FOM: London Review of Books: letters about Sokal-Bricmont

[Martin Davis]

At Steve's suggestion, I'm posting on fom some correspondence having
to do with the book (that I recommend to all) by Alan Sokal & Jean
Bricmont "Fashionable Nonsense: Postmodern Intellectual's Abuse of
Science." Sokal is the physicist whose (brilliant) hoax article was
published in an allegedly serious journal.  

The venue of the correspondence was the London Review of Books which
had a review of the book and letters afterwards. A recent letter came
from Cristian Calude a reputable computer scientist whose work has to
do with the Chaitin--Martin-Löv theory of randomness. Here's the text
of his letter:

> One aspect of the Sokal and Bricmont affair was not raised in the 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, they
> 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 to 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 reappears later in
> the book. Finally, the authors' 'expert' judgment dismisses any
> impact of Goedel's theory on the development of artificial
> intelligence, the theory of randomness, the philosophy of mathematics
> or the understanding of 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,
> New Zealand

Here's the reply I sent to the LRB yesterday. Of course, I have no
idea whether they will chose to publish it. Note that I decided to
ignore the misstatement by the authors over consistency vs.
omega-consistency as an irrelevant technicality.
 
> I am writing to express my astonishment over my friend Dr. Cristian
> Calude's attack on the competence of Sokal and Bricmont regarding
> their understanding of Gödel's famous incompleteness theorems. I have
> been teaching the incompleteness theorems to graduate students in
> mathematics and computer science for half a century and it has been
> crucial in my own research. Dr. Calude himself solicited my
> autobiographical essay for the recently published volume he edited
> entitled "People and Ideas in Theoretical Computer Science".
 
> It is not at all the case that Sokal and Bricmont's statement of
> Gödel's first theorem is "simply wrong". When Gödel's paper appeared
> in 1931, the advance by Alan Turing and Alonzo Church that made it
> possible to speak of "algorithms" in a rigorous manner was still five
> years way. So there was no way that Calude's demand for a
> "proof-checking algorithm" could have been part of Gödel's statement
> of his theorem, and it was not. With their explicit reference to the
> 1931 paper, Sokal and Bricmont simply refer to "the given formal
> system", which can readily be understood to refer to the systems to
> which Gödel's original proof applied.
> 
> Calude complains about the assertion that Gödel's theorems have had
> "very little impact on the bulk of mathematical research". Alas, this
> is unquestionably true. Calude lists "the development of artificial
> intelligence, the theory of randomness, the philosophy of mathematics
> or the understanding of Escher's art" as areas slighted in this
> connection. One may have varied judgements concerning the relevance
> of Gödel's work to these subjects, but it is difficult to see how
> they relate to the bulk of mathematical research, and none of them is
> mentioned by Sokal-Bricmont.
> 
> 							Martin Davis
> 							Berkeley, California