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.

--
Copyright 2023 Olcott

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