NABOKV-L post 0014061, Wed, 15 Nov 2006 22:37:23 -0500

Subject
More help for otherworldly logic (also Goedel Escher Bach)
From
Date
Body
Peter Dale:

Let's call VN's Statement P:
> "I know more than I can express in words, and the little I can express
> would not have been expressed, had I not known more."

I do appreciate your careful analysis. As you indicate, it's an ancient
philosophical-epistemological-linguistical-more-yet problem that can be
coarsly summed up as 'the limitations of language' or, by pessimists, as
'the curse of language' (see my posting on 'semantics.') There's a
delightfully challenging recursion (well, some of us have found it
rent-paying fun over the years -- the Liverpool Dockers talk of
STRETCHING
out a job!): we read VN expressing himself on what may or may not be
expressible. And we are then asked to express our views on how well VN
has
expressed himself! Note first that some listers found P totally
incomprehensible, reminding us that 'expressibility' involves both the
'expressers' and the 'expressees' (those trying to parse and judge that
which is 'expressed') Those of us exposed professionally from an early
age
to Russell, Goedel, Quine, et al. react to P with a touch of "Brother,
here
we go again" exasperation. It's down-right daunting, as Peter's response
illustrates, to phrase an interpretation of P accessible to those
unfamiliar
with the rather specialised languages used in epistemology and Formal
Systems. Those who have made a start with Goedel-Escher-Bach are urged
to
read
http://www.maa.org/mathhorizons/pdfs/september_2005_13.pdf

or my own
http://www.acmqueue.org/modules.php?name=Content&pa=showpage&pid=392

One might cut through the cackle by saying: "I accept your assertion
that
you KNOW certain things which you feel you can't adequately express in
WORDS. Perhaps there are no adequate words, or maybe you just can't
dredge
them up at the moment! Try some inadequate words like GOD and we may at
least get the gist. Or try drawing, whistling or waving your hands. Keep
trying. We are all in the same boat."

VN is sadly out-of-tune with _real_ mathematics in his The Art of
Literature
& Commonsense (Lectures on Literature, Harvest Harcourt 1982 esp p 374).
He confuses mathematics with the tiny, mundane 'commonsense' subset used
by
bean-counting accountants (although. of course, VN was ever alert on
such
banalities when negotiating his royalty percentages). He cites "Two and
two
makes four" as a failure of the "artificial logical world" and its
"commonsense" calculating machines. A old quip that's used to separate
the
mathematicians from the abacus-pushers is "2 + 2 = 5 for sufficiently
large
values of 2!" In fact, the value of 2 + 2 depends on the particular
system/notation in use (e.g., '+' as vector-addition, or '=' as modulo N
etc)

Stan Kelly-Bootle

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