Re: incompleteness of ZF

["R.A.G. Seely" <rags@math.mcgill.ca>]

On Tue, 6 Apr 1999, F W Lawvere wrote:

> Using an old logician's trick (see eg Feferman on paths thru O, or even
> Goedel's original papers) as an
> 			April Fool joke
> may be amusing to some within the closed gates of a British University,
> but is irresponsible on the world network. Think of the hundreds of
> lurkers (who hesitate to speak up so that misconceptions can
> be discussed and clarified openly, but) who are now furthering the rumor
> that mathematics has somehow been proved inconsistent.The waves of such
> disinformation can last for years or even decades.

Curiously, my reaction to this has been rather different.  We were
discussing Paul's note after the seminar here the other day, and apart
from one reply, I rather had the idea that most replies were aware
that this was a joke, but that it was a subtle one (not all that
subtle, perhaps, but a lot more subtle that what often passes as
humour on the net, for sure).  And that finding the error was a
respectable response.

As for spreading disinformation, there has been no shortage of people
who look serious, (I avoid the harder question as to whether they are,
and what exactly that ought to mean) and who have been spreading tales
of the inconsistency of maths for decades.  As a graduate student, I
often attended logic meetings where Edward Wette proved ever more
basic fragments of our subject inconsistent (I recall he got as far as
propositional logic, Peano arithmetic, and several branches of
physics.  I am not sure he made any serious distinction between the
last case and the others.)  Perhaps one point here is that anyone who
believes all he reads is a fool, and anyone who believes all he reads
on the net is a fool who cannot even learn from experience.  (It takes
about 5 minutes to uncover patently silly things on the net! - not
even counting this one...)  

So - I agree Bill raises a serious matter, but I think in this case it
may be an overreaction.  Paul's note was certainly "fishy" (French
reference for those not in a French environment), but it was
essentially harmless.  This group is comparitively closed (even your
average academic journal is probably more open).  And if anyone missed
the joke up to now, surely that has been remedied.  (If only in that
refutations appeared quickly.)

However, if I see a report on this on "60 minutes" I will eat my
hat...

 - all the best, Robert 

= rags =

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