Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

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

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Peter Percival Posts: 2,225 Registered: 10/25/10
Re: The Invalidity of Godel's Incompleteness Work.
Posted: Oct 19, 2013 4:06 PM
 Plain Text Reply

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.
>>

>>> iii) you admit that your claims about cGC and Gödel are wrong?
>>> 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.

> here in this context; and if
> you do understand, I'll fully respond to your quest about cGC above
> ( _but only per your post shown above_ ).
>
> The choice is yours.
>

--
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

© The Math Forum at NCTM 1994-2017. All Rights Reserved.