Here's a nice pic to use in discussion.... from GEB. The map for a
formal system (a tree). A formal system could not draw this picture. It
is entirely and only ever 'a tree'. Humans dance in the forest.
col
Bruno Marchal wrote:
> On 13 Aug 2009, at 10:53, 1Z wrote:
>
>
>>
>> On 13 Aug, 01:42, Colin Hales <c.ha....domain.name.hidden> 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.
>
> Bruno
>
>
>
>
>>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
> >
>
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Received on Fri Aug 14 2009 - 11:21:52 PDT