CONTENTS - ouroboros ponderosa

the quantum theory, is that which is to be comrrehc!l(lcd mathcmatical
ly." lUI
During thse first three decades of th 20th century, moreovr, the
great attempts by Russell and Whitehead, Hilbert, t aI., to provide a
completely unproblcmatic basis for thc wholc edific of math, referred
to above, went forward with considerable optimism. But in 1931 Kurt
Godcl dashed these bright hopes with his Incompleteness Theorem,
which demonstrates that any symbolic system can be either complet or
fully consistent, but not both. Godel's devastating mathematical proof of
this not only shows the limits of axiomatic number systems, but rules out
nclosing nature by any closed, consistent language. If there are
theorems or assertions within a system of thought which can neither be
proved nor disproved internally, it is impossible to give a proof of
consistency within the language used. As GOdel and immediate succes­
sors like Tarski and Church convincingly argued, "any system of
knowledge about the world is, and must remain, fundamentally incom­
plete, eternally subject to rcvision."1O'
Morris Kline's Mathemalics: The Loss of Certainty relatd the "calami­
tics" that have befallen the once seemingly inviolable "majesty of
mathematics,""J3 chiefly dating from Godel. Math, like language, used to
describe the world and itself, fails in its totalizing quest, in the same way
that capitalism cannot provide itself with unassailable grounding. Further,
with Godel's Theorem not only was mathematics "recognized to be much
more abstract and formal than had been traditionally supposed,"!C4 but
it also became clar that "the resources of the human mind have not
becn, and cannot be, fully formalized."'os
But who could deny that, in practice, quantity has been mastering us,
with or without definitively shoring up its theoretical basis? Human
hdplssness secms to be directly proportional to mathematical
technology's domination over naturc, or as Adorno phrased it, "the
subjection of outer nature is successful only in the measure of the
repression of inner nature."!D6 And certainly undrstanding is diminished
by number's hallmark, division of labor. Raymond Firth accidentally
exemplified th stupidity of advanced specialization, in a passing
comment on a crucial topic: "the proposition that symbols are instru­
ments of knowlcdge raises epistemological issues which anthropologists
arc not trained to handle."!D7 The connection with a more common
degradation is made by Singh, in the contcxt of an ever more refined
division of labor and a more and more technicized social life, noting that
"automation of computation immediately paved the way for automatizing
industrial operations."!OH
1.II'h·lI NT'> I)!- 1 1 ' 1 ' 11", · \1
!'Ill' l1l'i', htt'tled tnliUIl1 of computerized plTicc work is today's very
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