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

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 fom Posts: 1,968 Registered: 12/4/12
Re: The Invalidity of Godel's Incompleteness Work.
Posted: Oct 19, 2013 6:38 PM

On 10/19/2013 1:53 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)?
>>>
>>> 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,
> Not iii) I bet.
>

Goodness. Allow me to compliment you
on that piece of reasoning. Given Nam's
refusal to concede a non-classical basis
for his logic, you are correct.

By the way, Shelah has that on his list
of important things... a model theory for
arithmetic comparable to the one for
set theory.

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