judicial tyranny

[David Welch]

On Thu, May 17, 2001 at 04:00:34PM -0400, Wojtek Sokolowski wrote:
>
> >CB: Do you mean that all formal logics like legal reasoning or mathematics
> develop inherent paradoxes and can't be completely consistent with respect
> to their fundamental principle of non-contradiction ?
> >
> 
> Wasn't that Goedel?
>
Hardly, Goedel showed that formal, mathematical systems of sufficent
strength (e.g. first order logic with axioms for multiplication, addition and 
induction) contain sentences that are true but unprovable and in particular
their own consistency is unprovable. Goedel's result was of historical
significance because Hilbert's program required proofs of consistency to
justify the innovations in mathematics at the turn of century (principally
set theory), most modern mathematicians (I assume) are happy to do
mathematics without worrying about consistency at all.