[FOM] Response / critical review of Franzen's Gödel book
Aatu Koskensilta
Aatu.Koskensilta at uta.fi
Sun Apr 1 19:15:13 EDT 2012
[My apologies to the moderator if this message was posted twice.]
Quoting charlie <silver_1 at mindspring.com>:
> What exactly is meant by "serious" abuses of G's thms? I'm puzzled,
> since throwing around mistaken versions of G's th'm, Russell's
> Paradox, Heisenberg's Uncertainty Principle etc., are ubiquitous. I
> wouldn't know what would make them "serious". It seems clear to me
> that the purpose writers have in alluding to these principles is
> simply to appear impressive to their audience. Sokal & Bricmont
> indicate that flawed technical references often achieve this purpose.
Gödel this, quantum that -- so it goes. There are of course people
who use all sorts of heady bits and pieces from science, philosophy,
what have you, as an intellectual alibi and excuse for their
more-or-less far-fetched, ill-defined and vague visions and waffling.
But this is not what Franzén's _Gödel's Theorem_ is mainly about. As
he writes in the introduction:
Many references to the incompleteness theorem outside the field
of formal logic are rather obviously nonsensical and appear to
be based on gross misunderstandings or some process of free
association.
- - -
Thus Alan Sokal and Jean Brickmont, in their commentary on
postmodernism, remark that "Gödel's theorem is an inexhaustible
source of intellectual abuses" and give examples from the writings
of Regis Debray, Michel Serres, and others. But among the
nonmathematical arguments, ideas, and reflections inspired by
Gödel's theorem there are many that by no means represent
postmodernist excesses, but rather occur naturally to many
people with very different backgrounds when they think about
the theorem.
Among these ideas, reflections, nonmathematical consequences, that
naturally suggest themselves to perfectly sensible people when
encountering the theorem and pondering it, we find e.g. the
Lucas-Penrose argument, the idea that the second incompleteness
theorem shows there to be something dubious or fishy about the
foundations of mathematics and so on. These misconceptions or abuses
are serious in the sense that they're not just name dropping, peculiar
to intellectual charlatans or woolly thinkers who enjoy having their
heads swim with metaphysical confusion in a logical head trip. They
affect, in a very real way, the thinking of many students,
mathematicians, and even some professional philosophers of mathematics.
--
Aatu Koskensilta (aatu.koskensilta at uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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