[FOM] Did G?del's result come as a surprise to Bertrand Russell?

hdeutsch@ilstu.edu hdeutsch at ilstu.edu
Wed Mar 31 19:14:52 EDT 2010

Fascinating! Did Goedel actually regard his results as paradoxical.   
What is the evidence of this?  As I understand it, Carnap didn't  
understand the result at first, but was the first to produce an  
explicit proof of the diagonal lemma. Is that true?

Quoting Alasdair Urquhart <urquhart at cs.toronto.edu>:

> Russell's reference to the incompleteness results are disappointingly
> thin.  He was almost certainly aware of them in the 1930s.  I believe
> that Goedel sent him an offprint of the incompleteness paper.  The Russell
> Archives (McMaster University, Hamilton, Ontario) contain an offprint
> of the 1931 paper, though it is not, I believe, a copy of the offprint
> sent by Goedel.  It has no marginalia.
> The second edition of the "Principles of Mathematics" has a reference
> to the new "puzzles" presented by Goedel.  "An Inquiry into Meaning
> and Truth" (1940) has an explicit reference to the concept of Goedel
> numbering, so it is clear that Russell had understood this aspect
> of the result.
> This very sparse evidence perhaps suggests that Russell never entirely
> understood the results, conceivably interpreting them as some kind of
> new paradox, as Goedel himself thought.  The fact that Russell
> never broke free from the conceptual world of Principia Mathematica
> would make this reasonable -- in Principia Mathematica, the formalism
> is indissolubly wedded to its informal interpretation.
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