On Jul 17, 2008, at 10:27 AM, Roger Critchlow wrote:
> On Wed, Jul 16, 2008 at 8:57 PM, Owen Densmore <[EMAIL PROTECTED]>
> wrote:
>> No one who accepts mathematics as it is, however, considers it a
>> point
>> of philosophy. We do not argue about it, we try to grasp it.
>>
>> Arguing about it is for those of us who cannot understand it.
>>
> I suspect a category error: was Goedel's theorem mathematics or an
> argument
> about mathematics?
The former.
I do admit Gödel creates an interesting problem (not argument) for
mathematicians: You MUST be careful about your axioms, and you should
be aware of the problems they present.
My hazy understanding of Gödel's work is that basically an axiom set
can be over-specified (thus creating the potential for both T and !T
being provable) or under-specified (T is true but not provable). This
is old stuff for linear algebraists.
All that said, how many mathematicians are halted in their tracks by
Gödel, giving up all as foolish and pointless? Rather they use it as
a cautionary tale, much like computer scientists dealing with
decidability.
-- Owen
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
