[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
     - - -
     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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