bts%unc%CSNet-Relay@sri-unix.UUCP (11/04/83)
From: Bruce T. Smith <bts%unc@CSNet-Relay>
The most recent issue (Vol. 48, Number 3, September
1983) of the Journal of Symbolic Logic (JSL) has an
interesting review of Hofstadter's book "Godel, Escher,
Bach: an eternal golden braid.". (It's on pages 864-871, a
rather long review for the JSL. It's by Judson C. Webb, a
name unfamiliar to me, amateur that I am.)
This is a pretty favorable review-- I know better than
to start any debates over GEB-- but what I found most
interesting was its emphasis on the LOGIC in the book. Yes,
I know that's not all GEB was about, but it was unusual
to read a discussion of it from this point of view. Just to
let you know what to expect, Webb's major criticism is
Hofstadter's failure, in a book on self-reference, to dis-
cuss Kleene's fixed-point theorem,
which fuses these two phenomena so closely together.
The fixed-point theorem shows (by an adaptation of
Godel's formal diagonalization) that the strangest ima-
ginable conditions on functions have solutions computed
by self-referential machines making essential use of
their own Godel-numbers, provided only that the condi-
tions are expressible by partial recursive functions.
He also points out that Hofstadter didn't show quite how
shocking Godel's theorems were: "In short, Godel discovered
the experimental completeness of a system that seemed almost
too weak to bother with, and the theoretical incompleteness
of one that aimed only at experimental completeness."
Enough. I'm not going to type the whole 7.5 pages. Go
look for the newest issue of the JSL-- probably in your
Mathematics library. For any students out there, membership
in the Association for Symbolic Logic is only $9.00/yr and
includes the JSL. Last year they published around 1000
pages. It's mostly short technical papers, but they claim
they're going to do more expository stuff. The address to
write to is
The Association for Symbolic Logic
P.O.Box 6248
Providence, RI 02940
============================================
Bruce Smith, UNC-Chapel Hill
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