On 13 Aug 2009, at 10:53, 1Z wrote:

> On 13 Aug, 01:42, Colin Hales <c.ha...@pgrad.unimelb.edu.au> wrote:
>> I am not saying humans are magical. I am saying that humans do /not/
>> operate formally like COMP.... and that '/formally handling
>> inconsistency/' is not the same thing as '/delivering inconsistency  
>> by
>> being an informal/ /system/'. BTW I mean informal in the Godellian
>> sense...simultaneous inconsistency and incompleteness.
> You can have formal systems that are simultaneously inconsistent
> and incomplete too.

I guess you mean "you can't have formal systems ...".

Or you were talking about paraconsistent system, or relevant systems.  
Then I agree.

At least in classical and intuitionist logic, all inconsistent systems  
are complete, in the sense of proving all what is true, and also ...  
all what is false. This is due to the fact that (false->A) is a  
tautology. (A being any proposition)

Of course Colin could answer by saying that he was talking about  
"informal system". But thenas Quentin points out, he put the  
conclusion in the hypothesis.
And  what does he mean by "Godelian sense", which makes sense only for  
formal systems?

What Colin means by "informal", in his context, is a bit of a mystery.


> >


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