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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 24, 2013 10:35 AM

Nam Nguyen wrote:
> On 24/10/2013 6:58 AM, Peter Percival wrote:
>> Nam Nguyen wrote:
>>

>>>
>>> The game of symbol manipulation is there to stay with FOL=, nonetheless.
>>>
>>> It doesn't matter what philosophical motivation you might have had, it's
>>> part of the definition of reasoning with rules of inference in FOL with
>>> identity: either you'd conform to it, or betray it.
>>>
>>> Godel betrayed it, and so have we.

>>
>> Gödel's incompleteness theorem isn't about FOL=.

>
> You're wrong of course.
>
> What Godel wrote on his seminar paper:
>
> "This situation is not due in some way to the special nature of the
> systems set up, but holds for a very extensive class of formal
> systems".
>
> Note his "formal systems" would refer to what's known today as
> First Order Logic with equality, and note that his "class of formal
> systems" would include the "set theory of Zermelo-Fraenkel" (his words),
> which is today known as ZF (of First Order Logic with equality).
>

You are confusing first order logic with identity (which is surely what
"FOL=" stands for) with first order theories. FOL= has only logical
axioms (if it has any at all), that's why it's called logic. A first
order theory may have non-logical axioms. That "very extensive class of
formal systems" are theories with non-logical axioms. It is the
non-logical axioms that lead to incompleteness, FOL= is complete..

--
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
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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
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10/20/13 namducnguyen
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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
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10/20/13 fom
10/25/13 Rock Brentwood