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Topic: The Invalidity of Godel's Incompleteness Work.
Replies: 87   Last Post: Oct 25, 2013 2:44 PM

 Messages: [ Previous | Next ]
 Peter Percival Posts: 2,623 Registered: 10/25/10
Re: The Invalidity of Godel's Incompleteness Work.
Posted: Oct 19, 2013 4:21 PM

Nam Nguyen wrote:
> On 19/10/2013 2:06 PM, Peter Percival wrote:
>> Nam Nguyen wrote:
>>> On 19/10/2013 1:24 PM, Nam Nguyen wrote:
>>>> On 19/10/2013 12:53 PM, Peter Percival wrote:
>>>>> Nam Nguyen wrote:
>>>>>> On 19/10/2013 12:10 PM, Peter Percival wrote:
>>>>>>> Nam Nguyen wrote:
>>>>>>>> On 19/10/2013 11:32 AM, fom wrote:
>>>>>>>
>>>>>>>>> And, the meaning of "impossible to know"?
>>>>>>>>
>>>>>>>> Right there: right in front of you.
>>>>>>>>
>>>>>>>> _A meta truth_ is said to be impossible to know if it's not in the
>>>>>>>> collection of meta truths, resulting from all available
>>>>>>>> definitions,
>>>>>>>> permissible reasoning methods, within the underlying logic
>>>>>>>> framework
>>>>>>>> [FOL(=) in this case].

>>>>>>>
>>>>>>> We don't yet know if PA|-cGC or PA|-~cGC, so we don't know if
>>>>>>> "PA|-cGC"
>>>>>>> or "PA|-~cGC" is in the collection of meta truths. So we don't
>>>>>>> know if
>>>>>>> it's impossible to know cGC (or ~cGC). Why, then, do you claim that
>>>>>>> it's impossible to know cGC (or ~cGC)?

>>>>
>>>> "Fom" asked me a very specific DEFINITION-question and I've given a
>>>> very
>>>> specific answer to his question.
>>>>
>>>> Until you and fom let me know if this definition is understood by
>>>> you both, I'm not answering further to your endless postings resulted
>>>> from _your not understanding my definition_ .
>>>>
>>>> So, here it is again:
>>>>

>>>> > _Do you first understand the definition itself_ ?
>>>> >
>>>> > Would you please confirm you now do or still don't? Thanks.

>>>>
>>>>>>>
>>>>>>> Do you know that both cGC and ~cGC are not in the collection of meta
>>>>>>> truths? If so you must know that neither PA|-cGC nor PA|-~cGC. You
>>>>>>> should publish your proof. And stop claiming that Gödel's
>>>>>>> incompleteness theorem is invalid, because if neither PA|-cGC nor
>>>>>>> PA|-~cGC, then that is an example of incompleteness.
>>>>>>>
>>>>>>> Also if you know that neither PA|-cGC nor PA|-~cGC, then you've
>>>>>>> proved
>>>>>>> PA consistent. So you should stop claiming that its consistency is
>>>>>>> unprovable.

>>>>>>
>>>>>> _Do you first understand the definition itself_ ?
>>>>>>
>>>>>> Would you please confirm you now do or still don't? Thanks.

>>>>>
>>>>> If I've understood it (the definition of "impossible to know") then my
>>>>> argument above is valid. If it's valid then you're wrong about Gödel.
>>>>> So you should be careful about what you ask to be confirmed.
>>>>>
>>>>> You have been caught out in a contradiction. Now, what's it to be:
>>>>> i) you are too dim to recognize it,
>>>>> ii) you are too dishonest to recognize it,

>>>>
>>>> You forgot another possibility:
>>>>
>>>> You're too intellectually coward to admit my definition is sound,
>>>> which would lead to the fact you've been so stupid in this debate.
>>>>

>>>>> Not iii) I bet.

>>>
>>> I'll give you a breathing room: let me know if you understand my
>>> definition of "impossible to know"

>>
>> It is from your definition of "impossible to know" that I deduce that
>> you can prove that neither PA|-cGC nor PA|-~cGC. Hence you have proved
>> Gödel's incompleteness theorem and you have proved PA is consistent.

>
>

>> So
>> if I understood your definition then you are wrong about Gödel's
>> incompleteness theorem being invalid and you are wrong about PA not
>> being provably consistent.

>
> You see: it's your keep saying "if I understood your definition" that
> has raised a red flag to me. What happen if your understanding of my
> definition is incorrect? Should it be in that case we have to see eye
> to eye on the definition itself first, before you blaming me for the
> alleged being wrong about Gödel's work here?
>
> So please confirm if you indeed you understand my definition.

Do you want me to understand it? If I do, then I deduce that you can
prove that neither PA|-cGC nor PA|-~cGC. Hence you have proved Gödel's
incompleteness theorem and you have proved PA is consistent. So if I
incompleteness theorem being invalid and you are wrong about PA not
being provably consistent.

Perhaps for that reason you don't want me to understand it.

> (From what you've said I don't think you understand. But I'd
> rather hear it from you, than my own guessing!)
>

--
The world will little note, nor long remember what we say here
Lincoln at Gettysburg

Date Subject Author
10/4/13 namducnguyen
10/5/13 Peter Percival
10/6/13 LudovicoVan
10/6/13 LudovicoVan
10/9/13 fom
10/18/13 Peter Percival
10/18/13 namducnguyen
10/19/13 Peter Percival
10/19/13 fom
10/19/13 Peter Percival
10/19/13 fom
10/19/13 namducnguyen
10/19/13 fom
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 fom
10/19/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/19/13 namducnguyen
10/19/13 fom
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 fom
10/19/13 fom
10/19/13 namducnguyen
10/19/13 fom
10/19/13 fom
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/24/13 namducnguyen
10/24/13 fom
10/24/13 namducnguyen
10/24/13 Peter Percival
10/24/13 namducnguyen
10/24/13 Peter Percival
10/24/13 fom
10/24/13 fom
10/20/13 fom
10/25/13 Rock Brentwood