 AM, olcott wrote:
>>>>>>>>>>>>>>>>> On 4/27/2023 9:41 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 4/27/23 9:07 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> The standard definition of mathematical incompleteness:
>>>>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Remember, that if φ ∈ F then φ has a defined truth
>>>>>>>>>>>>>>>>>> value in F, it is either True of False, and thus can't
>>>>>>>>>>>>>>>>>> be the "Liar's Paradox".
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> How about this one?
>>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You use of terms that you do not define doesn't help you.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Incomplete means, in actual words, that there exists a
>>>>>>>>>>>>>>>> true statement in F that can not be proven in F, or
>>>>>>>>>>>>>>>> similarly a False statement in F that can not be
>>>>>>>>>>>>>>>> disproven (proven to be false).
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I don't think that there is any source that says it is a
>>>>>>>>>>>>>>> true statement in F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Except that Godel has PROVEN (in Meta-F) that G actually
>>>>>>>>>>>>>> IS true in F.
>>>>>>>>>>>>>>
>>>>>>>>>>>>> Please show me where it says that
>>>>>>>>>>>>>
>>>>>>>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Page 41 (marked as 44 of the PDF)
>>>>>>>>>>>>
>>>>>>>>>>>>  From the remark that [R(q); q] asserts its own
>>>>>>>>>>>> unprovability, it follows at once that [R(q); q] is correct,
>>>>>>>>>>>> since [R(q); q] is certainly unprovable (because
>>>>>>>>>>>> undecidable). So the proposition which is undecidable in the
>>>>>>>>>>>> system PM yet turns out to be decided by metamathematical
>>>>>>>>>>>> considerations. The close analysis of this remarkable
>>>>>>>>>>>> circumstance leads to surprising results concerning proofs
>>>>>>>>>>>> of consistency of formal systems, which are dealt with in
>>>>>>>>>>>> more detail in Section 4 (Proposition XI).
>>>>>>>>>>>
>>>>>>>>>>> As I suspected it says nothing about being true in PM.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It says it is CORRECT, which mean the assertion is TRUE (in P
>>>>>>>>>> and in the meta).
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> It says nothing about being correct or true in PM.
>>>>>>>>> In PM it is undecidable, thus not correct, true, false in PM.
>>>>>>>>
>>>>>>>> Nope, you don't understand that while it is undecideable in the
>>>>>>>> system PM (and thus not PROVABLE or REFUTABLE in PM), it IS
>>>>>>>> shown to be true in the metamathematical system, and thus also
>>>>>>>> true in PM,
>>>>>>>
>>>>>>> Epidemiologically that is not the way that truth is derived.
>>>>>>
>>>>>> Can you actually quote a RULE that says that?
>>>>>>
>>>>>> You can KNOW that something is true because you can prove that it
>>>>>> is true using another system with the right connections to that
>>>>>> original system.
>>>>>>
>>>>>> KNOWLEDGE is not constrained by the same rules that proofs are. A
>>>>>> proof "in a system" can only use the truth makers of that system.
>>>>>
>>>>> Hence G is not true in PM.
>>>>
>>>> Nope, you are just proving you don't know a thing about what you are
>>>> talking about.
>>>>
>>>> I said you couldn't PROVE G in PM, that says NOTHING about it not
>>>> being True in PM, or about what we can KNOW about G in PM.
>>>
>>> When PM is asked is G true or false PM says I have no idea.
>>>
>>>
>>
>> But you don't "Ask" the system for what it knows, that isn't how logic
>> works. That PM will "say" "I have no idea" just shows that in PM the
>> problem is undecidable (which deals with PROVALBE in PM, not TRUTH in
>> PM).
>>
>
> Epistemic closure ... It is the principle that if a subject S knows p,
> and S knows that p entails q, then S can thereby come to know q.
> https://en.wikipedia.org/wiki/Epistemic_closure
>
> Knowledge is really only truth that we are aware of. In this case the
> subject is PM and PM is helpless to entail anything about G.

But we are talking about TRUTH, not KNOWLEDGE.

You are just proving YOUR LACK of ACTUAL KNOWLEDGE, showing you are an
ignorant idiot.

You have sunk any possibility that anyone might be interested in your
concepts of truth, since you have shown you totally don't know what it
means.

>
>>
>> You are just PROVING you are a pathological lying idiot reguarding how
>> logic works.
>>
>> We can show that G *IS* true in PM, as we can prove that no such
>> number CAN exist in the mathematics of PM to make G false, that means
>> that G is true.
>>
>
> Since PM has no way to derive this, PM has no knowledge of this.

But WE do, and that is what matters.

You don't seem to understand the difference between Truth and Knowledge.

>
>> There is no such option as "Not a Truth Bearer" when asking if a
>> number exists that matchs a computable criteria.
>>
>
> "[R(q); q] asserts its own unprovability"
> The whole numerical aspect is intended to be an isomorphism to that.

On 5/6/2023 10:15 PM, Richard Damon wrote:
> On 5/6/23 11:07 PM, olcott wrote:
>> On 5/6/2023 9:49 PM, Richard Damon wrote:
>>> On 5/6/23 10:34 PM, olcott wrote:
>>>> On 5/6/2023 9:28 PM, Richard Damon wrote:
>>>>> On 5/6/23 10:13 PM, olcott wrote:
>>>>>> On 5/6/2023 8:46 PM, Richard Damon wrote:
>>>>>>> On 5/6/23 9:20 PM, olcott wrote:
>>>>>>>> On 5/6/2023 8:06 PM, Richard Damon wrote:
>>>>>>>>> On 5/6/23 8:49 PM, olcott wrote:
>>>>>>>>>> On 5/6/2023 7:31 PM, Richard Damon wrote:
>>>>>>>>>>> On 5/6/23 8:11 PM, olcott wrote:
>>>>>>>>>>>> On 5/6/2023 6:48 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 5/6/23 6:29 PM, olcott wrote:
>>>>>>>>>>>>>> On 5/6/2023 3:45 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 5/6/23 2:36 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 4/28/2023 6:40 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 4/28/23 12:23 AM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 4/27/2023 9:41 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 4/27/23 9:07 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> The standard definition of mathematical incompleteness:
>>>>>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Remember, that if φ ∈ F then φ has a defined truth
>>>>>>>>>>>>>>>>>>> value in F, it is either True of False, and thus
>>>>>>>>>>>>>>>>>>> can't be the "Liar's Paradox".
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> How about this one?
>>>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> You use of terms that you do not define doesn't help you.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Incomplete means, in actual words, that there exists a
>>>>>>>>>>>>>>>>> true statement in F that can not be proven in F, or
>>>>>>>>>>>>>>>>> similarly a False statement in F that can not be
>>>>>>>>>>>>>>>>> disproven (proven to be false).
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I don't think that there is any source that says it is a
>>>>>>>>>>>>>>>> true statement in F.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Except that Godel has PROVEN (in Meta-F) that G actually
>>>>>>>>>>>>>>> IS true in F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Please show me where it says that
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Page 41 (marked as 44 of the PDF)
>>>>>>>>>>>>>
>>>>>>>>>>>>>  From the remark that [R(q); q] asserts its own
>>>>>>>>>>>>> unprovability, it follows at once that [R(q); q] is
>>>>>>>>>>>>> correct, since [R(q); q] is certainly unprovable (because
>>>>>>>>>>>>> undecidable). So the proposition which is undecidable in
>>>>>>>>>>>>> the system PM yet turns out to be decided by
>>>>>>>>>>>>> metamathematical considerations. The close analysis of this
>>>>>>>>>>>>> remarkable circumstance leads to surprising results
>>>>>>>>>>>>> concerning proofs of consistency of formal systems, which
>>>>>>>>>>>>> are dealt with in more detail in Section 4 (Proposition XI).
>>>>>>>>>>>>
>>>>>>>>>>>> As I suspected it says nothing about being true in PM.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> It says it is CORRECT, which mean the assertion is TRUE (in P
>>>>>>>>>>> and in the meta).
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It says nothing about being correct or true in PM.
>>>>>>>>>> In PM it is undecidable, thus not correct, true, false in PM.
>>>>>>>>>
>>>>>>>>> Nope, you don't understand that while it is undecideable in the
>>>>>>>>> system PM (and thus not PROVABLE or REFUTABLE in PM), it IS
>>>>>>>>> shown to be true in the metamathematical system, and thus also
>>>>>>>>> true in PM,
>>>>>>>>
>>>>>>>> Epidemiologically that is not the way that truth is derived.
>>>>>>>
>>>>>>> Can you actually quote a RULE that says that?
>>>>>>>
>>>>>>> You can KNOW that something is true because you can prove that it
>>>>>>> is true using another system with the right connections to that
>>>>>>> original system.
>>>>>>>
>>>>>>> KNOWLEDGE is not constrained by the same rules that proofs are. A
>>>>>>> proof "in a system" can only use the truth makers of that system.
>>>>>>
>>>>>> Hence G is not true in PM.
>>>>>
>>>>> Nope, you are just proving you don't know a thing about what you
>>>>> are talking about.
>>>>>
>>>>> I said you couldn't PROVE G in PM, that says NOTHING about it not
>>>>> being True in PM, or about what we can KNOW about G in PM.
>>>>
>>>> When PM is asked is G true or false PM says I have no idea.
>>>>
>>>>
>>>
>>> But you don't "Ask" the system for what it knows, that isn't how
>>> logic works. That PM will "say" "I have no idea" just shows that in
>>> PM the problem is undecidable (which deals with PROVALBE in PM, not
>>> TRUTH in PM).
>>>
>>
>> Epistemic closure ... It is the principle that if a subject S knows p,
>> and S knows that p entails q, then S can thereby come to know q.
>> https://en.wikipedia.org/wiki/Epistemic_closure
>>
>> Knowledge is really only truth that we are aware of. In this case the
>> subject is PM and PM is helpless to entail anything about G.
>
> But we are talking about TRUTH, not KNOWLEDGE.
>

The only difference between truth and knowledge is that truth includes
expressions of language that we are unaware of or expressions of
language with unknown truth values. The G is unprovable in PM is
known by us and known by metamathematics and unknown by PM.

>> "[R(q); q] asserts its own unprovability"
>> The whole numerical aspect is intended to be an isomorphism to that.
>
> So, it is a FACT that [R(q); q] is actually TRUE, but unprovable within
> the system PM. You haven't found an error in that proof,

On 5/6/23 11:39 PM, olcott wrote:
> On 5/6/2023 10:15 PM, Richard Damon wrote:
>> On 5/6/23 11:07 PM, olcott wrote:
>>> On 5/6/2023 9:49 PM, Richard Damon wrote:
>>>> On 5/6/23 10:34 PM, olcott wrote:
>>>>> On 5/6/2023 9:28 PM, Richard Damon wrote:
>>>>>> On 5/6/23 10:13 PM, olcott wrote:
>>>>>>> On 5/6/2023 8:46 PM, Richard Damon wrote:
>>>>>>>> On 5/6/23 9:20 PM, olcott wrote:
>>>>>>>>> On 5/6/2023 8:06 PM, Richard Damon wrote:
>>>>>>>>>> On 5/6/23 8:49 PM, olcott wrote:
>>>>>>>>>>> On 5/6/2023 7:31 PM, Richard Damon wrote:
>>>>>>>>>>>> On 5/6/23 8:11 PM, olcott wrote:
>>>>>>>>>>>>> On 5/6/2023 6:48 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 5/6/23 6:29 PM, olcott wrote:
>>>>>>>>>>>>>>> On 5/6/2023 3:45 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 5/6/23 2:36 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 4/28/2023 6:40 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 4/28/23 12:23 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 4/27/2023 9:41 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 4/27/23 9:07 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> The standard definition of mathematical
>>>>>>>>>>>>>>>>>>>>> incompleteness:
>>>>>>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Remember, that if φ ∈ F then φ has a defined truth
>>>>>>>>>>>>>>>>>>>> value in F, it is either True of False, and thus
>>>>>>>>>>>>>>>>>>>> can't be the "Liar's Paradox".
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> How about this one?
>>>>>>>>>>>>>>>>>>> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> You use of terms that you do not define doesn't help you.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Incomplete means, in actual words, that there exists a
>>>>>>>>>>>>>>>>>> true statement in F that can not be proven in F, or
>>>>>>>>>>>>>>>>>> similarly a False statement in F that can not be
>>>>>>>>>>>>>>>>>> disproven (proven to be false).
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> I don't think that there is any source that says it is
>>>>>>>>>>>>>>>>> a true statement in F.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Except that Godel has PROVEN (in Meta-F) that G actually
>>>>>>>>>>>>>>>> IS true in F.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Please show me where it says that
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Page 41 (marked as 44 of the PDF)
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>  From the remark that [R(q); q] asserts its own
>>>>>>>>>>>>>> unprovability, it follows at once that [R(q); q] is
>>>>>>>>>>>>>> correct, since [R(q); q] is certainly unprovable (because
>>>>>>>>>>>>>> undecidable). So the proposition which is undecidable in
>>>>>>>>>>>>>> the system PM yet turns out to be decided by
>>>>>>>>>>>>>> metamathematical considerations. The close analysis of
>>>>>>>>>>>>>> this remarkable circumstance leads to surprising results
>>>>>>>>>>>>>> concerning proofs of consistency of formal systems, which
>>>>>>>>>>>>>> are dealt with in more detail in Section 4 (Proposition XI).
>>>>>>>>>>>>>
>>>>>>>>>>>>> As I suspected it says nothing about being true in PM.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> It says it is CORRECT, which mean the assertion is TRUE (in
>>>>>>>>>>>> P and in the meta).
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> It says nothing about being correct or true in PM.
>>>>>>>>>>> In PM it is undecidable, thus not correct, true, false in PM.
>>>>>>>>>>
>>>>>>>>>> Nope, you don't understand that while it is undecideable in
>>>>>>>>>> the system PM (and thus not PROVABLE or REFUTABLE in PM), it
>>>>>>>>>> IS shown to be true in the metamathematical system, and thus
>>>>>>>>>> also true in PM,
>>>>>>>>>
>>>>>>>>> Epidemiologically that is not the way that truth is derived.
>>>>>>>>
>>>>>>>> Can you actually quote a RULE that says that?
>>>>>>>>
>>>>>>>> You can KNOW that something is true because you can prove that
>>>>>>>> it is true using another system with the right connections to
>>>>>>>> that original system.
>>>>>>>>
>>>>>>>> KNOWLEDGE is not constrained by the same rules that proofs are.
>>>>>>>> A proof "in a system" can only use the truth makers of that system.
>>>>>>>
>>>>>>> Hence G is not true in PM.
>>>>>>
>>>>>> Nope, you are just proving you don't know a thing about what you
>>>>>> are talking about.
>>>>>>
>>>>>> I said you couldn't PROVE G in PM, that says NOTHING about it not
>>>>>> being True in PM, or about what we can KNOW about G in PM.
>>>>>
>>>>> When PM is asked is G true or false PM says I have no idea.
>>>>>
>>>>>
>>>>
>>>> But you don't "Ask" the system for what it knows, that isn't how
>>>> logic works. That PM will "say" "I have no idea" just shows that in
>>>> PM the problem is undecidable (which deals with PROVALBE in PM, not
>>>> TRUTH in PM).
>>>>
>>>
>>> Epistemic closure ... It is the principle that if a subject S knows
>>> p, and S knows that p entails q, then S can thereby come to know q.
>>> https://en.wikipedia.org/wiki/Epistemic_closure
>>>
>>> Knowledge is really only truth that we are aware of. In this case the
>>> subject is PM and PM is helpless to entail anything about G.
>>
>> But we are talking about TRUTH, not KNOWLEDGE.
>>
>
> The only difference between truth and knowledge is that truth includes
> expressions of language that we are unaware of or expressions of
> language with unknown truth values. The G is unprovable in PM is
> known by us and known by metamathematics and unknown by PM.