On Monday, January 16, 2023 at 9:17:09 AM UTC-6, olcott wrote:
> On 1/15/2023 11:05 AM, Richard Damon wrote:
> > On 1/15/23 11:15 AM, olcott wrote:
> >> On 1/14/2023 5:42 PM, Richard Damon wrote:
> >>> On 1/14/23 6:19 PM, olcott wrote:
> >>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
> >>>>> On 1/14/23 5:31 PM, olcott wrote:
> >>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
> >>>>>>> On 1/14/23 4:48 PM, olcott wrote:
> >>>>>>>> How does the formal system know that an expression of language
> >>>>>>>> of this
> >>>>>>>> formal system is true unless this expression of language has a
> >>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
> >>>>>>>>
> >>>>>>>>
> >>>>>>>
> >>>>>>> Becaue the formal system doesn't need to KNOW what is true.
> >>>>>>>
> >>>>>>
> >>>>>> So PA has no idea that:
> >>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
> >>>>>>
> >>>>>
> >>>>> Why do you say that.
> >>>>>
> >>>>> Just because truth doesn't NEED to be proven for it to be true,
> >>>>> doesn't mean it can't be.
> >>>>>
> >>>>> In fact, your statement just comes out of a simple application of
> >>>>> the addition AXIOMS of PA.
> >>>>>
> >>>>> a + 0 = a
> >>>>> a + Successor(b) = Successor(a + b)
> >>>>>
> >>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
> >>>>>
> >>>>
> >>>> Unless a formal system has a syntactic connection from an expression of
> >>>> its language to its truth maker axioms the expression is untrue in that
> >>>> formal system.
> >>>
> >>> Right, but the connection can be infinite in length, and thus not
> >>> provable.
> >>>
> >>>>
> >>>> Try and show an expression of language that is true in a formal system
> >>>> (not just true somewhere else) that does not have any connection to
> >>>> truth maker axioms in this formal system. You must show why it is true
> >>>> in this formal system not merely that it is true somewhere else.
> >>>>
> >>>
> >>> The connection might be infinite, and thus not SHOWABLE as a proof
> >>> strictly in the formal system.
> >>>
> >>> If the connection exists as an infinite connection within the system,
> >>> then it is TRUE in the system.
> >>>
> >>> Note, that if there is such an infinite connection, which thus can
> >>> not be proven within the formal system, it is still possible, that
> >>> another system, related to that system, with more knowledge, might be
> >>> able to show that there does exist within the original formal system
> >>> such an infinte connection.
> >>>
> >>> This is what happens to G in F and meta-F
> >>>
> >>> G states that there does not exist a Natural Number g that meets a
> >>> specific requirement (expressed as a primative recursive relationship).
> >>>
> >>> This statement turns out to be true, because it turns out that no
> >>> number g does meet that requirement, but it can't be proven in F that
> >>> this is true, because in F, to show this we need to test every
> >>> natuarl number, which requires an infinite number of steps (finite
> >>> for each number, but an infinite number of numbers to test).
> >>>
> >>> In meta-F, we can do better, because due to additional knowledge in
> >>> meta-F, we can show that if a number g could be found, then that
> >>> number g could be converted into a proof, in F, of the statement G
> >>> (which says that such a number does not exist).
> >>>
> >>> Thus, in meta-F, we can prove that G is true, and also show that no
> >>> proof of it can exist in F.
> >>>
> >> So your basic line-of-reasoning is that G is true in F even if the truth
> >> of G cannot even be expressed in F as long as the truth of G can be
> >> expressed in meta-F.
> >>
> >
> > Expect that it CAN be expressed in F, it just is an infinite expression..
> >
> So you changed your mind about infinite proofs in formal systems?
> We know the steps of the infinite proof for the Goldbach conjecture.
>
> What are the infinite steps to show that a self-contradictory expression
> is provable?
> --
> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

One day my coworker came up to me and said "Don Stockbauer, my twin girls were watching TV and they came running up to me saying "Mommy, mommy, there's a woman on TV and she's saying that she's a Man!!!!" My coworker went into the TV room and it was Boy George!!!!! I thought that was really funny!!!!!

On 1/15/2023 7:15 PM, Richard Damon wrote:
> On 1/15/23 7:56 PM, olcott wrote:
>> On 1/15/2023 6:47 PM, Richard Damon wrote:
>>> On 1/15/23 7:26 PM, olcott wrote:
>>>> On 1/15/2023 2:23 PM, Richard Damon wrote:
>>>>> On 1/15/23 3:12 PM, olcott wrote:
>>>>>> On 1/15/2023 1:46 PM, Richard Damon wrote:
>>>>>>> On 1/15/23 2:29 PM, olcott wrote:
>>>>>>>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>>>>>>>> On 1/15/23 2:00 PM, olcott wrote:
>>>>>>>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>>>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> How does the formal system know that an
>>>>>>>>>>>>>>>>>>>>>>>> expression of language of this
>>>>>>>>>>>>>>>>>>>>>>>> formal system is true unless this expression of
>>>>>>>>>>>>>>>>>>>>>>>> language has a
>>>>>>>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL
>>>>>>>>>>>>>>>>>>>>>>>> SYSTEM* ???
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW
>>>>>>>>>>>>>>>>>>>>>>> what is true.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) +
>>>>>>>>>>>>>>>>>>>>>> successor(0) is true ???
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for it
>>>>>>>>>>>>>>>>>>>>> to be true, doesn't mean it can't be.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually
>>>>>>>>>>>>>>>>>>>>> KNOWN to be true.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Unless a formal system has a syntactic connection
>>>>>>>>>>>>>>>>>>>> from an expression of
>>>>>>>>>>>>>>>>>>>> its language to its truth maker axioms the
>>>>>>>>>>>>>>>>>>>> expression is untrue in that
>>>>>>>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Right, but the connection can be infinite in length,
>>>>>>>>>>>>>>>>>>> and thus not provable.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Try and show an expression of language that is true
>>>>>>>>>>>>>>>>>>>> in a formal system
>>>>>>>>>>>>>>>>>>>> (not just true somewhere else) that does not have
>>>>>>>>>>>>>>>>>>>> any connection to
>>>>>>>>>>>>>>>>>>>> truth maker axioms in this formal system. You must
>>>>>>>>>>>>>>>>>>>> show why it is true
>>>>>>>>>>>>>>>>>>>> in this formal system not merely that it is true
>>>>>>>>>>>>>>>>>>>> somewhere else.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> The connection might be infinite, and thus not
>>>>>>>>>>>>>>>>>>> SHOWABLE as a proof strictly in the formal system.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> If the connection exists as an infinite connection
>>>>>>>>>>>>>>>>>>> within the system, then it is TRUE in the system.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Note, that if there is such an infinite connection,
>>>>>>>>>>>>>>>>>>> which thus can not be proven within the formal
>>>>>>>>>>>>>>>>>>> system, it is still possible, that another system,
>>>>>>>>>>>>>>>>>>> related to that system, with more knowledge, might be
>>>>>>>>>>>>>>>>>>> able to show that there does exist within the
>>>>>>>>>>>>>>>>>>> original formal system such an infinte connection.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> G states that there does not exist a Natural Number g
>>>>>>>>>>>>>>>>>>> that meets a specific requirement (expressed as a
>>>>>>>>>>>>>>>>>>> primative recursive relationship).
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> This statement turns out to be true, because it turns
>>>>>>>>>>>>>>>>>>> out that no number g does meet that requirement, but
>>>>>>>>>>>>>>>>>>> it can't be proven in F that this is true, because in
>>>>>>>>>>>>>>>>>>> F, to show this we need to test every natuarl number,
>>>>>>>>>>>>>>>>>>> which requires an infinite number of steps (finite
>>>>>>>>>>>>>>>>>>> for each number, but an infinite number of numbers to
>>>>>>>>>>>>>>>>>>> test).
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> In meta-F, we can do better, because due to
>>>>>>>>>>>>>>>>>>> additional knowledge in meta-F, we can show that if a
>>>>>>>>>>>>>>>>>>> number g could be found, then that number g could be
>>>>>>>>>>>>>>>>>>> converted into a proof, in F, of the statement G
>>>>>>>>>>>>>>>>>>> (which says that such a number does not exist).
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and
>>>>>>>>>>>>>>>>>>> also show that no proof of it can exist in F.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> So your basic line-of-reasoning is that G is true in F
>>>>>>>>>>>>>>>>>> even if the truth
>>>>>>>>>>>>>>>>>> of G cannot even be expressed in F as long as the
>>>>>>>>>>>>>>>>>> truth of G can be
>>>>>>>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Expect that it CAN be expressed in F, it just is an
>>>>>>>>>>>>>>>>> infinite expression.
>>>>>>>>>>>>>>>> That is false. It is not that G takes an infinite number
>>>>>>>>>>>>>>>> of steps to
>>>>>>>>>>>>>>>> reach its truth maker axioms in F it is that even after
>>>>>>>>>>>>>>>> an infinite
>>>>>>>>>>>>>>>> number of steps it never reaches is truth maker axioms
>>>>>>>>>>>>>>>> in F because G is
>>>>>>>>>>>>>>>> simply untrue in F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> No, YOUR problem is you aren't actually talking about G
>>>>>>>>>>>>>>> in F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> "This sentence is not true"
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Which isn't G.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Not true about what?
>>>>>>>>>>>>>>>> Not true about being not true.
>>>>>>>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> So you are just a MORON.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Since Gödel said:
>>>>>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be used
>>>>>>>>>>>>>>>> for a similar undecidability proof.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy for
>>>>>>>>>>>>>>>> his proof we
>>>>>>>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Ad Hominem attacks are the tactic that people having no
>>>>>>>>>>>>>> interest in any
>>>>>>>>>>>>>> honest dialogue use when they realize that their reasoning
>>>>>>>>>>>>>> has been
>>>>>>>>>>>>>> utterly defeated.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>>>>>>>
>>>>>>>>>>>>> You ARE a LYING MORON as you insist that Godel's G is a
>>>>>>>>>>>>> sentence that is actually provably isn't.
>>>>>>>>>>>>>
>>>>>>>>>>>>> You think it is because you are too stupid to actually read
>>>>>>>>>>>>> any of the paper, so you take that comment that the
>>>>>>>>>>>>> statment is "based" on that statement to mean it IS that
>>>>>>>>>>>>> statement.
>>>>>>>>>>>>>
>>>>>>>>>>>> All of your Ad Hominem attacks cannot possibly hide the fact
>>>>>>>>>>>> that you
>>>>>>>>>>>> are asserting this counter-factual statement:
>>>>>>>>>>>>
>>>>>>>>>>>> when a valid proxy for an argument is defeated this does not
>>>>>>>>>>>> defeat the
>>>>>>>>>>>> original argument.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Right, which is what YOU are doing, showing your arguement is
>>>>>>>>>>> INVALID.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> In other words you disagree that correctly refuting a valid
>>>>>>>>>> proxy for an
>>>>>>>>>> argument does correctly refute the original argument?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> VALID is the key word,
>>>>>>>>>
>>>>>>>>> Yours isn't (I don't think you actually know the meaning of the
>>>>>>>>> words)
>>>>>>>>>
>>>>>>>>> And you are an IDIOT to claim it is.
>>>>>>>> So Gödel is wrong when he says:
>>>>>>>>
>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>> similar undecidability proof.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> No, but you don't understand what he is saying.
>>>>>>>
>>>>>> He is saying that every epistemological antinomy is a valid proxy for
>>>>>> his proof. He is not saying that his expression is not an
>>>>>> epistemological antinomy.
>>>>>>
>>>>>
>>>>> Nope, that isn't what he is saying. How could it be, the ACTUAL G
>>>>> is a proven Truth Bearer, while the Liar's Paradox isn't
>>>>>
>>>>> Your arguement just shows its inconsistency.
>>>>>
>>>>> In part, because you don't actually understand what the sentence
>>>>> actually is.
>>>>>
>>>>>
>>>>>> The analogy between this result and Richard’s antinomy leaps to
>>>>>> the eye;
>>>>>> there is also a close relationship with the “liar” antinomy,14
>>>>>> since the
>>>>>> undecidable proposition [R(q); q] states precisely that q belongs
>>>>>> to K,
>>>>>> i.e. according to (1), that [R(q); q] is not provable. We are
>>>>>> therefore
>>>>>> confronted with a proposition which asserts its own unprovability.
>>>>>> (Gödel 1931:43)
>>>>>>
>>>>>> This <is> an isomorphism to a proposition that asserts its own
>>>>>> untruth.
>>>>>>
>>>>>>
>>>>>
>>>>> Nope, unless you erroneously think that statements about Truth ARE
>>>>> statements about provability, that isn't an isomoprhism.
>>>>>
>>>>> Note, you have even stated that *ALL* statements of the form
>>>>> "statement x is provable" or "Statment x is not provable" are Truth
>>>>> Bearers,
>>>>
>>>> I have most definitely never said this or anything that could be
>>>> unintentionally misconstrued to mean this.
>>>>
>>>> It is always the case that when-so-ever any expression of language only
>>>> refers to its own truth or provability that this expression is not a
>>>> truth bearer, thus not a member of any formal system of logic.
>>>>
>>>
>>> You admitted that it was TRUE that a statement could not be proven
>>> even if the only way to show that it could not be proven was to check
>>> the infinite set of all possible proofs to see that none of them were
>>> a proof.
>>>
>>
>> This is not related to what I just said. Every expression of language is
>> untrue unless it has a semantic connection to its truth maker axiom.
>
> I never disagreed with that, just that you keep on wavering between just
> saying there must be a connection, and then at times adding it must be a
> FINITE connection (which is actually only requried to be Proven)
>
> G, the statment about the non-existance of a natural number that
> satisfies the specified primative recursive relationship is TRUE,
> because it IS connected to the truth maker axioms of math via an
> infinite chain of steps.
>
> Each natural number can be shown to not meet that requirement in a
Gödel was actually talking about the expression:

On 1/16/23 4:51 PM, olcott wrote:
> On 1/15/2023 7:15 PM, Richard Damon wrote:
>> On 1/15/23 7:56 PM, olcott wrote:
>>> On 1/15/2023 6:47 PM, Richard Damon wrote:
>>>> On 1/15/23 7:26 PM, olcott wrote:
>>>>> On 1/15/2023 2:23 PM, Richard Damon wrote:
>>>>>> On 1/15/23 3:12 PM, olcott wrote:
>>>>>>> On 1/15/2023 1:46 PM, Richard Damon wrote:
>>>>>>>> On 1/15/23 2:29 PM, olcott wrote:
>>>>>>>>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>>>>>>>>> On 1/15/23 2:00 PM, olcott wrote:
>>>>>>>>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>>>>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> How does the formal system know that an
>>>>>>>>>>>>>>>>>>>>>>>>> expression of language of this
>>>>>>>>>>>>>>>>>>>>>>>>> formal system is true unless this expression of
>>>>>>>>>>>>>>>>>>>>>>>>> language has a
>>>>>>>>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS
>>>>>>>>>>>>>>>>>>>>>>>>> FORMAL SYSTEM* ???
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW
>>>>>>>>>>>>>>>>>>>>>>>> what is true.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) +
>>>>>>>>>>>>>>>>>>>>>>> successor(0) is true ???
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for
>>>>>>>>>>>>>>>>>>>>>> it to be true, doesn't mean it can't be.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually
>>>>>>>>>>>>>>>>>>>>>> KNOWN to be true.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Unless a formal system has a syntactic connection
>>>>>>>>>>>>>>>>>>>>> from an expression of
>>>>>>>>>>>>>>>>>>>>> its language to its truth maker axioms the
>>>>>>>>>>>>>>>>>>>>> expression is untrue in that
>>>>>>>>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Right, but the connection can be infinite in length,
>>>>>>>>>>>>>>>>>>>> and thus not provable.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Try and show an expression of language that is true
>>>>>>>>>>>>>>>>>>>>> in a formal system
>>>>>>>>>>>>>>>>>>>>> (not just true somewhere else) that does not have
>>>>>>>>>>>>>>>>>>>>> any connection to
>>>>>>>>>>>>>>>>>>>>> truth maker axioms in this formal system. You must
>>>>>>>>>>>>>>>>>>>>> show why it is true
>>>>>>>>>>>>>>>>>>>>> in this formal system not merely that it is true
>>>>>>>>>>>>>>>>>>>>> somewhere else.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> The connection might be infinite, and thus not
>>>>>>>>>>>>>>>>>>>> SHOWABLE as a proof strictly in the formal system.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> If the connection exists as an infinite connection
>>>>>>>>>>>>>>>>>>>> within the system, then it is TRUE in the system.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Note, that if there is such an infinite connection,
>>>>>>>>>>>>>>>>>>>> which thus can not be proven within the formal
>>>>>>>>>>>>>>>>>>>> system, it is still possible, that another system,
>>>>>>>>>>>>>>>>>>>> related to that system, with more knowledge, might
>>>>>>>>>>>>>>>>>>>> be able to show that there does exist within the
>>>>>>>>>>>>>>>>>>>> original formal system such an infinte connection.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> G states that there does not exist a Natural Number
>>>>>>>>>>>>>>>>>>>> g that meets a specific requirement (expressed as a
>>>>>>>>>>>>>>>>>>>> primative recursive relationship).
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> This statement turns out to be true, because it
>>>>>>>>>>>>>>>>>>>> turns out that no number g does meet that
>>>>>>>>>>>>>>>>>>>> requirement, but it can't be proven in F that this
>>>>>>>>>>>>>>>>>>>> is true, because in F, to show this we need to test
>>>>>>>>>>>>>>>>>>>> every natuarl number, which requires an infinite
>>>>>>>>>>>>>>>>>>>> number of steps (finite for each number, but an
>>>>>>>>>>>>>>>>>>>> infinite number of numbers to test).
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> In meta-F, we can do better, because due to
>>>>>>>>>>>>>>>>>>>> additional knowledge in meta-F, we can show that if
>>>>>>>>>>>>>>>>>>>> a number g could be found, then that number g could
>>>>>>>>>>>>>>>>>>>> be converted into a proof, in F, of the statement G
>>>>>>>>>>>>>>>>>>>> (which says that such a number does not exist).
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and
>>>>>>>>>>>>>>>>>>>> also show that no proof of it can exist in F.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> So your basic line-of-reasoning is that G is true in
>>>>>>>>>>>>>>>>>>> F even if the truth
>>>>>>>>>>>>>>>>>>> of G cannot even be expressed in F as long as the
>>>>>>>>>>>>>>>>>>> truth of G can be
>>>>>>>>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Expect that it CAN be expressed in F, it just is an
>>>>>>>>>>>>>>>>>> infinite expression.
>>>>>>>>>>>>>>>>> That is false. It is not that G takes an infinite
>>>>>>>>>>>>>>>>> number of steps to
>>>>>>>>>>>>>>>>> reach its truth maker axioms in F it is that even after
>>>>>>>>>>>>>>>>> an infinite
>>>>>>>>>>>>>>>>> number of steps it never reaches is truth maker axioms
>>>>>>>>>>>>>>>>> in F because G is
>>>>>>>>>>>>>>>>> simply untrue in F.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> No, YOUR problem is you aren't actually talking about G
>>>>>>>>>>>>>>>> in F.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> "This sentence is not true"
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Which isn't G.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Not true about what?
>>>>>>>>>>>>>>>>> Not true about being not true.
>>>>>>>>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> So you are just a MORON.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Since Gödel said:
>>>>>>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be used
>>>>>>>>>>>>>>>>> for a similar undecidability proof.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy for
>>>>>>>>>>>>>>>>> his proof we
>>>>>>>>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Ad Hominem attacks are the tactic that people having no
>>>>>>>>>>>>>>> interest in any
>>>>>>>>>>>>>>> honest dialogue use when they realize that their
>>>>>>>>>>>>>>> reasoning has been
>>>>>>>>>>>>>>> utterly defeated.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You ARE a LYING MORON as you insist that Godel's G is a
>>>>>>>>>>>>>> sentence that is actually provably isn't.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You think it is because you are too stupid to actually
>>>>>>>>>>>>>> read any of the paper, so you take that comment that the
>>>>>>>>>>>>>> statment is "based" on that statement to mean it IS that
>>>>>>>>>>>>>> statement.
>>>>>>>>>>>>>>
>>>>>>>>>>>>> All of your Ad Hominem attacks cannot possibly hide the
>>>>>>>>>>>>> fact that you
>>>>>>>>>>>>> are asserting this counter-factual statement:
>>>>>>>>>>>>>
>>>>>>>>>>>>> when a valid proxy for an argument is defeated this does
>>>>>>>>>>>>> not defeat the
>>>>>>>>>>>>> original argument.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Right, which is what YOU are doing, showing your arguement
>>>>>>>>>>>> is INVALID.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> In other words you disagree that correctly refuting a valid
>>>>>>>>>>> proxy for an
>>>>>>>>>>> argument does correctly refute the original argument?
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> VALID is the key word,
>>>>>>>>>>
>>>>>>>>>> Yours isn't (I don't think you actually know the meaning of
>>>>>>>>>> the words)
>>>>>>>>>>
>>>>>>>>>> And you are an IDIOT to claim it is.
>>>>>>>>> So Gödel is wrong when he says:
>>>>>>>>>
>>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>>> similar undecidability proof.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> No, but you don't understand what he is saying.
>>>>>>>>
>>>>>>> He is saying that every epistemological antinomy is a valid proxy
>>>>>>> for
>>>>>>> his proof. He is not saying that his expression is not an
>>>>>>> epistemological antinomy.
>>>>>>>
>>>>>>
>>>>>> Nope, that isn't what he is saying. How could it be, the ACTUAL G
>>>>>> is a proven Truth Bearer, while the Liar's Paradox isn't
>>>>>>
>>>>>> Your arguement just shows its inconsistency.
>>>>>>
>>>>>> In part, because you don't actually understand what the sentence
>>>>>> actually is.
>>>>>>
>>>>>>
>>>>>>> The analogy between this result and Richard’s antinomy leaps to
>>>>>>> the eye;
>>>>>>> there is also a close relationship with the “liar” antinomy,14
>>>>>>> since the
>>>>>>> undecidable proposition [R(q); q] states precisely that q belongs
>>>>>>> to K,
>>>>>>> i.e. according to (1), that [R(q); q] is not provable. We are
>>>>>>> therefore
>>>>>>> confronted with a proposition which asserts its own unprovability.
>>>>>>> (Gödel 1931:43)
>>>>>>>
>>>>>>> This <is> an isomorphism to a proposition that asserts its own
>>>>>>> untruth.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Nope, unless you erroneously think that statements about Truth ARE
>>>>>> statements about provability, that isn't an isomoprhism.
>>>>>>
>>>>>> Note, you have even stated that *ALL* statements of the form
>>>>>> "statement x is provable" or "Statment x is not provable" are
>>>>>> Truth Bearers,
>>>>>
>>>>> I have most definitely never said this or anything that could be
>>>>> unintentionally misconstrued to mean this.
>>>>>
>>>>> It is always the case that when-so-ever any expression of language
>>>>> only
>>>>> refers to its own truth or provability that this expression is not a
>>>>> truth bearer, thus not a member of any formal system of logic.
>>>>>
>>>>
>>>> You admitted that it was TRUE that a statement could not be proven
>>>> even if the only way to show that it could not be proven was to
>>>> check the infinite set of all possible proofs to see that none of
>>>> them were a proof.
>>>>
>>>
>>> This is not related to what I just said. Every expression of language is
>>> untrue unless it has a semantic connection to its truth maker axiom.
>>
>> I never disagreed with that, just that you keep on wavering between
>> just saying there must be a connection, and then at times adding it
>> must be a FINITE connection (which is actually only requried to be
>> Proven)
>>
>> G, the statment about the non-existance of a natural number that
>> satisfies the specified primative recursive relationship is TRUE,
>> because it IS connected to the truth maker axioms of math via an
>> infinite chain of steps.
>>
>> Each natural number can be shown to not meet that requirement in a
> Gödel was actually talking about the expression:
>
> We are therefore confronted with a proposition which asserts its own
> unprovability. (Gödel 1931:43)

On 1/16/23 10:17 AM, olcott wrote:
> On 1/15/2023 11:05 AM, Richard Damon wrote:
>> On 1/15/23 11:15 AM, olcott wrote:
>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>> How does the formal system know that an expression of language
>>>>>>>>> of this
>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>
>>>>>>>
>>>>>>> So PA has no idea that:
>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>>>
>>>>>>
>>>>>> Why do you say that.
>>>>>>
>>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>>> doesn't mean it can't be.
>>>>>>
>>>>>> In fact, your statement just comes out of a simple application of
>>>>>> the addition AXIOMS of PA.
>>>>>>
>>>>>> a + 0 = a
>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>
>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>>
>>>>>
>>>>> Unless a formal system has a syntactic connection from an
>>>>> expression of
>>>>> its language to its truth maker axioms the expression is untrue in
>>>>> that
>>>>> formal system.
>>>>
>>>> Right, but the connection can be infinite in length, and thus not
>>>> provable.
>>>>
>>>>>
>>>>> Try and show an expression of language that is true in a formal system
>>>>> (not just true somewhere else) that does not have any connection to
>>>>> truth maker axioms in this formal system. You must show why it is true
>>>>> in this formal system not merely that it is true somewhere else.
>>>>>
>>>>
>>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>>> strictly in the formal system.
>>>>
>>>> If the connection exists as an infinite connection within the
>>>> system, then it is TRUE in the system.
>>>>
>>>> Note, that if there is such an infinite connection, which thus can
>>>> not be proven within the formal system, it is still possible, that
>>>> another system, related to that system, with more knowledge, might
>>>> be able to show that there does exist within the original formal
>>>> system such an infinte connection.
>>>>
>>>> This is what happens to G in F and meta-F
>>>>
>>>> G states that there does not exist a Natural Number g that meets a
>>>> specific requirement (expressed as a primative recursive relationship).
>>>>
>>>> This statement turns out to be true, because it turns out that no
>>>> number g does meet that requirement, but it can't be proven in F
>>>> that this is true, because in F, to show this we need to test every
>>>> natuarl number, which requires an infinite number of steps (finite
>>>> for each number, but an infinite number of numbers to test).
>>>>
>>>> In meta-F, we can do better, because due to additional knowledge in
>>>> meta-F, we can show that if a number g could be found, then that
>>>> number g could be converted into a proof, in F, of the statement G
>>>> (which says that such a number does not exist).
>>>>
>>>> Thus, in meta-F, we can prove that G is true, and also show that no
>>>> proof of it can exist in F.
>>>>
>>> So your basic line-of-reasoning is that G is true in F even if the truth
>>> of G cannot even be expressed in F as long as the truth of G can be
>>> expressed in meta-F.
>>>
>>
>> Expect that it CAN be expressed in F, it just is an infinite expression.
>>
> So you changed your mind about infinite proofs in formal systems?
> We know the steps of the infinite proof for the Goldbach conjecture.

No, because I am showing that G is TRUE, not PROVABLE. Truth can use
infinte sets oc connections, proofs can't. Only YOU have perposed that
we think about infinite proofs.

>
> What are the infinite steps to show that a self-contradictory expression
> is provable?
>

There are, because an actually self-contradictory expression isn't true.

G is TRUE (in F and in meta-F) because it has an infinite set of
statements that connect it totally to the Truth Makers of F, through the
system F.

"This statement is false", your self-contradictory expression doesn't
have a connection to the Truth Makers (infinite or otherwise).

On 1/16/2023 7:51 PM, Richard Damon wrote:
> On 1/16/23 4:51 PM, olcott wrote:
>> On 1/15/2023 7:15 PM, Richard Damon wrote:
>>> On 1/15/23 7:56 PM, olcott wrote:
>>>> On 1/15/2023 6:47 PM, Richard Damon wrote:
>>>>> On 1/15/23 7:26 PM, olcott wrote:
>>>>>> On 1/15/2023 2:23 PM, Richard Damon wrote:
>>>>>>> On 1/15/23 3:12 PM, olcott wrote:
>>>>>>>> On 1/15/2023 1:46 PM, Richard Damon wrote:
>>>>>>>>> On 1/15/23 2:29 PM, olcott wrote:
>>>>>>>>>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/15/23 2:00 PM, olcott wrote:
>>>>>>>>>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>>>>>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> How does the formal system know that an
>>>>>>>>>>>>>>>>>>>>>>>>>> expression of language of this
>>>>>>>>>>>>>>>>>>>>>>>>>> formal system is true unless this expression
>>>>>>>>>>>>>>>>>>>>>>>>>> of language has a
>>>>>>>>>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS
>>>>>>>>>>>>>>>>>>>>>>>>>> FORMAL SYSTEM* ???
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW
>>>>>>>>>>>>>>>>>>>>>>>>> what is true.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) +
>>>>>>>>>>>>>>>>>>>>>>>> successor(0) is true ???
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for
>>>>>>>>>>>>>>>>>>>>>>> it to be true, doesn't mean it can't be.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> In fact, your statement just comes out of a
>>>>>>>>>>>>>>>>>>>>>>> simple application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually
>>>>>>>>>>>>>>>>>>>>>>> KNOWN to be true.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Unless a formal system has a syntactic connection
>>>>>>>>>>>>>>>>>>>>>> from an expression of
>>>>>>>>>>>>>>>>>>>>>> its language to its truth maker axioms the
>>>>>>>>>>>>>>>>>>>>>> expression is untrue in that
>>>>>>>>>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Right, but the connection can be infinite in
>>>>>>>>>>>>>>>>>>>>> length, and thus not provable.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Try and show an expression of language that is
>>>>>>>>>>>>>>>>>>>>>> true in a formal system
>>>>>>>>>>>>>>>>>>>>>> (not just true somewhere else) that does not have
>>>>>>>>>>>>>>>>>>>>>> any connection to
>>>>>>>>>>>>>>>>>>>>>> truth maker axioms in this formal system. You must
>>>>>>>>>>>>>>>>>>>>>> show why it is true
>>>>>>>>>>>>>>>>>>>>>> in this formal system not merely that it is true
>>>>>>>>>>>>>>>>>>>>>> somewhere else.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> The connection might be infinite, and thus not
>>>>>>>>>>>>>>>>>>>>> SHOWABLE as a proof strictly in the formal system.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> If the connection exists as an infinite connection
>>>>>>>>>>>>>>>>>>>>> within the system, then it is TRUE in the system.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Note, that if there is such an infinite connection,
>>>>>>>>>>>>>>>>>>>>> which thus can not be proven within the formal
>>>>>>>>>>>>>>>>>>>>> system, it is still possible, that another system,
>>>>>>>>>>>>>>>>>>>>> related to that system, with more knowledge, might
>>>>>>>>>>>>>>>>>>>>> be able to show that there does exist within the
>>>>>>>>>>>>>>>>>>>>> original formal system such an infinte connection.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> G states that there does not exist a Natural Number
>>>>>>>>>>>>>>>>>>>>> g that meets a specific requirement (expressed as a
>>>>>>>>>>>>>>>>>>>>> primative recursive relationship).
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> This statement turns out to be true, because it
>>>>>>>>>>>>>>>>>>>>> turns out that no number g does meet that
>>>>>>>>>>>>>>>>>>>>> requirement, but it can't be proven in F that this
>>>>>>>>>>>>>>>>>>>>> is true, because in F, to show this we need to test
>>>>>>>>>>>>>>>>>>>>> every natuarl number, which requires an infinite
>>>>>>>>>>>>>>>>>>>>> number of steps (finite for each number, but an
>>>>>>>>>>>>>>>>>>>>> infinite number of numbers to test).
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> In meta-F, we can do better, because due to
>>>>>>>>>>>>>>>>>>>>> additional knowledge in meta-F, we can show that if
>>>>>>>>>>>>>>>>>>>>> a number g could be found, then that number g could
>>>>>>>>>>>>>>>>>>>>> be converted into a proof, in F, of the statement G
>>>>>>>>>>>>>>>>>>>>> (which says that such a number does not exist).
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and
>>>>>>>>>>>>>>>>>>>>> also show that no proof of it can exist in F.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> So your basic line-of-reasoning is that G is true in
>>>>>>>>>>>>>>>>>>>> F even if the truth
>>>>>>>>>>>>>>>>>>>> of G cannot even be expressed in F as long as the
>>>>>>>>>>>>>>>>>>>> truth of G can be
>>>>>>>>>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Expect that it CAN be expressed in F, it just is an
>>>>>>>>>>>>>>>>>>> infinite expression.
>>>>>>>>>>>>>>>>>> That is false. It is not that G takes an infinite
>>>>>>>>>>>>>>>>>> number of steps to
>>>>>>>>>>>>>>>>>> reach its truth maker axioms in F it is that even
>>>>>>>>>>>>>>>>>> after an infinite
>>>>>>>>>>>>>>>>>> number of steps it never reaches is truth maker axioms
>>>>>>>>>>>>>>>>>> in F because G is
>>>>>>>>>>>>>>>>>> simply untrue in F.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> No, YOUR problem is you aren't actually talking about G
>>>>>>>>>>>>>>>>> in F.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> "This sentence is not true"
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Which isn't G.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Not true about what?
>>>>>>>>>>>>>>>>>> Not true about being not true.
>>>>>>>>>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> So you are just a MORON.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Since Gödel said:
>>>>>>>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be used
>>>>>>>>>>>>>>>>>> for a similar undecidability proof.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy
>>>>>>>>>>>>>>>>>> for his proof we
>>>>>>>>>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Ad Hominem attacks are the tactic that people having no
>>>>>>>>>>>>>>>> interest in any
>>>>>>>>>>>>>>>> honest dialogue use when they realize that their
>>>>>>>>>>>>>>>> reasoning has been
>>>>>>>>>>>>>>>> utterly defeated.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You ARE a LYING MORON as you insist that Godel's G is a
>>>>>>>>>>>>>>> sentence that is actually provably isn't.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You think it is because you are too stupid to actually
>>>>>>>>>>>>>>> read any of the paper, so you take that comment that the
>>>>>>>>>>>>>>> statment is "based" on that statement to mean it IS that
>>>>>>>>>>>>>>> statement.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>> All of your Ad Hominem attacks cannot possibly hide the
>>>>>>>>>>>>>> fact that you
>>>>>>>>>>>>>> are asserting this counter-factual statement:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> when a valid proxy for an argument is defeated this does
>>>>>>>>>>>>>> not defeat the
>>>>>>>>>>>>>> original argument.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Right, which is what YOU are doing, showing your arguement
>>>>>>>>>>>>> is INVALID.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> In other words you disagree that correctly refuting a valid
>>>>>>>>>>>> proxy for an
>>>>>>>>>>>> argument does correctly refute the original argument?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> VALID is the key word,
>>>>>>>>>>>
>>>>>>>>>>> Yours isn't (I don't think you actually know the meaning of
>>>>>>>>>>> the words)
>>>>>>>>>>>
>>>>>>>>>>> And you are an IDIOT to claim it is.
>>>>>>>>>> So Gödel is wrong when he says:
>>>>>>>>>>
>>>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>>>> similar undecidability proof.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> No, but you don't understand what he is saying.
>>>>>>>>>
>>>>>>>> He is saying that every epistemological antinomy is a valid
>>>>>>>> proxy for
>>>>>>>> his proof. He is not saying that his expression is not an
>>>>>>>> epistemological antinomy.
>>>>>>>>
>>>>>>>
>>>>>>> Nope, that isn't what he is saying. How could it be, the ACTUAL G
>>>>>>> is a proven Truth Bearer, while the Liar's Paradox isn't
>>>>>>>
>>>>>>> Your arguement just shows its inconsistency.
>>>>>>>
>>>>>>> In part, because you don't actually understand what the sentence
>>>>>>> actually is.
>>>>>>>
>>>>>>>
>>>>>>>> The analogy between this result and Richard’s antinomy leaps to
>>>>>>>> the eye;
>>>>>>>> there is also a close relationship with the “liar” antinomy,14
>>>>>>>> since the
>>>>>>>> undecidable proposition [R(q); q] states precisely that q
>>>>>>>> belongs to K,
>>>>>>>> i.e. according to (1), that [R(q); q] is not provable. We are
>>>>>>>> therefore
>>>>>>>> confronted with a proposition which asserts its own unprovability.
>>>>>>>> (Gödel 1931:43)
>>>>>>>>
>>>>>>>> This <is> an isomorphism to a proposition that asserts its own
>>>>>>>> untruth.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> Nope, unless you erroneously think that statements about Truth
>>>>>>> ARE statements about provability, that isn't an isomoprhism.
>>>>>>>
>>>>>>> Note, you have even stated that *ALL* statements of the form
>>>>>>> "statement x is provable" or "Statment x is not provable" are
>>>>>>> Truth Bearers,
>>>>>>
>>>>>> I have most definitely never said this or anything that could be
>>>>>> unintentionally misconstrued to mean this.
>>>>>>
>>>>>> It is always the case that when-so-ever any expression of language
>>>>>> only
>>>>>> refers to its own truth or provability that this expression is not a
>>>>>> truth bearer, thus not a member of any formal system of logic.
>>>>>>
>>>>>
>>>>> You admitted that it was TRUE that a statement could not be proven
>>>>> even if the only way to show that it could not be proven was to
>>>>> check the infinite set of all possible proofs to see that none of
>>>>> them were a proof.
>>>>>
>>>>
>>>> This is not related to what I just said. Every expression of
>>>> language is
>>>> untrue unless it has a semantic connection to its truth maker axiom.
>>>
>>> I never disagreed with that, just that you keep on wavering between
>>> just saying there must be a connection, and then at times adding it
>>> must be a FINITE connection (which is actually only requried to be
>>> Proven)
>>>
>>> G, the statment about the non-existance of a natural number that
>>> satisfies the specified primative recursive relationship is TRUE,
>>> because it IS connected to the truth maker axioms of math via an
>>> infinite chain of steps.
>>>
>>> Each natural number can be shown to not meet that requirement in a
>> Gödel was actually talking about the expression:
>>
>> We are therefore confronted with a proposition which asserts its own
>> unprovability. (Gödel 1931:43)
>
> No, that is a statement which is proven in Meta-F to have the identical
> truth value of G. G doesn't SAY it is unprovable, but a natural
> concesequence of G being True is that it is unprovable, and if it is
> provable, it can't be True. Since G must be True or False, if it is True
> it IS unprovable, and if it is Provable, then it must be False, which is
> a contradiction (since ALL provable statements are True), so that case
> is impossible. Thus, G MUST be True but Unprovable.
>
> If F includes an axiom that says all Truths are Provable, then F is
> proved to be inconsistent.
>
>>
>> He only used the whole natural numbers thing to be able to encode the
>> above expression in a language that did not have a provability
>> predicate.
>
> No, F might well have a provability predicate, ies of the Natural Numbers.
>

On 1/17/23 12:32 AM, olcott wrote:
> On 1/16/2023 7:51 PM, Richard Damon wrote:
>> On 1/16/23 4:51 PM, olcott wrote:
>>> On 1/15/2023 7:15 PM, Richard Damon wrote:
>>>> On 1/15/23 7:56 PM, olcott wrote:
>>>>> On 1/15/2023 6:47 PM, Richard Damon wrote:
>>>>>> On 1/15/23 7:26 PM, olcott wrote:
>>>>>>> On 1/15/2023 2:23 PM, Richard Damon wrote:
>>>>>>>> On 1/15/23 3:12 PM, olcott wrote:
>>>>>>>>> On 1/15/2023 1:46 PM, Richard Damon wrote:
>>>>>>>>>> On 1/15/23 2:29 PM, olcott wrote:
>>>>>>>>>>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/15/23 2:00 PM, olcott wrote:
>>>>>>>>>>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>>>>>>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> How does the formal system know that an
>>>>>>>>>>>>>>>>>>>>>>>>>>> expression of language of this
>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system is true unless this expression
>>>>>>>>>>>>>>>>>>>>>>>>>>> of language has a
>>>>>>>>>>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS
>>>>>>>>>>>>>>>>>>>>>>>>>>> FORMAL SYSTEM* ???
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW
>>>>>>>>>>>>>>>>>>>>>>>>>> what is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) +
>>>>>>>>>>>>>>>>>>>>>>>>> successor(0) is true ???
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for
>>>>>>>>>>>>>>>>>>>>>>>> it to be true, doesn't mean it can't be.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> In fact, your statement just comes out of a
>>>>>>>>>>>>>>>>>>>>>>>> simple application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually
>>>>>>>>>>>>>>>>>>>>>>>> KNOWN to be true.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Unless a formal system has a syntactic connection
>>>>>>>>>>>>>>>>>>>>>>> from an expression of
>>>>>>>>>>>>>>>>>>>>>>> its language to its truth maker axioms the
>>>>>>>>>>>>>>>>>>>>>>> expression is untrue in that
>>>>>>>>>>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Right, but the connection can be infinite in
>>>>>>>>>>>>>>>>>>>>>> length, and thus not provable.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Try and show an expression of language that is
>>>>>>>>>>>>>>>>>>>>>>> true in a formal system
>>>>>>>>>>>>>>>>>>>>>>> (not just true somewhere else) that does not have
>>>>>>>>>>>>>>>>>>>>>>> any connection to
>>>>>>>>>>>>>>>>>>>>>>> truth maker axioms in this formal system. You
>>>>>>>>>>>>>>>>>>>>>>> must show why it is true
>>>>>>>>>>>>>>>>>>>>>>> in this formal system not merely that it is true
>>>>>>>>>>>>>>>>>>>>>>> somewhere else.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> The connection might be infinite, and thus not
>>>>>>>>>>>>>>>>>>>>>> SHOWABLE as a proof strictly in the formal system.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> If the connection exists as an infinite connection
>>>>>>>>>>>>>>>>>>>>>> within the system, then it is TRUE in the system.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Note, that if there is such an infinite
>>>>>>>>>>>>>>>>>>>>>> connection, which thus can not be proven within
>>>>>>>>>>>>>>>>>>>>>> the formal system, it is still possible, that
>>>>>>>>>>>>>>>>>>>>>> another system, related to that system, with more
>>>>>>>>>>>>>>>>>>>>>> knowledge, might be able to show that there does
>>>>>>>>>>>>>>>>>>>>>> exist within the original formal system such an
>>>>>>>>>>>>>>>>>>>>>> infinte connection.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> G states that there does not exist a Natural
>>>>>>>>>>>>>>>>>>>>>> Number g that meets a specific requirement
>>>>>>>>>>>>>>>>>>>>>> (expressed as a primative recursive relationship).
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> This statement turns out to be true, because it
>>>>>>>>>>>>>>>>>>>>>> turns out that no number g does meet that
>>>>>>>>>>>>>>>>>>>>>> requirement, but it can't be proven in F that this
>>>>>>>>>>>>>>>>>>>>>> is true, because in F, to show this we need to
>>>>>>>>>>>>>>>>>>>>>> test every natuarl number, which requires an
>>>>>>>>>>>>>>>>>>>>>> infinite number of steps (finite for each number,
>>>>>>>>>>>>>>>>>>>>>> but an infinite number of numbers to test).
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> In meta-F, we can do better, because due to
>>>>>>>>>>>>>>>>>>>>>> additional knowledge in meta-F, we can show that
>>>>>>>>>>>>>>>>>>>>>> if a number g could be found, then that number g
>>>>>>>>>>>>>>>>>>>>>> could be converted into a proof, in F, of the
>>>>>>>>>>>>>>>>>>>>>> statement G (which says that such a number does
>>>>>>>>>>>>>>>>>>>>>> not exist).
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and
>>>>>>>>>>>>>>>>>>>>>> also show that no proof of it can exist in F.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> So your basic line-of-reasoning is that G is true
>>>>>>>>>>>>>>>>>>>>> in F even if the truth
>>>>>>>>>>>>>>>>>>>>> of G cannot even be expressed in F as long as the
>>>>>>>>>>>>>>>>>>>>> truth of G can be
>>>>>>>>>>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Expect that it CAN be expressed in F, it just is an
>>>>>>>>>>>>>>>>>>>> infinite expression.
>>>>>>>>>>>>>>>>>>> That is false. It is not that G takes an infinite
>>>>>>>>>>>>>>>>>>> number of steps to
>>>>>>>>>>>>>>>>>>> reach its truth maker axioms in F it is that even
>>>>>>>>>>>>>>>>>>> after an infinite
>>>>>>>>>>>>>>>>>>> number of steps it never reaches is truth maker
>>>>>>>>>>>>>>>>>>> axioms in F because G is
>>>>>>>>>>>>>>>>>>> simply untrue in F.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> No, YOUR problem is you aren't actually talking about
>>>>>>>>>>>>>>>>>> G in F.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> "This sentence is not true"
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Which isn't G.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Not true about what?
>>>>>>>>>>>>>>>>>>> Not true about being not true.
>>>>>>>>>>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> So you are just a MORON.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Since Gödel said:
>>>>>>>>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be
>>>>>>>>>>>>>>>>>>> used for a similar undecidability proof.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy
>>>>>>>>>>>>>>>>>>> for his proof we
>>>>>>>>>>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Ad Hominem attacks are the tactic that people having no
>>>>>>>>>>>>>>>>> interest in any
>>>>>>>>>>>>>>>>> honest dialogue use when they realize that their
>>>>>>>>>>>>>>>>> reasoning has been
>>>>>>>>>>>>>>>>> utterly defeated.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You ARE a LYING MORON as you insist that Godel's G is a
>>>>>>>>>>>>>>>> sentence that is actually provably isn't.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You think it is because you are too stupid to actually
>>>>>>>>>>>>>>>> read any of the paper, so you take that comment that the
>>>>>>>>>>>>>>>> statment is "based" on that statement to mean it IS that
>>>>>>>>>>>>>>>> statement.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> All of your Ad Hominem attacks cannot possibly hide the
>>>>>>>>>>>>>>> fact that you
>>>>>>>>>>>>>>> are asserting this counter-factual statement:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> when a valid proxy for an argument is defeated this does
>>>>>>>>>>>>>>> not defeat the
>>>>>>>>>>>>>>> original argument.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Right, which is what YOU are doing, showing your arguement
>>>>>>>>>>>>>> is INVALID.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> In other words you disagree that correctly refuting a valid
>>>>>>>>>>>>> proxy for an
>>>>>>>>>>>>> argument does correctly refute the original argument?
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> VALID is the key word,
>>>>>>>>>>>>
>>>>>>>>>>>> Yours isn't (I don't think you actually know the meaning of
>>>>>>>>>>>> the words)
>>>>>>>>>>>>
>>>>>>>>>>>> And you are an IDIOT to claim it is.
>>>>>>>>>>> So Gödel is wrong when he says:
>>>>>>>>>>>
>>>>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>>>>> similar undecidability proof.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No, but you don't understand what he is saying.
>>>>>>>>>>
>>>>>>>>> He is saying that every epistemological antinomy is a valid
>>>>>>>>> proxy for
>>>>>>>>> his proof. He is not saying that his expression is not an
>>>>>>>>> epistemological antinomy.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Nope, that isn't what he is saying. How could it be, the ACTUAL
>>>>>>>> G is a proven Truth Bearer, while the Liar's Paradox isn't
>>>>>>>>
>>>>>>>> Your arguement just shows its inconsistency.
>>>>>>>>
>>>>>>>> In part, because you don't actually understand what the sentence
>>>>>>>> actually is.
>>>>>>>>
>>>>>>>>
>>>>>>>>> The analogy between this result and Richard’s antinomy leaps to
>>>>>>>>> the eye;
>>>>>>>>> there is also a close relationship with the “liar” antinomy,14
>>>>>>>>> since the
>>>>>>>>> undecidable proposition [R(q); q] states precisely that q
>>>>>>>>> belongs to K,
>>>>>>>>> i.e. according to (1), that [R(q); q] is not provable. We are
>>>>>>>>> therefore
>>>>>>>>> confronted with a proposition which asserts its own unprovability.
>>>>>>>>> (Gödel 1931:43)
>>>>>>>>>
>>>>>>>>> This <is> an isomorphism to a proposition that asserts its own
>>>>>>>>> untruth.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Nope, unless you erroneously think that statements about Truth
>>>>>>>> ARE statements about provability, that isn't an isomoprhism.
>>>>>>>>
>>>>>>>> Note, you have even stated that *ALL* statements of the form
>>>>>>>> "statement x is provable" or "Statment x is not provable" are
>>>>>>>> Truth Bearers,
>>>>>>>
>>>>>>> I have most definitely never said this or anything that could be
>>>>>>> unintentionally misconstrued to mean this.
>>>>>>>
>>>>>>> It is always the case that when-so-ever any expression of
>>>>>>> language only
>>>>>>> refers to its own truth or provability that this expression is not a
>>>>>>> truth bearer, thus not a member of any formal system of logic.
>>>>>>>
>>>>>>
>>>>>> You admitted that it was TRUE that a statement could not be proven
>>>>>> even if the only way to show that it could not be proven was to
>>>>>> check the infinite set of all possible proofs to see that none of
>>>>>> them were a proof.
>>>>>>
>>>>>
>>>>> This is not related to what I just said. Every expression of
>>>>> language is
>>>>> untrue unless it has a semantic connection to its truth maker axiom.
>>>>
>>>> I never disagreed with that, just that you keep on wavering between
>>>> just saying there must be a connection, and then at times adding it
>>>> must be a FINITE connection (which is actually only requried to be
>>>> Proven)
>>>>
>>>> G, the statment about the non-existance of a natural number that
>>>> satisfies the specified primative recursive relationship is TRUE,
>>>> because it IS connected to the truth maker axioms of math via an
>>>> infinite chain of steps.
>>>>
>>>> Each natural number can be shown to not meet that requirement in a
>>> Gödel was actually talking about the expression:
>>>
>>> We are therefore confronted with a proposition which asserts its own
>>> unprovability. (Gödel 1931:43)
>>
>> No, that is a statement which is proven in Meta-F to have the
>> identical truth value of G. G doesn't SAY it is unprovable, but a
>> natural concesequence of G being True is that it is unprovable, and if
>> it is provable, it can't be True. Since G must be True or False, if it
>> is True it IS unprovable, and if it is Provable, then it must be
>> False, which is a contradiction (since ALL provable statements are
>> True), so that case is impossible. Thus, G MUST be True but Unprovable.
>>
>> If F includes an axiom that says all Truths are Provable, then F is
>> proved to be inconsistent.
>>
>>>
>>> He only used the whole natural numbers thing to be able to encode the
>>> above expression in a language that did not have a provability
>>> predicate.
>>
>> No, F might well have a provability predicate, ies of the Natural
>> Numbers.
>>
>
> Then it would not need any Gödel number.

On 1/16/2023 7:51 PM, Richard Damon wrote:
> On 1/16/23 10:17 AM, olcott wrote:
>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>> On 1/15/23 11:15 AM, olcott wrote:
>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>> How does the formal system know that an expression of language
>>>>>>>>>> of this
>>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>
>>>>>>>>
>>>>>>>> So PA has no idea that:
>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>>>>
>>>>>>>
>>>>>>> Why do you say that.
>>>>>>>
>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>>>> doesn't mean it can't be.
>>>>>>>
>>>>>>> In fact, your statement just comes out of a simple application of
>>>>>>> the addition AXIOMS of PA.
>>>>>>>
>>>>>>> a + 0 = a
>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>
>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>>>
>>>>>>
>>>>>> Unless a formal system has a syntactic connection from an
>>>>>> expression of
>>>>>> its language to its truth maker axioms the expression is untrue in
>>>>>> that
>>>>>> formal system.
>>>>>
>>>>> Right, but the connection can be infinite in length, and thus not
>>>>> provable.
>>>>>
>>>>>>
>>>>>> Try and show an expression of language that is true in a formal
>>>>>> system
>>>>>> (not just true somewhere else) that does not have any connection to
>>>>>> truth maker axioms in this formal system. You must show why it is
>>>>>> true
>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>
>>>>>
>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>>>> strictly in the formal system.
>>>>>
>>>>> If the connection exists as an infinite connection within the
>>>>> system, then it is TRUE in the system.
>>>>>
>>>>> Note, that if there is such an infinite connection, which thus can
>>>>> not be proven within the formal system, it is still possible, that
>>>>> another system, related to that system, with more knowledge, might
>>>>> be able to show that there does exist within the original formal
>>>>> system such an infinte connection.
>>>>>
>>>>> This is what happens to G in F and meta-F
>>>>>
>>>>> G states that there does not exist a Natural Number g that meets a
>>>>> specific requirement (expressed as a primative recursive
>>>>> relationship).
>>>>>
>>>>> This statement turns out to be true, because it turns out that no
>>>>> number g does meet that requirement, but it can't be proven in F
>>>>> that this is true, because in F, to show this we need to test every
>>>>> natuarl number, which requires an infinite number of steps (finite
>>>>> for each number, but an infinite number of numbers to test).
>>>>>
>>>>> In meta-F, we can do better, because due to additional knowledge in
>>>>> meta-F, we can show that if a number g could be found, then that
>>>>> number g could be converted into a proof, in F, of the statement G
>>>>> (which says that such a number does not exist).
>>>>>
>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
>>>>> proof of it can exist in F.
>>>>>
>>>> So your basic line-of-reasoning is that G is true in F even if the
>>>> truth
>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>> expressed in meta-F.
>>>>
>>>
>>> Expect that it CAN be expressed in F, it just is an infinite expression.
>>>
>> So you changed your mind about infinite proofs in formal systems?
>> We know the steps of the infinite proof for the Goldbach conjecture.
>
> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
> infinte sets oc connections, proofs can't. Only YOU have perposed that
> we think about infinite proofs.
>

Formal systems cannot ever use infinite connections from their
expressions of language to their truth maker axioms thus eliminating
these from consideration as any measure of true "in the system".

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

On 1/17/2023 5:02 AM, Richard Damon wrote:
> On 1/17/23 12:32 AM, olcott wrote:
>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>> On 1/16/23 4:51 PM, olcott wrote:
>>>> On 1/15/2023 7:15 PM, Richard Damon wrote:
>>>>> On 1/15/23 7:56 PM, olcott wrote:
>>>>>> On 1/15/2023 6:47 PM, Richard Damon wrote:
>>>>>>> On 1/15/23 7:26 PM, olcott wrote:
>>>>>>>> On 1/15/2023 2:23 PM, Richard Damon wrote:
>>>>>>>>> On 1/15/23 3:12 PM, olcott wrote:
>>>>>>>>>> On 1/15/2023 1:46 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/15/23 2:29 PM, olcott wrote:
>>>>>>>>>>>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/15/23 2:00 PM, olcott wrote:
>>>>>>>>>>>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> How does the formal system know that an
>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression of language of this
>>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system is true unless this expression
>>>>>>>>>>>>>>>>>>>>>>>>>>>> of language has a
>>>>>>>>>>>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS
>>>>>>>>>>>>>>>>>>>>>>>>>>>> FORMAL SYSTEM* ???
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW
>>>>>>>>>>>>>>>>>>>>>>>>>>> what is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) +
>>>>>>>>>>>>>>>>>>>>>>>>>> successor(0) is true ???
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven
>>>>>>>>>>>>>>>>>>>>>>>>> for it to be true, doesn't mean it can't be.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> In fact, your statement just comes out of a
>>>>>>>>>>>>>>>>>>>>>>>>> simple application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus
>>>>>>>>>>>>>>>>>>>>>>>>> actually KNOWN to be true.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Unless a formal system has a syntactic
>>>>>>>>>>>>>>>>>>>>>>>> connection from an expression of
>>>>>>>>>>>>>>>>>>>>>>>> its language to its truth maker axioms the
>>>>>>>>>>>>>>>>>>>>>>>> expression is untrue in that
>>>>>>>>>>>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Right, but the connection can be infinite in
>>>>>>>>>>>>>>>>>>>>>>> length, and thus not provable.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Try and show an expression of language that is
>>>>>>>>>>>>>>>>>>>>>>>> true in a formal system
>>>>>>>>>>>>>>>>>>>>>>>> (not just true somewhere else) that does not
>>>>>>>>>>>>>>>>>>>>>>>> have any connection to
>>>>>>>>>>>>>>>>>>>>>>>> truth maker axioms in this formal system. You
>>>>>>>>>>>>>>>>>>>>>>>> must show why it is true
>>>>>>>>>>>>>>>>>>>>>>>> in this formal system not merely that it is true
>>>>>>>>>>>>>>>>>>>>>>>> somewhere else.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> The connection might be infinite, and thus not
>>>>>>>>>>>>>>>>>>>>>>> SHOWABLE as a proof strictly in the formal system.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> If the connection exists as an infinite
>>>>>>>>>>>>>>>>>>>>>>> connection within the system, then it is TRUE in
>>>>>>>>>>>>>>>>>>>>>>> the system.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Note, that if there is such an infinite
>>>>>>>>>>>>>>>>>>>>>>> connection, which thus can not be proven within
>>>>>>>>>>>>>>>>>>>>>>> the formal system, it is still possible, that
>>>>>>>>>>>>>>>>>>>>>>> another system, related to that system, with more
>>>>>>>>>>>>>>>>>>>>>>> knowledge, might be able to show that there does
>>>>>>>>>>>>>>>>>>>>>>> exist within the original formal system such an
>>>>>>>>>>>>>>>>>>>>>>> infinte connection.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> G states that there does not exist a Natural
>>>>>>>>>>>>>>>>>>>>>>> Number g that meets a specific requirement
>>>>>>>>>>>>>>>>>>>>>>> (expressed as a primative recursive relationship).
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> This statement turns out to be true, because it
>>>>>>>>>>>>>>>>>>>>>>> turns out that no number g does meet that
>>>>>>>>>>>>>>>>>>>>>>> requirement, but it can't be proven in F that
>>>>>>>>>>>>>>>>>>>>>>> this is true, because in F, to show this we need
>>>>>>>>>>>>>>>>>>>>>>> to test every natuarl number, which requires an
>>>>>>>>>>>>>>>>>>>>>>> infinite number of steps (finite for each number,
>>>>>>>>>>>>>>>>>>>>>>> but an infinite number of numbers to test).
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> In meta-F, we can do better, because due to
>>>>>>>>>>>>>>>>>>>>>>> additional knowledge in meta-F, we can show that
>>>>>>>>>>>>>>>>>>>>>>> if a number g could be found, then that number g
>>>>>>>>>>>>>>>>>>>>>>> could be converted into a proof, in F, of the
>>>>>>>>>>>>>>>>>>>>>>> statement G (which says that such a number does
>>>>>>>>>>>>>>>>>>>>>>> not exist).
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and
>>>>>>>>>>>>>>>>>>>>>>> also show that no proof of it can exist in F.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> So your basic line-of-reasoning is that G is true
>>>>>>>>>>>>>>>>>>>>>> in F even if the truth
>>>>>>>>>>>>>>>>>>>>>> of G cannot even be expressed in F as long as the
>>>>>>>>>>>>>>>>>>>>>> truth of G can be
>>>>>>>>>>>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Expect that it CAN be expressed in F, it just is an
>>>>>>>>>>>>>>>>>>>>> infinite expression.
>>>>>>>>>>>>>>>>>>>> That is false. It is not that G takes an infinite
>>>>>>>>>>>>>>>>>>>> number of steps to
>>>>>>>>>>>>>>>>>>>> reach its truth maker axioms in F it is that even
>>>>>>>>>>>>>>>>>>>> after an infinite
>>>>>>>>>>>>>>>>>>>> number of steps it never reaches is truth maker
>>>>>>>>>>>>>>>>>>>> axioms in F because G is
>>>>>>>>>>>>>>>>>>>> simply untrue in F.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> No, YOUR problem is you aren't actually talking about
>>>>>>>>>>>>>>>>>>> G in F.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> "This sentence is not true"
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Which isn't G.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Not true about what?
>>>>>>>>>>>>>>>>>>>> Not true about being not true.
>>>>>>>>>>>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>>>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> So you are just a MORON.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Since Gödel said:
>>>>>>>>>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be
>>>>>>>>>>>>>>>>>>>> used for a similar undecidability proof.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy
>>>>>>>>>>>>>>>>>>>> for his proof we
>>>>>>>>>>>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Ad Hominem attacks are the tactic that people having
>>>>>>>>>>>>>>>>>> no interest in any
>>>>>>>>>>>>>>>>>> honest dialogue use when they realize that their
>>>>>>>>>>>>>>>>>> reasoning has been
>>>>>>>>>>>>>>>>>> utterly defeated.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> You ARE a LYING MORON as you insist that Godel's G is a
>>>>>>>>>>>>>>>>> sentence that is actually provably isn't.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> You think it is because you are too stupid to actually
>>>>>>>>>>>>>>>>> read any of the paper, so you take that comment that
>>>>>>>>>>>>>>>>> the statment is "based" on that statement to mean it IS
>>>>>>>>>>>>>>>>> that statement.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> All of your Ad Hominem attacks cannot possibly hide the
>>>>>>>>>>>>>>>> fact that you
>>>>>>>>>>>>>>>> are asserting this counter-factual statement:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> when a valid proxy for an argument is defeated this does
>>>>>>>>>>>>>>>> not defeat the
>>>>>>>>>>>>>>>> original argument.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Right, which is what YOU are doing, showing your
>>>>>>>>>>>>>>> arguement is INVALID.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> In other words you disagree that correctly refuting a
>>>>>>>>>>>>>> valid proxy for an
>>>>>>>>>>>>>> argument does correctly refute the original argument?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> VALID is the key word,
>>>>>>>>>>>>>
>>>>>>>>>>>>> Yours isn't (I don't think you actually know the meaning of
>>>>>>>>>>>>> the words)
>>>>>>>>>>>>>
>>>>>>>>>>>>> And you are an IDIOT to claim it is.
>>>>>>>>>>>> So Gödel is wrong when he says:
>>>>>>>>>>>>
>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>>>>>> similar undecidability proof.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> No, but you don't understand what he is saying.
>>>>>>>>>>>
>>>>>>>>>> He is saying that every epistemological antinomy is a valid
>>>>>>>>>> proxy for
>>>>>>>>>> his proof. He is not saying that his expression is not an
>>>>>>>>>> epistemological antinomy.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Nope, that isn't what he is saying. How could it be, the ACTUAL
>>>>>>>>> G is a proven Truth Bearer, while the Liar's Paradox isn't
>>>>>>>>>
>>>>>>>>> Your arguement just shows its inconsistency.
>>>>>>>>>
>>>>>>>>> In part, because you don't actually understand what the
>>>>>>>>> sentence actually is.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> The analogy between this result and Richard’s antinomy leaps
>>>>>>>>>> to the eye;
>>>>>>>>>> there is also a close relationship with the “liar” antinomy,14
>>>>>>>>>> since the
>>>>>>>>>> undecidable proposition [R(q); q] states precisely that q
>>>>>>>>>> belongs to K,
>>>>>>>>>> i.e. according to (1), that [R(q); q] is not provable. We are
>>>>>>>>>> therefore
>>>>>>>>>> confronted with a proposition which asserts its own
>>>>>>>>>> unprovability.
>>>>>>>>>> (Gödel 1931:43)
>>>>>>>>>>
>>>>>>>>>> This <is> an isomorphism to a proposition that asserts its own
>>>>>>>>>> untruth.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Nope, unless you erroneously think that statements about Truth
>>>>>>>>> ARE statements about provability, that isn't an isomoprhism.
>>>>>>>>>
>>>>>>>>> Note, you have even stated that *ALL* statements of the form
>>>>>>>>> "statement x is provable" or "Statment x is not provable" are
>>>>>>>>> Truth Bearers,
>>>>>>>>
>>>>>>>> I have most definitely never said this or anything that could be
>>>>>>>> unintentionally misconstrued to mean this.
>>>>>>>>
>>>>>>>> It is always the case that when-so-ever any expression of
>>>>>>>> language only
>>>>>>>> refers to its own truth or provability that this expression is
>>>>>>>> not a
>>>>>>>> truth bearer, thus not a member of any formal system of logic.
>>>>>>>>
>>>>>>>
>>>>>>> You admitted that it was TRUE that a statement could not be
>>>>>>> proven even if the only way to show that it could not be proven
>>>>>>> was to check the infinite set of all possible proofs to see that
>>>>>>> none of them were a proof.
>>>>>>>
>>>>>>
>>>>>> This is not related to what I just said. Every expression of
>>>>>> language is
>>>>>> untrue unless it has a semantic connection to its truth maker axiom.
>>>>>
>>>>> I never disagreed with that, just that you keep on wavering between
>>>>> just saying there must be a connection, and then at times adding it
>>>>> must be a FINITE connection (which is actually only requried to be
>>>>> Proven)
>>>>>
>>>>> G, the statment about the non-existance of a natural number that
>>>>> satisfies the specified primative recursive relationship is TRUE,
>>>>> because it IS connected to the truth maker axioms of math via an
>>>>> infinite chain of steps.
>>>>>
>>>>> Each natural number can be shown to not meet that requirement in a
>>>> Gödel was actually talking about the expression:
>>>>
>>>> We are therefore confronted with a proposition which asserts its own
>>>> unprovability. (Gödel 1931:43)
>>>
>>> No, that is a statement which is proven in Meta-F to have the
>>> identical truth value of G. G doesn't SAY it is unprovable, but a
>>> natural concesequence of G being True is that it is unprovable, and
>>> if it is provable, it can't be True. Since G must be True or False,
>>> if it is True it IS unprovable, and if it is Provable, then it must
>>> be False, which is a contradiction (since ALL provable statements are
>>> True), so that case is impossible. Thus, G MUST be True but Unprovable.
>>>
>>> If F includes an axiom that says all Truths are Provable, then F is
>>> proved to be inconsistent.
>>>
>>>>
>>>> He only used the whole natural numbers thing to be able to encode the
>>>> above expression in a language that did not have a provability
>>>> predicate.
>>>
>>> No, F might well have a provability predicate, ies of the Natural
>>> Numbers.
>>>
>>
>> Then it would not need any Gödel number.
>
> Maybe, but the key is that it DOESN'T use the operator, so your
> "special" rule based on using it doesn't apply.
>
> Godel showed that Meta-F we can construct a calculation in Meta-F that
> is the exact same caluclation in F that provides us proofs in Meta-F
> based on what is simply a calculation in F.
>
> Since it is just a calculation in F about the existance of a number
> based on a computable function, in F the stateement ALWAYS has a Truth
> Value, either such a number exsits or it doesn't.
>
> Because of the DEFINED relationship between F and Meta-F, that truth
> value transfers, and due to the extra axioms in Meta-F.
>
> Arguing that in Meta-F we have an epistemological antinomy means that
> your logic system makes the mathematics in F be able to create this same
> situation, which doesn't match the behavior of the Natural Numbers, so
> your F doesn't meet the requirements for it.
>
> YOU "PROOF" FAILS.
>
>
> If you want to make the sort of claims you are doing, you need to show
> exactly which step in his proof does something wrong. You are not
> allowed to rebut a proof by saying its answer must be wrong, or you
> disagree with a footnote. You need to find an actaul erroneous step in
> the proof itself.
>
> Since you have shown you don't actually understand the proof at all,
> this is probably impossible for you.
>
>>
>>>>
>>>> (G) F ⊢ GF ↔ ¬ProvF(┌GF┐). // with Gödel number
>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>
>> *paraphrased as: GF ↔ (F ⊬ GF) // without Gödel number*
>
> Nope, it only "means" that in Meta F, not in F.
>
> F doesn't have Truth Makers to establish that meaning, so that
> "parapharse" is incorrect.
>
> You are just showing you don't understand what logic does.
>
>>
>>>>
>>>>
>>>
>>>
>>> Which if you read, agrees with Godel, that this sentence must be
>>> neither provable or disprovable, and agrees with the right
>>> conditions, can be made True.
>>
>> I am removing the Gödel number and showing what's left.
>>
>
> Remove the Godel Number, and NOTHING is left of the statement in F,

On 1/17/2023 10:44 AM, Jeffrey Rubard wrote:
> On Tuesday, January 17, 2023 at 8:40:02 AM UTC-8, _ Olcott wrote:
>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>> On 1/16/23 10:17 AM, olcott wrote:
>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>> How does the formal system know that an expression of language
>>>>>>>>>>>> of this
>>>>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So PA has no idea that:
>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Why do you say that.
>>>>>>>>>
>>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>>>>>> doesn't mean it can't be.
>>>>>>>>>
>>>>>>>>> In fact, your statement just comes out of a simple application of
>>>>>>>>> the addition AXIOMS of PA.
>>>>>>>>>
>>>>>>>>> a + 0 = a
>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>
>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>> expression of
>>>>>>>> its language to its truth maker axioms the expression is untrue in
>>>>>>>> that
>>>>>>>> formal system.
>>>>>>>
>>>>>>> Right, but the connection can be infinite in length, and thus not
>>>>>>> provable.
>>>>>>>
>>>>>>>>
>>>>>>>> Try and show an expression of language that is true in a formal
>>>>>>>> system
>>>>>>>> (not just true somewhere else) that does not have any connection to
>>>>>>>> truth maker axioms in this formal system. You must show why it is
>>>>>>>> true
>>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>>
>>>>>>>
>>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>>>>>> strictly in the formal system.
>>>>>>>
>>>>>>> If the connection exists as an infinite connection within the
>>>>>>> system, then it is TRUE in the system.
>>>>>>>
>>>>>>> Note, that if there is such an infinite connection, which thus can
>>>>>>> not be proven within the formal system, it is still possible, that
>>>>>>> another system, related to that system, with more knowledge, might
>>>>>>> be able to show that there does exist within the original formal
>>>>>>> system such an infinte connection.
>>>>>>>
>>>>>>> This is what happens to G in F and meta-F
>>>>>>>
>>>>>>> G states that there does not exist a Natural Number g that meets a
>>>>>>> specific requirement (expressed as a primative recursive
>>>>>>> relationship).
>>>>>>>
>>>>>>> This statement turns out to be true, because it turns out that no
>>>>>>> number g does meet that requirement, but it can't be proven in F
>>>>>>> that this is true, because in F, to show this we need to test every
>>>>>>> natuarl number, which requires an infinite number of steps (finite
>>>>>>> for each number, but an infinite number of numbers to test).
>>>>>>>
>>>>>>> In meta-F, we can do better, because due to additional knowledge in
>>>>>>> meta-F, we can show that if a number g could be found, then that
>>>>>>> number g could be converted into a proof, in F, of the statement G
>>>>>>> (which says that such a number does not exist).
>>>>>>>
>>>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
>>>>>>> proof of it can exist in F.
>>>>>>>
>>>>>> So your basic line-of-reasoning is that G is true in F even if the
>>>>>> truth
>>>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>>>> expressed in meta-F.
>>>>>>
>>>>>
>>>>> Expect that it CAN be expressed in F, it just is an infinite expression.
>>>>>
>>>> So you changed your mind about infinite proofs in formal systems?
>>>> We know the steps of the infinite proof for the Goldbach conjecture.
>>>
>>> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
>>> infinte sets oc connections, proofs can't. Only YOU have perposed that
>>> we think about infinite proofs.
>>>

>> Formal systems cannot ever use infinite connections from their
>> expressions of language to their truth maker axioms thus eliminating
>> these from consideration as any measure of true "in the system".

>> --
>> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
>> hits a target no one else can see." Arthur Schopenhauer
>
> "What you've written is almost like formal logic."

I am filling in a key detail about the way that "true" in formal logic
actually works. Wittgenstein first pointed this out and no mathematician
has ever noticed. https://www.liarparadox.org/Wittgenstein.pdf

If any mathematician had noticed this then they would have noticed that
Gödel did not prove that formal systems are incomplete. He only proved
that some of the expressions of language of a formal system are simply
untrue which is a mere triviality that everyone already knew.

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

On 1/17/23 12:25 PM, olcott wrote:
> On 1/17/2023 10:44 AM, Jeffrey Rubard wrote:
>> On Tuesday, January 17, 2023 at 8:40:02 AM UTC-8, _ Olcott wrote:
>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>> On 1/16/23 10:17 AM, olcott wrote:
>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>> How does the formal system know that an expression of language
>>>>>>>>>>>>> of this
>>>>>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is
>>>>>>>>>>> true ???
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Why do you say that.
>>>>>>>>>>
>>>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>>>>>>> doesn't mean it can't be.
>>>>>>>>>>
>>>>>>>>>> In fact, your statement just comes out of a simple application of
>>>>>>>>>> the addition AXIOMS of PA.
>>>>>>>>>>
>>>>>>>>>> a + 0 = a
>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>
>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be
>>>>>>>>>> true.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>> expression of
>>>>>>>>> its language to its truth maker axioms the expression is untrue in
>>>>>>>>> that
>>>>>>>>> formal system.
>>>>>>>>
>>>>>>>> Right, but the connection can be infinite in length, and thus not
>>>>>>>> provable.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Try and show an expression of language that is true in a formal
>>>>>>>>> system
>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>> connection to
>>>>>>>>> truth maker axioms in this formal system. You must show why it is
>>>>>>>>> true
>>>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>>>>>>> strictly in the formal system.
>>>>>>>>
>>>>>>>> If the connection exists as an infinite connection within the
>>>>>>>> system, then it is TRUE in the system.
>>>>>>>>
>>>>>>>> Note, that if there is such an infinite connection, which thus can
>>>>>>>> not be proven within the formal system, it is still possible, that
>>>>>>>> another system, related to that system, with more knowledge, might
>>>>>>>> be able to show that there does exist within the original formal
>>>>>>>> system such an infinte connection.
>>>>>>>>
>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>
>>>>>>>> G states that there does not exist a Natural Number g that meets a
>>>>>>>> specific requirement (expressed as a primative recursive
>>>>>>>> relationship).
>>>>>>>>
>>>>>>>> This statement turns out to be true, because it turns out that no
>>>>>>>> number g does meet that requirement, but it can't be proven in F
>>>>>>>> that this is true, because in F, to show this we need to test every
>>>>>>>> natuarl number, which requires an infinite number of steps (finite
>>>>>>>> for each number, but an infinite number of numbers to test).
>>>>>>>>
>>>>>>>> In meta-F, we can do better, because due to additional knowledge in
>>>>>>>> meta-F, we can show that if a number g could be found, then that
>>>>>>>> number g could be converted into a proof, in F, of the statement G
>>>>>>>> (which says that such a number does not exist).
>>>>>>>>
>>>>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
>>>>>>>> proof of it can exist in F.
>>>>>>>>
>>>>>>> So your basic line-of-reasoning is that G is true in F even if the
>>>>>>> truth
>>>>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>>>>> expressed in meta-F.
>>>>>>>
>>>>>>
>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>> expression.
>>>>>>
>>>>> So you changed your mind about infinite proofs in formal systems?
>>>>> We know the steps of the infinite proof for the Goldbach conjecture.
>>>>
>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
>>>> infinte sets oc connections, proofs can't. Only YOU have perposed that
>>>> we think about infinite proofs.
>>>>
>
>>> Formal systems cannot ever use infinite connections from their
>>> expressions of language to their truth maker axioms thus eliminating
>>> these from consideration as any measure of true "in the system".
>
>>> --
>>> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
>>> hits a target no one else can see." Arthur Schopenhauer
>>
>> "What you've written is almost like formal logic."
>
> I am filling in a key detail about the way that "true" in formal logic
> actually works. Wittgenstein first pointed this out and no mathematician
> has ever noticed. https://www.liarparadox.org/Wittgenstein.pdf

And he was WRONG about that.

>
> If any mathematician had noticed this then they would have noticed that
> Gödel did not prove that formal systems are incomplete. He only proved
> that some of the expressions of language of a formal system are simply
> untrue which is a mere triviality that everyone already knew.
>

Nope, Mathematics doesn't work in a systme that restricts itself to that
axiom.

You need to take you chioce, you can include a axiom that Truth is
Provable, and limit how far you can go with mathematics, or you can
accept that not all truth is provable, and get the fullness of mathematics.

You just seem to not understand this, and try to do all of mathematics
with that axioms which makes your system inconsistent and thus worthless.

You are just to stupid to understand this.

On 1/17/23 12:07 PM, olcott wrote:
> On 1/17/2023 5:02 AM, Richard Damon wrote:
>> On 1/17/23 12:32 AM, olcott wrote:
>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>> On 1/16/23 4:51 PM, olcott wrote:
>>>>> On 1/15/2023 7:15 PM, Richard Damon wrote:
>>>>>> On 1/15/23 7:56 PM, olcott wrote:
>>>>>>> On 1/15/2023 6:47 PM, Richard Damon wrote:
>>>>>>>> On 1/15/23 7:26 PM, olcott wrote:
>>>>>>>>> On 1/15/2023 2:23 PM, Richard Damon wrote:
>>>>>>>>>> On 1/15/23 3:12 PM, olcott wrote:
>>>>>>>>>>> On 1/15/2023 1:46 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/15/23 2:29 PM, olcott wrote:
>>>>>>>>>>>>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/15/23 2:00 PM, olcott wrote:
>>>>>>>>>>>>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How does the formal system know that an
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression of language of this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system is true unless this
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression of language has a
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> FORMAL SYSTEM* ???
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to
>>>>>>>>>>>>>>>>>>>>>>>>>>>> KNOW what is true.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) +
>>>>>>>>>>>>>>>>>>>>>>>>>>> successor(0) is true ???
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven
>>>>>>>>>>>>>>>>>>>>>>>>>> for it to be true, doesn't mean it can't be.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> In fact, your statement just comes out of a
>>>>>>>>>>>>>>>>>>>>>>>>>> simple application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus
>>>>>>>>>>>>>>>>>>>>>>>>>> actually KNOWN to be true.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Unless a formal system has a syntactic
>>>>>>>>>>>>>>>>>>>>>>>>> connection from an expression of
>>>>>>>>>>>>>>>>>>>>>>>>> its language to its truth maker axioms the
>>>>>>>>>>>>>>>>>>>>>>>>> expression is untrue in that
>>>>>>>>>>>>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Right, but the connection can be infinite in
>>>>>>>>>>>>>>>>>>>>>>>> length, and thus not provable.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Try and show an expression of language that is
>>>>>>>>>>>>>>>>>>>>>>>>> true in a formal system
>>>>>>>>>>>>>>>>>>>>>>>>> (not just true somewhere else) that does not
>>>>>>>>>>>>>>>>>>>>>>>>> have any connection to
>>>>>>>>>>>>>>>>>>>>>>>>> truth maker axioms in this formal system. You
>>>>>>>>>>>>>>>>>>>>>>>>> must show why it is true
>>>>>>>>>>>>>>>>>>>>>>>>> in this formal system not merely that it is
>>>>>>>>>>>>>>>>>>>>>>>>> true somewhere else.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> The connection might be infinite, and thus not
>>>>>>>>>>>>>>>>>>>>>>>> SHOWABLE as a proof strictly in the formal system.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> If the connection exists as an infinite
>>>>>>>>>>>>>>>>>>>>>>>> connection within the system, then it is TRUE in
>>>>>>>>>>>>>>>>>>>>>>>> the system.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Note, that if there is such an infinite
>>>>>>>>>>>>>>>>>>>>>>>> connection, which thus can not be proven within
>>>>>>>>>>>>>>>>>>>>>>>> the formal system, it is still possible, that
>>>>>>>>>>>>>>>>>>>>>>>> another system, related to that system, with
>>>>>>>>>>>>>>>>>>>>>>>> more knowledge, might be able to show that there
>>>>>>>>>>>>>>>>>>>>>>>> does exist within the original formal system
>>>>>>>>>>>>>>>>>>>>>>>> such an infinte connection.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> G states that there does not exist a Natural
>>>>>>>>>>>>>>>>>>>>>>>> Number g that meets a specific requirement
>>>>>>>>>>>>>>>>>>>>>>>> (expressed as a primative recursive relationship).
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> This statement turns out to be true, because it
>>>>>>>>>>>>>>>>>>>>>>>> turns out that no number g does meet that
>>>>>>>>>>>>>>>>>>>>>>>> requirement, but it can't be proven in F that
>>>>>>>>>>>>>>>>>>>>>>>> this is true, because in F, to show this we need
>>>>>>>>>>>>>>>>>>>>>>>> to test every natuarl number, which requires an
>>>>>>>>>>>>>>>>>>>>>>>> infinite number of steps (finite for each
>>>>>>>>>>>>>>>>>>>>>>>> number, but an infinite number of numbers to test).
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> In meta-F, we can do better, because due to
>>>>>>>>>>>>>>>>>>>>>>>> additional knowledge in meta-F, we can show that
>>>>>>>>>>>>>>>>>>>>>>>> if a number g could be found, then that number g
>>>>>>>>>>>>>>>>>>>>>>>> could be converted into a proof, in F, of the
>>>>>>>>>>>>>>>>>>>>>>>> statement G (which says that such a number does
>>>>>>>>>>>>>>>>>>>>>>>> not exist).
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true,
>>>>>>>>>>>>>>>>>>>>>>>> and also show that no proof of it can exist in F.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> So your basic line-of-reasoning is that G is true
>>>>>>>>>>>>>>>>>>>>>>> in F even if the truth
>>>>>>>>>>>>>>>>>>>>>>> of G cannot even be expressed in F as long as the
>>>>>>>>>>>>>>>>>>>>>>> truth of G can be
>>>>>>>>>>>>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Expect that it CAN be expressed in F, it just is
>>>>>>>>>>>>>>>>>>>>>> an infinite expression.
>>>>>>>>>>>>>>>>>>>>> That is false. It is not that G takes an infinite
>>>>>>>>>>>>>>>>>>>>> number of steps to
>>>>>>>>>>>>>>>>>>>>> reach its truth maker axioms in F it is that even
>>>>>>>>>>>>>>>>>>>>> after an infinite
>>>>>>>>>>>>>>>>>>>>> number of steps it never reaches is truth maker
>>>>>>>>>>>>>>>>>>>>> axioms in F because G is
>>>>>>>>>>>>>>>>>>>>> simply untrue in F.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> No, YOUR problem is you aren't actually talking
>>>>>>>>>>>>>>>>>>>> about G in F.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> "This sentence is not true"
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Which isn't G.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Not true about what?
>>>>>>>>>>>>>>>>>>>>> Not true about being not true.
>>>>>>>>>>>>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>>>>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> So you are just a MORON.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Since Gödel said:
>>>>>>>>>>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be
>>>>>>>>>>>>>>>>>>>>> used for a similar undecidability proof.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy
>>>>>>>>>>>>>>>>>>>>> for his proof we
>>>>>>>>>>>>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Ad Hominem attacks are the tactic that people having
>>>>>>>>>>>>>>>>>>> no interest in any
>>>>>>>>>>>>>>>>>>> honest dialogue use when they realize that their
>>>>>>>>>>>>>>>>>>> reasoning has been
>>>>>>>>>>>>>>>>>>> utterly defeated.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> You ARE a LYING MORON as you insist that Godel's G is
>>>>>>>>>>>>>>>>>> a sentence that is actually provably isn't.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> You think it is because you are too stupid to actually
>>>>>>>>>>>>>>>>>> read any of the paper, so you take that comment that
>>>>>>>>>>>>>>>>>> the statment is "based" on that statement to mean it
>>>>>>>>>>>>>>>>>> IS that statement.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> All of your Ad Hominem attacks cannot possibly hide the
>>>>>>>>>>>>>>>>> fact that you
>>>>>>>>>>>>>>>>> are asserting this counter-factual statement:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> when a valid proxy for an argument is defeated this
>>>>>>>>>>>>>>>>> does not defeat the
>>>>>>>>>>>>>>>>> original argument.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Right, which is what YOU are doing, showing your
>>>>>>>>>>>>>>>> arguement is INVALID.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In other words you disagree that correctly refuting a
>>>>>>>>>>>>>>> valid proxy for an
>>>>>>>>>>>>>>> argument does correctly refute the original argument?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> VALID is the key word,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Yours isn't (I don't think you actually know the meaning
>>>>>>>>>>>>>> of the words)
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> And you are an IDIOT to claim it is.
>>>>>>>>>>>>> So Gödel is wrong when he says:
>>>>>>>>>>>>>
>>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>>>>>>> similar undecidability proof.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> No, but you don't understand what he is saying.
>>>>>>>>>>>>
>>>>>>>>>>> He is saying that every epistemological antinomy is a valid
>>>>>>>>>>> proxy for
>>>>>>>>>>> his proof. He is not saying that his expression is not an
>>>>>>>>>>> epistemological antinomy.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Nope, that isn't what he is saying. How could it be, the
>>>>>>>>>> ACTUAL G is a proven Truth Bearer, while the Liar's Paradox isn't
>>>>>>>>>>
>>>>>>>>>> Your arguement just shows its inconsistency.
>>>>>>>>>>
>>>>>>>>>> In part, because you don't actually understand what the
>>>>>>>>>> sentence actually is.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> The analogy between this result and Richard’s antinomy leaps
>>>>>>>>>>> to the eye;
>>>>>>>>>>> there is also a close relationship with the “liar”
>>>>>>>>>>> antinomy,14 since the
>>>>>>>>>>> undecidable proposition [R(q); q] states precisely that q
>>>>>>>>>>> belongs to K,
>>>>>>>>>>> i.e. according to (1), that [R(q); q] is not provable. We are
>>>>>>>>>>> therefore
>>>>>>>>>>> confronted with a proposition which asserts its own
>>>>>>>>>>> unprovability.
>>>>>>>>>>> (Gödel 1931:43)
>>>>>>>>>>>
>>>>>>>>>>> This <is> an isomorphism to a proposition that asserts its
>>>>>>>>>>> own untruth.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Nope, unless you erroneously think that statements about Truth
>>>>>>>>>> ARE statements about provability, that isn't an isomoprhism.
>>>>>>>>>>
>>>>>>>>>> Note, you have even stated that *ALL* statements of the form
>>>>>>>>>> "statement x is provable" or "Statment x is not provable" are
>>>>>>>>>> Truth Bearers,
>>>>>>>>>
>>>>>>>>> I have most definitely never said this or anything that could be
>>>>>>>>> unintentionally misconstrued to mean this.
>>>>>>>>>
>>>>>>>>> It is always the case that when-so-ever any expression of
>>>>>>>>> language only
>>>>>>>>> refers to its own truth or provability that this expression is
>>>>>>>>> not a
>>>>>>>>> truth bearer, thus not a member of any formal system of logic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> You admitted that it was TRUE that a statement could not be
>>>>>>>> proven even if the only way to show that it could not be proven
>>>>>>>> was to check the infinite set of all possible proofs to see that
>>>>>>>> none of them were a proof.
>>>>>>>>
>>>>>>>
>>>>>>> This is not related to what I just said. Every expression of
>>>>>>> language is
>>>>>>> untrue unless it has a semantic connection to its truth maker axiom.
>>>>>>
>>>>>> I never disagreed with that, just that you keep on wavering
>>>>>> between just saying there must be a connection, and then at times
>>>>>> adding it must be a FINITE connection (which is actually only
>>>>>> requried to be Proven)
>>>>>>
>>>>>> G, the statment about the non-existance of a natural number that
>>>>>> satisfies the specified primative recursive relationship is TRUE,
>>>>>> because it IS connected to the truth maker axioms of math via an
>>>>>> infinite chain of steps.
>>>>>>
>>>>>> Each natural number can be shown to not meet that requirement in a
>>>>> Gödel was actually talking about the expression:
>>>>>
>>>>> We are therefore confronted with a proposition which asserts its own
>>>>> unprovability. (Gödel 1931:43)
>>>>
>>>> No, that is a statement which is proven in Meta-F to have the
>>>> identical truth value of G. G doesn't SAY it is unprovable, but a
>>>> natural concesequence of G being True is that it is unprovable, and
>>>> if it is provable, it can't be True. Since G must be True or False,
>>>> if it is True it IS unprovable, and if it is Provable, then it must
>>>> be False, which is a contradiction (since ALL provable statements
>>>> are True), so that case is impossible. Thus, G MUST be True but
>>>> Unprovable.
>>>>
>>>> If F includes an axiom that says all Truths are Provable, then F is
>>>> proved to be inconsistent.
>>>>
>>>>>
>>>>> He only used the whole natural numbers thing to be able to encode the
>>>>> above expression in a language that did not have a provability
>>>>> predicate.
>>>>
>>>> No, F might well have a provability predicate, ies of the Natural
>>>> Numbers.
>>>>
>>>
>>> Then it would not need any Gödel number.
>>
>> Maybe, but the key is that it DOESN'T use the operator, so your
>> "special" rule based on using it doesn't apply.
>>
>> Godel showed that Meta-F we can construct a calculation in Meta-F that
>> is the exact same caluclation in F that provides us proofs in Meta-F
>> based on what is simply a calculation in F.
>>
>> Since it is just a calculation in F about the existance of a number
>> based on a computable function, in F the stateement ALWAYS has a Truth
>> Value, either such a number exsits or it doesn't.
>>
>> Because of the DEFINED relationship between F and Meta-F, that truth
>> value transfers, and due to the extra axioms in Meta-F.
>>
>> Arguing that in Meta-F we have an epistemological antinomy means that
>> your logic system makes the mathematics in F be able to create this
>> same situation, which doesn't match the behavior of the Natural
>> Numbers, so your F doesn't meet the requirements for it.
>>
>> YOU "PROOF" FAILS.
>>
>>
>> If you want to make the sort of claims you are doing, you need to show
>> exactly which step in his proof does something wrong. You are not
>> allowed to rebut a proof by saying its answer must be wrong, or you
>> disagree with a footnote. You need to find an actaul erroneous step in
>> the proof itself.
>>
>> Since you have shown you don't actually understand the proof at all,
>> this is probably impossible for you.
>>
>>>
>>>>>
>>>>> (G) F ⊢ GF ↔ ¬ProvF(┌GF┐). // with Gödel number
>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>
>>> *paraphrased as: GF ↔ (F ⊬ GF) // without Gödel number*
>>
>> Nope, it only "means" that in Meta F, not in F.
>>
>> F doesn't have Truth Makers to establish that meaning, so that
>> "parapharse" is incorrect.
>>
>> You are just showing you don't understand what logic does.
>>
>>>
>>>>>
>>>>>
>>>>
>>>>
>>>> Which if you read, agrees with Godel, that this sentence must be
>>>> neither provable or disprovable, and agrees with the right
>>>> conditions, can be made True.
>>>
>>> I am removing the Gödel number and showing what's left.
>>>
>>
>> Remove the Godel Number, and NOTHING is left of the statement in F,
>
> Here is what remains: GF ↔ (F ⊬ GF)
>

On 1/17/23 11:39 AM, olcott wrote:
> On 1/16/2023 7:51 PM, Richard Damon wrote:
>> On 1/16/23 10:17 AM, olcott wrote:
>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>> language of this
>>>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> So PA has no idea that:
>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>>>>>
>>>>>>>>
>>>>>>>> Why do you say that.
>>>>>>>>
>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>>>>> doesn't mean it can't be.
>>>>>>>>
>>>>>>>> In fact, your statement just comes out of a simple application
>>>>>>>> of the addition AXIOMS of PA.
>>>>>>>>
>>>>>>>> a + 0 = a
>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>
>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>>>>
>>>>>>>
>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>> expression of
>>>>>>> its language to its truth maker axioms the expression is untrue
>>>>>>> in that
>>>>>>> formal system.
>>>>>>
>>>>>> Right, but the connection can be infinite in length, and thus not
>>>>>> provable.
>>>>>>
>>>>>>>
>>>>>>> Try and show an expression of language that is true in a formal
>>>>>>> system
>>>>>>> (not just true somewhere else) that does not have any connection to
>>>>>>> truth maker axioms in this formal system. You must show why it is
>>>>>>> true
>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>
>>>>>>
>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>>>>> strictly in the formal system.
>>>>>>
>>>>>> If the connection exists as an infinite connection within the
>>>>>> system, then it is TRUE in the system.
>>>>>>
>>>>>> Note, that if there is such an infinite connection, which thus can
>>>>>> not be proven within the formal system, it is still possible, that
>>>>>> another system, related to that system, with more knowledge, might
>>>>>> be able to show that there does exist within the original formal
>>>>>> system such an infinte connection.
>>>>>>
>>>>>> This is what happens to G in F and meta-F
>>>>>>
>>>>>> G states that there does not exist a Natural Number g that meets a
>>>>>> specific requirement (expressed as a primative recursive
>>>>>> relationship).
>>>>>>
>>>>>> This statement turns out to be true, because it turns out that no
>>>>>> number g does meet that requirement, but it can't be proven in F
>>>>>> that this is true, because in F, to show this we need to test
>>>>>> every natuarl number, which requires an infinite number of steps
>>>>>> (finite for each number, but an infinite number of numbers to test).
>>>>>>
>>>>>> In meta-F, we can do better, because due to additional knowledge
>>>>>> in meta-F, we can show that if a number g could be found, then
>>>>>> that number g could be converted into a proof, in F, of the
>>>>>> statement G (which says that such a number does not exist).
>>>>>>
>>>>>> Thus, in meta-F, we can prove that G is true, and also show that
>>>>>> no proof of it can exist in F.
>>>>>>
>>>>> So your basic line-of-reasoning is that G is true in F even if the
>>>>> truth
>>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>>> expressed in meta-F.
>>>>>
>>>>
>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>> expression.
>>>>
>>> So you changed your mind about infinite proofs in formal systems?
>>> We know the steps of the infinite proof for the Goldbach conjecture.
>>
>> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
>> infinte sets oc connections, proofs can't. Only YOU have perposed that
>> we think about infinite proofs.
>>
>
> Formal systems cannot ever use infinite connections from their
> expressions of language to their truth maker axioms thus eliminating
> these from consideration as any measure of true "in the system".
>
>

Source? or is this just another of your made up "Facts"

WHERE in the definition of a "Formal System" does it say that the
connecti0on must be finite.

On 1/17/23 12:25 PM, olcott wrote:
>
> If any mathematician had noticed this then they would have noticed that
> Gödel did not prove that formal systems are incomplete. He only proved
> that some of the expressions of language of a formal system are simply
> untrue which is a mere triviality that everyone already knew.

And the statements that you claim have become untrue show that your
logic system can no longer support Mathematics.

The statement that you are rejecting is like: "There exists no n a
member of the Natural Numbers exists that make f(n) == 0, where f is a
computable function" CAN'T be a non-truth bearer in Mathematics, as
either a value of n exists or it doesn't.

Just like eithat a proof exists or it doesn't, that ALL statments about
provability are truth bearers.

THe fact that you say the statement isn't a Truth Bearer says you don't
have mathemeatics in your logic system any more.

YOU FAIL.

On Tuesday, January 17, 2023 at 9:25:11 AM UTC-8, olcott wrote:
> On 1/17/2023 10:44 AM, Jeffrey Rubard wrote:
> > On Tuesday, January 17, 2023 at 8:40:02 AM UTC-8, _ Olcott wrote:
> >> On 1/16/2023 7:51 PM, Richard Damon wrote:
> >>> On 1/16/23 10:17 AM, olcott wrote:
> >>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
> >>>>> On 1/15/23 11:15 AM, olcott wrote:
> >>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
> >>>>>>> On 1/14/23 6:19 PM, olcott wrote:
> >>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
> >>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
> >>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
> >>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
> >>>>>>>>>>>> How does the formal system know that an expression of language
> >>>>>>>>>>>> of this
> >>>>>>>>>>>> formal system is true unless this expression of language has a
> >>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
> >>>>>>>>>>>>
> >>>>>>>>>>>>
> >>>>>>>>>>>
> >>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
> >>>>>>>>>>>
> >>>>>>>>>>
> >>>>>>>>>> So PA has no idea that:
> >>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
> >>>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> Why do you say that.
> >>>>>>>>>
> >>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
> >>>>>>>>> doesn't mean it can't be.
> >>>>>>>>>
> >>>>>>>>> In fact, your statement just comes out of a simple application of
> >>>>>>>>> the addition AXIOMS of PA.
> >>>>>>>>>
> >>>>>>>>> a + 0 = a
> >>>>>>>>> a + Successor(b) = Successor(a + b)
> >>>>>>>>>
> >>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
> >>>>>>>>>
> >>>>>>>>
> >>>>>>>> Unless a formal system has a syntactic connection from an
> >>>>>>>> expression of
> >>>>>>>> its language to its truth maker axioms the expression is untrue in
> >>>>>>>> that
> >>>>>>>> formal system.
> >>>>>>>
> >>>>>>> Right, but the connection can be infinite in length, and thus not
> >>>>>>> provable.
> >>>>>>>
> >>>>>>>>
> >>>>>>>> Try and show an expression of language that is true in a formal
> >>>>>>>> system
> >>>>>>>> (not just true somewhere else) that does not have any connection to
> >>>>>>>> truth maker axioms in this formal system. You must show why it is
> >>>>>>>> true
> >>>>>>>> in this formal system not merely that it is true somewhere else.
> >>>>>>>>
> >>>>>>>
> >>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
> >>>>>>> strictly in the formal system.
> >>>>>>>
> >>>>>>> If the connection exists as an infinite connection within the
> >>>>>>> system, then it is TRUE in the system.
> >>>>>>>
> >>>>>>> Note, that if there is such an infinite connection, which thus can
> >>>>>>> not be proven within the formal system, it is still possible, that
> >>>>>>> another system, related to that system, with more knowledge, might
> >>>>>>> be able to show that there does exist within the original formal
> >>>>>>> system such an infinte connection.
> >>>>>>>
> >>>>>>> This is what happens to G in F and meta-F
> >>>>>>>
> >>>>>>> G states that there does not exist a Natural Number g that meets a
> >>>>>>> specific requirement (expressed as a primative recursive
> >>>>>>> relationship).
> >>>>>>>
> >>>>>>> This statement turns out to be true, because it turns out that no
> >>>>>>> number g does meet that requirement, but it can't be proven in F
> >>>>>>> that this is true, because in F, to show this we need to test every
> >>>>>>> natuarl number, which requires an infinite number of steps (finite
> >>>>>>> for each number, but an infinite number of numbers to test).
> >>>>>>>
> >>>>>>> In meta-F, we can do better, because due to additional knowledge in
> >>>>>>> meta-F, we can show that if a number g could be found, then that
> >>>>>>> number g could be converted into a proof, in F, of the statement G
> >>>>>>> (which says that such a number does not exist).
> >>>>>>>
> >>>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
> >>>>>>> proof of it can exist in F.
> >>>>>>>
> >>>>>> So your basic line-of-reasoning is that G is true in F even if the
> >>>>>> truth
> >>>>>> of G cannot even be expressed in F as long as the truth of G can be
> >>>>>> expressed in meta-F.
> >>>>>>
> >>>>>
> >>>>> Expect that it CAN be expressed in F, it just is an infinite expression.
> >>>>>
> >>>> So you changed your mind about infinite proofs in formal systems?
> >>>> We know the steps of the infinite proof for the Goldbach conjecture.
> >>>
> >>> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
> >>> infinte sets oc connections, proofs can't. Only YOU have perposed that
> >>> we think about infinite proofs.
> >>>
>
> >> Formal systems cannot ever use infinite connections from their
> >> expressions of language to their truth maker axioms thus eliminating
> >> these from consideration as any measure of true "in the system".
>
> >> --
> >> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> >> hits a target no one else can see." Arthur Schopenhauer
> >
> > "What you've written is almost like formal logic."
>
> I am filling in a key detail about the way that "true" in formal logic
> actually works. Wittgenstein first pointed this out and no mathematician
> has ever noticed. https://www.liarparadox.org/Wittgenstein.pdf
>
> If any mathematician had noticed this then they would have noticed that
> Gödel did not prove that formal systems are incomplete. He only proved
> that some of the expressions of language of a formal system are simply
> untrue which is a mere triviality that everyone already knew.
> --
> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

This is just really, really poor.

On Tuesday, January 17, 2023 at 6:46:00 PM UTC-6, Jeffrey Rubard wrote:
> On Tuesday, January 17, 2023 at 9:25:11 AM UTC-8, olcott wrote:
> > On 1/17/2023 10:44 AM, Jeffrey Rubard wrote:
> > > On Tuesday, January 17, 2023 at 8:40:02 AM UTC-8, _ Olcott wrote:
> > >> On 1/16/2023 7:51 PM, Richard Damon wrote:
> > >>> On 1/16/23 10:17 AM, olcott wrote:
> > >>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
> > >>>>> On 1/15/23 11:15 AM, olcott wrote:
> > >>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
> > >>>>>>> On 1/14/23 6:19 PM, olcott wrote:
> > >>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
> > >>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
> > >>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
> > >>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
> > >>>>>>>>>>>> How does the formal system know that an expression of language
> > >>>>>>>>>>>> of this
> > >>>>>>>>>>>> formal system is true unless this expression of language has a
> > >>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
> > >>>>>>>>>>>>
> > >>>>>>>>>>>>
> > >>>>>>>>>>>
> > >>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
> > >>>>>>>>>>>
> > >>>>>>>>>>
> > >>>>>>>>>> So PA has no idea that:
> > >>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
> > >>>>>>>>>>
> > >>>>>>>>>
> > >>>>>>>>> Why do you say that.
> > >>>>>>>>>
> > >>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
> > >>>>>>>>> doesn't mean it can't be.
> > >>>>>>>>>
> > >>>>>>>>> In fact, your statement just comes out of a simple application of
> > >>>>>>>>> the addition AXIOMS of PA.
> > >>>>>>>>>
> > >>>>>>>>> a + 0 = a
> > >>>>>>>>> a + Successor(b) = Successor(a + b)
> > >>>>>>>>>
> > >>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
> > >>>>>>>>>
> > >>>>>>>>
> > >>>>>>>> Unless a formal system has a syntactic connection from an
> > >>>>>>>> expression of
> > >>>>>>>> its language to its truth maker axioms the expression is untrue in
> > >>>>>>>> that
> > >>>>>>>> formal system.
> > >>>>>>>
> > >>>>>>> Right, but the connection can be infinite in length, and thus not
> > >>>>>>> provable.
> > >>>>>>>
> > >>>>>>>>
> > >>>>>>>> Try and show an expression of language that is true in a formal
> > >>>>>>>> system
> > >>>>>>>> (not just true somewhere else) that does not have any connection to
> > >>>>>>>> truth maker axioms in this formal system. You must show why it is
> > >>>>>>>> true
> > >>>>>>>> in this formal system not merely that it is true somewhere else.
> > >>>>>>>>
> > >>>>>>>
> > >>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
> > >>>>>>> strictly in the formal system.
> > >>>>>>>
> > >>>>>>> If the connection exists as an infinite connection within the
> > >>>>>>> system, then it is TRUE in the system.
> > >>>>>>>
> > >>>>>>> Note, that if there is such an infinite connection, which thus can
> > >>>>>>> not be proven within the formal system, it is still possible, that
> > >>>>>>> another system, related to that system, with more knowledge, might
> > >>>>>>> be able to show that there does exist within the original formal
> > >>>>>>> system such an infinte connection.
> > >>>>>>>
> > >>>>>>> This is what happens to G in F and meta-F
> > >>>>>>>
> > >>>>>>> G states that there does not exist a Natural Number g that meets a
> > >>>>>>> specific requirement (expressed as a primative recursive
> > >>>>>>> relationship).
> > >>>>>>>
> > >>>>>>> This statement turns out to be true, because it turns out that no
> > >>>>>>> number g does meet that requirement, but it can't be proven in F
> > >>>>>>> that this is true, because in F, to show this we need to test every
> > >>>>>>> natuarl number, which requires an infinite number of steps (finite
> > >>>>>>> for each number, but an infinite number of numbers to test).
> > >>>>>>>
> > >>>>>>> In meta-F, we can do better, because due to additional knowledge in
> > >>>>>>> meta-F, we can show that if a number g could be found, then that
> > >>>>>>> number g could be converted into a proof, in F, of the statement G
> > >>>>>>> (which says that such a number does not exist).
> > >>>>>>>
> > >>>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
> > >>>>>>> proof of it can exist in F.
> > >>>>>>>
> > >>>>>> So your basic line-of-reasoning is that G is true in F even if the
> > >>>>>> truth
> > >>>>>> of G cannot even be expressed in F as long as the truth of G can be
> > >>>>>> expressed in meta-F.
> > >>>>>>
> > >>>>>
> > >>>>> Expect that it CAN be expressed in F, it just is an infinite expression.
> > >>>>>
> > >>>> So you changed your mind about infinite proofs in formal systems?
> > >>>> We know the steps of the infinite proof for the Goldbach conjecture.
> > >>>
> > >>> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
> > >>> infinte sets oc connections, proofs can't. Only YOU have perposed that
> > >>> we think about infinite proofs.
> > >>>
> >
> > >> Formal systems cannot ever use infinite connections from their
> > >> expressions of language to their truth maker axioms thus eliminating
> > >> these from consideration as any measure of true "in the system".
> >
> > >> --
> > >> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > >> hits a target no one else can see." Arthur Schopenhauer
> > >
> > > "What you've written is almost like formal logic."
> >
> > I am filling in a key detail about the way that "true" in formal logic
> > actually works. Wittgenstein first pointed this out and no mathematician
> > has ever noticed. https://www.liarparadox.org/Wittgenstein.pdf
> >
> > If any mathematician had noticed this then they would have noticed that
> > Gödel did not prove that formal systems are incomplete. He only proved
> > that some of the expressions of language of a formal system are simply
> > untrue which is a mere triviality that everyone already knew.
> > --
> > Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > hits a target no one else can see." Arthur Schopenhauer
> This is just really, really poor.

On Tuesday, January 17, 2023 at 6:46:00 PM UTC-6, Jeffrey Rubard wrote:
> On Tuesday, January 17, 2023 at 9:25:11 AM UTC-8, olcott wrote:
> > On 1/17/2023 10:44 AM, Jeffrey Rubard wrote:
> > > On Tuesday, January 17, 2023 at 8:40:02 AM UTC-8, _ Olcott wrote:
> > >> On 1/16/2023 7:51 PM, Richard Damon wrote:
> > >>> On 1/16/23 10:17 AM, olcott wrote:
> > >>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
> > >>>>> On 1/15/23 11:15 AM, olcott wrote:
> > >>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
> > >>>>>>> On 1/14/23 6:19 PM, olcott wrote:
> > >>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
> > >>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
> > >>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
> > >>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
> > >>>>>>>>>>>> How does the formal system know that an expression of language
> > >>>>>>>>>>>> of this
> > >>>>>>>>>>>> formal system is true unless this expression of language has a
> > >>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
> > >>>>>>>>>>>>
> > >>>>>>>>>>>>
> > >>>>>>>>>>>
> > >>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
> > >>>>>>>>>>>
> > >>>>>>>>>>
> > >>>>>>>>>> So PA has no idea that:
> > >>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
> > >>>>>>>>>>
> > >>>>>>>>>
> > >>>>>>>>> Why do you say that.
> > >>>>>>>>>
> > >>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
> > >>>>>>>>> doesn't mean it can't be.
> > >>>>>>>>>
> > >>>>>>>>> In fact, your statement just comes out of a simple application of
> > >>>>>>>>> the addition AXIOMS of PA.
> > >>>>>>>>>
> > >>>>>>>>> a + 0 = a
> > >>>>>>>>> a + Successor(b) = Successor(a + b)
> > >>>>>>>>>
> > >>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
> > >>>>>>>>>
> > >>>>>>>>
> > >>>>>>>> Unless a formal system has a syntactic connection from an
> > >>>>>>>> expression of
> > >>>>>>>> its language to its truth maker axioms the expression is untrue in
> > >>>>>>>> that
> > >>>>>>>> formal system.
> > >>>>>>>
> > >>>>>>> Right, but the connection can be infinite in length, and thus not
> > >>>>>>> provable.
> > >>>>>>>
> > >>>>>>>>
> > >>>>>>>> Try and show an expression of language that is true in a formal
> > >>>>>>>> system
> > >>>>>>>> (not just true somewhere else) that does not have any connection to
> > >>>>>>>> truth maker axioms in this formal system. You must show why it is
> > >>>>>>>> true
> > >>>>>>>> in this formal system not merely that it is true somewhere else.
> > >>>>>>>>
> > >>>>>>>
> > >>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
> > >>>>>>> strictly in the formal system.
> > >>>>>>>
> > >>>>>>> If the connection exists as an infinite connection within the
> > >>>>>>> system, then it is TRUE in the system.
> > >>>>>>>
> > >>>>>>> Note, that if there is such an infinite connection, which thus can
> > >>>>>>> not be proven within the formal system, it is still possible, that
> > >>>>>>> another system, related to that system, with more knowledge, might
> > >>>>>>> be able to show that there does exist within the original formal
> > >>>>>>> system such an infinte connection.
> > >>>>>>>
> > >>>>>>> This is what happens to G in F and meta-F
> > >>>>>>>
> > >>>>>>> G states that there does not exist a Natural Number g that meets a
> > >>>>>>> specific requirement (expressed as a primative recursive
> > >>>>>>> relationship).
> > >>>>>>>
> > >>>>>>> This statement turns out to be true, because it turns out that no
> > >>>>>>> number g does meet that requirement, but it can't be proven in F
> > >>>>>>> that this is true, because in F, to show this we need to test every
> > >>>>>>> natuarl number, which requires an infinite number of steps (finite
> > >>>>>>> for each number, but an infinite number of numbers to test).
> > >>>>>>>
> > >>>>>>> In meta-F, we can do better, because due to additional knowledge in
> > >>>>>>> meta-F, we can show that if a number g could be found, then that
> > >>>>>>> number g could be converted into a proof, in F, of the statement G
> > >>>>>>> (which says that such a number does not exist).
> > >>>>>>>
> > >>>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
> > >>>>>>> proof of it can exist in F.
> > >>>>>>>
> > >>>>>> So your basic line-of-reasoning is that G is true in F even if the
> > >>>>>> truth
> > >>>>>> of G cannot even be expressed in F as long as the truth of G can be
> > >>>>>> expressed in meta-F.
> > >>>>>>
> > >>>>>
> > >>>>> Expect that it CAN be expressed in F, it just is an infinite expression.
> > >>>>>
> > >>>> So you changed your mind about infinite proofs in formal systems?
> > >>>> We know the steps of the infinite proof for the Goldbach conjecture.
> > >>>
> > >>> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
> > >>> infinte sets oc connections, proofs can't. Only YOU have perposed that
> > >>> we think about infinite proofs.
> > >>>
> >
> > >> Formal systems cannot ever use infinite connections from their
> > >> expressions of language to their truth maker axioms thus eliminating
> > >> these from consideration as any measure of true "in the system".
> >
> > >> --
> > >> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > >> hits a target no one else can see." Arthur Schopenhauer
> > >
> > > "What you've written is almost like formal logic."
> >
> > I am filling in a key detail about the way that "true" in formal logic
> > actually works. Wittgenstein first pointed this out and no mathematician
> > has ever noticed. https://www.liarparadox.org/Wittgenstein.pdf
> >
> > If any mathematician had noticed this then they would have noticed that
> > Gödel did not prove that formal systems are incomplete. He only proved
> > that some of the expressions of language of a formal system are simply
> > untrue which is a mere triviality that everyone already knew.
> > --
> > Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > hits a target no one else can see." Arthur Schopenhauer
> This is just really, really poor.

On Wednesday, January 18, 2023 at 11:11:45 PM UTC-6, Don Stockbauer wrote:
> On Tuesday, January 17, 2023 at 6:46:00 PM UTC-6, Jeffrey Rubard wrote:
> > On Tuesday, January 17, 2023 at 9:25:11 AM UTC-8, olcott wrote:
> > > On 1/17/2023 10:44 AM, Jeffrey Rubard wrote:
> > > > On Tuesday, January 17, 2023 at 8:40:02 AM UTC-8, _ Olcott wrote:
> > > >> On 1/16/2023 7:51 PM, Richard Damon wrote:
> > > >>> On 1/16/23 10:17 AM, olcott wrote:
> > > >>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
> > > >>>>> On 1/15/23 11:15 AM, olcott wrote:
> > > >>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
> > > >>>>>>> On 1/14/23 6:19 PM, olcott wrote:
> > > >>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
> > > >>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
> > > >>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
> > > >>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
> > > >>>>>>>>>>>> How does the formal system know that an expression of language
> > > >>>>>>>>>>>> of this
> > > >>>>>>>>>>>> formal system is true unless this expression of language has a
> > > >>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
> > > >>>>>>>>>>>>
> > > >>>>>>>>>>>>
> > > >>>>>>>>>>>
> > > >>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
> > > >>>>>>>>>>>
> > > >>>>>>>>>>
> > > >>>>>>>>>> So PA has no idea that:
> > > >>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
> > > >>>>>>>>>>
> > > >>>>>>>>>
> > > >>>>>>>>> Why do you say that.
> > > >>>>>>>>>
> > > >>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
> > > >>>>>>>>> doesn't mean it can't be.
> > > >>>>>>>>>
> > > >>>>>>>>> In fact, your statement just comes out of a simple application of
> > > >>>>>>>>> the addition AXIOMS of PA.
> > > >>>>>>>>>
> > > >>>>>>>>> a + 0 = a
> > > >>>>>>>>> a + Successor(b) = Successor(a + b)
> > > >>>>>>>>>
> > > >>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
> > > >>>>>>>>>
> > > >>>>>>>>
> > > >>>>>>>> Unless a formal system has a syntactic connection from an
> > > >>>>>>>> expression of
> > > >>>>>>>> its language to its truth maker axioms the expression is untrue in
> > > >>>>>>>> that
> > > >>>>>>>> formal system.
> > > >>>>>>>
> > > >>>>>>> Right, but the connection can be infinite in length, and thus not
> > > >>>>>>> provable.
> > > >>>>>>>
> > > >>>>>>>>
> > > >>>>>>>> Try and show an expression of language that is true in a formal
> > > >>>>>>>> system
> > > >>>>>>>> (not just true somewhere else) that does not have any connection to
> > > >>>>>>>> truth maker axioms in this formal system. You must show why it is
> > > >>>>>>>> true
> > > >>>>>>>> in this formal system not merely that it is true somewhere else.
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
> > > >>>>>>> strictly in the formal system.
> > > >>>>>>>
> > > >>>>>>> If the connection exists as an infinite connection within the
> > > >>>>>>> system, then it is TRUE in the system.
> > > >>>>>>>
> > > >>>>>>> Note, that if there is such an infinite connection, which thus can
> > > >>>>>>> not be proven within the formal system, it is still possible, that
> > > >>>>>>> another system, related to that system, with more knowledge, might
> > > >>>>>>> be able to show that there does exist within the original formal
> > > >>>>>>> system such an infinte connection.
> > > >>>>>>>
> > > >>>>>>> This is what happens to G in F and meta-F
> > > >>>>>>>
> > > >>>>>>> G states that there does not exist a Natural Number g that meets a
> > > >>>>>>> specific requirement (expressed as a primative recursive
> > > >>>>>>> relationship).
> > > >>>>>>>
> > > >>>>>>> This statement turns out to be true, because it turns out that no
> > > >>>>>>> number g does meet that requirement, but it can't be proven in F
> > > >>>>>>> that this is true, because in F, to show this we need to test every
> > > >>>>>>> natuarl number, which requires an infinite number of steps (finite
> > > >>>>>>> for each number, but an infinite number of numbers to test).
> > > >>>>>>>
> > > >>>>>>> In meta-F, we can do better, because due to additional knowledge in
> > > >>>>>>> meta-F, we can show that if a number g could be found, then that
> > > >>>>>>> number g could be converted into a proof, in F, of the statement G
> > > >>>>>>> (which says that such a number does not exist).
> > > >>>>>>>
> > > >>>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
> > > >>>>>>> proof of it can exist in F.
> > > >>>>>>>
> > > >>>>>> So your basic line-of-reasoning is that G is true in F even if the
> > > >>>>>> truth
> > > >>>>>> of G cannot even be expressed in F as long as the truth of G can be
> > > >>>>>> expressed in meta-F.
> > > >>>>>>
> > > >>>>>
> > > >>>>> Expect that it CAN be expressed in F, it just is an infinite expression.
> > > >>>>>
> > > >>>> So you changed your mind about infinite proofs in formal systems?
> > > >>>> We know the steps of the infinite proof for the Goldbach conjecture.
> > > >>>
> > > >>> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
> > > >>> infinte sets oc connections, proofs can't. Only YOU have perposed that
> > > >>> we think about infinite proofs.
> > > >>>
> > >
> > > >> Formal systems cannot ever use infinite connections from their
> > > >> expressions of language to their truth maker axioms thus eliminating
> > > >> these from consideration as any measure of true "in the system".
> > >
> > > >> --
> > > >> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > > >> hits a target no one else can see." Arthur Schopenhauer
> > > >
> > > > "What you've written is almost like formal logic."
> > >
> > > I am filling in a key detail about the way that "true" in formal logic
> > > actually works. Wittgenstein first pointed this out and no mathematician
> > > has ever noticed. https://www.liarparadox.org/Wittgenstein.pdf
> > >
> > > If any mathematician had noticed this then they would have noticed that
> > > Gödel did not prove that formal systems are incomplete. He only proved
> > > that some of the expressions of language of a formal system are simply
> > > untrue which is a mere triviality that everyone already knew.
> > > --
> > > Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > > hits a target no one else can see." Arthur Schopenhauer
> > This is just really, really poor.
> Jeffrey, I'll second that emotion.

On Thursday, January 19, 2023 at 5:35:08 AM UTC-8, Don Stockbauer wrote:
> On Wednesday, January 18, 2023 at 11:11:45 PM UTC-6, Don Stockbauer wrote:
> > On Tuesday, January 17, 2023 at 6:46:00 PM UTC-6, Jeffrey Rubard wrote:
> > > On Tuesday, January 17, 2023 at 9:25:11 AM UTC-8, olcott wrote:
> > > > On 1/17/2023 10:44 AM, Jeffrey Rubard wrote:
> > > > > On Tuesday, January 17, 2023 at 8:40:02 AM UTC-8, _ Olcott wrote:
> > > > >> On 1/16/2023 7:51 PM, Richard Damon wrote:
> > > > >>> On 1/16/23 10:17 AM, olcott wrote:
> > > > >>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
> > > > >>>>> On 1/15/23 11:15 AM, olcott wrote:
> > > > >>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
> > > > >>>>>>> On 1/14/23 6:19 PM, olcott wrote:
> > > > >>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
> > > > >>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
> > > > >>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
> > > > >>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
> > > > >>>>>>>>>>>> How does the formal system know that an expression of language
> > > > >>>>>>>>>>>> of this
> > > > >>>>>>>>>>>> formal system is true unless this expression of language has a
> > > > >>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
> > > > >>>>>>>>>>>>
> > > > >>>>>>>>>>>>
> > > > >>>>>>>>>>>
> > > > >>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
> > > > >>>>>>>>>>>
> > > > >>>>>>>>>>
> > > > >>>>>>>>>> So PA has no idea that:
> > > > >>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
> > > > >>>>>>>>>>
> > > > >>>>>>>>>
> > > > >>>>>>>>> Why do you say that.
> > > > >>>>>>>>>
> > > > >>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
> > > > >>>>>>>>> doesn't mean it can't be.
> > > > >>>>>>>>>
> > > > >>>>>>>>> In fact, your statement just comes out of a simple application of
> > > > >>>>>>>>> the addition AXIOMS of PA.
> > > > >>>>>>>>>
> > > > >>>>>>>>> a + 0 = a
> > > > >>>>>>>>> a + Successor(b) = Successor(a + b)
> > > > >>>>>>>>>
> > > > >>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
> > > > >>>>>>>>>
> > > > >>>>>>>>
> > > > >>>>>>>> Unless a formal system has a syntactic connection from an
> > > > >>>>>>>> expression of
> > > > >>>>>>>> its language to its truth maker axioms the expression is untrue in
> > > > >>>>>>>> that
> > > > >>>>>>>> formal system.
> > > > >>>>>>>
> > > > >>>>>>> Right, but the connection can be infinite in length, and thus not
> > > > >>>>>>> provable.
> > > > >>>>>>>
> > > > >>>>>>>>
> > > > >>>>>>>> Try and show an expression of language that is true in a formal
> > > > >>>>>>>> system
> > > > >>>>>>>> (not just true somewhere else) that does not have any connection to
> > > > >>>>>>>> truth maker axioms in this formal system. You must show why it is
> > > > >>>>>>>> true
> > > > >>>>>>>> in this formal system not merely that it is true somewhere else.
> > > > >>>>>>>>
> > > > >>>>>>>
> > > > >>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
> > > > >>>>>>> strictly in the formal system.
> > > > >>>>>>>
> > > > >>>>>>> If the connection exists as an infinite connection within the
> > > > >>>>>>> system, then it is TRUE in the system.
> > > > >>>>>>>
> > > > >>>>>>> Note, that if there is such an infinite connection, which thus can
> > > > >>>>>>> not be proven within the formal system, it is still possible, that
> > > > >>>>>>> another system, related to that system, with more knowledge, might
> > > > >>>>>>> be able to show that there does exist within the original formal
> > > > >>>>>>> system such an infinte connection.
> > > > >>>>>>>
> > > > >>>>>>> This is what happens to G in F and meta-F
> > > > >>>>>>>
> > > > >>>>>>> G states that there does not exist a Natural Number g that meets a
> > > > >>>>>>> specific requirement (expressed as a primative recursive
> > > > >>>>>>> relationship).
> > > > >>>>>>>
> > > > >>>>>>> This statement turns out to be true, because it turns out that no
> > > > >>>>>>> number g does meet that requirement, but it can't be proven in F
> > > > >>>>>>> that this is true, because in F, to show this we need to test every
> > > > >>>>>>> natuarl number, which requires an infinite number of steps (finite
> > > > >>>>>>> for each number, but an infinite number of numbers to test)..
> > > > >>>>>>>
> > > > >>>>>>> In meta-F, we can do better, because due to additional knowledge in
> > > > >>>>>>> meta-F, we can show that if a number g could be found, then that
> > > > >>>>>>> number g could be converted into a proof, in F, of the statement G
> > > > >>>>>>> (which says that such a number does not exist).
> > > > >>>>>>>
> > > > >>>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
> > > > >>>>>>> proof of it can exist in F.
> > > > >>>>>>>
> > > > >>>>>> So your basic line-of-reasoning is that G is true in F even if the
> > > > >>>>>> truth
> > > > >>>>>> of G cannot even be expressed in F as long as the truth of G can be
> > > > >>>>>> expressed in meta-F.
> > > > >>>>>>
> > > > >>>>>
> > > > >>>>> Expect that it CAN be expressed in F, it just is an infinite expression.
> > > > >>>>>
> > > > >>>> So you changed your mind about infinite proofs in formal systems?
> > > > >>>> We know the steps of the infinite proof for the Goldbach conjecture.
> > > > >>>
> > > > >>> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
> > > > >>> infinte sets oc connections, proofs can't. Only YOU have perposed that
> > > > >>> we think about infinite proofs.
> > > > >>>
> > > >
> > > > >> Formal systems cannot ever use infinite connections from their
> > > > >> expressions of language to their truth maker axioms thus eliminating
> > > > >> these from consideration as any measure of true "in the system".
> > > >
> > > > >> --
> > > > >> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > > > >> hits a target no one else can see." Arthur Schopenhauer
> > > > >
> > > > > "What you've written is almost like formal logic."
> > > >
> > > > I am filling in a key detail about the way that "true" in formal logic
> > > > actually works. Wittgenstein first pointed this out and no mathematician
> > > > has ever noticed. https://www.liarparadox.org/Wittgenstein.pdf
> > > >
> > > > If any mathematician had noticed this then they would have noticed that
> > > > Gödel did not prove that formal systems are incomplete. He only proved
> > > > that some of the expressions of language of a formal system are simply
> > > > untrue which is a mere triviality that everyone already knew.
> > > > --
> > > > Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > > > hits a target no one else can see." Arthur Schopenhauer
> > > This is just really, really poor.
> > Jeffrey, I'll second that emotion.
> these people could be out raising corn, doing something useful.

On Thursday, January 19, 2023 at 10:59:26 AM UTC-6, Jeffrey Rubard wrote:
> On Thursday, January 19, 2023 at 5:35:08 AM UTC-8, Don Stockbauer wrote:
> > On Wednesday, January 18, 2023 at 11:11:45 PM UTC-6, Don Stockbauer wrote:
> > > On Tuesday, January 17, 2023 at 6:46:00 PM UTC-6, Jeffrey Rubard wrote:
> > > > On Tuesday, January 17, 2023 at 9:25:11 AM UTC-8, olcott wrote:
> > > > > On 1/17/2023 10:44 AM, Jeffrey Rubard wrote:
> > > > > > On Tuesday, January 17, 2023 at 8:40:02 AM UTC-8, _ Olcott wrote:
> > > > > >> On 1/16/2023 7:51 PM, Richard Damon wrote:
> > > > > >>> On 1/16/23 10:17 AM, olcott wrote:
> > > > > >>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
> > > > > >>>>> On 1/15/23 11:15 AM, olcott wrote:
> > > > > >>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
> > > > > >>>>>>> On 1/14/23 6:19 PM, olcott wrote:
> > > > > >>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
> > > > > >>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
> > > > > >>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
> > > > > >>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
> > > > > >>>>>>>>>>>> How does the formal system know that an expression of language
> > > > > >>>>>>>>>>>> of this
> > > > > >>>>>>>>>>>> formal system is true unless this expression of language has a
> > > > > >>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
> > > > > >>>>>>>>>>>>
> > > > > >>>>>>>>>>>>
> > > > > >>>>>>>>>>>
> > > > > >>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
> > > > > >>>>>>>>>>>
> > > > > >>>>>>>>>>
> > > > > >>>>>>>>>> So PA has no idea that:
> > > > > >>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
> > > > > >>>>>>>>>>
> > > > > >>>>>>>>>
> > > > > >>>>>>>>> Why do you say that.
> > > > > >>>>>>>>>
> > > > > >>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
> > > > > >>>>>>>>> doesn't mean it can't be.
> > > > > >>>>>>>>>
> > > > > >>>>>>>>> In fact, your statement just comes out of a simple application of
> > > > > >>>>>>>>> the addition AXIOMS of PA.
> > > > > >>>>>>>>>
> > > > > >>>>>>>>> a + 0 = a
> > > > > >>>>>>>>> a + Successor(b) = Successor(a + b)
> > > > > >>>>>>>>>
> > > > > >>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
> > > > > >>>>>>>>>
> > > > > >>>>>>>>
> > > > > >>>>>>>> Unless a formal system has a syntactic connection from an
> > > > > >>>>>>>> expression of
> > > > > >>>>>>>> its language to its truth maker axioms the expression is untrue in
> > > > > >>>>>>>> that
> > > > > >>>>>>>> formal system.
> > > > > >>>>>>>
> > > > > >>>>>>> Right, but the connection can be infinite in length, and thus not
> > > > > >>>>>>> provable.
> > > > > >>>>>>>
> > > > > >>>>>>>>
> > > > > >>>>>>>> Try and show an expression of language that is true in a formal
> > > > > >>>>>>>> system
> > > > > >>>>>>>> (not just true somewhere else) that does not have any connection to
> > > > > >>>>>>>> truth maker axioms in this formal system. You must show why it is
> > > > > >>>>>>>> true
> > > > > >>>>>>>> in this formal system not merely that it is true somewhere else.
> > > > > >>>>>>>>
> > > > > >>>>>>>
> > > > > >>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
> > > > > >>>>>>> strictly in the formal system.
> > > > > >>>>>>>
> > > > > >>>>>>> If the connection exists as an infinite connection within the
> > > > > >>>>>>> system, then it is TRUE in the system.
> > > > > >>>>>>>
> > > > > >>>>>>> Note, that if there is such an infinite connection, which thus can
> > > > > >>>>>>> not be proven within the formal system, it is still possible, that
> > > > > >>>>>>> another system, related to that system, with more knowledge, might
> > > > > >>>>>>> be able to show that there does exist within the original formal
> > > > > >>>>>>> system such an infinte connection.
> > > > > >>>>>>>
> > > > > >>>>>>> This is what happens to G in F and meta-F
> > > > > >>>>>>>
> > > > > >>>>>>> G states that there does not exist a Natural Number g that meets a
> > > > > >>>>>>> specific requirement (expressed as a primative recursive
> > > > > >>>>>>> relationship).
> > > > > >>>>>>>
> > > > > >>>>>>> This statement turns out to be true, because it turns out that no
> > > > > >>>>>>> number g does meet that requirement, but it can't be proven in F
> > > > > >>>>>>> that this is true, because in F, to show this we need to test every
> > > > > >>>>>>> natuarl number, which requires an infinite number of steps (finite
> > > > > >>>>>>> for each number, but an infinite number of numbers to test).
> > > > > >>>>>>>
> > > > > >>>>>>> In meta-F, we can do better, because due to additional knowledge in
> > > > > >>>>>>> meta-F, we can show that if a number g could be found, then that
> > > > > >>>>>>> number g could be converted into a proof, in F, of the statement G
> > > > > >>>>>>> (which says that such a number does not exist).
> > > > > >>>>>>>
> > > > > >>>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
> > > > > >>>>>>> proof of it can exist in F.
> > > > > >>>>>>>
> > > > > >>>>>> So your basic line-of-reasoning is that G is true in F even if the
> > > > > >>>>>> truth
> > > > > >>>>>> of G cannot even be expressed in F as long as the truth of G can be
> > > > > >>>>>> expressed in meta-F.
> > > > > >>>>>>
> > > > > >>>>>
> > > > > >>>>> Expect that it CAN be expressed in F, it just is an infinite expression.
> > > > > >>>>>
> > > > > >>>> So you changed your mind about infinite proofs in formal systems?
> > > > > >>>> We know the steps of the infinite proof for the Goldbach conjecture.
> > > > > >>>
> > > > > >>> No, because I am showing that G is TRUE, not PROVABLE. Truth can use
> > > > > >>> infinte sets oc connections, proofs can't. Only YOU have perposed that
> > > > > >>> we think about infinite proofs.
> > > > > >>>
> > > > >
> > > > > >> Formal systems cannot ever use infinite connections from their
> > > > > >> expressions of language to their truth maker axioms thus eliminating
> > > > > >> these from consideration as any measure of true "in the system".
> > > > >
> > > > > >> --
> > > > > >> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > > > > >> hits a target no one else can see." Arthur Schopenhauer
> > > > > >
> > > > > > "What you've written is almost like formal logic."
> > > > >
> > > > > I am filling in a key detail about the way that "true" in formal logic
> > > > > actually works. Wittgenstein first pointed this out and no mathematician
> > > > > has ever noticed. https://www.liarparadox.org/Wittgenstein.pdf
> > > > >
> > > > > If any mathematician had noticed this then they would have noticed that
> > > > > Gödel did not prove that formal systems are incomplete. He only proved
> > > > > that some of the expressions of language of a formal system are simply
> > > > > untrue which is a mere triviality that everyone already knew.
> > > > > --
> > > > > Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> > > > > hits a target no one else can see." Arthur Schopenhauer
> > > > This is just really, really poor.
> > > Jeffrey, I'll second that emotion.
> > these people could be out raising corn, doing something useful.
>
> You're full of shit, but the writing on logic *is* bad.