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.

You don't understand what "based" means.

The fact that you can't actually SHOW that your statement is a correct
proxy, and in fact you have claimed that it is "esentially the same
thing" when it isn't, just shows how badly you understand the field.

Your Claim is effectively that it is not a Truth Bearer that a Natural
Number exists (or not exists) that satisfies a specific computable funciton.

That make your logic inconsistent, as there is no middle ground between
existing and not-existing.