Sonic Boom

One aspect of the Sokal and Bricmont affair was not raised in the {\em LRB} 
correspondence (29 October 1998): namely, the authors' scientific 
competence.  They state rightly that 'Goedel's theorem is an inexhaustible 
source of intellectual abuses'.  Unfortunately, the authors themselves, 
suffer from 'Goedelitis'!  Their 'explanation'--'Goedel's first theorem 
exhibits a proposition that is neither provable nor refutable in the given 
system, provided that this system is consistent'--is simply wrong.  An 
essential property--namely the existence of a proof-checking algorithm--is 
omitted.  Without this proviso the whole edifice falls into pieces 
essentially in the same way it did when Kristeva replaced 'consistency' by 
'inconsistency' in Goedel's second theorem: sometimes consistency cannot be 
proved within the system, but an inconsistent system can prove its own 
inconsistency.  The omission is not accidental: it reapers on later in the 
book.  Finally, the authors' 'expert' judgement dismisses any impact of 
Goedel's theory on the development of artificial intelligence, theory of 
randomness, philosophy of mathematics or understanding Escher's art (to 
name only a few areas): 'Metatheorems in mathematical logic, such as 
Goedel's theorem ...  have ...  very little impact on the bulk of 
mathematical research and almost no impact on the natural sciences'.

C.S. Calude, Auckland
London Review of Books, 4 February, 1999, 4